STQ6D: [NBAA: P17 INTERNATIONAL FINANCE MAY 2003 Q4b]b) Suppose the interest rate on £ is 15% in London, and the interest rate on a comparable Tanzanian shilling investment in Dar Es Salaam is 10%.

Managementand Cost A ccounting Instructor’s Manual COLIN DRURY Management and Cost A ccounting Instructor’s Manual EIGHTH EDITION Australia Brazil Japan Korea Mexico Singap ore Spain United Kingdom United States Management and Cost Accountingighth Edition Colin Drury Publishing Director: Linden Harris Publisher: Brendan George Development Editor: Annabel Ainscow Editorial Assistant: Lauren Darby Production Editor: Lucy Arthy Production Controller: Eyvett Davis Marketing Manager: Amanda Cheung Typesetter: Integra, India Cover design: Design Deluxe Text design: Design Deluxe ª , Colin Drury ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transmitted, stored or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section or of the United States Copyright Act, or applicable copyright law of another jurisdiction, without the prior written permission of the publisher.

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For your lifelong learning solutions, visit www.cengage.co.uk Purchase your next print book, e-book or e-chapter at www.cengagebrain.com , I nstructor's Manual, E 978-1-4080-6431-3 Contents Preface vii Part I Solutions 1 An introduction to cost terms and concepts 3 Cost assignment 5 Accounting entries for a job costing system 17 Process costing 25 Joint and by-product costing 39 Income effects of alternative cost accumulation systems 52 Cost–volume–profit analysis 60 Measuring relevant costs and revenues for decision-making 69 83 Decision-making under conditions of risk and uncertainty 107 Capital investment decisions: appraisal methods 120Capital investment decisions: the impact of capital rationing, taxation, inflation and risk 131 The budgeting process 147 Management control systems 154 Standard costing and variance analysis 1 165 Standard costing and variance analysis 2: further aspects 176Divisional financial performance measures 188 Transfer pricing in divisionalized companies 200Cost management 210 Strategic management accounting 214 Cost estimation and cost behaviour 220 Quantitative models for the planning and control of inventories 229 The application of linear programming to management accounting 239 Part II Solutions to website learning note questions 253 Pricing decisions and profitability analysis Activity based costing 97 Preface This manual is complementary to the main textbook, Management and Cost Accounting , and the accompanying Student’s Manual . Throughout the main text the illustrations have been kept simple to enable readers to understand the principles involved in designing and evaluating management and cost accounting systems. It isessential that students work through a wide range of problems to gain experience onthe application of principles, but there is insufficient classroom time for tutorial guid-ance to meet this requirement. The Students’ Manual provides this guidance byenabling students to work independently on problems and compare their answerswith the suggested solutions. In addition, tutors require feedback information on the students’ understanding of the subject and the ability to solve problems independently. Tutors also require that arange of problems is available where the solutions are not generally available to stu-dents. The Instructors’ Manual aims to meet these requirements. Recently some pro-fessional accountancy examining bodies have made solutions to examinationquestions available on their websites and other examining bodies provide publishedanswers that can be purchased by students. To ensure that the problems are not avail-able from published sources the problems applicable to the instructors’ manual tendto be approximately ten years old and thus do not appear on publication lists or web- The solutions given in this manual are my own and not the approved solutions of the professional body setting the question. Where an essay question is asked and a fullanswer requires an undue repetition of the main book, either references are made toappropriate sections of the book, or an answer guide or outline is provided. Finally, Iwould like to thank once again, the Association of Accounting Technicians, theInstitution of Chartered Accountants in England and Wales, the CharteredAssociation of Certified Accountants and the Chartered Institute of ManagementAccountants for permission to reproduce questions which have appeared in pastexaminations. sites of the professional examining bodies. All of the questions and answers that appeared in the seventh edition have been retained in the eighth edition. However, many of these questions and answers have been updated to reflect the current envi- ronment. For example, some monetary values have been changed (e.g wage rates) and references to entries for specific years have been changed from the early years of the millennium to reflect years relating to the current edition. Lecturers should therefore exercise care when using questions that appeared in the seventh edition. A huge amount of additional questions that have not been extracted from examinations set by pro- fessional accountancy bodies is available in the ac companying ExamView®. Part I Solutions (1) (a); (2) (d); (3) (e); (4) (f); (5) (i); (6) (b); (7) (h).(i) Direct materials (ii) Direct labour (iii) Direct expenses 91 610 (iv) Indirect production (v) Research and (vi) Selling and overhead development costs distribution costs12 07 61 1 81 2 18 13 19 17 (vii) Administration costs (viii) Finance costs 25 34 1415 (a) Variable cost per running hour of Machine XR1 (£) (£27 500/1100 hours)= 25 Fixed cost „„„„„„„„„ (£20 000/1100 hours) = 18.182 Cost of brain scan on Machine XRI: (£) Variable machine cost (4 hours × £25) 100 X-ray plates 40 Total variable cost 140 Fixed machine cost (4 hours × £18.182) 72.73 Total cost of a scan212.73 Total cost of a satisfactory scan (£212.73/0.9) 236.37 (b) It is assumed that fixed costs will remain unchanged and also that they are not relevant to the decision. The relevant costs are the incremental costs of an additional scan: Machine XR1: (£) Variable cost per scan 140 Variable cost per satisfactory scan (£140/0.9) 155.56Machine XR50: (£) Solution IM 2.1 Solution IM 2.2 Solution IM 2.3 AN INTRODUCTION TO COST TERMS AND CONCEPTS 3 An introduction to cost terms and concepts Solutions to Chapter 2 questions Variable machine cost per scan (£64 000/2000 hours × 1.8 hours) 57.60 X-ray plates55.00 Variable cost per scan112.60 Variable cost per satisfactory scan (£112.60/0.94) 119.79 The relevant costs per satisfactory scan are cheaper on Machine XR50 and therefore brain scans should be undertaken on this machine.

(a) Standard cost sheet (per unit) (£) (£) Direct materials 40 m at £5.30 per m 2 212 Direct wages: Bonding dept 48 hours at £12.50 per hour 600 Finishing dept 30 hours at £9.50 per hour 285 (i) Prime cost 1097 Variable overhead: a Bonding dept 48 hours at £0.75 per hour 36 Finishing dept 30 hours at £0.50 per hour 15 51 (ii) Variable production cost 1148 Fixed production overheadb 40 (iii) Total production cost 1188 Selling and distribution cost c 20 Administration costc 10 30 (iv) Total cost 1218 Notes a Variable overhead rates: Bonding = £375 000 = £0.75 500 000 hours Finishing = £150 000 = £0.50 300 000 hours b Fixed production overhead rate per unit of output = £392 000 = £40 9800 units The fixed production overhead rate per unit of output has been calculated because there appears to be only one product produced. Alternatively, a fixed production hourly overhead rate can be calculated and charged to the product on the basis of the number of hours which the product spends in each department.

c Selling and production cost per unit of output = £196 000 = £20 9800 units Administration cost per unit of output = £98 000 = £10 9800 units (b) Selling price per unit £1218 1 80 50 = 1433 Solution IM 2.4 4 AN INTRODUCTION TO COST TERMS AND CONCEPTS885 2 COST ASSIGNMENT5 Solution IM 3.1 Solution IM 3.2 Solution IM 3.3 Solution IM 3.4 (a) For the answer to this question see ‘Budgeted overhead rates’ in Chapter 3. (b) A lower production overhead rate does not necessarily indicate that factory X is more efficient than factory Y. The reasons for this are:(i) Factory Y’s operations might be highly mechanized, resulting in large depreciation costs, whereas factory X’s operations might be labour-intensive.Consequently products produced in factory Y will incur higher overhead andlower labour costs, whereas products produced in factory X will incur loweroverhead and higher labour costs.

(ii) Factory Y may have invested in plant with a larger operating capacity inorder to meet future output. This will result in larger fixed costs and a higheroverhead rate.

(iii) Both factories may use different denominators in calculating the overheadrates. For example, if factory Y uses normal capacity and factory X usesmaximum practical capacity then factory Y will have a higher overhead rate.

(iv) Current budgeted activity might be used by both firms to calculate theoverhead rate. The level of budgeted sales will determine budgeted activity.The lower overhead rate of factory X might be due to a higher sales volumerather than efficient factory operations.

(v) Different cost classification might result in different overhead rates. Factory X might treat all expenditure as a direct cost wherever possible. For example, employers’ costs might be charged out by means of an inflatedhourly wage rate. Factory Y may treat such items as overhead costs.

See answer to Question 3.22 in the text for the answer to this question.

(a) For the answer to this question see ‘Blanket overhead rates’ in Chapter 3.

(b) For the answer to this question see Learning Note 3.1 on the open access website.

(a) Production department Service Total department ABC (£) (£) (£) (£) (£) Direct 261 745 226 120 93 890 53 305 635 060 Indirect 135 400 (40%) 118 475 (35%) 67 700 (20%) 16 925 (5%) 338 500Service dept appointment 23 410 ( 1 3 ) 23 410 ( 13 ) 23 410 ( 13 ) (70 230) ––––––– ––––––– ––––––– –––––– ––––––– 420 555 368 005 185 000 — 973 560 ––––––– ––––––– ––––––– –––––– ––––––– Allocation base (1) 17 760 5 760 148 000 =£23.68 =£63.89 =£1.25 per direct per m/c per hour labour hour hour Cost assignment Solutions to Chapter 3 questions 6COST ASSIGNMENT Note:

1. Dept. A direct labour hours = 10 × 37 × 48= 17 760Dept. B machine hours= 5 × 24 × 48=5760Dept. C units = 148 000 (b) Dept A £ 9 direct labour hours at £23.68 213.12 Dept B 3 m/c hours at £63.89 191.67 Dept C 100 units at £1.25 125.00 529.79 Cost per unit = £5.30 (£529.79/100) (a) Overhead analysis sheet Production Service Total Cutting Tents Bags Stores Canteen Maintenance(£) (£) (£) (£) (£) (£) (£) Indirect wages 147 200 6 400 19 500 20 100 41 200 15 000 45 000 Consumable materials 54 600 5 300 4 100 2 300 — 18 700 24 200 Plant depreciation 84 200 31 200 17 500 24 600 2 500 3 400 5 000Power a 31 700 5 389 12 046 10 144 951 2 536 634 Heat and light b 13 800 Rent and rates b 14 400 11 120 13 900 9 730 2 085 3 475 1 390 Building insurance b 13 500 359 400 59 409 67 046 66 874 46 736 43 111 76 224 Reapportionment:Stores c – 29 210 5 842 5 842 (46 736) — 5 842 Canteen d – 2 694 18 476 21 941 (43 111) — Maintenance e – 1 887 37 731 42 448 (82 066) 359 400 93 200 129 095 137 105 Machine hours 87 000 2 000 40 000 45 000 Labour hours 112 000 7 000 48 000 57 000 Machine hour rate £46.60 £3.23 £3.05 Overheads per labour hour £13.31 £2.69 £2.41 Notes Bases of apportionment: a estimated power usage; b area; c value of issues; d direct labour hours; e machine hours. Actual basis for other costs.

(b) See section on budgeted overhead rates in Chapter 3 for the answer to this question. In addition the following points should be made:(i) It draws attention to the under /over recovery of overheads arising from changes in production levels.

(ii) There is difficulty in determining estimated overheads and an appropriate level of activity when calculating predetermined overhead rates. Solution IM 3.5 COST ASSIGNMENT7 (a) Percentage of direct labour cost method = (£600 000/£200 000) 100 = 300% of direct labour cost Direct labour hour method = (£600 000 /40 000 direct labour hours) = £15 per direct labour hour Machine hour method = (£600 000 /50 000 machine hour) = £12 per machine hour (b) See ‘Predetermined overhead rates’ in Chapter 3 for the answer to this question.

(c) The question states that the company has become machine-intensive and implies that in the long term there is a closer association between overhead expenditureand machine hours than the other two methods. Therefore the best measure ofoverhead resources consumed by jobs or products is machine hours.

(d) Job Ax (£) Direct material 3788 Direct labour 1100 Direct expenses 422 Prime cost 5310 Production overhead (120 machine hours £12) 1440 Factory cost 6750 Administrative overheads (20% £6750) 1350 Total cost 8100 Profit (£8100/0.90 £8100) 900 Selling price 9000 Workings Administration overhead absorption rate = Total admin. overheads /total factory cost = £328 000 /£1 640 000 = 20% of factory cost (e) The general characteristics of incentive schemes should ensure that: (i) the scheme is simple to understand and administer; (ii) payment should be made as quickly as possible after production; (iii) there should be no limit on earnings and employees must be safe-guardedfrom earning lower wages than time rate wages arising from problems whichare outside their control.

The advantages of incentive schemes are: (i) increased production and lower average unit costs; (ii) increased morale of the workforce; (iii) attraction of more efficient workers to the company. Solution IM 3.6 8COST ASSIGNMENT (a) Predetermined machine hour rate =machine department overheads (£1 080 000) machine hours (80 000) Machining department = £13.50 per machine hour Hand finishing department = £760 000 /120 000 labour hours = £6.33 per labour hour (b) (i) Machine department Hand finishing department (£) (£) Overhead incurred 84 500 67 100 Overhead absorbed 81 000 (6000 £13.50) 60 800 (9600 £6.33) Under recovery of 3 500 6 300 overheads (ii) Overheads that are apportioned to cost centres tend to be on an arbitrary basis and are unlikely to be controllable by the cost centre manager. Managers should be held accountable for only those overheads that they can control. See‘Guidelines for applying the controllability principle’ in Chapter 16 for a moredetailed discussion of controllable and non-controllable costs.

(c) Absorption costing is used by companies to ensure that all products /services bear an equitable share of company overheads. The Statement of Standard AccountingPractice (SSAP 9) requires that stocks should be valued at full production cost.Therefore absorption costing is required to allocate overheads to products inorder to meet financial accounting requirements.

(a) In order to ascertain the actual overhead traced to the production departments, it is necessary to allocate the service department overheads to the filling and sealingdepartments: Filling Sealing Maintenance Canteen(£) (£) (£) (£) Allocated 74 260 38 115 25 050 24 375Reallocation of: Canteen 14 625 (60%) 7 800 (32%) 1 950 (8%) (24 375) Maintenance 18 900 (70%) 7 290 (27%) (27 000) 810 (3%) Canteen 486 (60%) 259 (32%) 65 (8%) (810) Maintenance 47 (70 /97) 18 (27 /97) – – 108 318 53 482 Predetermined overhead rates:

Filling Sealing(£) (£) Budgeted overheads 110 040 53 300 Budgeted direct labour hours 13 100 10 250 Direct labour hour overhead rate 8.40 5.20 Overhead incurred 108 318 53 482 Overhead allocated 107 688 (12 820 £8.40) 52 390 (10 075 £5.20)(Under) /over recovery (630) (1 092) Solution IM 3.8 Solution IM 3.7 (b) The objectives of overhead apportionment and absorption are:(i) To meet the stock valuation and profit measurement requirements forfinancial accounting purposes. Financial accounting regulations in most countries require that all manufacturing overheads be traced to products forstock valuation purposes.

(ii) For various decisions, such as pricing decisions, management requireestimates of the total product costs.

(iii) Overhead costs may be traced to different segments of the business, such asproduct groups or geographical regions, in order to assess the performanceof each segment.

Overhead apportionment and absorption can be criticized on the followinggrounds: (i) The process includes many arbitrary apportionments and does not provide an accurate indication of the resources consumed by each product. In tracingoverheads to products, the allocation procedure assumes that all overheadsare related to volume. This is inappropriate for many fixed overheads, sincethey are fixed in the short term, and tend to be caused by factors other thanvolume, such as the diversity of the product range, number of set-ups andrange of component parts which the firm stocks.

(ii) Fixed overheads are sunk costs, and will tend not to change in the shortterm. Hence they are unaffected in the short term, irrespective of whichdecisions are taken. Arbitrary overhead allocations should not be used fordecision-making purposes.

(iii) Overhead allocations are normally undertaken for stock valuation purposes.

The procedures are not intended to meet other requirements, such asdecision-making and performance evaluation.

(iv) Individuals should not be held accountable for costs which they cannotcontrol. Arbitrary apportionment of overheads is therefore inappropriate forcost control and performance measurement purposes.

(a) (i) An over-absorption of overheads occurs because the actual overhead charged to products (or clients) exceeds the overheads incurred. Therefore £747 360 (£742 600 actual overheads + £4760 over-absorption were charged to clientsduring direct hours worked, the actual professional staff hours worked during the period were 99 648 (£747 360/£7.50 hourly overhead rate). Therefore budgeted professional staff hours = 98 288 (99 648 1360).

(ii) Budgeted overhead expenditure = Budgeted hours (98 288) × Overhead rate (£7.50) = £737 160 (b) To determine the overhead rate the senior staff hours should be weighted by a factor of 1.4 and the junior staff hours by a factor of 1.0:Senior staff= 21 600 × 1.4 = 30 240 Junior staff= 79 300 × 1.0 = 79 300 109 540 Allocation of overheads:

Senior staff= 30 240/109 540 × £784 000 = £216 434 Junior staff= 79 300/109 540 × £784 000 = £567 566 £784 000 Solution IM 3.9 COST ASSIGNMENT 9 Senior staff overhead allocation rate = £216 434/21 600= £10.020 per hour Junior staff overhead allocation rate = £567 566/79 300 hours = £7.157 per hour (c) Presumably the senior staff consume a greater proportion of the overhead costs than the junior staff and the revised method is an attempt to reflect this difference in resource consumption. For example, senior staff are likely to require moreoffice space and make greater demands on secretarial time, telephones, etc. Therevised method creates two separate cost centres and overhead rates whereas theprevious method used a single blanket rate for the whole organization.

(d) See the section on under- and over-recovery of overheads in Chapter 3 for the answer to this question. Differences between overhead incurred and overheadabsorbed may be due to:(1) differences between actual and budgeted expenditure; (2) differences between actual and budgeted activity level.

(i) With the step-wise method the costs of the first service department (Department G specified in the question) are reapportioned to the second department but returnallocations are not made from the second department back to the first department.

Production depts Internal services12 G H (£000) (£000) (£000) (£000) Overheads 870 690 Costs 160 82 G apportioned 96 (60%) 48 (30%) 160 16 (10%) –––– –––– 98 H apportioned 61 ( 50 /80 )3 7(30 /80 ) 98 –––– –––– –––– 1027 775 –––– –––– (ii) Let G = Service Department G overheads Let H = Service Department H overheads G = 160 + 0.2H H = 82 + 0.1G Rearranging the above equations 0.2H + G = 160 (1) 1H 0.1 G = 82 (2) Multiply equation (1) by 1 and equation (2) by 10 0.2H + G = 160 10H G = 820 Add the above equations together: 9.8H = 980H = 100 Substituting for the value of H in equation (1) 0.2 (100) + G = 160 G = 180 Solution IM 3.10 10 COST ASSIGNMENT COST ASSIGNMENT11 Production depts Internal Total 1 2 Services (£000) (£000) (£000) G (180 × 90%) 162 ( 69 ) 108 ( 39 )5 4 H (100 × 80%) 80 ( 5 8 )5 0( 3 8 )3 0 ––– –––– ––– 242 158 84 Overheads (given) 870 690 –––– ––– 1028 774 –––– ––– (iii) The simultaneous equation method will yield more accurate allocations because it takes into account the fact that service departments serve each other whereas thestep-wise method ignores such reciprocal usage. The step-wise method involvessimpler computations and, in this question, does not give a significantly differentanswer. However, the step-wise method may yield inaccurate results whereservice costs are high and there are more than two service departments withsignificantly different usage ratios between the departments.

(a) Overhead analysis (ignoring reciprocal allocations) General Service cost Production cost factory centres centres overhead 1 2 A B (£) (£) (£) (£) (£) Primary allocation 210 000 93 800 38 600 182 800 124 800Apportionment of general factoryoverhead a (210 000) 10 500 21 000 31 500 147 000 ––––––– ––––––– –––––– –––––––– –––––––– — 104 300 59 600 214 300 271 800 ––––––– ––––––– Charges by service cost centre 1 b (104 300) — 91 262 13 038 ––––––– –––––– –––––––– –––––––– — 59 600 305 562 284 838 –––––––––––––– Charges by service cost centre 2 c (59 600) 8 221 51 379 –––––– –––––––– –––––––– — £313 783 £336 217 –––––– –––––––– –––––––– –––––– –––––––– –––––––– Budgeted direct labour hours 120 000 20 000 –––––––– –––––––– –––––––– –––––––– Absorption rates £2.61 £16.81 –––––––– –––––––– –––––––– –––––––– Notes a General factory overhead is apportioned to service cost centres before reallocation to production centres as indicated in note (i) of the question.b Because reciprocal allocations are not made, the costs allocated to service cost cen- tre 1 are reallocated as follows:

£91 262 (63/72 £104 300) to production cost centre A £13 038 (9 /72 £104 300) to production cost centre B c Reciprocal charges are not made. Therefore the allocation is as follows:

4 000/29 000 £59 600 = £8 221 to production cost centre A 25 000 /29 000 £59 600 = £51 379 to production cost centre B Solution IM 3.11 12COST ASSIGNMENT (b) The difference may be due to the following:

(i) Changes occurred in projected overhead expenditure compared withexpenditure which was used to determine the current year’s overhead rate.

(ii) Current overhead rates do not include a proportion of the service cost centres overhead.

(iii) Budgeted activity for the next year is greater than the current year forproduction cost centre A. If this is not matched by a corresponding increasein overhead expenditure then the hourly overhead rate will decline.Budgeted activity for production cost centre B is lower than the current year,resulting in an increase in the overhead rate. Because fixed overheads do notchange in relation to activity, the hourly overhead rate will fluctuatewhenever changes in activity occur. (See Example 3.2 in Chapter 3 for anillustration.) (c) This question can be answered by using either the repeated distribution or simultaneous equation methods. Both methods are illustrated in Appendix 3.1 toChapter 3. The simultaneous equation method is illustrated below: Let X= total overhead of service cost centre 1 Y = total overhead of service cost centre 2 Then X= 104 300 + 31 0 Y (i.e. 1000 /30 000 hrs of service cost centre 2 overheads) Y = 59 600 + 1 5 X (i.e. 18% out of total of 90% of service cost centre 1 overheads) Rearranging the above equations: X 31 0 Y = 104 300 (1) 1 5 X + Y = 59 600 (2) Multiply equation (1) by 1 and equation (2) by 5: X 31 0 Y = 104 300 X+ 5 Y = 298 000 Adding the above equations together: 149 Y= 402 300 30 Y = 402 300 30 149 Y = 81 000 Substituting for Yin equation (1) results in the following equation:

X 31 0 81 000 = 104 300 X= 107 000 The service cost centre overheads of £107 000 (service cost centre 1) and £81 000 (service cost centre 2) are now apportioned to the production cost centres as follows: General Service cost Production costfactory centre centre overhead 1 2 A B (£) (£) (£) (£) (£) Primary allocation 210 000 93 800 38 600 182 800 124 800 Apportionment of general factory overhead (210 000) 10 500 21 000 31 500 147 000 –––––––– –––––– –––––– ––––––– ––––––– — 104 300 59 600 214 300 271 800 –––––––– –––––––– Charges by service cost centre 1 a (107 000) 21 400 74 900 10 700 Charges by service cost centre 2 b 2 700 (81 000) 10 800 67 500 –––––– –––––– ––––––– ––––––– — — £300 000 £350 000 –––––– –––––– ––––––– ––––––– –––––– –––––– ––––––– ––––––– Budgeted direct labour hours 120 000 20 000 –––––– –––––– –––––– –––––– Absorption rates £2.50 £17.50 –––––– –––––– –––––– –––––– Notes a 18 /90 £107 000 = £21 400 to service cost centre 2 (18% out of 90%) 63 /90 £107 000 = £74 900 to production cost centre A 9 /90 £107 000 = £10 700 to production cost centre B b 1000 /30 000 £81 000 = £2700 to service cost centre 1 4000 /30 000 £81 000 = £10 800 to production cost centre A 25 000 /30 000 £81 000 = £67 500 to production cost centre B (d) The answer should include the following points: (i) The overhead rate calculations do not distinguish between fixed and variableelements. Such an analysis is necessary for decision-making purposes.

(ii) The majority of service cost centre 1 costs are variable. It is preferable to determine an activity measure which exerts most influence on the variablecosts and apportion the costs on the basis of this measure. The presentmethod of apportionment appears to be inappropriate.

(iii) Service cost centre 2 is the maintenance department and the majority of costs are fixed, thus suggesting preventive maintenance be undertaken. Thequestion does not make it clear which hourly base is used for allocatingoverheads (direct labour hours or machine hours). Machine hours should beused for allocating variable costs, since these costs are likely to vary with thisactivity base. Preventive maintenance should be apportioned on the basis of the planned hours which the maintenance staff intend to allocate to eachdepartment.

(iv) Production cost centre B is highly mechanized, thus suggesting that amachine hour rate might be preferable to the present direct labour hour rate. COST ASSIGNMENT 13 14COST ASSIGNMENT (a)Department cost statement Belts Braces Administration Maintenance Warehousing Total (£000) (£000) (£000) (£000) (£000) (£000) Direct variable costs: Materials 120 130 — 20 ) 30) 300 Labour 80 70 50 ) 80) 20) 300 –––– –––– –––– –––– –––– ––––– 200 200 50 ) 100 ) 50) 600 Factory-wide indirect cost per floorspace 400 400 50 ) 100 ) 50) 1000 –––– –––– –––– –––– –––– ––––– 600 600 100 ) 200 ) 100 ) 1600 Service departments Administration a 40 40 (100) 10 ) 10) — –––– –––– –––– –––– –––– ––––– 640 640 — 210 ) 110 ) 1600 Maintenance b 79 79 — (264) 106 ) — Warehousing b 108 54 — 54 ) (216) — –––– –––– –––– –––– –––– ––––– £827 £773 — — — £1600 –––– –––– –––– –––– –––– ––––– Cost per unit: Belts £827 000 = £8.27 100 000 Braces £773 000 = £15.46 50 000 Notes a Administration does not receive any charges from the other service departments.

Therefore the reciprocal basis does not apply.b The simultaneous equation method is used to allocate the maintenance and ware- house costs.

Let M= total cost of the maintenance department W = total cost of the warehousing department Then M= 210 + 0.25 W (1) W = 110+ 0.4 M (2) Multiplying equation (1) by 4 and equation (2) by 1, and rearranging the resulting equa- tions: 4M W = 840 0.4 M+ W = 110 3.6 M = 950 M = £263.89 Substituting the value of Minto equation (2):

W= 110 + 0.4 263.89 W = £215.56 (b) Kaminsky Ltd has spare capacity, and therefore any sales revenue in excess of variable costs will provide a contribution towards fixed costs and profit. Therefore it is necessary to calculate the variable cost per unit for belts and braces.The calculations of the unit variable cost are as follows: Solution IM 3.12 COST ASSIGNMENT15 Belts Braces Administration Maintenance Warehousing Total (£000) (£000) (£000) (£000) (£000) (£000) Direct variable costs: Materials 120 130 — )) 20) 30) 300 Labour 80 70 50 ) 80) 20) 300 –––– –––– ––– ––––– –––– ––– 200 200 50 ) 100 ) 50) 600 Service departments Administration 20 20 (50) 5 ) 5) — –––– –––– ––– ––––– –––– ––– 220 220 — )) 105 ) 55) 600 Maintenance a 39.6 39.6 — )) (132) 52.8 ) — Warehousing a 53.9 26.9 — )) 26.95 ) (107.8) — –––– –––– ––– ––––– –––– ––– 313.5 286.5 — )) —) —) 600 –––– –––– ––– ––––– –––– ––– Variable cost per unit: Belts £313 500 = £3.135 100 000 Braces £286 500 = £5.73 50 000 Note a The simultaneous equation method is used to allocate the service department costs as follows: Let M= maintenance department variable costs W = warehousing department variable costs Then M= 105 + 0.25 W (1) W = 55 + 0.4 M (2) Multiplying equation (1) by 4 and equation (2) by 1: 4M W = 420 0.4 M+ W = 55 3.6 M = 475 M = 131.94 Substituting in equation (2): W= 55 + 0.4 131.94 W = 107.8 Camfan order (£) Contract price 5000 Variable costs (1000 belts at £3.135) 3135 Contribution 1865 If this order is accepted, profits will increase by £1865, provided that better opportunities are not available and the normal selling price will not be affected. Itis unlikely that such a small order will affect the normal selling price. Mixon Spenders contract The normal unit cost based on a normal activity of 100 000 belts is £8.27. If thisunit cost is used as the basis for determining the ‘cost-plus’ selling price then the agreed selling price will be £9.10 (£8.27 + 10%). The normal selling price will be £9.92 (£8.27 + 20%). The contribution from supplying 100 000 belts will be £596 500 [(£9.10 £3.135 variable cost) 100 000]. Total demand will now be 200 000 belts, but maximum output is 150 000 belts. Therefore existing sales will be reduced by 50 000 belts. The lost contribution is £339 250 [50 000 (£9.92 £3.135)]. Consequently total contribution will increase by £257 250. Alternatively, Kaminsky might base selling price on unit costs at maximum capacity of 150 000 units. The revised unit cost will be as follows:

Fixed costs apportioned to belts = £513 500 (£827 000 total cost £313 500 variable cost) Fixed costs per unit (£) = 3.42 (£513 500 /150 000 units) Variable cost per unit (£) = 3.135 –––– Total cost per unit (£) = 6.555 –––– Selling price for contract = £7.21 (£6.555 + 10%).

The total contribution from the contract will be £407 500, consisting of 100 000 units at a contribution per unit of £4.075 (£7.21 £3.135). This will still cover the contribution sacrificed on existing business. On the basis of the abovequantitative information, the contract should be accepted. However, beforeacceptance, the following qualitative factors should be considered: (i) Will the long-term disadvantages from a loss of customer goodwill from depriving normal customers of 50 000 units outweigh the short-term advan-tage of taking on the contract?

(ii) An attractive feature of the contract is that it will result in certain sales of 2000 units per week, thus enabling production, cash flows etc. to be fore-casted more accurately.

(c) For the answer to this question see ‘alternative denominator level measures’ in Chapter 7. In addition the answer should emphasize that normal overhead ratesreflect a long-term planned activity base which is expected to satisfy demandlevels over a series of years. Over this period, fluctuations in customer demand,seasonal and cyclical changes will be incorporated into an annual rate. Anormalized overhead rate recognizes that the company’s overhead costcommitment is related to the long-run demand for its products. A normalizedoverhead rate is preferable for pricing purposes, since the alternative of basingoverhead rates on the activity for next year will result in higher selling priceswhen demand is low if cost-plus pricing is used. Prices should be lower whendemand is depressed. A normalized overhead rate should avoid suchinconsistencies. 16 COST ASSIGNMENT ACCOUNTING ENTRIES FOR A JOB COSTING SYSTEM17 Solution IM 4.1 (a) and (b) Fixed assets (£000) Balance b /f 275 ) Share capital (£000) Balance b /f 500 ) Creditors control (£000) ) (£000) ) Bank 150 ) Stores control 525 ) Balance c /f 487.5 Production overhead control 47.5 Production overhead control 26 ) Production overhead control 39 ) ––––– ––––– 637.5 637.5 ––––– ––––– Balance b /f 487.5 Provision for depreciation (£000) Production overhead control 15 ) Bank (£000) (£000) Balance b /f 225 Wages control 500 Debtors 520 Production overhead control 20 Sales overhead control 40 Administration overhead control 25 Creditors control 150Balance c/f1 0 ––– ––– 745 745 ––– ––– Balance b /f1 0 Wages control (£000) (£000) Bank 500 WIP: Department A 300 .5 Wage deductions 175 WIP: Department B 260 .5 Production overhead control 42.5 Sales overhead control 47.5 Administration overhead control 25 .5 ––– –––– 675 675 .5 ––– –––– Accounting entries for a job costing system Solutions to Chapter 4 questions 18ACCOUNTING ENTRIES FOR A JOB COSTING SYSTEM Wage deductions (£000) Wages control 175 .5 Stores control (£000) (£000) Creditors control 525 WIP: Department A 180 .5 WIP: Department B 192.5 Production overhead control 65 .5 Balance c /f 87.5 ––– –––– 525 525 .5 ––– –––– Balance b /f 87.5 Production overhead control(£000) (£000) Creditors control 47.5 WIP control: Department A 110 Bank 20 .5 WIP control: Department B 120 Stores control 65 .5 Profit and loss 25 Wages control 42.5 Creditors control 26 .5 Creditors control 39 .5 Provision for depreciation 15 .5 ––––– ––– 255 .5 255 ––––– ––– WIP control: Department A (£000) (£000) Stores control 180 Finished goods control 570 Wages control 300 Balance c /f2 0 Production overhead control 110 ––– ––– 590 590 ––– ––– Balance b /f2 0 WIP control: Department B (£000) (£000) Stores control 192.5 Finished goods control 555 .0 Wages control 260 .0 Balance c /f 17.5 Production overhead control 120 .0 ––––– ––––– 572.5 572.5 ––––– ––––– Balance b /f 17.5 Selling overhead control(£000) (£000) Bank 40 .0 Profit and loss 87.5 Wages control 47.5 ––––– ––––– 87.5 87.5 ––––– ––––– Administration overhead control (£000) (£000) Bank 25 Profit and loss 50 Wages control 25 ––––– ––––– 50 50 ––––– ––––– ACCOUNTING ENTRIES FOR A JOB COSTING SYSTEM19 Debtors control (£000) (£000) Sales 870 Bank 520 Balance c/f 350 ––––– ––––– 870 870 ––––– ––––– Balance b /f 350 Finished goods control(£000) (£000) WIP Control: Department A 570 Cost sales 700 WIP Control: Department B 555 Balance c /f 425 ––––– ––––– 1125 1125 ––––– ––––– Balance b /f 425 Cost of sales (£000) (£000) Finished goods control 700 Profit and loss 700 ––––– ––––– 700 700 ––––– ––––– Sales (£000) (£000) Profit and loss 870 Debtors 870 ––––– ––––– (c) (i) Profit statement for the period 1 February to 30 April (£000) (£000) Sales 870 Cost of sales 700 ––––– Gross profit 170 Under-absorption of production overheads 25 Selling overheads 87.5 Administration overheads 50 162.5 –––– ––––– Net profit 12 7.5 ––––– (ii) Balance sheet as at 30 April (£000) (£000) (£000) Fixed assets at cost 275 Provision for depreciation 15 ––––– Written down value 260 Current assets Stock: Finished goods 425 WIP: Department A 20 WIP: Department B 17.5 37.5 –––– Raw materials 87.5 ––––– 550 Debtors 350 Bank 10 –––––910 Current liabilities Creditors 487.5 Wage deductions 175 662.5 247.5 ––– ––––– ––––– 507.5 ––––– Financed:

Capital 500 Profit 7.5 ––––– 507.5 ––––– 20ACCOUNTING ENTRIES FOR A JOB COSTING SYSTEM Solution IM 4.2 (a) See the comparison between management accounting and financial accounting in Chapter 1 for the answer to this question.

(b) Note that the job ledger control account shown in the question is equivalent to the work in progress control account described in Chapter 4.

Stores ledger control account(£000) (£000) Opening balance 176.0 Job ledger control A/c Financial ledger (64 500 kg × £3.20) 206.4 control A/c 224.2 Production o’head control A/c (Balancing figure) 24.3 Closing blanace 169.5 ––––––– ––––––– 400.2 400.2 ––––––– ––––––– Production wages control account (£000) (£000) Financial ledger Job ledger control A/c (75%) 147.0 control A/c 196.0 Production o’head control A/c (25%) 49.0 ––––––– ––––––– 196.0 196.0 ––––––– ––––––– Production overhead control account (£000) (£000) Financial ledger Job ledger control A/c (1) 191.1 control A/c 119.3 Under-absorbed overheadStores ledger control A/c 24.3 (Balance to profit and loss Production wages contol A/c) 1.5 A/c 49.0 ––––––– ––––––– 192.6 192.6 ––––––– ––––––– Job ledger control account (£000) (£000) Opening balance 114.9 Cost of sales A/c (balancing Stores ledger control A/c 206.4 figure) 506.4 Production wages control Closing balance 153.0 A/c 147.0 Production o’head control A/c 191.1 ––––––– ––––––– 659.4 659.4 ––––––– ––––––– Note:

(1) Direct labour hours = = 14700 hours Overhead charged to production = 14700 direct labour hours × direct labour rate (£13) = £191 100. Direct labour wages (£147 000) Direct labour wage rate (£10) ACCOUNTING ENTRIES FOR A JOB COSTING SYSTEM21 Solution IM 4.3 (a)Raw material control account (£) (£) Opening balance 87 460 Work-in-progress (1) 194 550 Cost ledger control 200 740 Manufacturing overhead control a/c (1) 6 917 Closing balance 86 733 ––––––– ––––––– 288 200 288 200 ––––––– ––––––– Manufacturing overhead control account (£) (£) Raw material control 6 917 Opening balance 5 123 Wages control 74 887 Work-in-progress (2) 191 200 Cost ledger control 112 194 Closing balance 2 325 ––––––– ––––––– 196 323 196 323 ––––––– ––––––– Work-in-progress account (£) (£) Raw material control 194 550 Finished goods (3) 570 308 Wages control 186 743 Abnormal loss to profit and Manufacturing overhead loss account (3) 2 185 control a/c 191 200 ––––––– ––––––– 572 493 572 493 ––––––– ––––––– Finished goods account (£) (£) Opening balance 148 352 Production cost of sales 534 508 Work-in-progress (3) 570 308 Closing balance 184 152 ––––––– ––––––– 718 660 718 660 ––––––– ––––––– Workings (1) Raw material: Material A Material B Indirect Total (kg) (£) (kg) (£) (£) (£) Opening balance 18 760 52 715 4 242 29 994 4 751 87 460 Purchases 34 220 97 527 13 520 95 992 7 221 200 740 –––––– ––––––– –––––– –––––– –––––– ––––––– 52 980 150 242 17 762 125 986 11 972 288 200 Issues a 35 176 99 759 13 364 94 791 6 917 201 467 –––––– ––––––– –––––– –––––– –––––– ––––––– Closing balance 17 804 50 483 4 398 31 195 5 055 86 733 –––––– ––––––– –––––– –––––– –––––– ––––––– Total direct materials issue cost = £194 550 (£99 759 + £94 791) Total input of direct materials = 48 540 kg (35 176 + 13 364) Notes a The cost of the materials issues is calculated as follows:

Material A = £2.836 per kg (£150 242/52 980 kg) Material B = £7.093 per kg (£125 986/17 762 kg) Direct materials issued = 48 540 kg (35 176 + 13 364) £194 550 (99 759 + 94 791) (2) Overheads absorbed = 11 950 hrs at £16.00 = £191 200 (3) Calculation of cost of finished goods transfer and abnormal lossExpected output (48 540 kg × 0.95) = 46 113 kg Actual output 45 937 kg –––––– Abnormal loss 176 kg –––––– Cost per kg = £12.415 per kg (£572 493/46 113 kg) Output = 45 937 kg at £12.415 = £570 308 Abnormal loss = 176 kg at £12.415 = £2 185 (4) Calculation of cost of sales (kg) (Total £) Opening balance 12 160 148 352 Production 45 937 570 308 –––––– ––––––– 58 097 718 660 Cost of sales a 43 210 534 508 –––––– ––––––– Closing balance 14 887 184 152 –––––– ––––––– Notes a Issue cost = £718 660/58 097 kg = £12.37 Cost of sales = 43 210 kg × £12.37 = £534 508 (b) See ‘Equivalent production’ in Chapter 5 for the answer to this question.

(a) The costs of labour turnover include: (i) leaving costs associated with completing the appropriate documentation andlost production if the employees cannot be immediately replaced; (ii) recruitment costs resulting from the advertising, selection and engagement of new staff; (iii) learning costs including training costs, the cost arising from lower productiv- ity and defective work during the learning period.

(b) Workings: Basic time = 40 workers × 38 hours per week for 4 weeks = 6080 hoursOvertime = Total hours (6528) Basic time (6080) = 448 hours (£) Total wages = Basic pay (6528 hours × £10) =65Overtime premium (448 hours × £3.50) 1 568 –––––– Less deductions (30% × £66 848) 0 – Net amount paid 46 794 Cost of productive time (6.528 hours 188 hours idle time) × £10 63 400 Cost of idle time (188 hours × £10) 1 880 Journal entries: Dr Cr Wages control £66 848Bank £46 794 Employee deductions 20 054 Being analysis of gross wages for direct workers Work in progress £63 400 Production overhead (1) £3 448 Wages control £66 848 Being the allocation of gross wages for the period 22 ACCOUNTING ENTRIES FOR A JOB COSTING SYSTEM Solution IM 4.4 280 20 54 66 848 –––––– –––––– ACCOUNTING ENTRIES FOR A JOB COSTING SYSTEM23 Note:

(1) Production overhead = Idle time (£1 880) + Overtime premium (£1 568) (a) WorkingsGross wages paid (£) Direct (25 520 hours £14.40) 367 448 Direct (2120 overtime hours £4.32) 9 158 –––––––– –––––––– Indirect (4430 hours £11.70) 51 831 Indirect (380 hours £3.51) 1 334 –––––––– –––––––– Tax and employees’ national insurance (£) Direct (£376 646 £293 865) 82 781 Indirect (£53 165 £41 577) 11 588 –––––––– 31 456.40 –––––––– Productive hours (7200 + 11 600 + 4400) 23 200 hours Direct labour unproductive labour hours (25 520 23 200) 2 320 hours Productive hours charged to WIP (23 200 £14.40) £334 080 Charge to production overhead (£) (£) Gross wages of indirect workers 53 165 Overtime premium (direct workers) 9 158 Unproductive time of direct workers (2320 £14.40) 33 408 95 731 Wages control account (£) (£) Cash /bank (net wages): WIP 334 080 Direct 293 865 Production overhead 95 731 Indirect 41 577Tax and national insurance 94 369 ––––––– ––––––– ––––––– ––––––– (b) The cost of the proposed piecework scheme based on the production for the current period is as follows: (£) Product 1 (36 000 units £3) 108 000 Product 2 (116 000 units £1.50) 174 000 Product 3 (52 800 units £1.20) 0 ––––––– Unproductive time (see note*) 20 300 ––––––– ––––––– * Calculation of wages paid for unproductive time Solution IM 4.5 376 646 53 165 429 811 429 811 36 63 345 360 365 660 24ACCOUNTING ENTRIES FOR A JOB COSTING SYSTEM Productive time is:

Product 1 (36 000 units /6 units per hour) 6 000 hours Produc 2 (116 000 units /12 units per hour) 9 666.67 hours Produc 3 (52 800 units /14.4 units per hour) 3 666.67 hours –––––––– 19 333.34 hours –––––––– Wages paid for unproductive time (10% 19 333.34 hours £10.50) £20 300 The direct labour cost per unit for the current scheme is: Product 1 (7200 hours £14.40) /36 000 units = £2.88 Product 2 (11 600 hours £14.40) /116 000 units= £1.44 Product 3 (4400 hours £14.40) /52 800 units = £1.20 The current piecework rates exceed the above unit costs but the overall costs are lower with the piecework scheme because of less unproductive time and a saving inovertime. It is also likely that overhead costs will be reduced because of a reductionin overtime in respect of indirect labour. PROCESS COSTING25 Solution IM 5.1 Solution IM 5.2 (a) See section on job and process costing systems in Chapter 2 and the introduction to Chapter 5 for the answer to this problem.

(b) It would appear that a job costing system provides more accurate product costs because a separate cost is calculated for each job whereas with a process costing system the cost per unit is an average cost. On the other hand, a greater proportionof the costs are likely to be direct under process costing. With a job costing system, alarge proportion of costs will be treated as overheads and the problem ofapportioning and allocating overheads will result in inaccurate product costs. In thissense process costing might yield more accurate product costs. However, oneproblem with process costing is that there is a need to estimate the degree ofcompletion of closing stocks of WIP in order to estimate equivalent units and costper unit. If it is difficult to produce an accurate estimate of the degree of completionthen the product costs will also be inaccurate. Therefore it depends on thecircumstances – in some situations job costing product costs will be more accurateand in other situations process costing product costs may be more accurate.

(a) The question does not indicate the method of overhead recovery. It is assumed that overheads are to be absorbed using the direct wages percentage method.

Process A account Units Price Amount Units Price Amount (£) (£) (£) (£) Direct materials 6000 12 000 Normal loss (scrap Direct materials added 5 000 account) 300 1.5 450 Direct wages 4 000 Process B 5760 5.5 31 680 Direct expenses 800 Production overhead 10 000 –––––– (250% direct wages) 31 800 Abnormal gain account 60 5.5 330 –––––––––– –––––––––– 6060 32 130 6060 32 130 –––– –––––– –––––––––– Cost per unit = cost of production scrap value of normal loss expected output = £31 800 £450 = £5.50 5700 units Process B account Units Price Amount Units Price Amount (£) (£) (£) (£) Process A 5760 5.5 31 680 Normal loss (scrap Direct materials added 9 000 account) 576 2.0 1 152 Direct wages 6 000 Process C 5100 12.0 61 200 Direct expenses 1 680 Abnormal loss 84 12.0 1 008Production overhead (250% direct wages) 15 000 –––––––––– –––––––––– 5760 63 360 5760 63 360 –––– –––––– –––––––––– Process costing Solutions to Chapter 5 questions 26PROCESS COSTING Cost per unit =£63 360 £1152 = £12 5760 576 units Process C account Units Price Amount Units Price Amount (£) (£) (£) (£) Process B 5100 61 200 Normal loss (scrap Direct materials added 4 000 account) 255 4.0 1 020 Direct wages 2 000 Finished goods 4370 16.0 69 920 Direct expenses 2 260 Process D 510 8.0 4 080Production overhead (250% direct wages) 5 000 –––––– 74 460 Abnormal gain 35 16.0 560 –––––––––– –––––––––– 5135 75 020 5135 75 020 –––– –––––– –––––––––– Cost per unit = £74 460 £1020 £4080 = £16 5100 255 510 units Process D account (by-product) Units Price Amount Units Price Amount (£) (£) (£) (£) Process C 510 4080 Normal loss (scrap Direct materials added 220 account) 51 2.0 102 Direct wages 200 Finished goods 450 11.0 4950 Direct expenses 151 Abnormal loss 9 11.0 99Production overhead (250% direct wages) 500 ––– –––– ––– –––– 510 5151 510 5151 ––– –––– ––– –––– Cost per unit = £5151 £102 = £11 510 51 units (b) Abnormal gain account Units Price Amount Units Price Amount (£) (£) (£) (£) Normal loss account 60 1.5 90 Process A 60 330 Normal loss account 35 4.0 140 Process C 35 560 Profit and loss account 660 –– ––– –– ––– 95 890 95 890 –– ––– –– ––– Abnormal loss account Units Price Amount Units Price Amount (£) (£) (£) (£) Process B 84 1008 Normal loss account 84 2.0 168 Process D 9 99 Normal loss account 9 2.0 18 Profit and loss account 921 –– –––– –– –––– 93 1107 93 1107 –– –––– –– –––– Normal loss account (income due) (£) (£) Process A normal loss 450 Abnormal gain account 90 Process B normal loss 1152 Abnormal gain account 140 Process C normal loss 1020 Process D normal loss 102 Abnormal loss account 168 Abnormal loss account 18 PROCESS COSTING27 Solution IM 5.3 (a) See ‘Methods of apportioning joint costs to products’ and ‘Limitations of joint cost allocations for decision-making’ in Chapter 6 for the answer to this question.

(b) Process 1 Units (£) Units (£) Stock – material 3000 15 000 Process 2 2800 33 600 Components stock 1 000 Normal loss 300 600 Wages 4 000 Expenses 10 000 Production overhead 3 000 –––––– 33 000 Abnormal gain 100 1 200 –––––––––– –––––––––– 3100 34 200 3100 34 200 –––– –––––– –––––––––– Cost per unit = £33 000 £600 = £12 2700 Process 2 Units (£) Units (£) Process 1 2800 33 600 Finished goods 2600 59 800 Components stock 780 Normal loss 140 700 Wages 6 000 Abnormal loss 60 1 380 Expenses 14 000 Production overhead 7 500 –––––––––– –––––––––– 2800 61 880 2800 61 880 –––– –––––– –––––––––– Cost per unit = £61 880 £700 = £23 2600 units Finished goods (£) (£) Balance b /f 20 000 Cost of sales 56 800 Process 2 59 800 Balance 23 000 –––––– –––––– 79 800 79 800 –––––– –––––– Normal loss/scrap (£) (£) Process 1 600 Abnormal gain (process 1) 200 Process 2 700 Cash 1100 –––– –––– 1300 1300 –––– –––– Abnormal loss (£) (£) Process 2 1380 Cash 300 Profit and loss account 1080 –––– –––– 1380 1380 –––– –––– Abnormal gain (£) (£) Normal loss (100 £2) 200 Process 1 1200 Profit and loss account 1000 –––– –––– 1200 1200 –––– –––– Profit and loss account(£) (£) Abnormal loss 1080 Abnormal gain 1000 (a) Input – materials 12 000 ––––– ––––– Normal loss (5%) 600 Abnormal loss 100 Completed production 9 500 Balance (Closing WIP) 1 800 (b) Statement of completed production and calculation of cost per unit a Cost element Total cost Completed Closing WIP Abnormal Total Cost per (£) units equiv. units loss b equiv. units unit (£) Materials 79 800 c 9 500 1 800 100 11 400 7.00 Labour and overhead 41 280 9 500 720 100 10 320 4.00 ––––– 11.00 ––––– Value of WIP Materials (1800 units at £7) 12 600 Labour and overhead (720 units at £4) 2 880 15 480 ––––– Abnormal loss (100 units at £11) 1 100 Completed units (9500 units at £11) 104 500 ––––––– 121 080 ––––––– Note a The short cut method is used because the calculations suggest that it was the examiner’s intention that this method should be used.

b It is assumed that losses are detected at the completion stage.

c See process account for calculation.

(c) Mixing process account Materials: A 6 000 48 000 Normal loss 600 — B 4 000 24 000 Abnormal loss 100 1 100 C 2 000 7 800 Completed production 9 500 104 500––––– ––––– 12 000 79 800 Closing WIP 1 800 15 480 Labour and overheads 41 280 ––––– ––––– ––––– –––––– 12 000 121 080 12 000 121 080 ––––– ––––– ––––– –––––– (d) See ‘Abnormal gains’ in Chapter 5 for the answer to this question 28 PROCESS COSTING Solution IM 5.4 PROCESS COSTING29 (a) See Chapter 5 for a description of each of the terms.

(b) See ‘Normal and abnormal losses’ in Chapter 5 for the answer to this question. (c)Workings Process 1 abnormal gain = input (9000) (7300 completed units + 1800 normal loss) = 100 units.

Process 2 abnormal loss = input (7300) (4700 completed units + 2000 WIP + 530 normal loss) = 70 units. It is assumed that the intention of the question is that normal loss is 10% of the input which reached the final inspection stage where the inspection occurs.Therefore normal loss is 530 units [10% (7300 input 2000 WIP)]. The cost per unit of output for process 1 is: cost of production scrap value of normal loss expected output = £14 964 + 14 700 (1800 £1.20) (80% 9000) = £3.82 Process 1 Units (£) Units (£) Materials 9000 14 964 Completed units Conversion cost 14 700 (7300 £3.82) 7300 27 886 Abnormal gain Normal loss (100 £3.82) 100 382 (1800 £1.20) 1800 2 160 –––––– –––––– 30 046 30 046 –––––– –––––– Abnormal gain account (£) (£) Normal loss 120 Process 1 382 Profit and loss account 262 ––– ––– 382 382 ––– ––– Normal loss (income due) account (£) (£) Process 1 2160 Abnormal gain (100 £1.20) 120 Process 1 753 Cash (balance) 2793 –––– –––– 2913 2913 –––– –––– Process 2 account (£) (£) Process 1 27 886 Finished goods ( W1) 24 456 Conversion cost 6 300 Normal loss (530 £1.42) 753 Abnormal loss ( W1) 337 Closing WIP ( W1) 8 640 –––––– –––––– 34 186 34 186 –––––– –––––– Abnormal loss account (£) (£) Process 2 337 Cash (sale of £70 units at £1.42) 99 Profit and loss account 238 ––– ––– 337 337 ––– ––– Solution IM 5.5 30PROCESS COSTING Working (W1 ) The cost per unit calculation for Process 2 (not using the short cut method) is as follows:

WIP Total Cost Completed Normal Abnormal equivalent equivalent per WIP units loss loss units units unit value (£) (£) (£) Previous process 27 886 4700 530 70 2000 7300 3.82 7640 Conversion cost 6 300 4700 530 70 1000 6300 1.00 1000 –––––– –––––––– 34 186 4.82 8640 –––––– –––––––– (£) (£) Completed units (4700 £4.82) 22 654 Share of normal loss (530 £4.82) 2554.60 Less sale proceeds (530 £1.42) 752.60 1 802 ––––––– –––––– Cost of completed units 24 456 Abnormal loss (70 £4.82) 337 WIP 8 640 –––––– 33 433 –––––– Note that the cost of the input (£34 186) less the sale proceeds of the normal loss equals the cost of the output. The question specifically states that losses occur at theend of the process. This statement, and the above calculations, suggests that theexaminer’s intention was that the short cut method should not be applied. The nor-mal loss of £1802 ought to be apportioned between completed units and abnormalloss where this will have a significant impact on the value of completed units andabnormal loss. If this approach is adopted, the normal loss of £1802 could beapportioned as follows:

Completed units [4700/(4700 + 70)] £1802 = £1776 Abnormal loss [70/(4700 + 70)] £1802 = £26 Given that the above adjustment will only have a minor effect on the process costs, there is little point in reflecting this apportionment in the process accounts.

Statement of input and output (Kgs) Process 1 Process 2 Opening WIP 3000 2250 Input for the period 4000 2400 –––– –––– Total input 7000 4650 –––– –––– Transferred to next process/finished stock 2400 2500 Closing WIP 3400 2600 Normal loss (10%) 400 240 Balance – Abnormal loss/(gain) 800 (690) –––– –––– 7000 4 650 –––– –––– Statement of completed production and calculation of cost per unit a (Process 1) Opening Current Total Completed Closing Abnormal Total Cost WIP cost cost units WIP loss b equiv. per units unit (£) (£) (£) (£) Materials 4 400 22 000 26 400 2 400 3 400 800 6 600 4.00 Conversion cost 3 744 30 000c 33 744 2 400 1 360 800 4 560 7.40 –––––– ––––– 60 144 11.40 –––––– ––––– Solution IM 5.6 PROCESS COSTING31 Completed production (2400 units at £11.40) 27 360 Closing WIP: Materials (3400 units at £4) 13 600 Conversion cost (1360 units at £7.40) 10 064 23 664 –––––– Abnormal loss (800 units at £11.40) 9 120 –––––– 60 144 –––––– Statement of completed production and calculation of cost per unit a (Process 2) Opening Current Total Completed Closing Abnormal Total Cost WIP cost cost units WIP gain b equiv. per units unit (£) (£) (£) (£) Previous process cost 4431 27 360 31 791 Less normal loss (480) –––––– (240 units at £2) 31 311 2500 2600 (690) 4410 7.10 Conversion cost 5250 37 500 c 42 750 2500 1040 (690) 2850 15.00 –––––– ––––– 73 061 22.10 –––––– ––––– Completed production (2500 units at £22.10) 55 250 Closing WIP: Previous process cost (2600 units at £7.10) 18 460 Conversion cost (1040 units at £15) 15 600 34 060 ––––– Abnormal gain (690 units at £22.10) (15 249) –––––– 74 061 –––––– Notes a The short cut method is used based on the assumption that the calculations suggest that it was the examiner’s intention to apply this method.

b It is assumed that losses/gains are detected at the completion stage c Labour cost plus overheads (150% of overhead cost) Process 1 (kgs) (£) (kgs) (£) WIP b/fwd 3000 8144 Normal loss 400 — Stock control 4000 22 000 Process 2 2400 27 360 Wages control 12 000 Abnormal loss 800 9 120 Overhead control 18 000 WIP c/fwd 3400 23 664 –––– –––––– –––– –––––– 7000 60 144 7000 60 144 –––– –––––– –––– –––––– Process 2 (kgs) (£) (kgs) (£) WIP b/fwd 2250 9 681 Normal loss 240 480 Process 1 2400 27 360 Finished goods 2500 55 250 Wages control 15 000 WIP c/fwd 2600 34 060 Overhead control 22 500 Abnormal gain 690 15 249 –––– –––––– –––– –––––– 5340 89 790 5340 89 790 –––– –––––– –––– –––––– Abnormal loss(£) (£) B/fwd 1 400 Profit and loss a/c 10 520 Process 1 9 120 ––––– ––––– 10 520 10 520 ––––– ––––– 32PROCESS COSTING Abnormal gain (£) (£) Normal loss 1 380 B/fwd 300 Profit and loss a/c 14 169 Process 2 15 249 ––––– –––––– 15 549 15 549 ––––– –––––– Overhead control (£) (£) Bank/expense creditors 54 000 B/fwd 250 Process 1 18 000 Process 2 22 500 Profit and loss a/c 13 250 ––––– –––––– 54 000 54 000 ––––– –––––– Sales (£) (£) Proft and loss a/c 637 000 B/fwd 585 000 Debtors 52 000 ––––––– ––––––– 637 000 637 000 ––––––– ––––––– Finished goods (£) (£) B/fwd 65 000 Cost of sales 60 250 Process 2 55 250 C/fwd 60 000 –––––– –––––– 120 250 120 250 –––––– –––––– Cost of sales (£) (£) B/fwd 442 500 Profit and loss a/c 502 750 Finished goods 60 250 ––––––– ––––––– 502 750 502 750 ––––––– ––––––– ABC plc – Profit and loss account for the year ended September (£) (£) Cost of sales 502 750 Sales 637 000 Abnormal loss 10 520 Abnormal gain 14 169 Overhead control 13 250 Profit 124 649 ––––––– ––––––– 651 169 651 169 ––––––– ––––––– ––––––– ––––––– Statement of cost per unit using the short-cut method: Completed Abnormal Total equiv. Cost perunits gain units unit(£) (£) Material 16 245 9580 (80) 9.500 1.71Labour and overhead 28 596 9580 (48) 9.532 3.00 ––––– –––– 44 841 4.71 ––––– –––– Solution IM 5.7 PROCESS COSTING33 (£) Cost of completed production (9850 × £4.71) 45 121.80 Abnormal gain: Materials (80 units × £1.71) 136.80 Labour and overhead (48 × £3) 144.00 280.80 –––––– –––––––– Net cost 44 841.00 –––––––– Process account (£) (£) Materials 16 445 Finished goods 45 121.80 Labour and overhead 28 596 Normal scrap 200.00 Abnormal gain 280.80 –––––––– ––––––––– 45 321.80 45 321.80 –––––––– ––––––––– Normal loss (Income due) (£) (£) Process account 200 Abnormal gain (80 × 40p) 32 Cash from scrap sold(420 × 40p) 168 ––– ––– 200 200 ––– ––– Abnormal gain account (£) (£) Normal loss account 32 Process account 280.80 Profit and loss account 248.80 ––––– –––––– 280.80 280.80 ––––– –––––– (a) (i) Production statement Input: (£) Opening WIP 21 700 Materials input 105 600 ––––––– 127 300 ––––––– Output: Completed units 92 400 Closing WIP 28 200 Normal loss (balance) 6 700 ––––––– 127 300 ––––––– Losses are detected at the start of the process and should be allocated between completed units and closing WIP. Therefore it is appropriate to use the short cut method. The calculations are:

WIP Total Total Completed equiv. equiv. Cost per costs units units unit unit (£) (£) Materials 330 077 a 92 400 28 200 120 600 2.737 1 Conversion cost 256 792 a 92 400 14 100 106 500 2.4112 –––––– 5.1482 –––––– Solution IM 5.8 34PROCESS COSTING Note a £333 092 total cost (opening WIP plus current cost) less scrap value of normal loss (£3015).

(a) (ii) Production statement Input: (kg) Opening WIP 21 700 Materials input 105 600 ––––––– 127 300 ––––––– Output: Completed units 92 400 Closing WIP 28 200Normal loss (5% 105 600) 5 280 Abnormal loss (balance) 1 420 ––––––– 127 300 ––––––– Statement of equivalent production and calculation of cost of completed production and WIP Completed Abnormal Closingunits less loss WIP Total Cost Current opening WIP equiv. equiv. equiv. per cost requirements units units units unit(£) (£) Materials 274 296 a 70 700 1420 28 200 100 320 2.7342 Conversion cost 226 195 79 380 — 14 100 93 480 2.4197 –––––– 5.1539 –––––– Note a £276 672 current cost less the scrap value of the normal loss (5 280 kg £0.45). Cost of completed production: Opening WIP (£56 420 + £30 597) 87 017 Materials (70 700 £2.7342) 193 309 Conversion cost (79 380 £2.4197) 192 076 472 402 Abnormal loss: Materials (1 420 £2.7342) 3 882 Closing WIP: Materials (28 200 £2.7342) 77 106 Conversion cost (14 100 £2.4197) 34 118 111 224 –––––– ––––––– 587 508––––––– (b) Process account Opening WIP: Completed units 472 402 Materials 56 420 Abnormal loss 3 882 Conversion costs 30 597 Normal loss (sale proceeds) 2 376 87 017 Closing WIP 111 224 Input costs: Materials 276 672 Conversion costs 226 195 ––––––– ––––––– 589 884 589 884 ––––––– ––––––– PROCESS COSTING35 (c) See introduction to Chapter 6 and ‘Accounting for by-products’ in Chapter 6 for the answer to this question.

(a) The answer should include an explanation of the accounting treatment of normal and abnormal losses as indicated in Chapter 5. A discussion of the alternative treatment of losses might include the following:(i) The stage where the loss is assumed to occur will determine how much of the loss is allocated to completed production and closing WIP. If the loss isassumed to occur at the end of the process, it will be charged to completedproduction only.

(ii) The normal loss may be charged to the good output only or apportionedbetween the good output and the abnormal loss.

(iii) Losses may be valued at variable cost or absorption cost. If the loss hasresulted in the consumption of scarce resources then a charge might be addedto reflect the opportunity cost of the scarce capacity.

(b) (i) Calculation of units in closing WIP Units Total input: Opening assembly WIP 50 000 Units added to assembly process 112 000 ––––––– 162 000 ––––––– Output to be accounted for (162 000 units): Good units completed 90 000Spoiled units 10 000 Lost units 2 000 Closing WIP (difference) 60 000 ––––––– 162 000 ––––––– (ii) Calculation of equivalent units processed Equivalent units Total units Components Assembly Finishing Units started and finished a 40 000 40 000 40 000 40 000 Completion of opening WIP a 50 000 Nil 25 000 50 000 Spoilage b 10 000 10 000 10 000 10 000 Losses 2 000 2 000 2 000 Nil Closing WIP 60 000 60 000 20 000 Nil 162 000 112 000 97 000 100 000 Notes a The opening WIP completed in this period is 50 000 units. Therefore 40 000 units out of the 90 000 completed units will be started and finished during the period. The opening WIP will be fully completed as far as components are con-cerned, so no additional equivalent units will be completed in this period. Theopening WIP for assembly is 50% complete. Therefore the remaining 50% (i.e.25 000 units) will be completed in this period. All the opening work inprogress will be completed in this period in the finishing process. b Spoilage is recognized at the end of the finishing process. The 10 000 spoilt units will be passed from the assembly to finishing process and willnot be considered to be spoilt until the end of the finishing process.Therefore it is inappropriate to allocate a share of the normal loss to theclosing WIP of the assembly process. Solution IM 5.9 36PROCESS COSTING (iii)Calculation of cost per equivalent unit: assembly process Completed units Closingless opening WIP Total Cost Current WIP equivalent Spoiled Lost equivalent equivalent per Cost element costs units units units units units unit (£) (£) Bought in components 120 000 40 000 10 000 2000 60 000 112 000 1.071 43 Direct costs 40 000 65 000 10 000 2000 20 000 97 000 0.824 74 ––––––– Overhead 40 000 1.896 17 ––––––– ––––––– 200 000 ––––––– (£) Closing WIP: Components (60 000 £1.071 43) 64 286 Closing WIP: Direct costs and overheads (20 000 £0.824 74) 16 495 80 781 –––––– Completed units plus spoiled units transferred:

Components (50 000 £1.071 43) 53 571 Direct costs etc. (75 000 £0.824 74) 61 856 Add opening WIP (£60 000 + £25 000 + £25 000) 110 000 225 427 ––––––– Lost units (2000 £1.896 17) written off 3 792 ––––––– Total assembly costs accounted for 310 000 ––––––– Finishing process Completed units transferred from assembly process: 90 000 + 10 000 =100 000 units. Finishing process costs: (£) (£) Transferred from assembly 225 427 Finishing costs 30 000 255 427 ––––––– Completed cost per unit = £2.554 27 (£255 427/100 000 units). Of the 100 000 units transferred, 90 000 units are completed and 10 000 units are spoiled. Therefore Normal loss = 5000 units ( 11 8 90 000) Abnormal loss = 5000 units (balance) The costs of £255 427 can be analysed as follows: Completed units = £242 656 (95 000 £2.554 27) Abnormal loss = £12 771 (5000 £2.554 27) Note that the normal loss is charged to the completed units.

(a) The closing stock valuation for October which is given in the question does not distinguish between materials and conversion cost. It is therefore necessary toprepare the following statement for October:

October cost schedule (weighted average basis) Total Completed Closing WIP Total Cost per WIP cost units equivalent units equivalent units unit value(£) (£) (£) Materials 58 500 2400 1500 3900 15.00 22 500 Conversion cost 99 000 2400 1200 3600 27.50 33 000 ––––– –––––– 42.50 55 500 ––––– –––––– November cost schedule (weighted average basis) Closing WIP Total Opening Current Total Completed equivalent equivalent Cost per WIP WIP cost cost units units units unit value(£) (£) (£) (£) (£) Materials 22 500 48 600 71 100 2400 1800 4200 16.9286 30 471 Conversion cost 33 000 84 000 117 000 2400 900 3300 35.4545 31 909 ––––––– –––––– 52.3831 62 380 ––––––– –––––– Solution IM 5.10 PROCESS COSTING37 November cost schedule (FIFO basis) Completed units Closing WIP Current less opening WIP equivalent Current total Cost per WIP cost equivalent units units equivalent units unit value(£) (£) (£) Materials 48 600 900 1800 2700 18 32 400 Conversion cost 84 000 1200 900 2100 40 36 000 –– –––––– 58 68 400 –– –––––– Profit statements Weighted average FIFO (£) (£) (£) (£) Sales revenue 120 000 ) 120 000 Opening WIP 55 500 55 500 Variable costs 69 600 69 600 Fixed costs 63 000 63 000 ––––––– ––––––– 188 100 188 100 Closing WIP 62 380 68 400 ––––––– ––––––– Cost of sales 125 720 ) 119 700 ––––––– ) ––––––– Profit /(loss) (5 720) 300 ––––––– ) ––––––– (b) The difference in profits is due entirely to the difference between the average cost and FIFO stock valuations. Unit costs increased from £42.50 in October to £58 in November. With the average cost method, the stock valuation is based on bothOctober and November costs. This is because the opening WIP value forNovember is merged with the current costs to calculate the average cost per unit.With the FIFO method, the cost per unit is based entirely on November costs. Theclosing WIP is assumed to come from the new units which have been startedduring the period.

(c) 1. Use of standard costs : The statement is correct. Standard costs per equivalent unit produced would be used to value stocks, and costs per unit would be thesame each period (except for where standards are periodically changed).Consequently standard cost per equivalent unit for the opening WIP would beidentical to the standard cost per equivalent unit for the current period, andthe two alternative methods of allocating opening WIP to the current periodwould result in the calculation of identical unit costs. The use of standardcosts would also provide useful information for cost control purposes.Periodic comparisons of actual and standard performance could be made todetermine whether the process was running efficiently. The standard costingsystem should pinpoint costs which may be out of control. It is necessary toensure that standards set are attainable and that variances are not a result ofunreasonable standards.

2. Use of current costs : If current costs are used for stock valuation purposes, it will be necessary to adjust this valuation for financial accounting purposes.Therefore using current costs is likely to involve additional work. In addition,profit will be affected by temporary price changes. The comparison of actual costs with standard costs can be inappropriate when costs change frequently throughout the year. The standard cost islikely to represent an average target cost for the year. If costs increaserapidly throughout the year then favourable variances will arise in the earlypart of the year and these variances will be compensated by adverse vari-ances in the later part of the year. A possible solution is to change the stan-dards each month or to separate the variances into their planning andoperational elements (see Chapter 18 for a discussion of planning and oper-ating variances). 38PROCESS COSTING 3.Use of direct cost valuation : Variable costing is preferable to absorption cost- ing for managerial purposes. Monthly profit is a function of sales with a vari- able costing system, whereas monthly profit will be a function of sales andproduction with an absorption costing system. Managers might also be moti-vated to increase stocks in order to reduce the amount of fixed overheadsallocated to an accounting period. For a more detailed discussion of theadvantages of variable costing see ‘Some arguments in favour of variable cost-ing’ in Chapter 7. The disadvantage of variable costing is that the control offixed costs might be ignored. If a variable costing system is used, it will be necessary to convert the stock valuation to an absorption costing basis for financial accounting. Note that if avariable costing system is used, a decision will still have to be made whether touse the FIFO or the weighted average stock valuations.

4. Use of cash flow reports : It is important that profit statements be prepared at frequent intervals for control purposes. Annual profit statements are inade-quate for control purposes. If stock levels change significantly during a period,cash flow statements will not provide an indication of profit and productionperformance for the period. Management should receive periodic profitstatements and cash flow statements. It is important that both cash flows andprofits be monitored at frequent intervals. JOINT AND BY-PRODUCT COSTING39 Solution IM 6.1 Solution IM 6.2 (a) See Chapter 6 for the answer to this question.

(b) The answer should stress that joint cost apportionment should not be used for decision-making purposes. The sole purpose of joint cost apportionments is tovalue closing stock at the end of each accounting period in order to determineprofit. If all production for the period were sold, the problem of joint costapportionment would not exist. The two main methods of apportioning jointcosts are the physical measures method and the sales value method. The salesvalue method is recommended. For an explanation of why this method isrecommended see Chapter 6.

(c) See ‘Opening and closing work in progress’ in Chapter 5 for the answer to this question.

(a) See Chapter 6 for the answer to this question.

(b) (i) It is rational to undertake a common process if the total revenue from the sale of the products from the joint process exceeds the joint costs plus furtherprocessing costs of those products which are further processed. Consider thefollowing example.A joint process costs £600, and joint products A, B and C emerge. The further processing costs and sales revenue from the finished products are asfollows:

Additional Product finishing costs Sales revenue from finished product (£) (£) A 300 600 B 400 800 C 500 1000 –––– –––– 1200 2400 –––– –––– In the above example total revenue (£2400) is greater than joint costs (£600)plus the additional costs of processing (£1200). Therefore it is rational toundertake the joint process.

(ii) It is rational to ‘finish off’ each of the products from the joint process if the additional revenues from further processing exceed the additional costs offurther processing. For an illustration of this statement see Example 6.3 inChapter 6. Joint and by-product costing Solutions to Chapter 6 questions 40JOINT AND BY-PRODUCT COSTING For the answer to this question see ‘Methods of allocating joint costs to products’ and ‘Limitations of joint cost allocations for decision-making’ in Chapter 6. (a)Statement of input and output (litres) Input Output Opening WIP 5 000 Joint product X 30 000 Transferred from process 1 65 000 Joint product Y 25 000 By-product Z 7 000 Normal loss (5% × 65 000) 3 250 Closing WIP 6 000–––––– 71 250 Difference = Abnormal gain (1 250) –––––– –––––– 70 000 70 000 –––––– –––––– In Chapter 6 it was pointed out the by-products should not be charged with any portionof the joint costs that are incurred before the split-off point. Therefore the completed production for calculating the cost per unit of the joint process consists of 55 000 litresfor X and Y and excludes the output of the by-product. It was also pointed out inChapter 6 that by-product net revenues (the sales revenue of the by-product less theadditional further processing costs after split-off point) should be deducted from the costof the joint production process. In order to simplify the answer the short-cut method is used. Also note that the opening WIP value of £60 000 is not analysed by the elements of cost. The question can therefore only be answered using the FIFO method. It is assumed that losses andgains consist of fully complete units. Statement of cost per unit: Completedunits lessopening Closing Current Current WIP WIP total Cost Cost period equivalent Abnormal equivalent equivalent per element cost units gain units units unit (£) (£) Previous processcost 1 547 500 50 000 (1250) 6000 54 750 10.00 Conversion cost 221 400 53 000 (1250) 3600 55 350 4.00 ––––––– –––– 768 900 14.00 ––––––– –––– Completed production: (£) (£) Opening WIP 60 000 Previous process cost (50 000 × £10) 500 000 Conversion cost (53 000 × £4) 212 000 772 000 ––––––– Closing WIP Previous process cost (6000 × £10) 60 000 Conversion cost (3600 × £4) 14 400 74 400 –––––– Abnormal gain (1250 × £14) (17 500) ––––––– 828 900 ––––––– Note:

(1) Previous process cost = £578 500 by-product net revenue (7000 × £3.50) Scrap value of normal loss (3250 × £2) Solution IM 6.3 Solution IM 6.4 JOINT AND BY-PRODUCT COSTING41 Solution IM 6.5 It is assumed that joint costs are to be allocated on the basis of net realizable value at split-off point:

(£) Paint X (30 000 × (£15 £0.50)) = 435 000 Paint Y (25 000 × (£18 £2)) = 400 000 ––––––– 835 000 ––––––– Allocated to Paint X (£435/£835 × £772 000) = £402 180 Allocated to Paint Y (£400/£835 × £772 000) = £369 820 Process 2 account, October 1997 (litres) (£) (litres) (£) Opening WIP 5 000 60 000 Normal loss 3 250 6 500 Process 1 65 000 578 500 Paint X 30 000 402 180 Direct labour 101 400 Paint Y 25 000 369 820 Variable overhead 80 000 By-product Z 7 000 24 500 Fixed overhead 40 000 Closing WIP 6 000 74 400 Abnormal gain 1 250 17 500 –––––– ––––––– –––––– ––––––– 71 250 877 400 71 250 877 400 –––––– ––––––– –––––– ––––––– (b) To help you understand the answer the normal loss account is also shown below: Normal loss (income due)(£) (£) Process 2 account 6500 Abnormal gain (1250 × £2) 2500 Cash from scrap sold(2000 × £2) 4000 –––– –––– 6500 6500 –––– –––– Abnormal gain account: (£) (£) Normal loss account 2 500 Process 2 Account 17 500 Profit and loss account 15 000 ––––– ––––– 17 500 17 500 ––––– ––––– (c) See the section on methods of allocating joint costs to joint products for the answer to this question.

(a) Costs beyond Net Joint Sales split-off sales Proportion costs Product value point value of total apportioned (£000) (£000) (£000) (%) (£000) Q 768 160 608 62.30 456 R 232 128 104 10.65 78 S 32 — 32 3.28 24 T 240 8 232 23.77 174 –––– ––– ––– ––– 1272 296 976 732 –––– ––– ––– ––– 42JOINT AND BY-PRODUCT COSTING Solution IM 6.6 Budgeted product profitability statement Q R S T Total (£000) (£000) (£000) (£000) (£000) Sales 768 232 32 240 1272 Joint process costs (456) (78) (24) (174) (732) Further processing costs (160) (128) (8) (296) Profit 152 26 8 58 244 (b) Sales 512 144 32 180 868 Joint process costs (456) (78) (24) (174) (732) Profit 56 66 8 6 136 (c) Q R T (£000) (£000) (£000) Incremental revenue from further processing 256 (768 512) 88 (232 144) 60 (240 180) Additional processing costs 160 128 8 Incremental net revenue 96 (40) 52 Product R should be sold at split-off point, since the additional further processing costs exceed the incremental revenues. The overall profit will therefore rise from£244 000 to £284 000.

(a) Process 1 account Litres CPU Litres CPU (£) (£) (£) (£) Direct materials 80 000 1.25 100 000 Normal loss 8 000 0.50 4 000 Direct wages 48 000 Output A 22 000 2.50 55 000 Production overhead 36 000 Output B 20 000 2.50 50 000 (75% of direct Output C 10 000 2.50 25 000 wages) Output D 18 000 2.50 45 000 Abnormal loss 2 000 2.50 5 000 –––––– ––––––– –––––– ––––––– 80 000 184 000 80 000 184 000 –––––– ––––––– –––––– ––––––– Cost per unit = £184 000 £4000 = £2.50 per litre 72 000 litres Profit and loss statement A B C D Total Sales (litres) 22 000 20 000 10 000 18 000 Selling price per litre (£) 4325 Sales (£000) 88 60 20 90Joint cost apportionment from Process A (£000) (55) (50) (25) (45) Post separation costs: direct wages + overhead (£000) (21) (14) (7) (28) Profit /(loss) 12 (4) (12) 17 13 Note that the profit will be reduced by the £5000 abnormal loss. JOINT AND BY-PRODUCT COSTING43 Solution IM 6.7 (b) Profit from the present output can be maximized by further processing only those products whose incremental revenues exceed the incremental costs.

A B C D Total Incremental revenue per litre (£) 1.50 0.20 0.80 2.00 Output (litres) 22 000 20 000 10 000 18 000 Incremental revenue (£000) 33 4 8 36Incremental costs of further processing (£000) (21) (14) (7) (28) Contribution to joint costs 12 (10) 1 8 11 Product B should not be subject to further processing, since it yields £10 000 negative contribution. It is assumed that overheads and direct labour are avoidablecosts. If the overheads are fixed costs (i.e. not avoidable costs) and the direct wagesare avoidable costs, it is still not worthwhile further processing product B.

Revised profit statementA B C D Total Sales (£000) 88 56 20 90 Post separation costs (£000) 21 — 7 28 Contribution to joint costs (£000) 67 56 13 62 198 Less joint costs (£000) 175 ––– Revised profit (£000) 23 ––– Note the above profit will be reduced by the £5000 abnormal loss.

(c) Product B should not be processed beyond process 1, and the abnormal loss should be investigated. Product C makes a loss, but an alternative apportionmentmethod (e.g. the sales value method) might indicate that it makes a profit. The important point to note is that the process as a whole yields a profit. If product C were abandoned, the common and unavoidable joint costs would still continue,but the company would lose the sales revenue of £20 000.

(a) The diagram shown in Figure Q6.7 illustrates the production process. The relevant costs and revenues over the two-year period are:

Without further With furtherprocessing processing(£000) (£000) Sales 1200 3720 Transport costs (148) — Variable costs (1200) Annual fixed costs (74) Transport and vats (200) –––– –––– Excess of relevant revenues over relevant costs 1052 2246 –––– –––– Further processing increases profits by £1 194 000, or £597 000 per annum.

(b) (i) D C Total (£000) (£000) (£000) Sales 10 400 600 Variable costs (1 560) — Fixed costs (177) (74) –––– ––––––– Net realizable value 8 663 526 9189 Less joint costs a (8 155) (495) (8650) Plant administration costs a (89) (6) (95) –––– ––– –––– 419 25 444 –––– ––– –––– 44JOINT AND BY-PRODUCT COSTING Figure Q6.7 (ii) D E Total (£000) (£000) (£000) Sales 10 400 1860 Variable costs (1 560) (600) Fixed production costs (177) (37)Depreciation b (100) –––– –––– Net realizable value 8 663 1123 9786Less joint costs a (7 657) (993) (8650) Plant administration costs a (84) (11) (95) –––– ––– –––– 922 119 1041 –––– ––– –––– Notes a Several alternatives may be used to apportion joint costs. In this answer joint costs are apportioned in proportion to net realizable values. (See ‘Sales value method’ in Chapter 6 for an explanation of why this method is preferred.) b Transport and vats are written off on a straight-line basis over a period of two years.

The layout of the above statements emphasizes the benefit each joint product contributes to joint costs. The joint product contributions (i.e. net realizable values) can be used for performance evaluation because they do not include unavoidable non-controllable joint costs.

(c) Assuming that the projected costs for 2013 and 2014 are appropriate for 2012 and joint costs are apportioned on the basis of net realizable values, the stock valuations are:(i) Stock of C = (10 /120) (£495 000 + £6000) = £41 750 Note that the £74 000 transport costs are non-manufacturing costs, andtherefore are not included in the stock valuation.

(ii) Stock of E = (10 /120) (£737 000 + £1 004 000) = £145 083 (d) It is necessary to adjust the joint costs and the apportionment of joint costs in order to calculate the revised stock valuation. The revised calculation is: BD CE A Joint cost 400 000 galls. p.a. £20 per gall.

+ FC £650 000 p.a.

120 000 galls.

FC £74 000 p.a.

SP = £5 per gall. VC = £5 per gall.

FC = £37 000 p.a.

+ £200 000 SP = £15.50 per gall.

260 000 gall. VC = £6 per gall.

FC = £177 000 p.a.

SP = £40 per gall. (£000) Original joint cost calculation 8 650 Add replacement cost adjustment for material A (0.25 £8000) 2 000 Plant administration costs 95 10 745 Costs apportioned to E [(£1123 /£9786) £10 745] 1 233 Add further processing costs of E 737 Total cost of E1 970 Stock valuation = (10 /120) £1 970 000 = £164 167 Replacement cost stock valuation is preferred because it provides a better approximation of the value of the stock to the business than historic cost valuations.

(a) Preliminary calculations A B Z Total Production of separable products (tonnes) 3600 4000 380 Evaporation beyond split-off point (%) 10 20 5 Yield after evaporation (%) 90 80 95 Yield from joint process (tonnes) 4000 5000 400 9 400Input to joint process (tonnes) 10 000 Therefore the yield from joint distillation is 94%The cost of the joint distillation process is as follows: (£) (£) 10 000 tonnes at £5 variable cost 50 000Fixed cost 5 000 –––––– 55 000 Less by-product Z sales: 380 tonnes at £5 1 900 Less variable cost 400 tonnes at £1 400 Fixed cost 500 ––– 900––– 1 000 –––––– 54 000 –––––– –––––– We now apportion the above costs to joint products using an acceptable basis of apportionment. Either units produced or net realizable value at split-off point canbe used. In order to simplify the calculations, the joint costs are apportioned on aunits-produced basis. The calculations of the unit costs for products A and B andthe profit for the year are: A B Total (£) (£) (£) Joint costs 24 000 [(4000 /9000) £54 000] 30 000 [(5000 /9000) £54 000] Added variable cost 44 000 (4000 £11) 10 000 (5000 £2) Fixed cost 4 000 8 000 –––––– –––––– 72 000 48 000 Sales 86 400 (3600 £24) 58 000 (4000 £14.50) –––––– –––––– Profit 14 400 10 000 24 400 –––––– –––––– Cost per unit £20 (£72 000 /3600) £12 (£48 000 /4000) (a) (i) (a) (i) (a) (ii) JOINT AND BY-PRODUCT COSTING 45 Solution IM 6.8 46JOINT AND BY-PRODUCT COSTING (b) A B Z Total Revised yield fromjoint process (tonnes) 3600 (0.9 4000) 4500 (0.9 5000) 360 (0.9 4000) 8460 (previous yieldless 10%) Input to jointprocess [(100/94) 8460] 9000 The calculation of the revised joint costs is as follows: Cost of joint process: (£) Variable costs (9000 £5) 45 000 Fixed cost 5 000 Plant overhead 17 000 –––––– 67 000 Less income from by-product Z: Variable cost (360 £1) 360 Fixed cost 500 Sales (342 £5) (1710) 850 ––––––––––– 66 150 –––––– The joint cost of £66 150 is now apportioned to products A and B:

AB (£) (£) Joint costs 29 400 (£66 150 3600 /8100) 36 750 (£66 150 4500 /8100) Added variable costs 39 600 (3600 £11) 9 000 (4500 £2) Added fixed cost 4 000 8 000 –––––– –––––– 73 000 53 750 –––––– –––––– Cost per unit £22.53 (£73 000 /3240) £14.93 (£53 750 /3600) (c) AB (£) (£) Production costs per (b) 73 000 53 750 Imported cost a 9 000 (360 tonnes at £25) 6 000 (400 tonnes £15) –––––– –––––– Revised total costs 82 000 59 750 Sales 86 400 (3600 £24) 58 000 (4000 £14.50) –––––– –––––– Profit 4 400 (1 750) Profit = £2650 Note AB (tonnes) (tonnes) a Revised yield from joint process 3600 4500 a Evaporation beyond split-off point 360 (10%) 900 (20%) –––– –––– a Revised output of final product 3240 3600a Original production 3600 4000 –––– –––– a Lost output imported 360 400–––– –––– JOINT AND BY-PRODUCT COSTING47 (d) (i) Comparing proposal (i) with the answer to (b) and (c), the differential costs are calculated as follows:

A B Z Total (tonnes) (tonnes) (tonnes) (tonnes) Yield from joint process 3800 (3600 + 200) 4300 (4500 200) 360 8460 Final output 3420 (90% 3800) 3440 (80% 4300) Sales demand 3600 4000 Required imports 180 560 Differential costs (£) (£) Additional VC in joint process (2% £45 000) 900 ) Additional VC after split-off point (A = 200 £11) 2200 ) Additional VC after split-off point (B = 200 £2) (400) 1800 ) Savings in imports of A (180 360 at £25) (4500) Additional import cost of B (560 400 at £15) 2400 ) (2100) –––– ) –––– ) Additional costs 600 ) –––– ) Therefore proposal (i) should be rejected.

(ii) With proposal (ii), the by-product residue is apportioned to A and B in proportion to their output from the joint process (i.e. A = 360 3600 /8100 = 160, B = 360 4500 /8100 = 200).

AB Z (tonnes) (tonnes) (tonnes) Revised yield from joint process 3760 (3600 + 160) 4700 (4500 + 200) Final output 3346 (89% 3760) 3713 (79% 4700) Sales demand 3600 4000 Required imports 254 287 Previous imports in (c) 360 400 Saving in imports 106 113 Differential costs (£) (£) (£) Increase in fixed costs (5% £4000) + (5% £8000) 600 Increase in variable costs (A = 160 £11) 1760 Increase in variable costs (B = 200 £2) 400 2160 Loss of contribution from by-product Z (1710 360 per part (b)) 1350 4110 –––– Savings in import costs (A = 106 £25) 2650 Savings in import costs (B = 113 £15) 1695 (4345) –––– –––– Net gain from the proposal 235 –––– 48JOINT AND BY-PRODUCT COSTING (a) Figure Q6.9 shows a flow chart based on 100 gallons input (i.e. 50 gallons of L and 50 gallons of M). It appears that this alternative should be chosen. However, before the final decision is made, the following items should be considered, sincethey cannot be quantified:(i) Loss of customer for by-product. (Can this customer be retained or replaced, given that this is a temporary situation only?) (ii) The suggestions appear to be experiments. What degree of confidence doesmanagement have in these estimates?

(b) The sales limitation restricts output of B to 54 000 gallons. Figure Q6.9 indicates that for 50 gallons input for each of L and M we obtain an output of 36 gallons ofB. Therefore an output of 54 000 gallons of B requires an input of 75 000 gallonsof L and M (54 000 50 /36).

Process 1 account Units CPU (£) Units CPU (£) Material L 75 000 0.20 15 000 Evaporation Material M 75 000 0.50 37 500 loss (10%) 15 000 — — Direct wages and Process 2 135 000 0.60 81 000 variable overhead (150 000 £0.15) 22 500 Fixed overhead 6 000 –––––– –––––– 81 000 81 000 –––––– –––––– Solution IM 6.9 Fluid A Fluid B Fluid B 6×6 Fluid A 54 × 1 6×6 36 54 54 Process 4 DrumsRaw material N 18 Process 3 AB Labels 100 99 54 × Raw material N 18 AB (18) (36) Process 2 90 Process 1 10 By-product C (18) Heating loss (18) Evaporation loss (10) Raw material L (50) Raw material M (50) 50 50 Bottles Figure Q6.9 JOINT AND BY-PRODUCT COSTING49 Process 2 account Units CPU (£) Units CPU (£) From Process 1 135 000 0.60 81 000 Boiling loss (20%) 27 000 — — Wages and variable By-product C 27 000 0.50 13 500 a overhead 0.35 47 250 Process 3 (A) 54 000 90 000 a Fixed overhead 20 250 Process 3 (B) 27 000 45 000 a ––––––– ––––––– 148 500 148 500 a ––––––– ––––––– Note a Joint netcosts of £135 000 are apportioned on a physical units basis as follows: A = 54 000 £135 000 81 000 B = 27 000 £135 000 81 000 Process 3 account (extract A) Units CPU (£) Units CPU (£) Process 2 54 000 1.67 90 000 Process 4 (A) 81 000 2.22 180 000 Material N 27 000 2.0 0 54 000 Labour and variable overhead(81 000 £0.3) 24 300 Fixed overhead a 11 700 ––––––– ––––––– 180 000 180 000 ––––––– ––––––– Process 3 account (extract B) Units CPU (£) Units CPU (£) Process 2 27 000 1.67 45 000 Process 4 (B) 54 000 2.27 123 000 Material N 27 000 2.0 0 54 000 Labour and variable overhead(54 000 £0.3) 16 200 Fixed overhead a 7 800 ––––––– ––––––– 123 000 123 000 ––––––– ––––––– Note a Fixed overheads of Process 3 are apportioned according to the output of this process; e.g. for extract A 81 000 £19 500 135 000 Process 4 account (extract A) Units CPU (£) Units CPU (£) Process 3 81 000 2.22 180 000 Finished stock 81 000 243 000 Wages and variableoverhead (81 000 £0.4) 32 400 Fixed overhead a 8 550 Bottles (81 000 0.27) 21 870 Labels b 180 ––––––– ––––––– 243 000 243 000 ––––––– ––––––– 50JOINT AND BY-PRODUCT COSTING Process 4 account (extract B) Units CPU (£) Units CPU (£) Process 3 54 000 2.27 123 000 Finished stock 54 000 202 500 Wages and variableoverhead(54 000 £0.40) 21 600 Fixed overhead a 5 700 Drums (9000 £5.80) 52 200 ––––––– ––––––– 202 500 202 500 ––––––– ––––––– Notes a Fixed overhead is apportioned according to the output of process 4 (i.e. 60% to A and 40% to B).

b 81 000 (100 /99) (£2.20 /1000) Manufacturing costs Production Cost per unit (£) (gallons) (£) Fluid A 243 000 81 000 3.00 Fluid B 202 500 54 000 3.75 (i) (ii) –– –– –– –– (iii) Selling price structure (%) Analysis of net selling price: Selling and distribution cost 12 Administration cost 5 Profit 8 ––– 25 Manufacturing cost 75 ––– Net selling price 100 = 1 1 3 times manufacturing cost ––– Fluid A Fluid B (£) (£) Manufacturing cost 3.00 3.75Net selling price ( 1 1 3 ) 4.00 5.00 List price ( 1 1 4 ) 5.00 List p rice ( 1 1 2 ) 7.50 (iv) Profit for the year (£) Fluid A: 81 000 gallons at £0.32 a 25 920 Fluid B: 54 000 gallons at £0.40 a 21 600 –––––– 47 520 –––––– Note a Profit margins are 8% of net selling prices.

(c) The answer is based on the following assumptions: (i) That the incidental production of fluid A (1 12 gallons per gallon of fluid B) as well as the by-product C would be saleable at usual prices.

(ii) That no additional fixed manufacturing overhead would be incurred.

(iii) That fluid A would incur marketing and administrative costs at the normal rate of £0.68 per gallon (17% of net selling price). One would expect suchcosts to include a ‘fixed’ element, but since no breakdown is given and sincethey are stated in the question as percentages of net selling price, it isassumed that they are intended to be treated as ‘variable’. (iv) That the exported fluid B would incur marketing and administrative costs of£1260 only, i.e. £0.42 per gallon.

The fixed overhead included in the manufacturing costs must be removed in order to calculate the incremental cost of production. The calculations are as follows: Total Fluid A Fluid B(£) (£) (£) Processes 1 and 2 26 250 17 500 ( 2 3 ) 8 750 ( 13 ) Processes 3 and 4 33 750 20 250 (60%) 13 500 (40%) –––––– –––––– –––––– 60 000 37 750 22 250 –––––– –––––– –––––– Output (gallons) 81 000 54 000 Per gallon £0.47 £0.41 The incremental costs per gallon and required selling price are:

Fluid A Fluid B(£) (£) Total cost of manufacture 3.00 3.75 Less fixed overhead 0.47 0.41 –––– –––– Marginal cost of manufacture 2.53 3.34Marketing and administration cost:

(normal) 0.68 (special) 0.42 –––– –––– 3.21 3.76 Net selling price (fluid A) 4.00 –––– Contribution:

1 gallon fluid A 0.79 –––– 1 1 2 gallons fluid A 1.19 (1.19) –––– Break-even selling price of fluid B 2.57 –––– (d) It is not possible to quote a price based on cost factors alone. We need information on the state of market demand, competitors’ prices, qualitydifferences etc. If the prices in the overseas market are low and this chemicalcompany wishes to establish a market to unload its spare capacity of B then anyprice above £2.57 would increase company profits. However, the companyshould not undercut competitors too much, since this may result in a price warwith a resulting long- term reduction in profits for the chemical company. A price of £3 may be appropriate if the company merely wishes to unload its spare capacity [profit increase = 3000 (£3 £2.57)].

However, if the chemical company wishes to sell B overseas and to pay for itself (not being subsidized by A in the UK market) then any selling price in excess of£3.76 would be acceptable. If the market is tight or the company wishes todevelop a market in the long term then a price of £4 may be appropriate. Alternatively, if the company wishes merely to dispose of the spare capacity and the prices in the export country are similar to the UK then the normal selling priceof £5 may be appropriate. The cost information merely indicates the minimum prices for certain policies, and the final price depends on the interaction of cost with a number of otherimportant variables which are not given in the question. JOINT AND BY-PRODUCT COSTING 51 52INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS Solution IM 7.1 Solution IM 7.2 Solution IM 7.3 See Chapter 7 for the answer to this question. See Chapter 7 for the answer to this question.

Fixed cost per unit (£6000/500) £12 Variable cost per unit 30 –– Total cost 42 –– (a) Operating statement for periods 1–4 (marginal costing) Total Period 1 Period 2 Period 3 Period 4(£) (£) (£) (£) (£) Sales 104 500 27 500 22 000 30 250 24 750 –––––– ––––– –––––– ––––– ––––– Opening stock 0 0 0 3 000 0 Production at £30 per unit 58 500 15 000 15 000 13 500 15 000 Closing stock (1 500) 0 (3 000) 0 (1 500) –––––– ––––– ––––– ––––– ––––– Marginal cost of sales 57 000 15 000 12 000 16 500 13 500 –––––– ––––– ––––– ––––– ––––– Contribution 47 500 12 500 10 000 13 750 11 250 Fixed costs (24 000) (6 000) (6 000) (6 000) (6 000) –––––– ––––– ––––– ––––– ––––– 23 500 6 500 4 000 7 750 5 250 –––––– ––––– ––––– ––––– ––––– (b) Operating statement for periods 1–4 (absorption costing) Total Period 1 Period 2 Period 3 Period 4(£) (£) (£) (£) (£) Sales 104 500 27 500 22 000 30 250 24 750 –––––– ––––– –––––– ––––– ––––– Opening stock 0 0 0 4 200 0 Production (at £42 per unit) 81 900 21 000 21 000 18 900 21 000 Closing stock (2 100) 0 (4 200) 0 (2 100) –––––– ––––– ––––– ––––– ––––– Total cost of sales 79 800 21 000 16 800 23 100 18 900 –––––– ––––– ––––– ––––– ––––– Sub-total 24 700 6 500 5 200 7 150 5 850Over/(under) absorbed Overheads (600) 0 0 (600) 0 –––––– ––––– ––––– ––––– ––––– Net profit 24 100 6 500 5 200 6 550 5 850 –––––– ––––– ––––– ––––– ––––– (c) In period 1 production equals sales and there are no stock movements so that profits are the same with both systems. When production exceeds sales (periods 2and 4) absorption costing reports the greater profits because fixed costs aredeferred in the stock valuations. For example, in period 2 stocks increase by 100units thus resulting in fixed costs of £1200 (100 × £12) being deferred as an Income effects of alternative cost accumulation systems Solutions to Chapter 7 questions INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS53 expense with the absorption costing system. Therefore absorption costing profits exceed marginal costing profits by £1200. When sales exceed production theopposite situation occurs and marginal costing reports the higher profits. For amore detailed explanation of these issues see ‘Variable costing and absorptioncosting: a comparison of their impact on profit’ in Chapter 7.

(a) (i) Absorption costing September October(£000) (£000) Opening stock — 730.24 (28 000 £26.08) Production cost 2999.20 (115 000 £26.08) 2034.24 (78 000 £26.08) Less closing stock 730.24 (28 000 £26.08) 130.40 (5000 £26.08) ––––––– ––––––– 2268.96 2634.08 Under /(over) absorption ( W1) (208.80) 45.44 ––––––– ––––––– 2060.16 2679.52 Non-manufacturing overheads 200.00 200.00 ––––––– ––––––– Total cost 2260.16 2879.52 Sales 2784.00 (87 000 £32) 3232.00 (101 000 £32) ––––––– ––––––– Net profit 523.84 352.48 ––––––– ––––––– Working (W1 ) 100% capacity production = 1 008 000 /0.7 = 1 444 000 gross per annum = 120 000 gross per month September October Production (units) 115 000 78 000 Capacity 96% 65% Fixed costs (£) 656 000 632 000Fixed overhead absorbed (£): 115 000 £7.52 864 800 — 78 000 £7.52 — 586 560 ––––––– ––––––– Under /(over) absorption (£) (208 800) 45 440 ––––––– ––––––– (a) (ii) Marginal costing September October (£000) (£000) Opening stock — 519.68 (28 000 £18.56) Production cost 2134.40 (115 000 £18.56) 1447.68 (78 000 £18.56) Less closing stock 519.68 (28 000 £18.56) 92.80 (5000 £18.56) ––––––– ––––––– 1614.72 1874.56 Fixed production costs 656.00 632.00 Non-manufacturing overheads 200.00 200.00 ––––––– ––––––– 2470.72 2706.56 Sales 2784.00 (87 000 £32) 3232.00 (101 000 £32) ––––––– ––––––– Net profit 313.28 525.44 ––––––– ––––––– Solution IM 7.4 54INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS (b) For cost control purposes flexible budgets should be used and costs should be separated into their fixed and flexible elements. Using absorption costing for stock valuation and profit measurement purposes therefore does not preclude theanalysis of fixed and variable costs for cost control purposes.Marginal costing does not eliminate any distortion of interim profits where seasonal fluctuations in sales occur and production is at a fairly constant level.Marginal costing exerts a smoothing effect only when sales are relatively stableand production fluctuates from period to period. The adoption of a relevant costing /variable costing approach for decision- making is not dependent upon stocks being valued on an absorption costing basis.The statement is confusing decision-making applications with cost informationrequired for stock valuation and profit measurement purposes. However, break-even analysis is based on the assumption that profits are measured on a marginalcosting basis, and consequently marginal costing is preferable for profit planningpurposes.

(a) Calculation of fixed manufacturing overhead rate (£000) Prodn Prodn Service General dept 1 dept 2 dept factory Total Allocated 380.0 465.0 265 230 1340 Allocation of general factory 92.0 (40%) 115.0 (50%) 23 (10%) (230) Share of service department: 288 3 Labour related costs (60%) 76.8 (8 /18) 96.0 (10 /18) (172.8) Machine related costs (40%) 57.6 57.6 (115.2) ––––– ––––– –––– 606.4 733.6 1340 ––––– ––––– –––– Units of output (000) 120 120 Overhead rate per unit (£) 5.0533 6.1133 Calculation of total manufacturing cost per unit (£) Direct materials 7.00 Direct labour 5.50 Variable overhead 2.00 Fixed overhead: department 1 5.0533 Fixed overhead: department 26.1133 ––––––– Manufacturing cost 25.6666 ––––––– Absorption costing profit statement (£000) ; Production cost (116 000 £25.666) 2977.33 Less closing stocks (2000 £25.6666) 51.33 Cost of sales 2926.00 Under absorption of overhead: Department 1 (£20 000 + (4000 £5.0533)) 40.21 Department 2 (4000 units £6.1133) 24.45 Non-manufacturing costs 875.00 –––––– Total cost 3865.66 Sales (114 000 £36) 4104.00 –––––– Net profit 238.34 –––––– Solution IM 7.5 INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS55 Note that the under recovery of fixed overheads consists of £20 000 arising from actual overheads exceeding estimated overheads plus 4000 times the fixed overheadrate because actual volume was 4000 units less than estimated volume.

(b) Marginal costing profit statement (£000) Variable production cost (116 000 £14.50) 1682 Less closing stocks (2000 £14.50) 29 –––– 1653 Fixed manufacturing overhead (1340 + 20) 1360Non-manufacturing overhead 875 –––– 3888 Sales 4104 –––– Net profit 216 (c) See ‘Variable costing and absorption costing: A comparison of their impact on profit’ in Chapter 7 for the answer to this question. The answer should also explainwhy the profits calculated on an absorption costing basis in (a) exceed the variablecosting profit computation in (b) by £22 340 (£238 340 £216 000). This is because stocks have increased by 2000 units and with the absorption costing profit computation fixed manufacturing overheads of approximately £22 340 (2000 units £11.166 fixed overhead rate) are included in the closing stock valuation. Therefore £22 340 of the fixed overheads is incurred as an expense inthe following period. The total fixed manufacturing overhead charged as anexpense against the current period is £1 337 660 ((116 000 £11.166) (2000 £11.166) + £64 660 under absorption). With the variable costing system all of the fixed overheads incurred during the period of £1 360 000 is charged as an expense against the current accounting period. The differencebetween the fixed overheads charged as an expense (£1 337 660 – £1 360 000)accounts for the difference in the profit computation.

(a) Calculation of fixed overhead rates per unit:

Product 1 = £6 (£180 000/30 000) Product 2 = £8 (£480 000 /60 000) Therefore the unit overhead costs can be analysed as follows:

Product 1 Product 2(£) (£) Fixed 6 8 Variable (balance) 1 1 –– Total 7 9 –– The total overheads included in the income statement presented in the question are as follows: Product 1 Product 2 (£) (£) Variable overheads 24 000 (24 000 £1) 60 000 (60 000 £1) Fixed overheads 180 000 480 000 ––––––– ––––––– 204 000 540 000 ––––––– ––––––– Therefore the under /over recovery of fixed overheads is not shown separately in the profit statement in the question, but is included within the total overhead charge. In Solution IM 7.6 56INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS order to be consistent, this approach is adopted in the answer to part (a).

To construct the profit statement for the quarter commencing January, it is necessary to determine the budgeted opening stocks. The calculation is as follows:

Product 1 Product 2(units) (units) Budgeted opening stock ? ?

Budgeted production 30 000 52 500 Budgeted closing stock (8 000) (3 000) –––––– –––––– Budgeted units available for sale (as April quarter) 30 000 57 000 –––––– –––––– Opening stock (difference) 8 000 7 500 –––––– –––––– Budgeted income statement for January, February and March Product 1 Product 2 Budgeted sales quantity (units) 30 000 57 000 ––––––––––––––– Budgeted production quantity (units) 30 000 52 500 ––––––––––––––– Budgeted sales revenue (£) 450 000 1 026 000 ––––––––––––––– Budgeted production costs (£) (£) Direct material 60 000 157 500 Direct labour 30 000 105 000 Factory overhead a 210 000 532 500 ––––––– –––––––– 300 000 795 000 Add budgeted finished goods stock at 1 January (8000) units 80 000 (7500 units)105 000 ––––––– ––––––– 380 000 900 000 Less budgeted finished goods stock at 31 March (8000 units) 80 000 (3000 units) 42 000 ––––––– ––––––– Budgeted manufacturing cost of budgeted sales 300 000 858 000 ––––––– ––––––– Budgeted manufacturing profit 150 000 168 000 Budgeted administrative and selling costs (fixed) 30 000 48 000 ––––––– ––––––– Budgeted profit 120 000 120 000 ––––––– ––––––– ––––––– ––––––– Note a Product 1 = £180 000 fixed + £30 000 variable (30 000 units at £1) Product 2 = £480 000 fixed + £52 500 variable (52 500 units at £1) (b) Budgeted income statements for the two quarters to the 30 June January/February /March April /May /June Product 1 Product 2 Product 1 Product 2 Budgeted sales quantity (units) 30 000 57 000 30 000 57 000 ––––––––––––––– ––––––––––––––– Budgeted production quantity (units) 30 000 52 500 24 000 60 000 ––––––––––––––– ––––––––––––––– (£) (£) (£) (£) Budgeted sales revenue 450 000 1 026 000 450 000 1 026 000 ––––––––––––––– ––––––––––––––– Budgeted production costs Direct material 60 000 157 500 48 000 180 000 Direct labour 30 000 105 000 24 000 120 000 Factory overhead (variable) 30 000 52 500 24 000 60 000 ––––––––––––––– ––––––––––––––– 120 000 315 000 96 000 360 000 INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS57 Add budgeted opening finished goods stock 32 000 45 000 32 000 18 000 ––––––––––––––– ––––––––––––––– 152 000 360 000 128 000 378 000 Less budgeted closing finished goods stock 32 000 18 000 8 000 36 000 ––––––––––––––– ––––––––––––––– Budgeted manufacturing cost of budgeted sales (variable) 120 000 342 000 120 000 342 000 ––––––––––––––– ––––––––––––––– Product 1 Product 2 Product 1 Product 2 (£) (£) (£) (£) Budgeted manufacturing contribution 330 000 684 000 330 000 684 000 Budgeted fixed manufacturing overheads (180 000) (480 000) (180 000) (480 000) Budgeted administrative and selling costs (fixed) (30 000) (48 000) (30 000) (48 000) ––––––––––––––– ––––––––––––––– Budgeted profit 120 000 156 000 120 000 156 000 ––––––––––––––– ––––––––––––––– ––––––– –––––––– ––––––––––––––– (c) The profits in the budgeted profit statements have been calculated on the basis of absorption costing. With a system of absorption costing, fixed manufacturingoverheads are included in the stock valuations. The effect of this is that the fixedoverheads charged against profits for a period may not be the same as the fixed overheads incurred during a period. When stocks are decreasing, fixedoverheads charged will be greater than the fixed overheads incurred. This occursin the second quarter for product 2.With an absorption costing system, profits are a function of sales and production.

This can result in a distortion in the profit calculations, thus causing the situationwhich has occurred in the question. This situation can be avoided by adopting amarginal (variable) costing system. From the answer to part (b) we can see thatprofits are identical for both periods when a marginal costing system is adopted. The following differences between absorption and marginal costing statements can arise:

(i) Production = sales : absorption and marginal costing profit calculations will be identical. This situation occurs with product 1 in the first quarter.

(ii) Production > sales (second quarter for product 2) : profits will be greater with an absorption costing system.

(iii) Production < sales : profits will be lower with an absorption costing system.

This situation occurs with product 1 in the second quarter.

For a detailed explanation of the above differences see ‘Variable costing andabsorption costing: a comparison of their impact on profit’ in Chapter 7.

(a) (£000) Actual variable cost profit 60 Less adjustment for stock reduction using absorption costing method a 12 –– Actual absorption cost profit 48 Add adjustment for apportionment of cost variances to closing stocks b 9 –– Actual costing profit 57 –– Notes a Stocks are reduced by 2000 units and fixed production overheads are absorbed at the rate of £6 per unit. Therefore an additional £12 000 fixed production overhead Solution IM 7.7 is charged as an expense with the absorption cost method. Variable costing charges £66 000 fixed production overhead as an expense for the period (£80 000 fixedproduction overhead – £14 000 fixed production overhead expenditure variance),whereas the absorption cost method charges £78 000 fixed production overhead asan expense for the period (£140 000 absorption cost of sales – £80 000 variable costof sales – £14 000 expenditure variance + £32 000 volume variance). b The total of the production cost variances is £14 000 adverse. With the standard absorption costing method, £14 000 is written off as a period cost. Consequently the production costs charged as an expense for the period are £154 000 (£140 000cost of sales + £14 000 production cost variances). The production costs charged asan expense with the actual cost system are £145 000 cost of sales. The £9000difference is because 18 000 /28 000 of the cost variance of £14 000 is apportioned to the closing stock valuation. Therefore the actual costing profit is £9000 higher.

(b) The answer should include a discussion of the relative merits of absorption costing and variable costing. For a discussion of the relative merits see ‘Some arguments insupport of variable costing and absorption costing’ in Chapter 7. In addition theanswer should indicate that a change to a standard costing system will providebetter information for decision-making and cost control purposes.

(c) The report should emphasize that for decision-making and cost control purposes the standard variable costing system is recommended. However, to meet therequirements of external reporting, it will be necessary to adjust the variable costaccounts to an absorption costing basis.

Projected profit and loss accounts for November and December 2012 (variable costing basis) November December (£000) (£000) (£000) (£000) Sales (10 000 units at £25) 250Sales (12 000 units at £25) 300 Opening stock 160 144 Production costs 64 112 ( W1) ––– ––– 224 256 Closing stock 144 80 160 ( W2)9 6 ––– ––– ––– ––– 170 204 Variable selling costs 10 12 ––– ––– Contribution 160 192 Other expenses Production: fixed 80 80 Administration: fixed 28 28 Selling: fixed 16 124 16 124 ––– ––– ––– ––– Standard variable cost profit 36 68 Variance: Production:Variable: expenditure (4) 4 ( W3) Fixed: expenditure (14) 10 ( W4) Administration: expenditure (5) (3.5) ( W5) Selling: Variable: expenditure 1 – ( W6) Fixed: expenditure (2) (24) (1) ( W7)9 .5 ––– ––– ––– –––– Actual variable cost profit 60 58.5 ––– –––– 58 INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS59 Workings (W1 ) 14 000 units £8.

( W2 ) 18 000 units opening stock + 14 000 units production 12 000 units sales = 20 000 units closing stock valued at £8 per unit.

( W3 ) Variable production cost variance: (14 000 £8) £116 000 = £4000.

( W4 ) Fixed production expenditure variance: £80 000 £90 000 = £10 000.

( W5 ) Administration expenditure variance: £28 000 £24 500 = £3500 (F).

( W6 ) Variable selling cost variance: (12 000 £1) £12 000 = nil.

( W7 ) Fixed selling cost variance: £16 000 £15 000 = £1000 (F).

The budgeted fixed production overheads calculation is: (160 000 units £6) /12 months. 60COST–VOLUME–PROFIT ANALYSIS Solution IM 8.1 Solution IM 8.2 Solution IM 8.3 (a) The selling price is in excess of the variable cost per unit, thus providing a contribution towards fixed costs and profit. At point (A) sales are insufficient to generate a contribution to cover the fixed costs (difference between total cost andvariable cost lines in the diagram). Consequently a loss occurs. Beyond the break-even point sales volume is sufficient to provide a contribution to cover fixed costs,and a profit is earned. At point (B) the increase in volume is sufficient to generatea contribution to cover fixed costs and provide a profit equal to the difference(represented by the dashed line) between the total revenue and cost line.

(b) See Chapter 8 for the answer to this question. The comparisons of CVP models represented in management accounting and economic theory are presented in the first half of Chapter 8. Additional points include thefollowing: (i) Both models are concerned with explaining the relationship between changes in costs and revenues and changes in output. Both are simplifications of cost and revenue functions because variables other than output affect costs and revenues.

(ii) The value of both models is reduced when arbitrary cost allocation methods areused to apportion joint costs to products or divisions.

(iii) The economic model indicates two break-even points whereas the managementaccounting model indicates one break-even point.

(iv) Both models are based on single value estimates of total costs and revenues. It ispossible to incorporate uncertainty into the analysis using the methods outlined inChapter 12.

(v) The model based on economic theory provides a theoretical presentation of the relationship between costs, revenues and output. The model is intended to providean insight into complex inter-relationships. The management accounting modelshould be seen as a practical decision-making tool which provides a usefulapproximation for decision-making purposes if certain conditions apply (e.g. relevant range assumption).

(a) See ‘Cost–volume–profit analysis assumptions’ in Chapter 8 for the answer to this question.

(b) Examples of the circumstances where the underlying assumptions are violated include:(i) Variable cost per unit remaining constant over the entire range : This assumption is violated where quantity discounts can be obtained from thepurchase of larger quantities. Consequently the variable cost per unit will notbe constant for all output levels. However, over a restricted range, or severalrestricted ranges, a linear relationship or a series of linear relationships mayprovide a reasonable approximation of the true cost function.

(ii) Selling price is constant per unit : In order to increase sales volume, the selling price might be reduced. Therefore selling price will not be a linear functionof volume. A series of linear relationships may provide a reasonable approximation of the true revenue function.

Cost–volume–profit analysis Solutions to Chapter 8 questions COST–VOLUME–PROFIT ANALYSIS61 (iii)The sales mix is known : It is unlikely that the planned sales mix will be equal to the actual sales mix. To incorporate the possibility that the actual sales mix may differ from the planned sales mix, a range of total cost and revenue curvesshould be prepared corresponding to each possible sales mix. This will give arange of break-even points and profit /losses for possible mixes of sales.

See ‘Cost–volume–profit analysis assumptions’ in Chapter 8 and ‘Decision-making underconditions of risk and uncertainty’ in Chapter 12 for the answer to this question.

(a) Product Unit Sales volume Total Total sales contribution (units) contribution revenue (£000) (£000) J 6 10 000 60 200 K 32 10 000 320 400 L (0.20) 50 000 (10) 200 M 3 20 000 60 200 –––––– ––– –––– 90 000 430 1000 –––––– ––– –––– Average contribution = 43% of sales revenue (b) and (c) The profit arising from the most profitable product (Product K) is drawn first on the profit-volume graph (see Fig. Q8.5). At £400 000 sales revenue a profit of £80 000 (£320 000 contribution – £240 000 fixed costs) is plotted Solution IM 8.4 Solution IM 8.5 200 400 600 800 1000 Sales (£000)Break-even point (£558 140) K J M L (£000) Profit 200190 140 100 80 Loss 100 200 240 Fixed costs Figure Q8.5 62COST–VOLUME–PROFIT ANALYSIS on the graph. The profits arising from the remaining products are then entered on the graph. Since fixed costs have already been covered by Product K, the next product (Product J) will increase profits by £60 000 (i.e. total contribution of £60 000). The second point to be plotted is thereforecumulative sales of £600 000 and profits of £140 000. The addition of Product M results in cumulative profits of £200 000 (£140 000 + £60 000)and cumulative sales revenue of £800 000. Finally, the addition of product Lreduces total profits to £190 000.

The dashed line on the graph represents the average contribution per £1 of sales (43%) arising from the planned sales mix. The break-even point insales value is £558 140 [fixed costs (£240 000) /contribution ratio (0.43)].

This is the point where the dashed line cuts the horizontal axis. At zero saleslevel a loss equal to the fixed costs will be incurred and at the maximum saleslevel profits will be £190 000 [(£1m 0.43) – £240 000].

Product K yields the largest contribution /sales ratio (80%) and Products J and M yield identical ratios. Product L has a negative contribution anddiscontinuation will result in profits increasing by £10 000.

(d) The contribution /sales ratio can be improved by:

(i) increasing selling price; (ii) reducing unit variable costs by improving labour efficiency or obtainingcheaper materials from different suppliers; (iii) automating production and substituting variable costs with fixed costs.

(a) See ‘Cost–volume–profit analysis assumptions’ in Chapter 8 for the answer to this question.

(b) (i) Holiday resort cost and income statement Guests Income Variable Contribution Fixed Surplus in residence p.a. costs costs (deficit) (£) (£) (£) (£) (£) 6 18 000 7 740 10 260 16 000 (5740) 7 21 000 9 030 11 970 16 000 (4030) 8 24 000 10 320 13 680 16 000 (2320) 9 27 000 11 610 15 390 16 000 (610) 10 30 000 12 900 17 100 16 000 1100 11 33 000 14 190 18 810 22 000 (3190) 12 36 000 15 480 20 520 22 000 (1480) 13 39 000 16 770 22 230 22 000 230 14 42 000 18 060 23 940 22 000 1940 15 45 000 19 350 25 650 22 000 3650 There are two break-even points. If provision is made for between 6 and 10guests, the first break-even point occurs just in excess of 9 guests per week (or270 guests per annum). If provision is made for 11 or more guests per week,the break-even point changes to 13 guests per week.

(ii) The total costs for various activity levels are as follows:

Guests Total costs(£) 6 23 740 10 28 900 11 36 190 15 41 350 The above costs are plotted on the break-even chart shown in Figure Q8.6. Solution IM 8.6 COST–VOLUME–PROFIT ANALYSIS63 (a) For the answer to this question you should refer to ‘cost behaviour’ in Chapter 2.

(b) Output Total cost (units) (£) Lowest activity 11 500 102 476 Highest activity 14 000 113 201 ––––– –––––– 2 500 10 725 ––––– –––––– Variable cost per unit of output = = £4.29 per unit The fixed cost can be estimated at any level of activity by subtracting the variable cost portion from the total cost. At an activity level of 11 500 units the total cost is £102 476 and the total variable cost is £49 335 (11 500 units × £4.29). The balance of £53 141 is assumed to represent the fixed costs. Difference in cost (£10 725) Difference in output (2500 units) Solution IM 8.7 50 40 £36 190 £28 900 £23 740 22 30 20 16 10 Fixed costs 45 000 41 350 BEP BEP Revenue T otal cost 2 4 6 8 10 12 14 15 Guests 0 Revenue and Costs (£000) Figure Q8.6 64COST–VOLUME–PROFIT ANALYSIS (c) Break-even point = = 8422 units Because the break-even point is outside the range of observations that were used to estimate the variable and fixed costs it is possible that estimates of costbehaviour may not be accurate. However, given that the lowest observed level ofactivity is significantly above the break-even point output level there is a very highprobability that profits will be generated at all likely levels of activity.

Task 1 – Preliminary workingsPlanned sales volume for draft budget = 0.75 × 3.2m = 2.4m unitsDraft budget = 2/3 of maximum capacityTherefore maximum capacity = 2.4m × 3/2 = 3.6m units The following is an analysis of the draft budget: (£m) (£ per unit) Sales revenues 960.0 400 Less variable costs 777.6 324 –––– ––– Contribution 182.4 76 Less fixed costs 171.0 –––– Net profit 11.4 –––– Break-even point in units (£171m/£76) 2.25m Break-even point in sales revenues (2.25m × £400 selling price) £900m (a) (i) and (a)(ii) Proposal A Commission per unit in the draft budget (£38.4m/2.4m units)= £16 Revised commission per unit = £18 Revised unit contribution = £74 Revised sales volume (units) 2.64m Projected total contribution (2.64m × £74) £195.36m Less fixed costs (£171m + £14m) 185.00m –––––––– Projected profit 10.36m –––––––– Break-even point in units (£185m/£74) 2.5m Break-even point in sales revenues (2.5m × £400) £1 000mChange in profit £1.04m Proposal B Reduction in selling price (5% × £400) £20 Projected sales volume 3.2m Reduction in cost of materials per unit £4 Revised unit contribution (£76 – £20 + £4) £60 Projected total contribution (3.2m × £60) £192mLess fixed costs 171m ––––– Projected profit 21m ––––– Break-even point in units (£171m/£60) 2.85m Break-even point in sales revenues (2.85m × £380) £1 083mChange in profit +£9.60m Fixed costs (£53 141) Contribution per unit (£10.60 £4.29) Solution IM 8.8 Proposal C Reduction in selling price (10% × £400) £40 Projected unit sales volume (restricted to maximum capacity) 3.6m Reduction in cost of materials per unit £4 Revised unit contribution (£76 – £40 + £4) £40 Projected total contribution (3.6m × £40) £144m Less fixed costs (£171m – £45m) 126m––––– Projected profit 18m ––––– Break-even point in units (£126m/£40) 3.15m Break-even point in sales revenues (3.15m × £360) £1.134mChange in profit +£6.6m (b) Proposal B would appear to be the best strategy in terms of profitability. All three proposals increase the break-even point although proposal A shows the smallestincrease. However, provided that management is confident that the predictedsales can be achieved proposal B should be chosen.

(c) Before making a final decision the following issues should be considered: (i) the promotion campaign might generate increased sales beyond the currentyear; (ii) the price reduction for proposals B and C may cause competitors to react thus provoking a price war; (iii) the price reduction for proposals B and C may not result in the predicted sales volume if customers perceive the product to be of low quality; (iv) proposal C will result in the company operating at full capacity. This mayresult in changes in cost structure if the company is operating outside the relevant output range.

Task 2(a) (£m) (£m) Proposed selling price 3.0 Less relevant costs:

Material A (replacement cost) 0.8 Material B (0.1 NRV + 0.3 replacement cost) 0.4Direct labour a (1.0 – 0.2) 0.8 Variable factory overhead 0.9 Fixed factory overhead nil 2.9 ––– ––– Contribution to fixed costs and profit 0.1 ––– Note: a It is assumed that the direct labour of £0.8m charged to the order includes the opportunity cost of the direct labour since the question implies that this labour willbe utilized elsewhere if the order is not accepted.

(b) The relevant cost approach described in Chapter 9 has been used in part (a). It is assumed that it is a one time short-term special order and that no other costs canbe avoided if the order is accepted. COST–VOLUME–PROFIT ANALYSIS 65 66COST–VOLUME–PROFIT ANALYSIS Task 1 (1) Production volume (packs) 40 000 50 000 60 000 70 000 (2) Average cost £430 £388 £360 £340 (3) Total cost (1 × 2) £17 200 000 £19 400 000 £21 600 000 £23 800 000 (4) Cost per extra 10 000 packs £2 200 000 £2 200 000 £2 200 000 (5) Unit variable cost ((4)/10 000) £220 £220 £220 (a)(£) Total cost for 40 000 packs 17 200 000 less Variable costs (40 000 × £220) 8 800 000 ––––––––– Fixed costs 8 400 000 ––––––––– (b) Unit contribution (£420 £220) 200 Total contribution (£200 × 65 000 packs) 13 000 000 less Fixed costs 8 400 000 ––––––––– Profit 4 600 000 ––––––––– (c) Break-even point (packs) = Fixed costs/Unit contribution = £8 400 000/£200 = 42 000 (d) Margin of safety = (65 000 42 000)/65 000 = 35.4% Task 2 (a) Additional contribution = 5000 × (£330 £220) = £550 000 Fixed costs are assumed to remain unchanged. Therefore profits should increase by £550 000.

(b) Additional contribution from the order = 15 000 × (£340 £220) = £1 800 000 Lost contribution from current sales = 10 000 × (£420 £220) = £2 000 000 ––––––––– Loss from the order £200 000 ––––––––– (c) The order for 5000 units at £330 should be accepted since this yields an additional contribution of £550 000. Fixed costs are assumed to remain unchanged for both orders. However, accepting an order for 15 000 units can only be met by reducing current sales by 10 000 units (planned existing sales are 65 000 units and capacity is restricted to 70 000 units). The order can only be justified if the lost sales can berecouped in future periods with no loss in customer goodwill.

(d) Non-financial factors that should be considered include: (i) The effect on existing customers if they become aware that the company isselling at a lower price to other customers.

(ii) The long-term potential of the new order. If the order is likely to result inrepeat sales it might be financially viable to increase capacity and obtain theincreased contribution without the loss of contribution from existing sales.The financial appraisal should compare the present value of the increase incontribution with the additional costs associated with increasing capacity.

(a) Absorption costing unitizes fixed production overheads and includes them in the stock valuation whereas marginal costing does not include fixed overheads in thestock valuation. Instead, total fixed production overheads incurred are treated as period costs. Therefore, the total fixed overheads of £385 000 (250 000 units of A plus 100 000 units of B valued at £1.10 per unit) are charged as an expensewith a marginal costing system. Solution IM 8.9 Solution IM 8.10 COST–VOLUME–PROFIT ANALYSIS67 Total production is 350 000 units (250 000 of A plus 100 000 units of B) and total sales volume is 335 000 units (225 000 units of A plus 110 000 units of B). Production exceeds sales by 15 000 units resulting in an equivalent increase instocks. With an absorption costing £16 500 (15 000 units × £1.10) out of a total fixed overheads incurred of £385 000 will be included in the stock valuation andnot recorded as an expense for the current period. Therefore the cost of sales withan absorption costing system will be £16 500 lower than marginal costing cost ofsales thus resulting in absorption costing showing an extra £16 500 profits for theperiod.

(b) Total fixed overheads for the period is calculated as follows: (£) Production fixed overhead(350 000 units normal production × £1.10) 385 000 Other fixed overheads (335 000 units sales × £0.50) 167 500 ––––––– 552 500 ––––––– It is assumed that other fixed overheads are absorbed on the basis of sales volumerather than production volume. The cost–volume–profit analysis should be based on the assumption that sales will be in accordance with the planned sales mix of 225 000 units of A and 110 000 units of B. This sales mix will yield the following total contribution:

Product A Product B Total (1) Selling price 5.70 6.90 (2) Variable cost 3.45 4.80 ––––– ––––– (3) Unit contribution 2.25 2.10 (4) Sales volume (units) 225 000 110 000 (5) Total contribution (3 × 4) £506 250 £231 000 £737 250 (6) Total sales revenue (1 × 4) £1 282 500 £759 000 £2 041 500 Average contribution per unit = £737 250/335 000 units total sales = £2.2007 Average selling price per unit = Total sales revenue (£2 041 500)/Total sales volume (335 0000) =£6.094 Break-even point (units) = Total fixed costs/Average contribution per unit = £552 500/£2.2007 = 251 056 units Break-even point (sales value) = 251 056 units × average selling price (£6.094) = £1 529 935 Alternatively, the break-even point in sales value can be computed using thefollowing formula:

× Total sales (£2 041 500) = £1 529 913.

Total fixed costs (£552 500) Total contribution (£737 250) (a) The capacity usage in single-room days is as follows:Days Single rooms: Peak period:60 rooms 6 weeks 7 days 2 520 Non-peak period: 60 rooms 14 weeks 7 days 80% 4 704 ––––– 7 224 Double rooms 35 rooms 7 days 20 weeks = 4900 days Double rooms expressed as equivalent single-room days 7 840 (4900 160%) –––––– Total equivalent single-room days 15 064 –––––– Required contribution = fixed costs (£29 900) + target profit (£10 000) = £39 900 Required contribution per single-room day = £2.65 (£39 900 /15 064) Required charge per single room = £6.65 (£2.65 + £4 variable cost)Required charge per double room = £10.64 (£2.65 160%) + £6.40 variable cost The following calculations can be used to check that the above charges will yield£10 000 profit. (£) Single-rooms contribution [7224 days (£6.65 £4 variable cost)] 19 144 Double-rooms contribution [4900 days (£10.64 £6.40 variable cost)] 20 776 ––––– Total contribution 39 920 Fixed costs 29 900 ––––– Profit 10 020 ––––– (b) (£) (£) Accommodation 10 020 Sports centre: Residential guests: Single rooms (7224 £2) 14 448 Double rooms (4900 2 £2) 19 600 Casual visitors: (30 20 weeks 7 days = 4200 £3) 12 600 –––––– 46 648 Fixed costs 15 500 31 148 –––––– Sports shop (7224 + 9800 + 4200 = 21 224 persons £1) 21 224 Fixed costs 8 250 12 974 –––––– Cafeteria (21 224 persons £1.50) 31 836 Fixed costs 12 750 19 086 –––––– –––––– Total profit 73 228 –––––– (c) It is assumed that the fixed costs do not include any depreciation and that the profit calculated in (b) is equivalent to cash flow. It is also assumed that the cash flows will remain at £73 228 per annum for the next 5 years.

PV of cash flows (£73 228 3.791 10% annuity factor for 5 years) = £277 607 The PV of the cash flows from operating the centre is in excess of the £250 000 offer from the private leisure company. Therefore the decision would be to reject theoffer. Note that the annual cash flows (and thus the PV) would be higher ifdepreciation has been deducted in the calculation of profit in (b). 68 COST–VOLUME–PROFIT ANALYSIS Solution IM 8.11 MEASURING RELEVANT COSTS AND REVENUES FOR DECISION-MAKING69 Measuring relevant costs and revenues for decision-making Solutions to Chapter 9 questions (a) See ‘Product mix decisions when capacity constraints exist’ in Chapter 9 for the answer to this question.

(b) See ‘Product mix decisions when capacity constraints exist’ in Chapter 9 and the early part of Chapter 25 for the answer to this question.

(c) See appendix to Chapter 9 and the solution to 9.25 for the answer to this question.

(a) The relevant costs for the production of 400 components are as follows: (£) (£) Materials: M1 (1200 kg at £5.50 replacement cost) 6 600 P2 (800 kg at £2 per kg) a 1 600 Part no. 678 (400 at £50 replacement cost) 20 000 28 200 –––––– Labour: Skilled (2000 hours at £13 per hour) 26 000 Semi-skilled (2000 hours at £10 per hour) 20 000 46 000 –––––– Overheads: Variable (1600 machine hours at £7 per hour) 11 200Fixed: Incremental fixed costs 3 200 –––––– Total relevant cost 88 600 Contract price (400 components at £250 per component) 10 ~0 000 –––––– Contribution to general fixed costs 11 400 –––––– –––––– The incremental revenues exceed the incremental costs. Therefore the contract should be accepted subject to the comments in (b) below. Note a If materials P2 are not used on the contract, they will be used as a substitute for material P4. Using P2 as a substitute for P4 results in a saving of £2 (£3.60 £1.60) per kg. Therefore the relevant cost of P2 consists of the opportunity cost of £2 per kg.

(b) Three factors which should be considered are: (i) Can a price higher than £250 per component be negotiated? The contractonly provides a contribution of £11 400 to general fixed costs. If the companygenerates insufficient contribution from its activities to cover general fixedcosts then it will incur losses and will not be able to survive in the long term.It is assumed that acceptance of the contract will not lead to the rejection ofother profitable work.

(ii) Will acceptance of the contract lead to repeat orders which are likely toprovide a better contribution to general fixed costs? Solution IM 9.1 Solution IM 9.2 – – – – – –– –– –– 70MEASURING RELEVANT COSTS AND REVENUES FOR DECISION-MAKING (iii)Acceptance of the contract will provide additional employment for 12 months, and this might have a significant effect on the morale of theworkforce.

(a) Revised cost estimate: (£) Direct materials: paper 2500 (1) inks 3000 (2) –––– 5500 Direct labour (£1750 + £2188) 3938 (3) Unskilled labour — (4) Variable overhead 1400 (5)Printing 600 (6) Printing press depreciation — (7) Fixed production costs — (7) Estimating department costs — (8) –––– –––– Notes: (1) The alternative use of the paper is to sell it for £2500. Therefore the cashflowimpact is £2500.

(2) The incremental cost of undertaking the work is £3000.

(3) Is is assumed that 125 hours not undertaken at weekends is in scarce supply and the decision to undertake the work will result in a lost contribution. Therelevant cost is the hourly labour rate plus the lost contribution per hour. Thelost contribution is not given in the question and therefore cannot be ascertained. The hourly labour rate consisting of 125 hours at £14 per hour isincluded in the above answer. It is assumed that the weekend hours representan incremental cost and do not involve a lost contribution. The incrementalcost of weekend work is £2188 (125 hours × £17.50).

(4) At present 200 unskilled hours are recorded as idle time and the work to be undertaken entails 100 plus 50 hours time off in lieu. Therefore idle time willbe reduced but no additional expenditure will be incurred.

(5) It is assumed that £1400 is an incremental cost of undertaking the work.

(6) The lost contribution of £600 (200 hours at £3 per hour) is included in the cost estimate. It is assumed that the variable cost of the printing press hourshave already been included in the cost estimate.

(7) Fixed overheads and depreciation are fixed costs and therefore do not involve incremental cash flows.

(8) The cost of estimating time has already been incurred and is a sunk cost.

(b) See the introductory sections in Chapter 9 for the answer to this question.

(c) See opportunity costs in Chapters 2 and 9 for the answer to this question. (a) (£) (£) Direct materials: Material A: (30 kg /0.9) £5.13 /kg ( W1) 171.00 Others: £1.34 /unit 100 134.00 305.00 –––––– Direct labour: Department 1: 40 hours £12 /hour 480 Department 2: 15 hours £13 /hour 195 675 –––––– Solution IM 9.3 Solution IM 9.4 11 438–– ––– – –– 00 .00 .00 .50 MEASURING RELEVANT COSTS AND REVENUES FOR DECISION-MAKING71 Production overhead:

Department 1: Variable, 40% £480.00 192.00 Fixed, 90% £480.00 432.00 Department 2: Variable, £0.9 per DLH 15 hours ( W2) 13.50 Fixed, £2.05 per DLH 15 hours ( W3) 30.75 668.25 –––––– Other overhead: Variable: £0.70 per unit 100 70.00 Fixed: £1.95 per unit 100 195.00 265.00 –––––– ––––––– Total cost 1913.25 ––––––– Workings ( W1 ) 2 400 000 30 /0.9 per 100 kg = 800 000 purchases p.a.

= 66 667 per month ( W2 ) Department 2 overhead:

Variable £1 980 000 Fixed £3 444 000 (balance) ––––––––– £5 424 000 ––––––––– Variable overhead rate = £1 980 000 /2 200 000 hours = £0.90 per direct labour hour ( W3 ) Expected usage of direct labour hours:

Expected capacity (excluding new product) =1.32 million hours (0.6 2.2 m) Capacity required for new product =0.36 million hours (2.4 m 15 /100) –––– Total hours 1.68 –––– Fixed overhead rate = £3 444 000 /1 680 000 direct labour hours = £2.05 per direct labour hour (b) The total cost per unit of £19. (£1913.25 /100) is below the expected selling price of £16 and it appears that the product is not profitable. However, the new product provides a contribution of £3.445 per unit towards fixed costs. The calculation is as follows:

(£) Variable costs: Direct materials 3.05 Direct labour 6.75 Variable production overhead 2.055 Other variable overhead 0.70 ––––– Selling price 16.000 ––––– Contribution 3.445 ––––– A total annual contribution of £8.268 m (£3.445 2.4 m annual sales) towards fixed costs will be obtained if the new product is introduced. If fixed costs will notbe affected by the decision to introduce the new product then the new product should be launched because it will provide an annua l contribution of £8.268 m which would not otherwise be obtained. The company is currently working at60% capacity and, with the introduction of the new product, utilization ofavailable capacity will be increased to 76% (1.68 m hours /2.2 m maximum capacity). Therefore sufficient capacity is available to meet the demand for the 1325 12.555 –– –––– ––– new product and no opportunity cost is involved resulting from a need to reduce existing output.With the introduction of the new product, spare capacity would remain, and the company should seek to utilize this capacity with other profitable work. If noother profitable work is likely to be obtained in the long term, then thecompany should consider reducing capacity to either 60% or 76% of existingcapacity. If the annual fixed costs that can be saved from reducing capacity from 76% to 60% exceed the £8.268 m contribution generat ed by the new product then it is more profitable to reduce capacity to 60% and not introduce the new product.

(c) At a selling price of £15.50 per unit, contribut ion per unit will be reduced by £0.50, and the annual contribution will be £8.5405m (£2.945 2.9 m sales). At a selling price of £16 the expected contribution is £8.268 m. It is therefore moreprofitable to reduce selling price if management are confident that the pricereduction will increase sales volume by 500 000 units (approximately 20%) andwill not affect the selling prices of other products. There is sufficient capacity tomeet the additional sales volume and it is assumed that the increase in demandwill not result in a change in fixed costs.

(a) Product ABCD Contribution £16 £17 £23 £22Unit m/c hours 4345 Contribution per m/c hour £4 £5.67 £5.75 £4.40Ranking 4213 Product Quantity Machine Contribution units hours (£) C 250 1000 5750 B 180 540 3060 D 92 460 2024 –––– ––––– 2000 10 834 Fixed costs 8000 ––––– Profit 2834 ––––– (b) (i) Sales Unit Additional Revised Net shortfall contribution cost per unit benefit units unit a contribution (£) (£) (£) (£) A 200 16.00 3.50 12.50 2500 D 8 22.00 7.00 15.00 120 –––– 2620 –––– Note:

a Labour cost at an overtime premium of £8 per labour hour plus a 50% increase in variable overheads.

(b) (ii) (£ per unit) Variable cost of B 13 Cost of external purchase 20 –– Increase in cost 7 –– 72 MEASURING RELEVANT COSTS AND REVENUES FOR DECISION-MAKING Solution IM 9.5 MEASURING RELEVANT COSTS AND REVENUES FOR DECISION-MAKING73 Reduction in contribution = £7 × 180 units = £1260 Hours released = 540 Allocated as follows: Product D 8 units (at 5 hours per unit) 40 hours Product A 125 units (at 4 hours per unit) 500 hours Additional Additional production contribution (£) D 8 at £22 176 A 125 at £16 2000 –––– 2176 B Contribution lost 1260 –––– Net benefit 916 –––– The report should draw attention to the fact that both options result in an increasein profits. The first option, however, results in the higher profit. Other factors toconsider are the extent to which the work force finds overtime to be desirable. Thesecond option involves a loss of control in terms of quality and reliability. Bothoptions have the advantage of satisfying customer demand and increasing customer goodwill.

(a) C D (£) (£) Selling price 127 161 Variable costs 66 87 ––– ––– Contribution 61 74 ––– ––– The drilling and grinding hours required to meet the production requirements for the period are calculated as follows:

A B C D Total Hours per unit: Drilling 2134 Hours per unit: Grinding2413 Units of output 50 100 250 500 Drilling hours required 100 100 750 2000 2950 Grinding hours required 100 400 250 1500 2250 Drilling hours are the limiting factor (1650 hours are available). The contribu- tions per drilling hour are £20.33 for product C (£61 /3 hours) and £18.50 (£74 /4 hours) for product D. Therefore the maximum demand of product C should be met, resulting in 950 drilling hours being utilized (750 for product C and 200 hours for components A and B). The remaining capacity of 700 hourscan be used to produce 175 units of product D. It is assumed that the internaldemand for components A and B must have priority over meeting the demandfor product D. The estimated profit per week is:

(£) Contribution from product C (250 units at £61) 15 250 Contribution from product D (175 units at £74) 12 950 –––––– Total contribution 28 200 Allocated fixed overheads (250 £23) + (175 £39) 12 575 –––––– 15 625 –––––– Solution IM 9.6 (b) (i) Components A and B are not used to produce either of the finished productsbut if they are purchased drilling time can be freed up to expand production of product D. The variable costs of components A and B are £32 and £78respectively and the outside purchasing costs are £50 and £96. Thus variablecosts will increase by £18 per unit for both components but the contributionper drilling hour from producing product D is £18.50. Purchase of com-ponent A releases 2 drilling hours (yielding £37 additional product Dcontribution) and purchase of component B releases 1 drilling hour (yielding£18.50 additional contribution). Thus components A and B should bepurchased from outside and this will free up 200 drilling hours (50components 2 hours for component A plus 100 1 hour for component B). This will enable output of product D to be expanded by 50 units (200hours /4 hours per unit). The increase in contribution is calculated as follows:

(£) (£) Additional contribution from Product D (50 £74) 3700 Less additional purchasing costs: Component A (50 £18) 900 Component B (100 £18) 1800 2700 –––– –––– Additional contribution 1000 –––– (ii) For the answer to this question see ‘Single-resource constraints’ and ‘Tworesource constraints’ in Chapter 25.

(a) Machine hours are the limiting factor and profits will be maximized by allocating machine hours on the basis of a product’s contribution per machine hour. In orderto do this it is necessary to compute the output per machine hour for eachproduct. Calculation of output per machine hour Manufacturing overhead rate = £427 500 /2250 hrs = £190 per machine hour Output per machine hour = machine hour rate overhead allocated per unit of output Product W = 222.2 (£190 /£0.855) units per hour X = 200 (£190 /£0.950) units per hour Y = 400 (£190 /£0.475) units per hour Z = 250 (£190 /£0.76) units per hour Calculation of contribution per machine hour Product WX Y Z (£) (£) (£) (£) Selling price per unit 3.650 3.900 2.250 2.950 Variable costs per unit 1.865 2.110 1.272 1.589 Contribution per unit 1.785 1.790 0.978 1.361 Output per machine hour (units) 222.2 200 400 250 Contribution per machine hour (£) 396.6 358 391.2 340.25 Ranking 1 3 2 4 74 MEASURING RELEVANT COSTS AND REVENUES FOR DECISION-MAKING Solution IM 9.7 MEASURING RELEVANT COSTS AND REVENUES FOR DECISION-MAKING75 Required machine hours to meet the maximum demand Product W= 855 hours (190 000 /222.2) X= 625 hours (125 000 /200) Y= 360 hours (144 000 /400) Z= 568 hours (142 000 /250) –––– 2408 hours Practical capacity is only 2250 machine hours and therefore there is a shortfall of 158 hours. Output of product Z should be reduced by 39 500 units (158 hours 250 units per hour). The optimum output schedule is to produce 102 500 (142 000 39 500) units of product Z and maximum demand as per the sales forecast for products W, X and Z.

(b) Calculation of profits with overtime Product Total W X Y Z (£) Sales volume (units) 190 000 125 000 144 000 142 000 Contribution per unit (£) 1.785 1.790 0.978 1.361Total contribution (excluding overtime premium) 339 150 223 750 140 832 193 262 896 994 Less overtime premium a (10 053) –––––– 886 941 Less fixed costs: Manufacturing (427 500) Selling and administration (190 000) Additional (24 570) –––––– Net profit 244 871 –––––– Note a The production shortfall of 158 machine hours could be made up by working overtime on any of the four products. The direct labour cost per machine hour for each product is:

Product W = £134.20 (222.2 £0.604) X = £130.20 (200 £0.651) Y = £162 (400 £0.405) Z = £127.25 (250 £0.509) Therefore it is cheaper to work overtime on product Z. The overtime premium will be 39 500 (£0.509 0.5) (c) (£) Additional contribution from working overtime on product Z (39 500 units £1.361) 53 759 Less: Overtime premium (10 053) Additional fixed costs (24 570) –––––– Additional profit 19 136 –––––– Prior to making the decision management should ensure that staff are prepared to work overtime and that this will not result in lower productivity due to workinglonger hours. 76MEASURING RELEVANT COSTS AND REVENUES FOR DECISION-MAKING (a) (i) Hectares suitable for squash, kale, lettuce and beans 680 Hectares suitable for kale and lettuce only 280 ––– 960 ––– Minimum requirement: 10 000 boxes of each rounded to nearest Maximum requirement: 227 500 boxes of each whole hectare. Squash Kale Lettuce Beans Boxes per hectare 350 100 70 180 Minimum requirements (hectares) 29 100 143 56 Cost per hectare: (pesos) (pesos) (pesos) (pesos) Materials 476 216 192 312 Labour: growing 896 608 372 528 Labour: harvesting etc. 1260 328 308 936 Labour: transport 1820 520 280 1728 –––– –––– –––– –––– Total variable costs 4452 1672 1152 3504 –––– –––– –––– –––– Selling price: (pesos) (pesos) (pesos) (pesos) Per box 15.38 15.87 18.38 22.27 Per hectare 5383.00 1587.00 1286.60 4008.60 Contribution per hectare 931.00 (85.00) 134.60 504.60Ranking 1432 280 hectares are suitable for kale and lettuce only. Given the negative contribution of kale, production should be restricted to the minimum require-ments of 10 000 boxes, thus requiring the allocation of 100 hectares. Theremaining 180 hectares should be allocated to lettuce. The 680 hectares whichare suitable for all four vegetables should be allocated as follows: Minimum requirements to beans 56 hectares Balance to squash 624 hectares (680 56) The maximum demand for squash is 227 500 boxes. This output requires 650 hectares (227 500 /350). Therefore the maximum requirement will not be exceeded.

(ii) Largest total profit (pesos) Squash 624 hectares at a contribution of 931 pesos per hectare 580 944.0 Beans 56 hectares at a contribution of 504.6 pesos per hectare 28 257.6 Lettuce 180 hectares at a contribution of 134.6 pesos per hectare 24 228.0 Kale 100 hectares at a contribution of (85.0) pesos per hectare (8 500.0) ––––––– 624 929.6 Fixed costs 444 000.0 –––––––– Profit 180 929.6 –––––––– Solution IM 9.8 (iii)The drainage work will make land which is at present only suitable for kale and lettuce suitable for all four vegetables. Therefore 280 hectares could beconverted to being suitable for all four vegetables. However, in order to meetminimum production requirements, it is necessary to allocate 100 hectaresfor kale and 143 hectares for lettuce. This leaves a balance of 37 hectareswhich should be considered for drainage in order to grow squash and beans.

Proposed production of squash in (i) requires 624 hectares yielding 218 400 boxes (624 350 boxes). An additional 9100 boxes (227 500 – 218 400) could be grown using 26 hectares (9100 /350). The balance of 11 hectares would be allocated to produce 1980 boxes of beans (this is stillwithin the maximum production requirement for beans). Alternatively, the37 hectares could be used to produce 6660 boxes of beans, and this will stillbe within the maximum output. The calculation of the change from normalharvesting costs per hectare for these alternatives are as follows: Squash: (pesos) First 10 hectares: 350 boxes 1.2 pesos +420 Second 10 hectares: 350 boxes 1.3 pesos +455 Third 10 hectares: 350 boxes 1.4 pesos +490 Fourth 7 hectares: 350 boxes 1.5 pesos +525 Beans: (pesos) 180 boxes 1.2 pesos 216 180 boxes 1.3 pesos 234 180 boxes 1.4 pesos 252 180 boxes 1.5 pesos 270 The revised contributions per hectare are:Squash (pesos) First 10 hectares: 931 existing less 420 =511 Second 10 hectares: 931 existing less 455 =476 Third 10 hectares: 931 existing less 490 =441 Fourth 7 hectares: 931 existing less 525 =406 Beans: (pesos) 504.6 existing plus 216 =720.6504.6 existing plus 234 =738.6504.6 existing plus 252 =756.6504.6 existing plus 270 =774.6 It is therefore more profitable to use all 37 hectares to substitute beans for lettuce. This substitution process will result in the following additionalcontributions (in pesos): Incremental contribution Incremental Beans Lettuce per hectare contribution First 10 hectares 720.6 134.6 586.0 5860 Second 10 hectares 738.6 134.6 604.0 6040 Third 10 hectares 756.6 134.6 622.0 6220 Fourth 7 hectares 774.6 134.6 640.0 4480 MEASURING RELEVANT COSTS AND REVENUES FOR DECISION-MAKING 77 78MEASURING RELEVANT COSTS AND REVENUES FOR DECISION-MAKING Solution IM 9.9 The NPV calculation (in pesos) using a 15% discount rate for a four year period are as follows:

Cash Present Cumulativeflow value Investment NPV NPV First 10 hectares 5860 16 730 19 000 (2270) (2270) Second 10 hectares 6040 17 244 17 500 (256) (2536) Third 10 hectares 6220 17 758 15 000 2758 232 Fourth 7 hectares 4480 12 790 12 950 (160) 72 NPV is maximized if 30 hectares of land are drained to grow beans instead of lettuce.

(b) Financial dangers associated with going ahead with the drainage work include: (i) Drainage work may take longer than expected, thus delaying the timing ofthe cash inflows.

(ii) Drainage work may cost more than expected.

(iii) Capital costs or the discount rate might be underestimated. Note that thereturn is only slightly in excess of the 15% cost of capital.

(iv) Demand and selling prices of the products might change or the changes incosts might be different from the predictions.

(a) The relevant costs of the contract are as follows: (£) (£) Salary of G. Harrison 2 000 Supervision cost a 10 000 Cost of craftsmen a 16 000 Cost of equipment b 3 000 Material costs: c A (100 £3) + (900 £3) 3000 B (1000 £0.90) 900 C (100 £6) 600 D (100 £2) + (100 £3) 500 E (5000 £0.20) 1000 F (1000 £1) + (2000 £2) 5000 11 000 –––– Other direct expenses 6 500 Owner’s opportunity cost d 3 000 –––––– 51 500 Less savings on maintenance work e (1 500) –––––– Minimum contract price 50 000 –––––– Notes a The costs given in the question include apportioned fixed overheads which are not a relevant cost. Therefore £1000 has been deducted from the supervision cost (10% £10 000) and £800 from each of the craftsmen’s costs.

b The historical cost of the equipment is a sunk cost. It is assumed that the existing equipment would have been sold if the contract were not accepted. Therefore therelevant cost of using the equipment is the reduction in the scrap value over theduration of the contract.

c Material A : It is assumed that the usage of the 100 units in stock will be replaced in the coming year and be used on property maintenance. This is more profitable thanthe alternative of selling the materials for £2 and replacing them at a later date at£3. The remaining quantities will be replaced at the current purchase price.Material B : It is assumed that the 1000 units issued from stock for the contract will be replaced at £0.90 per unit. This material is used regularly in the business. Material C : This material is purchased specially for the contract. MEASURING RELEVANT COSTS AND REVENUES FOR DECISION-MAKING79 Solution IM 9.10 Materials D and F: The stocks of these materials have no alternative use within the business and will be sold if not used on the contract. Hence the sale price represents the opportunity cost of using these materials. The remainder of the materials will bepurchased at current prices.Material E : It is assumed that the material taken from stock for this contract will be replaced at the current purchase price. This material is used regularly in the business. d It is assumed that the alternative is for Johnson to pay out £12 000 to maintain the existing business while he earns £15 000 on the one year appointment. If the contract is undertaken then Johnson will lose £3000. e It is assumed that the contract could be completed and maintenance programme carried out during the period in which the supervisor and craftsmen are employed(one year). It is also assumed that the supervision and craftsmen will be employedfor one year only. A further assumption is that the lowest quotation will be accepted. Other assumptions : The lease of the yard would have to be paid even if the contract were not accepted.

(b) (i) What is the likelihood that Johnson will obtain other contract work during the year? If there is a possibility then any lost contribution should be covered in the minimum contract price.

(ii) Given that the profit was £12 000 last year, Johnson should consider closing operations and obtaining a permanent salary of £15 000 per annum.

(iii) Do any alternative uses for the accommodation of the yard exist? If so then appropriate opportunity cost should be added.

(iv) The contract price represents a minimum price. Johnson should aim to earn a surplus on the contract.

(v) Will the loss of one-quarter of Johnson’s time to the existing business result in a reduction in profit? If this is the case then the lost profits should beincluded as an opportunity cost.

Discontinue Discontinueat 30 June at 30 November (£) (£) Relevant inflows Sale of printing material 10 000Sale of pallets a 380 Sub-letting income 12 500Sale of machines b 27 000 25 000 Sale of vehicles b 48 000 44 000 –––––– –––––– 97 880 69 000 –––––– –––––– Relevant outflowsSalaries and wages: c Printing 15 000 90 000 Distribution — 20 000 Publishing vacancy 7 000 6 500 Materials and supplies: Printing [(5 £31 000) – £18 000] 137 000 Distribution a 500 5 500 Cancellation charge a 100 Occupancy costs: d Apportioned 29 112 34 250 Directly attributable — 14 250 Printing and distribution fee (£65 000 5) 325 000 – ––––––– ––––––– 376 712 307 500 ––––––– ––––––– Net cash outflow 278 832 238 500 On the basis of the above information, printing and publishing should be discontinued on 30 November. Notes a If pallets are taken for July and August and resold to Longplant Ltd, the cash outflow will be £240 (£1000 760). If the pallets are taken for July only, the cash outflow will be £220 (£500 + £100 £380). Therefore the lowest cash outflow option should be chosen and the August delivery should be cancelled.

b Only incremental sale proceeds should be included in the analysis. Depreciation and the written-down value of assets represent sunk costs and are not relevant for decision- making purposes.

c Two specialist staff (£3000 5 months) will continue to be paid if the department is closed in June. If the department is closed in November, it is assumed the publishingvacancy will be filled for five months at a cost of £6500. With a June closure, thepublishing vacancy will cost the company £7000 (£1400 5). Redundancy payments are not relevant, since the same amount will be paid to all staff irrespective of the date ofclosure.

d The occupancy costs for five months are:

Printing Distribution Total(£) (£) (£) Total 42 500 6000 48 500 Directly attributable 12 750 (30%) 1500 (25%) 14 250 Apportioned (balance) 29 750 4500 34 250 It is assumed that company cash flows, in respect of the costs which are apportioned to activities, will be reduced by £5138 (15% £34 250) if the department is closed in June. In other words, it is assumed cash flows will be reduced and not merely theproportion of costs which are allocated to the department. 80 MEASURING RELEVANT COSTS AND REVENUES FOR DECISION-MAKING Lecturers please note that this question and answer appeared in the Students Manual accompanying the seventh edition of the book so it is possible that students may be able to access the answer to the question. (a) Total hours = 36 750 (120 000 0.25) + (45 000 0.15) Fixed overhead rate per hour = £40 (£1470 000/36 750 hours) Product A (£) Product B (£) Direct materials 2 40 Variable production overhead 28 4 Fixed production overhead 10 (0.25 £40) 6 (0.15 40) Total cost 40 50 Selling price 60 70 Pro t 20 20 Assuming that the company focuses on pro ts per unit it will be indifferent between the 2 products. Total net pro t = £3 300 000 (120 000 £20) + (45 000 £20) Solution IM 9.11 (b)Product A Product B Contribution per unit £30 (60-30) £26 (70-44) Bottleneck hours 0.02 0.015 Contribution per bottleneck hour £1 500 £1 733 Based on the contribution per bottleneck hour the maximum demand of product B should be produced. The maximum demand of product B requires 810 hours (54 000 0.015) leaving 2 265 hours (3 075 – 810) to be allocated to product A.

This will result in the production of 113 250 units (2 265 hours/0.02) of A. The maximum pro t is calculated as follows:

£ Contribution from product A (113 250 £30) 3 397 500 Contribution from product B (54 000 £26) 1 404 000 4 801 500 Less Fixed overhead cost 1 470 000 Net pro t 3 331 500 (c) (i) Return per bottleneck hour = (Selling price – material cost)/(Time on bottleneck resource) Product A = £2 900 [(£60-£2)/0.02 hours] Product B = £2 000 [(£70 - £40)/0.015 hours] Product A should be sold up to its maximum capacity of utilizing 2 880 bottleneck hours (144 000 units 0.02 hours). This will leave 195 hours for product B thus enabling 13 000 units (195/0.015) to be produced. The maximum pro t is calculated as follows: £ Throughput return from product A (144 000 x £58) 8 352 000 Contribution from product B (13 000 £30) 390 000 8 742 000 Less: variable overheads a 3 540 000 xed overhead cost 1 470 000 Net pro t 3 732 000 a It is assumed that the variable overheads (e.g. direct labour) are xed in the short-term. They are derived from part (a) – [(120 000 £28) + (45 000 £4)] (c) (ii) Total overhead cost (£3 540 000 + £1 470 000) = £5 010 000 Overhead cost per bottleneck hour = £1 629.27 (£5 010 000/3 075 hours) Throughput return per bottleneck hour = £2 000 (see c(i)) Throughput accounting ratio = 1.2275 (£2 000/£1 629.27) MEASURING RELEVANT COSTS AND REVENUES FOR DECISION-MAKING 81 Note (c) (iii) With throughput accounting a product should be sold if the throughput return per bottleneck hour is greater than the production cost (excluding direct materials) per throughput hour. In other words, the throughput accounting ratio should exceed 1.00. Increasing a product’s throughput ratio can increase pro ts. The throughput ratio can be increased by: 1. Increasing the selling price or reducing material costs (note that product B has a very high material cost).

2. Reducing the time required on the bottleneck resource.3. Creating more capacity of the bottleneck resource and if possible increase the capacity so that the bottleneck can be removed (subject to any additional nancial outlays being justi ed).

Note that product B should be sold because its throughput ratio exceeds 1 but product A has the higher ranking because it has a higher throughput ratio. (c) (iv)If material costs increase by 20% for product B the revised return per bottleneck hour will be £1 467 [(£70 - £48)/0.015] giving a throughput ratio of 0.9 (£1 467/£1 629.27). Although this is less than 1 production of B can be justi ed in the short-term, given the special circumstances that apply. Product A is being produced up to its maximum demand and the balance of capacity applied to product B has no incremental cost and is thus xed in the short-term. Therefore product B will contribute a cash ow of £22 (£70 - £48) per unit. 82 MEASURING RELEVANT COSTS AND REVENUES FOR DECISION-MAKING PRICING DECISIONS AND PROFITABILITY ANALYSIS83 Solution IM 10.1 (a) The ROCE approach would be likely to yield an inadequate return because:

(i) Prime cost does not include any overheads. Consequently the profit marginmay be insufficient to recover overheads and provide sufficient profits to yield an adequate ROCE.

(ii) The company is working at full capacity, which might suggest underpricing.

Consequently limiting factors will apply, and the resources should be costedat their opportunity cost. This approach is not adopted with the current pricing method.

(iii) Incremental or marginal cost represents the minimum short-run price. Prime cost does not include variable overheads, and therefore provides anunderestimate of the minimum short-run price. If the industry is verycompetitive, there is a danger that the company might tender on the basis ofan incorrect short-run price.

(iv) The profit margin bears no relation to an attempt to earn an adequateROCE. Tenders involving the use of a large amount of capital equipment donot include a charge for its use – in terms of either depreciation or a targetROCE. It is unlikely that the percentage added to prime cost will besufficient to cover the depreciation of the equipment or a fair return from theuse of the equipment.

(b) The stages are as follows: (i) Decide on a target ROCE employed from fixed and current assets and howthe ROCE is to be measured (on book value or replacement cost?).

(ii) Estimate how many working days per year the equipment will be inproductive use.

(iii) For a particular contract estimate the number of days the equipment will be used on the contract.

(iv) The charge to the contract will be:

estimated number of days on contract per (iii) value of equipment required ROCE estimated days in year when in use per (ii) (v) Estimate the average amount of incremental working capital resulting from the contract and the number of days for which it is required, and calculate the required monetary ROCE following the procedure outlined in(iv).

(vi) The tender price will be calculated by adding the required ROCE in (iv) and (v) expressed in monetary terms to the total costs of the contract (total costwould consist of prime cost plus manufacturing overhead plus non-manufacturing overheads).

(vii) It is assumed in (vi) that all assets can be allocated to contracts. The required ROCE on any assets which cannot be directly allocated to contracts (e.g.fixed assets related to administration) should be apportioned to contracts onsome acceptable basis.

(c) The problems likely to be encountered in meeting a pre-set profit target on a ROCE basis are: Pricing decisions and profitability analysis Solutions to Chapter 1 questions 0 PRICING DECISIONS AND PROFITABILITY ANALYSIS (i) The approach ignores demand and the competitive position of the company.If ROCE pricing is strictly applied when competition is keen and there is surplus capacity in the industry then it is unlikely that tenders will becompetitive. Consequently sales will decline and insufficient contributionwill be earned to obtain an adequate ROCE.

(ii) Strict application of the pricing method will result in fixed costs and the overall required monetary ROCE being spread over a smaller number ofcontracts when demand is declining. Consequently costs and selling priceswill be higher per contract when demand is falling. There is a danger that thecompany will not be competitive, and sales will decline dramatically whereasfixed costs will remain unchanged. Adopting ROCE pricing might thereforelead to reduced profits and ROCE.

(iii) The approach involves circular reasoning because estimates of demand arerequired to estimate the cost, which in turn is used to estimate the tenderprice, which in turn determines demand.

(iv) There may be difficulty in estimating which assets will be allocated tocontracts and the number of days they will be assigned. If the actual period ofthe contract is longer than anticipated or if the contract requires moreequipment than originally estimated then the return on capital employedincluded in the tender price will be significantly under estimated.

(a) See ‘Customer profitability analysis’ in Chapter 10 for the answer to this question.

(b) The answer should include a discussion of the benefits derived from customer profitability analysis (CPA) that are described in Chapter 10. The question asksfor a critical appraisal. Possible criticisms include: (i) Some organizations have thousands of different customers and it is very expensive, or not feasible, to analyse profits by individual customers. Theseorganizations concentrate on customer segment profitability analysis.However, for some companies it is difficult to identify appropriate customersegments which provide suitable feedback information for decision-making.

(ii) The difficulty in accurately measuring the cost of joint resources consumed by individual customers or customer segments.

(iii) CPA is unlikely to provide useful information in those organizations whosecustomers do not make repeated purchases.

(iv) The focus is on past profitability and there is a danger that organizations may focus excessively on existing customers rather than creating new customersand developing new markets and products.

(a) The company could adopt one of the following three approaches for pricing the new car:(i) A high-price market skimming policy.

(ii) A medium-price policy.

(iii) A low-price market penetration policy.

The new car is expected to have a reputation for high quality, and it appears that the company has a differential advantage over its competitors in terms of quality perceived by its customers. By setting a high price initially, the company can takefull advantage of the high demand which is expected. It appears that initialdemand will be in excess of supply, and the company should adopt a marketskimming policy in order to equate demand with supply. If it does not, some ofthe potential excess profits may be creamed off by second-hand car dealers. Ahigh price will be consistent with the car’s ‘quality image’ whereas a lower pricemay create the impression of lower quality. If the launch is supported with a highlevel of marketing and advertising, a demand will be created which should, atleast, be equivalent to its current production capacity. After setting the initial highprice, the price can be progressively reduced to stimulate further demand once theinitial inelastic demand has been met. One disadvantage of this policy is that itmight encourage competitors to enter this market segment. Solution IM 10.2 Solution IM 10.3 84 PRICING DECISIONS AND PROFITABILITY ANALYSIS A medium price would ensure that the company’s existing market share for this type of car is maintained or improved. However, this policy might lead to demand initially being in excess of production, and it might be preferable to curtail demandat the launch stage by setting a high price initially and then adopting a medium priceat a later stage in the product’s life cycle. A medium price at this stage may also benecessary as competitors come along with new models. The market for luxury cars is likely to be inelastic, and there is little point creating unfulfilled sales demand at a low selling price. At the decline stage of theproduct’s life cycle a low price may be necessary in order to stimulate demand.

(b) In the early stages of the product life cycle a high-price market skimming pricing strategy is likely to be appropriate. Customers will be prepared to pay a premiumprice for a quality product which is perceived to be superior to the competitors’products. The price should be high enough to limit initial demand to theestimated production output. At a later stage in the product’s life cycle, whencompetitors introduce new models which compete in this market segment, priceshould be lowered in order to expand the market and maintain market share.

(c) Demand for this type of car is likely to be elastic, and a low market penetration pricing policy is therefore appropriate. A pricing policy should be adopted whichmaximizes sales volumes at the early stage of the product life cycle, thus ensuringthat the high volume of fixed development costs are recovered as quickly aspossible.

(a) Cost per packet for Cohin tender (£) Raw materials 0.30 Operating wages 0.12 Manufacturing overheads 0.24 Administration overheads 0.12 Packaging and transport 0.10 –––– Full cost 0.88 –––– –––– Normal selling price for 50 000 = £0.88 1.15 = £1.012 (say £1.01) Selling price for 60 000 = £0.88 1.145= £1.0076 (say £1.01) Selling price for 70 000 = £0.88 1.14 = £1.0032 (say £1.00) (b) Cohin tender 50 000 units 60 000 units 70 000 units(£) (£) (£) Revenue 50 500 60 600 70 000 Variable costs at £0.52 per unit (26 000) (31 200) (36 400) Incremental fixed costs (10 900) (11 900) (11 900) –––––– –––––– –––––– Contribution to general fixed overheads 13 600 17 500 21 700 Stamford tender (£) Contribution [60 000 (£1.20 0.67)] 31 800 Less incremental fixed costs 11 900 –––––– Contribution to general fixed overheads 19 900 –––––– –––––– Recommendation The Cohin tender is preferable only if sales reach 70 000 units. The decisiondepends on management’s attitude towards risk. The Stamford contract will yielda contribution of £19 900 with certainty, whereas the contribution from theCohin contract will range from £13 600 to £21 700. Without estimates of Solution IM 10.4 85 PRICING DECISIONS AND PROFITABILITY ANALYSIS probabilities of the likely demand for the Cohin contract, it is not possible to make a specific recommendation.

(c) See ‘Limitations of cost-plus pricing’ and ‘Reasons for cost-plus pricing’ in Chapter 10 for the answer to this question.

(d) It is recommended that relevant costs should be used for pricing decisions and these cost estimates should be combined with demand estimates in order to settarget selling prices. For a detailed discussion of the approach see ‘Pricing non-customized products’ in Chapter 10.

(e) Expected value of Cohin tender = 0.8 (0.3 £13 600 + 0.5 £17 500 + 0.2 £21 700) = £13 736 Expected value of Stamford tender = 0.7 £19 900 = £13 930 Based on the expected value decision rule, Stamford should get the greater saleseffort.

(f) Any price which just covers the incremental cost per unit should represent the minimum selling price. However, a selling price which just covers incrementalcost is unlikely to cover general fixed costs, and can only be recommended in theshort term. The incremental cost per unit for an output of 80 000 units is:(i) Cohin tender = £0.67 [£0.52 variable cost + (£11 900 /80 000 units)] (ii) Stamford tender = £0.82 [£0.67 variable cost + (£11 900 /80 000 units)] The recommended price is the maximum price at which demand for the productis 80 000 units per week. Clearly this is less than £1 for Cohin and £1.20 forStamford, because neither company is prepared to order 80 000 units at theseprices. To determine the recommended price, it is necessary for Josun to negotiatewith both companies to ascertain the maximum price at which demand will be 80 000 units.

(a) (i) Second-year demand of 3600 units Selling Net cash price /unit Cash inflows Cash outflows inflow to Year to Year to Year to Two-year Year to Year to Two-year 31 July 2016 31 July 2015 31 July 2015 31 July 2016 total 31 July 2015 31 July 2016 total Total (£) (£000) (£000) (£000) (£000) (£000) (£000) (£000)20 40 80 a 120 32 32 d 64 56 30 48 96 b 144 32 32 64 80 40 48 112 c 160 32 32 64 96 50 55 116 171 32 32 64 107 60 60 120 180 32 32 64 116 70 49 132 181 32 32 64 117 80 32 144 176 32 32 64 112 The initial launch price should be set at £70 per unit in order to maximize the net benefits of the company. Notes a 2000 units maximum production at £40 per unit. There are no stocks at the end of the first year. b 2400 units at £40 per unit (2000 units maximum production plus 400 units closing stock at the end of the first year).c 2800 units at £40 per unit (2000 units maximum production plus 800 units closing stock at the end of the first year).

d For all output levels maximum production of 2000 units is required in year 2 in order to meet demand. Solution IM 10.5 86 PRICING DECISIONS AND PROFITABILITY ANALYSIS (a) (ii)Second-year demand of 1000 units Selling price /unit Cash inflows Cash outflows Net cash Year to Year to Year to Two-year Year to Year to Two-year inflow to 31 July 2015 31 July 2015 31 July 2016 total 31 July 2015 31 July 2016 total 31 July 2016 Total (£) (£000) (£000) (£000) (£000) (£000) (£000) (£000) 20 40 a40a 80 32 b16b 48 32 30 48 40 88 32 b9.6 b 41.6 46.4 40 48 40 88 32 b3.2 d 35.2 52.8 50 55 40 95 32 1.6 33.6 61.4 60 60 40 100 32 nil e 32 68 70 49 40 89 32 nil e 32 57 80 32 40 72 32 nil e 32 40 The initial launch price should be set at £60 per unit in order to maximize the net benefits to the company. Notes a In the second year there is sufficient production capacity (irrespective of demand in the first year) to meet sales demand. Therefore second-year sales will be 1000 units.

b 1000 units at £16.

c 600 units at £16 (1000 units less opening stock of 400 units).

d 200 units at £16 (1000 units less opening stock of 800 units).

e Opening stocks are sufficient to meet demand in the second year.

(b) In (a) (i) no spare capacity exists, and all production in the year to 31 July 2016 will be sold. In (a) (ii) zero production is required in the second year for initiallaunch prices of £60, £70 or £80. Stocks at the end of the second year are asfollows:

Launch price (£) 60 70 80 Units produced (first year) 2000 2000 2000 Units sold (first year) 1000 700 400 –––– –––– –––– Closing stock 1000 1300 1600 Units sold (second year) 1000 1000 1000 –––– –––– –––– Closing stock (second year) Nil 300 600 –––– –––– –––– The answer requires the calculation of the selling price of the unsold stock whichwill result in the overall net benefit to the company being greater than themaximum profit in (a) (ii) of £68 000. Let x= minimum selling price of unsold stock. Then, at a launch price of £70, 300x= £68 000 £57 000 x = £36.67 At a launch price of £80, 600x= £68 000 £40 000 x = £46.67 In other words, at a launch price of £70, unsold stock would have to be sold at a price in excess of £36.67 before this launch price will maximize company profits.At the £80 launch price, the unsold stock would have to be sold at a price inexcess of £46.67 before this launch price will maximize total company profits.

(c) At a launch price of £60, £70 or £80, zero production will be required in the second year. Production in the second year is maximized at a launch price of £20.

87 If the company can apply the spare capacity in the second year to alternative uses then the contribution from year 2 unused capacity should be incorporated into theanalysis. Also any expected increases in costs in year 2 might lead management toconsider selecting a launch price which minimizes production in the second year.

(a) (i) Calculation of cost per unit Labour hours Machine hours recovery method recovery method XY XY (£) (£) (£) (£) Direct labour 5 28 5 28 Direct materials 6 16 6 16Directly attributable overhead a 32 8 32 8 General factory overhead b 6(1 £6) 48 (8 £6) 16 (4 £4) 8 (2 £4) –– ––– –– –– Cost per unit 20 120 30 80 –– ––– –– –– Selling price at cost plus 20% 24 144 36 96 Notes a Fixed overheads directly attributable to the product divided by maximum production (X = 40 000 units, Y = 10 000 units).

b The calculations of the general fixed overhead rates are as follows:

Labour hours Machine hours(000) (000) X 40 (40 000 1) 160 (40 000 4) Y 80 (10 000 8) 20 (10 000 2) ––– ––– Total hours 120 180 ––– ––– General fixed overhead (£000) 720 720 Hourly overhead rate (£) 6 4 The hourly overheads are based on maximum production.

(ii) and (iii) Calculation of disclosed profits and stock values Labour hours Machine hours recovery method recovery method XYXY 1. Cost per unit (£) 20 120 30 80 b 2. Selling price per unit (£) 24 144 36 96 b 3. Sales quantity (000) a 36 7 18 10 b 4. Production (000) 40 10 40 10 b 5. Closing stock (4) (3) 4 3 22 0 b –– –– –– –– b –– –– –– –– b (£000) (£000) (£000) (£000) Sales revenues, (2) (3) 864 1008 648 960 b ––– –––– –––– ––– b Manufacturing costs, (1) (4) 800 1200 1200 800 b Less closing stock, (1) (5) 80 360 660 0 b ––– ––– ––– ––– b Cost of goods sold 720 840 540 800 b ––– ––– ––– ––– b Disclosed profit 144 168 108 160 b Total = 312 Total = 268 PRICING DECISIONS AND PROFITABILITY ANALYSIS Solution IM 10.6 88 PRICING DECISIONS AND PROFITABILITY ANALYSIS Notes a Sales demand based on estimated demand for different selling prices as given in the question. b Sales limited to maximum production of 10 000 units for product Y.

(b) The cost allocation methods result in different unit costs and selling prices. Price / demand relationships result in significant changes in sales quantities for different output levels. Units sold vary because of changes in accounting methods whencost-plus pricing is used. It is most unlikely that such an approach will produceoptimal selling prices. Selling prices should be determined on the basis of ananalysis of price /demand relationships and cost structure for different activity levels and selling prices. They should not be influenced by arbitrary costapportionments. See ‘Limitations of cost-plus pricing’ and ‘Relevant costs forpricing decisions’ in Chapter 10 for a more detailed discussion of a possibleanswer to this question.

(c) Where year 2 demand is below productive capacity (case 1) then French Ltd should concentrate on maximizing year 1 profits. Year 1 sales will not result inany lost sales in year 2 because demand can be met from year 2 production.Where year 2 demand is in excess of productive capacity then sales in year 1 will reduce the units available for sale in year 2. Any unsold stocks at the end ofyear 1 can be sold at the year 2 prices in year 2. In other words, the presence ofstocks in year 1 will enable greater sales revenue to be earned in year 2. Thequestion is whether it is more profitable to sell more in year 1 (thus reducingclosing stocks which can be sold in year 2) or to reduce the sales in year 1 and sellmore in year 2. With case 1, our analysis is for year 1 only; but with case 2, it is necessary to analyse the output of year 1 production over 2 years. Fixed costs are not includedin the analysis because they remain unchanged for all activity levels. The followinginformation enables the optimal selling price to be established:

Case 1 (product X) Case 2 (product Y) Contribution from Total contribution Contribution Sales Total closing stock from year 1 per unit a quantity contribution sold in year 2 b production c (£) (000) (£000) (£000) (£000) 13 (24 11) 36 468 76 544 19 (30 11) 32 608 d 152 760 25 (36 11) 18 450 418 868 d 31 (42 11) 8 244 608 852 Notes a Maximum selling price per price /demand estimates given in the question less unit variable cost.

b Maximum production in year 1 is 40 000. Unsold production can be sold in year 2 at a selling price of £30 per unit. Contribution is calculated on the basis of a £30selling price less £11 per unit variable cost. c Case 1 total contribution + contribution from closing stock sold in year 2.

d For case 1 a selling price of £30 maximizes total contribution, whereas for case 2 a selling price of £36 maximizes total contribution. The calculations for product Yare as follows:

89 90PRICING DECISIONS AND PROFITABILITY ANALYSIS Case 1 (product Y) Case 2 Contribution from Total contribution Contribution Sales Total closing stock from year 1 per unit quantity contribution sold in year 2 a production b (£) (000) (£000) (£000) (£000) 52 (96 44) 10 520 0 520 64 (108 44) 10 640 0 640 76 (120 44) 9 684 86 770 88 (132 44) 8 704 c 172 876 c 100 (144 44) 7 700 c 258 958 c 112 (156 44) 5 560 c 430 990 c Notes a Maximum production of year 1 is 10 000 units. Unsold production can be sold in year 2 at a selling price of £130 per unit. Contribution is calculated on the basis of a selling price of £130 less £44 per unit variable cost.

b Case 1 total contribution + contribution from closing stock sold in year 2.

c For case 1 a selling price of £132 maximizes total contribution, whereas for case 2 a selling price of £156 maximizes total contribution.

(a) Existing capacity = 80 000 machine hours [(20 000 2) + (40 000 1)] Fixed cost per unit = £480 000 /80 000 machine hours = £6 per machine hour Alpha Beta(£) (£) Total cost per unit 20 40 Fixed cost per unit 12 (2 £6) 6 (1 £6) –– –– Variable cost per unit 8 34 Selling price per unit 25 50 Contribution per unit 17 16 Contribution per machine hour 8.50 (£17 /2) 16 The question states that machine hours are fully utilized at the existing production level. Therefore demand is in excess of current capacity. Profits will be maximizedby concentrating on Beta, since this yields the larger contribution per machine hour.In order to meet the maximum demand for Beta, 50 000 machine hours will berequired. The remaining capacity of 30 000 hours (80 000 – 50 000) should beallocated to producing 15 000 units of Alpha. The total profit for this output level isas follows: (£) Alpha (15 000 units £17 contribution per unit) 255 000 Beta (50 000 units £16 contribution per unit) 800 000 –––––––– 1 055 000 Less fixed costs 480 000 –––––––– Profit 575 000 The above profit exceeds the profit arising from the proposed plan given in thequestion.

(b) The answer to this question should include a discussion of the limitations of cost- plus pricing and an explanation of why it is widely used in practice. For a discussion of these issues see ‘Limitations of cost-plus pricing’ and ‘Reasons forusing cost-based pricing formulae’ in Chapter 10.

(c) An increase in the selling price of Alpha by £10 reduces demand by 30 000 units. Assuming a linear relationship between price and demand, this price /demand Solution IM 10.7 PRICING DECISIONS AND PROFITABILITY ANALYSIS91 Solution IM 10.8 relationship indicates that to increase/decrease demand by 1 unit, the selling price must be decreased /increased by £0.000 333 (£10 /30 000 units). Estimated demand is 15 000 units at a selling price of £30. At a selling price of £35 (£30 + (15 000 £0.000 333)), demand will be zero. To increase demand by one unit, selling price must be reduced by £0.000 333. Thus the maximum selling price (SP)for an output of xunits is:

SP = £35 £0.000 333 x Total revenue (TR) = x(£35 £0.000 333 x) = £35 x £0.000 333 x2 Marginal revenue (MR) = d(TR) = £35 – £0.000 666 x d x Marginal cost = £8 Optimal output is where MR = MC:

35 £0.000 666 x=8 x = 40 540 units SP = £35 £0.000 333 40 540 = £21.50 An increase in the selling price of Beta by £10 reduces demand by 40 000 units. This implies that an increase /decrease in demand by 1 unit requires a decease /increase in price of £0.000 25 [£55 + (30 000 £0.000 25)]. To increase demand by one unit, selling price must be reduced by £0.000 25. Thus the maximum selling price(SP) for an output of xunits is:

SP = £62.50 £0.000 25 x TR = x(£62.50 £0.000 25 x) MR = £62.50 x £0.000 25 x2 d(TR) = £62.50 £0.0005 x d x MC = £34 Optimal output is where: 62.50 0.0005 x=34 x = 57 000 units SP = £62.50 £0.000 25 57 000 = £48.25 It is assumed that capacity is sufficient to meet demand at the above selling prices.

(d) The approach used in (c) was based on a knowledge of price /demand relationships and total cost functions and adopted the theoretical economist’s pricing model approach to pricing described in Learning Note 10.1 on the open access website.It is assumed that accurate cost and revenue functions can be obtained at zeroincremental cost and that optimal selling prices can be determined.

(a) (i) In order to answer this question, it is necessary to express output in terms of the number of unrefined tonnes processed prior to separation. If the numberof tonnes processed is Qthen the quantity of crude Alpha ( Q a) and crude Beta ( Q b) processed can be expressed as:

Qa = 0.4Q and Q b= 0.6Q 92PRICING DECISIONS AND PROFITABILITY ANALYSIS Total revenue from: Alpha (TR a) = 1250 Q a 100 Q a2 32 = 1250 (0.4 Q) 100 (0.4 Q)2 32 = 500 Q 0.5 Q 2 Beta (TR b) = 666.67 Q b– 100 Q b2 18 = 666.67 (0.6 Q) 100 (0.6 Q)2 18 = 400 Q 2Q 2 The marginal revenue from each product is: MRa= 500 Q MR b= 400 4Q The marginal revenue from total production is: MRa+ MR b= 900 5Q The marginal cost of processing one tonne is: £170 + £100 + 0.4 (£125) + 0.6 (£50) = £350 Optimal output is where MR = MC: 900 5Q = 350 Q = 110 110 tonnes of the raw materials should be processed, with 44 tonnes refined into Alpha and 66 into Beta. Alpha price ( P a) = 1250 – 100 44 = £1112.50 per tonne 32 Beta price ( P b) = 666.67 100 66 = £300 per tonne 18 (ii) When Q= 110, MRa= 500 110 = 390 MR b= 400 4 110 = 40 Therefore Alpha is the major product and Beta the minor.

(b) (i) Since Beta is not worth producing at an output level of 110 units, profit is maximized where the marginal cost of producing refined Alpha is equal to its marginal revenue:

170 + 100 + (0.4 125) = 500 Q Q = 180 180 tonnes should be processed and 72 tonnes (0.4 180) of Alpha refined.

Alternatively the answer could have been obtained by equating the separationprocess marginal cost with Alpha’s net marginal revenue (NMR):

125 = 1250 6.25 Q Q = 180 PRICING DECISIONS AND PROFITABILITY ANALYSIS93 Note that NMR is derived from the price equation given in the question.

(ii) Refining of Beta should be continued until its marginal revenue is equal to its marginal cost of refining:

400 4Q = 0.6 50 Q = 92.5 Q b = 0.6 92.5 Q b = 55.5 Alternatively the answer could have been obtained by equating the marginal cost with Beta’s net marginal revenue: 50 = 666.67 – 11.11Q Q = 55.5 Beta’s NMR is derived from the price equation given in the question.

(c) The answer should consider the following methods: (i) Physical measurement methods.

(ii) Sales value at split-off point.

(iii) Net-realizable value. (iv) Constant gross profit percentage.

You should refer to Chapter 6 for a discussion of these. The answer should stress that there is no ‘right way’ of allocating joint costs to products and that whichevermethod is selected will be based on arbitrary apportionments. The answer couldalso stress that joint costs should not be apportioned to by-products for stockvaluation purposes (see ‘Accounting for by-products’ in Chapter 6).

(a) (i) Sales only in the home market It is assumed that ‘unit variable cost’ represents average unit variable cost.Total variable cost = 19 Q Q2 Therefore marginal cost = 19 – 2 Q Total sales revenue = 68 Q 8Q 2 Therefore marginal revenue = 68 16 Q Profit is maximized when MR = MC:

68 16 Q = 19 2Q 14 Q =49 Q = 3.5 Optimum selling price = 68 8 3.5 = £40 Average variable cost = 19 3.5 = £15.50 Total contribution 3500 (£40 £15.50) = £85 750 (ii) Sales only in the export marketPrice in £ = (110 – 10 Q)/2 Total sales revenue = 55 Q 5Q 2 Marginal revenue = 55 10 Q Profit is maximized when MR = MC:

55 10 Q = 19 2Q 8 Q =36 Q = 4.5 Optimum selling price = 55 5 4.5 = £32.50 = $65 Average variable cost = 19 4.5 = £14.50 Total contribution = 4500 (£32.50 – £14.50) = £81 000 (iii) Sales in both marketsThe revised optimum position is established by equating the marginal costfunction with the sum of the marginal revenue functions in the two separatemarkets: Solution IM 10.9 PRICING DECISIONS AND PROFITABILITY ANALYSIS Home: MR = 68 16 Q 1 (1) Export: MR = 55 10 Q 2 (2) Divide equation (1) by 16 and equation (2) by 10: 0.0625 MR = 4.25 Q 1 (3) 0.1 MR = 5.5 Q 2 (4) Adding these:

0.1625 MR = 9.75 Q 1 Q 2 Let Qrepresent the total of Q 1and Q 2: MR = 9.75 Q (5) 0.1625 The profit-maximizing output is where MR = MC: 9.75 Q = 19 2Q 0.1625 9.75 Q = 0.1625 (19 2Q ) 9.75 Q = 3.0875 0.325 Q 0.675 Q= 6.6625 Q = 9.870 Substituting for Qin the combined marginal revenue function [equation (5)]:

MR = 9.75 9.87 = 0.738 0.1625 The allocation of the total quantity ( Q) between the two markets will be deter- mined by the need to keep MR equal to 0.738.

In the home market Q1= 4.25 0.0625 ( 0.738) [equation (3)] Q 1= 4.296 and P= 68 8 4.296 P = £33.63 In the export market Q2= 5.5 0.1 ( 0.738) [equation (4)] Q 2= 5.574 and P= 55 5 5.574 = £27.13 = $54.26 Average variable cost = 19 9.87 = £9.13 Total contribution = [4296 (£33.63 £9.13)]+[5574 (£27.13 £9.13)] = £205 584 (b) For every two units produced, one must be sold in the home market and one in the export market. The marginal revenue from the sale of these two units will be:

MR = (68 16 Q) + (55 10 Q) = 123 26 Q Note that the above expression refers to the sale of two units (one in each market).

94 PRICING DECISIONS AND PROFITABILITY ANALYSIS If Q is expressed in pairs of output (represented by qfor the sale of 1 unit in each market) then 2q = Qor q= 1 2 Q Total variable cost = 19 Q Q2 = 38 q 4q2 Marginal cost per pair = 38 8q Profit is maximized where MR = MC:

123 26 q= 38 8q q = 4.722 Total production should be 9444 units (4722 units in each market). In the home market P= 68 8 4.722 = £30.22 In the export market P= 55 5 4.722 = £31.39 = $62.78 Average variable cost = 19 9.444 = £9.556 Total contribution = (4722 £30.22) + (4722 £31.39) (9444 £9.556) = £200 676 Sensitivity analysis Exchange rate $1 = £0.25 $1 = £1 Price (£) (110 10 Q)/4 110 10 Q = 27.5 2.5 Q Total revenue (£) 27.5 Q 2.5 Q2 110Q 10 Q2 Marginal revenue (£) 27.5 5Q 110 20 Q MR for one unit sold in (68 16 Q) + (27.5 5Q ) (68 16 Q) + (110 20 Q) each market £ = 95.5 21 Q = 178 36 Q MR = MC where 95.5 21 Q= 38 8Q 178 36 Q = 38 8Q Q = 4.423 Q= 5 Home market P(£) 68 8 4.423 = 32.62 68 8 5 = 28 Export market P(£) 27.5 2.5 4.423 110 10 5 = 60 = 16.44 P ($) 16.44 4 = 65.76 60 Average variable cost 19 8.846 = £10.154 19 10 = £9 Total contribution 4423 (£32.62 + £16.44) 5000 (£60 + £28) 8846 £10.154 10 000 £9 = £127 170 £350 000 Summary $1 = £0.25 Home market price: 7.9% increase 32.62 30.22 30.22 Export market price: 4.75% increase in dollar 65.76 62.78 terms 62.78 Contribution: 36.6% decrease 200 676 127 170 200 676 $1 = £1 Home market price: 7.3% decrease 30.22 28 30.22 Export market price: 4.4% increase in dollar 62.78 60 terms 62.78 95 PRICING DECISIONS AND PROFITABILITY ANALYSIS Contribution: 74.4% decrease 350 000 200 676 200 676 It can be seen that, while the changes in exchange rates have relatively little impact on either the quantities sold in the two markets or the prices charged within each market, the overall effect of such changes on the total sterlingcontribution is significant.

(c) The answer should draw attention to the need to take steps to reduce the risk of currency exposure when foreign exchange rates are volatile. In particular thefollowing points should be included:(i) Exporters should consider invoicing in foreign currency so that the currency can be converted at the spot rate applicable on the date of payment.

(ii) During the period between invoicing and the date of payment, firms cancover their position in the foreign exchange market by selling foreigncurrency forward at the appropriate foreign exchange rate.

(iii) There is a greater need to continuously review selling prices and monitorcompetitors’ prices charged in the exporting country.

(iv) The period between the invoice date and the payment date should be shorter than for home sales so that exposure to changes in exchange rates is minimized.

96 ACTIVITY-BASED COSTING Solution IM 11.1 Solution IM 11.2 Solution IM 11.3 The answer to this question should describe cost allocation, cost apportionment and absorption within a traditional product costing system. Both traditional and ABCsystems use the two-stage allocation procedure. In the first stage costs are assigned tocost centres and in the second stage costs are charged to products passing through thecost centres using appropriate overhead absorption rates.The terms ‘cost allocation’ and ‘cost apportionment’ are often used interchangeably to describe methods that are used in the first stage to arbitrarily share out costs to costcentres on some logical basis (e.g. rent may be apportioned on the basis of floor areaof each department and works management on the basis of number of employees ineach department). However, some textbooks distinguish between the two terms.Allocations are used to describe those overheads that can be specifically attributed to acost centre (e.g. depreciation of machinery or the wages of a supervisor located in aspecific cost centre). The term ‘apportionment’ is used where a cost cannot bespecifically attributed to a cost centre and the costs have to be apportioned on somelogical basis (e.g. rent apportioned to cost centres on the basis of floor area). The term ‘absorption’ is normally used to refer to the second stage of the two-stage overheads process by which cost centre overheads are charged to products (i.e.absorbed by products) passing through the cost centre. Direct labour hours ormachine hours are the most widely used absorption methods to assign the cost centreoverheads to products. The answer should then go on to describe activity-based-costing systems and also the limitations of traditional product costing systems (see Chapter 11 for a descriptionof ABC). For the answer to this question see ‘A comparison of traditional and ABC systems’ and ‘volume-based and non-volume based cost drivers’ in Chapter 11.

(a) See ‘The emergence of ABC systems’ and ‘Costs versus benefits considerations’ in Chapter 11 for the answer to this question.

(b) Organizations may decide not to use or to abandon ABC for the following reasons:

(i) the high cost of operating an ABC system (ii) the lack of sufficient employees with the necessary expertise (iii) the lack of a ‘champion’ and top management support to promote ABC (iv) the resources required to set up an ABC system may not be available (v) difficulty in replacing existing systems that have become embedded in the organization and the resistance to change by employees (vi) employee hostility if it is viewed purely as a cost reduction technique that will be accompanied by redundancies (vii) a low proportion of costs that can be more effectively controlled and assigned to cost objects using ABC techniques. Activity-based costing Solutions to Chapter 11 questions 97 (c) The usefulness of distinguishing between value-added and non-value-addedactivities is discussed in Chapter 21.

(a) Production cost per unit (conventional method) Product X Product Y Product Z(£) (£) (£) Direct labour at £14 per hour Direct materials 20 12 25Production overhead at £28 per machine hour 42 (1 12 hours) 28 (1 hour) 84 (3 hours) –– –– ––– 69 61 123 –– –– ––– (b) The total production overhead is derived from the overheads allocated to the product in part (a):

(£) Product X 31 500 (750 £42) Product Y 35 000 (1250 £28) Product Z 588 000 (7000 £84) ––––––– 654 500 ––––––– Overhead costs traced to cost pools: (£) Set-up cost 229 075 (35%) Machining 130 900 (20%) Materials handling 98 175 (15%) Inspection 196 350 (30%) ––––––– 654 500 ––––––– Cost driver rates: (£) Cost per set-up 341.903 (£229 075 /670) Cost per machine hour 5.60 (£130 900 /23 375 a ) Cost per material movement 818.125 (£98 175 /120) Cost per inspection 196.35 (£196 350 /1 000) Note a Machine hours = (750 1 1 2 ) + (1250 1) + (7000 3) = 23 375 Overhead cost assigned to each product: Product X Product Y Product Z(£) (£) (£) Set-up costs at £341.903 25 643 (75) 39 319 (115) 164 113 (480) Machining at £5.60 per machine hour 6 300 (1125) 7 000 (1250) 117 600 (21 000) Materials handling at £818.125 per movement 9 817 (12) 17 181 (21) 71 177 (87) Inspection at £196.35 per inspection 29 453 (150) 35 343 (180) 131 554 (670) ––––––– ––––––– ––––––– 71 213 98 843 484 444 ––––––– ––––––– ––––––– Number of units 750 1250 7000 Overhead cost per unit £95 £79 £69 ACTIVITY-BASED COSTING Solution IM 11.4 7 21 14 98 Production cost per unit (ABC principles)Product X Product Y Product Z(£) (£) (£) Direct labour 7 Materials 20 12 25 Production overhead 95 79 69 ––– ––– ––– 122 112 108 ––– ––– ––– Change (compared with traditional method) +77% +84% 12% (c) The traditional method allocates overheads in proportion to machine hours to products (4.8% to X, 5.3% to Y and 89.9% to Z). However, when overheads areassigned on the basis of number of set-ups, movements of materials andinspections the proportion of overheads assigned to product Z are 72% (480 /670) for set-up costs, 72% (87 /120) for materials handling costs and 67% (670 /1000) for inspection costs. In contrast, the traditional method allocates approximately90% of all costs to product Z. Therefore the unit cost for product is higher with the traditional method. The opposite situation applies with products X and Yand, as a result, unit costs are lower with the traditional method.

(i) Traditional volume-based systemThe first stage of the two-stage overhead allocation procedure requires that theservice department overheads are reallocated to the production departments(Machinery and Fittings). Typical allocation bases are:

Materials handling – Direct material cost Material procurement – Direct material cost Set-up – Direct labour hours Maintenance – Machine cost or maintenance hours Quality control – Direct labour hours It is assumed that the £10 500 service department costs will be apportioned as follows: (£000) Machinery 6500 Fittings 4000 (Note that students will require details of the above allocation since the details are not given in the question.) The computation of the departmental overhead rates is as follows: Machinery Fitting department department (£) (£) Original overhead allocation 2 500 000 2 000 000 Service department reallocations 6 500 000 4 000 000 –––––––– –––––––– Total production overhead cost (£) 9 000 000 6 000 000 Total direct labour hours 1 100 000 350 000 Overhead rate £8.182 per DLH £17.143 per DLH ACTIVITY-BASED COSTING Solution IM 11.5 21 14 99 Product costsProduct A Product B(£) (£) Machinery department: 500 000 DLH £8.182 4 091 000 600 000 DLH £8.182 4 909 200 Fitting department: 150 000 DLH £17.143 2 571 500 200 000 DLH £17.143 3 428 600 –––––––– –––––––– Total production overhead cost (£) 6 662 500 8 337 800 Production volume (£) 300 000 300 000 Unit product overhead cost (£) 22.21 27.79 (ii) Activity-based costing system Computation of cost driver rates:

Overhead Annual Annual cost driver volume Cost driver rate cost (£000) Material handling 1500 2540 material movements £590.55 per material movement Material procurement 2000 6500 orders £307.69 per order Set-up 1500 624 set-ups £2403.85 per set-up Maintenance 2500 30 000 maintenance hours £83.33 per maintenance per hour Quality control 3000 4120 inspections £728.16 per inspection Machinery 2500 1 100 000 direct labour hours £2.27 per DLH Fitting 2000 350 000 direct labour hours £5.71 per DLH Overheads assigned to part numbers Material Material Quality Total handling procurement Set-up Maintenance control Machinery Fitting (£000) Part 1: Cost driver consumption 180 200 12 7000 360 150 000 50 000 Cost driver rate (£) 590.55 307.69 2 403.85 83.33 728.16 2.27 5.71 Total cost (£000) 106.30 61.54 28.85 583.31 262.14 340.50 285.50 1 668 Part 2: Cost driver consumption 160 300 12 5000 360 350 000 100 000 Cost driver rate (£) 590.55 307.69 2 403.85 83.33 728.16 2.27 5.71 Total cost (£000) 94.49 92.31 28.85 416.65 262.14 794.50 571.00 2 260 Part 3: Cost driver consumption 1000 2000 300 10 000 2400 200 000 60 000 Cost driver rate (£) 590.55 307.69 2 403.85 83.33 728.16 2.27 5.71 Total cost (£000) 590.55 615.38 721.16 833.30 1 747.58 454.00 342.60 5 305 Part 4: Cost driver consumption 1200 4000 300 8000 1000 400 000 140 000 Cost driver rate (£) 590.55 307.69 2 403.85 83.33 728.16 2.27 5.71 Total cost (£000) 708.66 1 203.76 721.16 666.64 728.16 908.00 799.40 5 763 Product costs Product A Product B(£) (£) Part 1 1 668 000 Part 2 2 260 000Part 3 5 305 000 Part 4 5 763 000 –––––––– ––––––––– Production overhead cost (£) 3 928 000 11 068 000 Production volume 300 000 units 300 000 units Unit cost (£) 13.09 36.89 ACTIVITY-BASED COSTING 100 (a) (i)Budgeted analysis of net profit based on the sales value allocation base Operating profit 840 000 370 000 290 000 Central cost allocation in ratio 5000: 4000: 3000 416 667 333 333 250 000 ––––––– ––––––– ––––––– Net profit 423 333 36 667 40 000 ––––––– ––––––– ––––––– The report should draw attention to the following:

Traditional costing systems allocate costs on the basis of volume measures such as direct labour hours, machine hours and sales values or volumes.

Using sales values assumes that central costs are caused by sales values thusdepartments with the higher sales values are allocated with higher proportions ofcentral costs. The result is that the high sales value stores will be overcosted andlow sales values stores will be undercosted if central costs are caused by factorsunrelated to sales volumes or values.

Central costs should be traced to stores on the basis of cost drivers that are thecause of the costs being incurred. Cost drivers are the events or forces that aresignificant determinants of the warehousing activities and the activitiesundertaken at head office.

In many cases it is the complexity of dealing with different products, customers orstores locations that are the cause of overhead costs, rather than volume. Activity-based-costing systems attempt to capture complexity by using cost drivers such as thenumber of dispatches. For example, some warehousing costs will be caused by thenumber of dispatches. Thus, if a low sales volume store dispatches many smallorders and a high sales volume store dispatches a small number of high volumeorders, using the number of dispatches as the cost driver will capture the greatercomplexity and the warehouse resources consumed by the low sales volume store. Incontrast, using sales values as the cost driver will not capture the complexity andhigh sales value stores will be overcosted and low sales values stores will beundercosted.

(a) (ii) Budgeted analysis of net profit based on the revised allocation bases Warehouse operationsTotal A B C Head Office (£) (£) (£) (£) (£) Salary a 200 000 20 000 60 000 60 000 60 000 Advertising b 80 000 — 33 333 26 667 20 000 Establishment c 120 000 12 000 36 000 36 000 36 000 –––––– 32 000 Warehouse Depreciation d 100 000 — 40 000 30 000 30 000 Storage e 80 000 32 000 24 000 24 000 Operating and despatch f 152 000 55 000 45 000 52 000 Delivery g 300 000 100 000 71 429 128 571 ––––––– ––––––– ––––––– 356 333 293 096 350 571 ––––––– ––––––– ––––––– Operating profit 840 000 370 000 290 000 Net profit/(loss) 483 667 76 904 (60 571) Notes a Allocated on the basis of note 1 in the question b Allocated on the basis of note 2 in the question c Allocated on the basis of note 1 in the question d Allocated on the basis of storage space occupied e Allocated on the basis of storage space occupied ACTIVITY-BASED COSTING Solution IM 11.6 101 ACTIVITY-BASED COSTING f£120 000 given in the question plus £32 000 allocated to warehousing operations in the above analysis g Allocated on the basis of delivery distances The revised allocations show that the costs identified to store C exceed the current level of operating profit and an overall loss is disclosed. Stores B and C showimproved results based on the revised allocations. The allocation bases selected beara closer cause-and-effect relationship than the current method of cost allocation.However, for some costs (e.g., advertising and depreciation) it is difficult toestablish meaningful cause-and-effect relationships. Nevertheless, the revised basisprovides more meaningful profitability analysis attention directing information. Itshows that the viability of maintaining store C should be subject to a more detailedspecial study. Some of the costs, such as depreciation, may represent facility orbusiness-sustaining costs that are unavoidable and that would still continue if Cwere closed. Such factors should be taken into account when the special study isundertaken. If the special study still suggests that C is unprofitable steps should betaken to reduce costs by reducing the demand for activities, such as by reducing thenumber of low volume dispatches so that resource consumption is reduced withoutreducing sales revenues. In addition, direct deliveries from some suppliers and themore efficient routing of deliveries should be considered. The important point tonote is that the revised profitability analysis has highlighted issues for investigationwhich were not highlighted by the previous allocation method.

(b) Regression analysis and tests of reliability can be used to examine the relationship between some of the costs and the allocation bases (cost drivers) proposed. Details of the costs of activities and the potential cost drivers should be accumulated atfrequent intervals (e.g. monthly) and a regression equation established andreliability tests undertaken. For a more detailed explanation of these issues youshould refer to Chapter 23.

(a) (i) Preliminary workings Making Estimated minutes for the making activity (5000 × 5.25) + (3000 × 5.25) 42 000 Variable conversion costs absorption rate ( £350 000/42 000 minutes) per minute £8.333 Fixed conversion costs absorption rate (£210 000/42 000 minutes) per minute £5 Variable conversion costs charged to both products (5.25 minutes × £8.333) £43.75 Fixed conversion costs charged to both products (5.25 minutes × £5) £26.25 Product specific fixed conversion costs charged to both products (40% × £26.25) £10.50 Packing Estimated minutes for the packing activity (5000 × 6) + (3000 × 4) 42 000 Variable conversion costs absorption rate (£280 000/42 000 minutes) per minute £6.666 Fixed conversion costs absorption rate (£140 000/42 000 minutes) per minute 3.333 Variable conversion costs charged to product VG4U (6 minutes × £6.666) £40 Variable conversion costs charged to product VG2 (4 minutes × £6.666) £26.67 Solution IM 11.7 102 Fixed conversion costs charged to product VG4U (6 minutes × £3.333) £20 Fixed conversion costs charged to product VG2 (4 minutes × £3.333) £13.33 Product specific fixed costs are 40% of £20 for VGU4 and 40% of £13.33 for VG2 The unit cost calculations are as follows: VG4U VG2(£) (£) Direct material 30 30 variable conversion cost – Making 43.75 43.75 – Packing 40.00 26.67––––– ––––– 113.75 100.42 Product specific fixed costs: Making 10.50 10.50 Packing 8.00 5.33 ––––– ––––– Total product specific (relevant) cost 132.25 116.25Company fixed cost:

Making 15.75 15.75 Packing 12.00 8.00 ––––– ––––– Total cost 160.00 140.00 ––––– ––––– (a) (ii) The management suggestion is presumably based on the fact that the reported cost for VG4U exceeds the selling price. However, the relevant oravoidable costs for the product are £132.25 and if the company fixed costsremain unchanged if the product is discontinued then the company will losea contribution of £17.75 (£150 – £132.25) on sales of 5000 units. This willresult in profits for the period being reduced by £88 750 (5000 × £17.75)unless there is an alternative opportunity for the production capacity.

(b) Costs are charged to each activity in the estimated proportions and then to each product using the cost driver proportions given in the question.

Total VG4U VG2 Product units 5000 3000 (%) (£) (£) (£) Variable conversion cost: Moulding (temperature) (60) 210 000 140 000 70 000 Trimming (consistency) (40) 140 000 40 000 100 000 Packing (time) (70) 196 000 117 600 78 400 Packing material (complexity) (30) 84 000 21 000 63 000 ––––––– ––––––– –––––––318 600 311 400––––––– ––––––– Cost per product unit 63.72 103.80 Product specific fixed costs: Moulding (60% × (40% of £210 000)) 50 400 33 600 16 800 Trimming (40% × (40% of £210 000)) 33 600 9600 24 000 Packing (70% × (40% of £140 000)) 39 200 23 520 15 680 Packing material (30% × (40% of £140 000)) 16 800 4200 12 600 ––––––– ––––––– –––––––70 920 69 080 ––––––– ––––––– Cost per product unit 14.18 23.03 Company fixed costs = 60% × £350 000 total fixed costs = £210 000 ACTIVITY-BASED COSTING 103 Overall average cost per unit = £210 000/8000= £26.25 Hence amended unit costs are as follows: VG4U VG2(£) (£) Direct material cost 30.00 30.00 Variable conversion costs 63.72 103.80 –––––– ––––––93.72 133.80 Product specific fixed costs 14.18 23.03 –––––– –––––– Relevant costs 107.90 156.83 Company fixed cost 26.25 26.25 –––––– –––––– 134.15 183.08 –––––– –––––– (c) The ABC unit costs should provide a more accurate measure of resource consumption by the products because several different cost drivers are used thatare related to the resources consumed by the products for the different activities.A different message emerges from the reported product costs. Product VG2appears to be a loss making product. A more detailed analysis indicates that theselling price exceeds the relevant costs and VG2 should not be discontinuedunless discontinuation enables company fixed costs to be reduced by an amountin excess of the product’s current contribution to these fixed costs.

(d) For the answer to this question you should refer to ‘Target costing’ in Chapters 10 and 21. In particular, the answer should stress that the existing selling prices, costsand volumes results in a net profit margin on sales of approximately 5%. Ifexisting selling prices cannot be changed, or they have been determined by marketforces, and volumes are to remain unchanged the focus will be on cost reductionto meet the target profit. This might be achieved by product redesign (such as theuse of fewer component parts and eliminating non-standard materials) and theelimination or reduction of activities. For an illustration of the approach youshould refer to Chapter 21. Note that kaizencosting is applicable here rather than target costing. Target costing is applied to new products whereas kaizencosting is applied to existing products. ACTIVITY-BASED COSTING Lecturers please note that this question appeared in a recent examination of a pro- fessional body so it is possible that students may be able to access the answer to the question. (a) Calculation of single overhead rate based on sales revenue Small Medium Large Total$$$$ Sales revenue $1,800 300 $540,000 $4,800 800 $3,840,000 $9,000 500 $4,500,000 $8,880,000 Overheads $1,596,000 Overheads/ Sales revenue 18% Cost per machine $1,800 18%$324 S4,800 18%$86459,000 18% $1,620 104 Solution IM 11.8 Small Medium Large$$ $ Copy charge per machine (60,000 $0.03) 1,800 (120,000 0.04) 4,800 (180,000 $0.05) 9,000 Cost of parts per machine ($100 5) (500) ($300 7) (2,100) ($400 14) (5,600) Labour cost per machine ($60 5) (300) ($80 7) (560) ($100 14) (1,400) Overhead cost (324) (864) (1,620) Pro t per machine 676 1,276 380Pro t per machine Activity Cost Driver Overheads $000No. of cost drivers Cost per driver $ Customer account handling Number of customers 126 (300/2) (800/2) (500/2) 800 $157.50 per customers Planned maintenance scheduling Number of planned maintenance visits 480 (300 4) (800 6) (500 12) 12,000 $ 40 per planned maintenance visit Unplanned maintenance Number of unplanned maintenance visits 147 (300 1) (800 1) (500 2) 2,100 $ 70 per unplanned maintenance visit Spare part procurement Number ofpurchase orders 243 (500 1,200 1,000) 2,700 $ 90 per Other overheads Number ofmachines 600(300 800 500) 1,600 $ 375 per machine Cost driver rates ACTIVITY-BASED COSTING 105 sheduling purchase order Small Medium Large Customer account handling ($157.50 /2) = $79 ($157.50 /2) = $79 ($157.50 /2) = $79 Planned maintenance scheduling ($40 4) = $160 ($40 6) = $240 ($40 12) = $480 Unplanned maintenance scheduling ($70 1) = $70 ($70 1) = $70 ($70 2) = $140 Spare part procurement ($90 500/300) = $150 ($90 1,200/800) = $135 ($90 1,000/500) = $180 Other overheads $375 $375 $375 Total overhead cost per machine $834 $899 $1,254Overhead cost per machine Small $ Medium $ Large $ Copy charge per machine 1,800 4,800 9,000 Parts and per (800) (2,660) (7,000) Overhead cost per machine (834) (899) (1,254) Pro t per machine using ABC 166 1,241 746ABC pro tability analysis (c) The answer should include the following points: The generation of more accurate product/service costs resulting in improved decision-making; Improved cost management by focusing on activity cost management (see Chapter 21 for a more detailed answer relating ABC cost management); More accurate pro tability analysis (you should discuss the difference in pro t rankings with the ABC system compared with the existing volume-based costing system); The implementation of ABC will enable the company to adopt activity-based budgeting (see Chapter 15 for a discussion of the bene ts of ABB). ACTIVITY-BASED COSTING 106 labour machine DECISION-MAKING UNDER CONDITIONS OF RISK AND UNCERTAINTY107 Solution IM 12.1 (a)Tabulation of cost and profit – colour printed catalogues Capacity utilization 80% 100% 120% Quantities 40 000 50 000 60 000 Total Unit Total Unit Total Unit(£) (£) (£) (£) (£) (£) Variable costs Direct materials 180 000 4.50 225 000 4.50 270 000 4.50 Direct wages 120 000 3.00 150 000 3.00 180 000 3.00 Direct expenses 52 000 1.30 65 000 1.30 78 000 1.30 ––––––– –––– ––––––– –––– ––––––– –––– 352 000 8.80 440 000 8.80 528 000 8.80 Semi-variable costs Indirect materials 46 800 1.17 47 000 0.94 74 400 1.24 Indirect wages 51 200 1.28 55 000 1.10 72 000 1.20 Indirect expenses 6 000 0.15 8 000 0.16 9 600 0.16 ––––––– ––––– ––––––– ––––– ––––––– ––––– 456 000 11.40 550 000 11.00 684 000 11.40 ––––––– ––––– ––––––– ––––– ––––––– ––––– ––––––– ––––– ––––––– ––––– ––––––– ––––– Fixed costs 60 000 1.50 60 000 1.20 60 000 1.00 ––––––– ––––– ––––––– ––––– ––––––– ––––– Total costs 516 000 12.90 610 000 12.20 744 000 12.40 Sales price of £16.00 per unit 640 000 16.00 800 000 16.00 960 000 16.00 ––––––– ––––– ––––––– ––––– ––––––– ––––– Profit 124 000 3.10 190 000 3.80 216 000 3.60 ––––––– ––––– ––––––– ––––– ––––––– ––––– Comments (i) Only at an activity level of 40 000 units is the contract not worth undertaking. At activity levels of 50 000 and 60 000 units, profits are inexcess of £132 000 annual profits from other customers.

(ii) Profits are maximized at an activity level of 60 000 units per annum.

(b) The expected direct material cost is £4.85 [(£4.50 0.5) + (£5 0.3) + (£5.50 0.2)]. The revised profits based on the expected direct material cost of £4.85 are as follows:

40 000 units 50 000 units 60 000 units(£) (£) (£) Profit calculation in (a) using a material cost of £4.50 per unit 124 000 190 000 216 000 Adjustment to reflect expected material cost (14 000) (17 500) (21 000) Revised profit 110 000 172 500 195 000 Expected profit (0.4 £110 000) + (0.5 £172 500) + (0.1 £195 000) = £149 750 Decision-making under conditions of risk and uncertainty Solutions to Chapter 12 questions 108DECISION-MAKING UNDER CONDITIONS OF RISK AND UNCERTAINTY (c) The expected profit of £149 750 is in excess of the estimated profit from the ‘other customers’. However, the £149 750 represents an average profit based on the weighted average of the possible outcomes. If the worst possible outcomeoccurs (an order for 40 000 catalogues and a direct material cost of £5.50), theprofit from the order will be £84 000. The probability of this event occurring is0.08 (0.4 0.2). It would be preferable to construct a probability distribution of the range of possible outcomes in order that management can decide whether ornot the risk of undertaking the order which has an uncertain outcome is justified. The long-term impact of accepting the order should also be considered. Will the contract be renewed after one year? Will the company become dependent onone major customer? Will the company still be able to earn £132 000 per annumprofits after the contract has been completed? It is important that qualitativeinformation which cannot be quantified should be taken into account whenchoosing between the alternatives.

Profit/ Joint Demand Inflation Contribution a Fixed costs b (loss) probability (%) (£) (£) (£) Pessimistic 10 33 000 40 600 (7 600) 0.12 Pessimistic 5 31 500 40 300 (8 800) 0.15 Pessimistic 1 30 300 40 060 (9 760) 0.03 Most likely 10 49 500 40 600 8 900 0.24 Most likely 5 47 250 40 300 6 950 0.30 Most likely 1 45 450 40 060 5 390 0.06 Optimistic 10 66 000 40 600 25 400 0.04 Optimistic 5 63 000 40 300 22 700 0.05 Optimistic 1 60 600 40 060 20 540 0.01 Notes a Demand at current selling prices (1 + inflation rate) contribution percentage.

For example, with £50 000 demand at current prices, sales revenue will increase to £55 000 if the inflation rate is 10%. The contribution margin percentageremains constant at 60%, and therefore contribution will be £33 000.

b £40 000 fixed costs + (inflation rate 0.15 fixed costs) Summary of probability distribution Probability of loss = 0.30 Probability of at least breaking even = 0.70 Probability of at least a profit of £20 000 = 0.10 Alternatively the entire probability distribution could be presented:

Probability of a loss of more than £9000 = 0.03 Probability of a loss of more than £8000 = 0.18 Probability of a loss of more than £7000 = 0.30 Probability of a profit of at least £5000 = 0.70 Probability of a profit of at least £6000 = 0.64 Probability of a profit of at least £7000 = 0.34 Probability of a profit of at least £8000 = 0.34 Probability of a profit of at least £20 000 = 0.10 Probability of a profit of at least £22 000 = 0.09 Probability of a profit of at least £25 000 = 0.04 It should be noted that it is inappropriate to assume that all costs and selling prices will alter in line with each other. Also the existence of stocks will introduce a lag inthe system. Solution IM 12.2 DECISION-MAKING UNDER CONDITIONS OF RISK AND UNCERTAINTY109 Part A (a)Scenario 1 Expected value = average long-run demand of 350 tickets Scenario 2 (1) (2) (3) (4) Type of artiste Ticket sales Probability Weighted average, (2) (3) Popular 500 0.45 225 Lesser known 350 0.30 105 Unknown 200 0.25 50 ––– Expected value 380 tickets ––– (b) Purchase 200 tickets Type of Purchase Sale by Profit /Expected artiste Revenue costs box office (loss) Probability value (£) (£) (£) (£) (£) Popular 600 a480 a 0 120 0.45 54 Lesser known 600 480 0 120 0.30 36 Unknown 600 480 0 120 0.25 30 ––– 120 ––– Purchase 300 tickets Popular 900 b675 b 0 225 0.45 101.25 Lesser known 900 675 0 225 0.30 67.50 Unknown 600 675 c18 c (57) 0.25 (14.25) ––––– 154.50 ––––– Purchase 400 tickets Popular 1200 d840 d 0 360 0.45 162.0 Lesser known 1050 840 e9 e 219 0.30 65.7 Unknown 600 840f36 f (204) 0.25 (51.0) ––––– 176.7 ––––– Purchase 500 tickets Popular 1500 g900 g 0 600 0.45 270.0 Lesser known 1050 900 h27 h 177 0.30 53.1 Unknown 600 900i54 i (246) 0.25 (61.5) ––––– 261.6 ––––– Notes a Purchase price = £2.40.

b Purchase price = £2.25.

c 10% of 100 unsold tickets at £1.80.

d Purchase price = £2.10.

e 10% of 50 unsold tickets at £1.80.

f 10% of 200 unsold tickets at £1.80.

g Purchase price = £1.80.

h 10% of 150 unsold tickets at £1.80.

i 10% of 300 unsold tickets at £1.80.

Scenario 1 The schedule of expected values indicates that for lesser known artistes thehighest profit is £225 when 300 tickets are purchased. Scenario 2 The purchase of 500 tickets yields the highest expected profit (£261.60) Solution IM 12.3 110DECISION-MAKING UNDER CONDITIONS OF RISK AND UNCERTAINTY Part B: Specialist prediction Type of artiste No. of tickets purchased to yield maximum profitPopular 500 Lesser known 300 Unknown 200 The expected value if the specialist is employed is equal to the sum of the maximumprofit for each possible outcome times the probability of the outcome occurring: Outcome Profit Probability Expected value (£) (£) Popular 600 0.45 270.0 Lesser known 225 0.30 67.5 Unknown 120 0.25 30.0 ––––– 367.5 ––––– The maximum sum payable per concert is equal to the expected value of certain information (£367.50) prior to appointing the specialist less the maximum expectedvalue under uncertainty (£261.60). Therefore the maximum sum payable is £105.90 perconcert. With 60 concerts per year, the maximum sum payable per annum is £6354(£105.90 60).

(a) Maximum monthly capacity = 2400 nights (80 30 days) Contribution per normal guest = £21 (£20 £4 + £5) Contribution per air-travel guest = £11 [(0.6 £20) £4 + £3] Monthly fixed costs = £28 000 The number of nights to be considered for the contract are: (i) 960 (2400 1440) (ii) 720 (2400 1680) (iii) 480 (2400 1920) (iv) 2400 (assuming air travel takes all the available capacity) (i) Contract 960 nights : If 960 nights are contracted, the remaining capacity of 1440 nights will be used whatever the weather conditions. Expected contribution = (960 £11) + (1440 £21) = £40 800 (ii) Contract 720 nights : If 720 nights are contracted, the remaining capacity will be 1680 nights. There is a 0.3 probability that weather condition A will apply and demand will be 1440 nights, resulting in the hotel being partlyempty. There is a 0.7 probability that weather conditions B or C will apply,thus resulting in the remaining capacity of 1680 nights being fully used. Expected contribution = (720 £11) + (0.3 1440 + 0.7 1680) £21 = £41 688 (iii) Contract 480 nights : The remaining capacity is now 1920 nights. There is a 0.3 probability that demand will be for 1440 nights, 0.4 that demand will be for 1680 nights, and 0.3 that demand will be for 1920 nights. Expected contribution =(480 £11) + (0.3 1440 + 0.4 1680 + 0.3 1920) £21 = £40 560 (iv) Contract 2400 nights : Expected contribution = 2400 £11 = £26 400 Solution IM 12.4 DECISION-MAKING UNDER CONDITIONS OF RISK AND UNCERTAINTY111 Using the expected value decision rule, 720 nights should be contracted. It would be possible to use other approaches, such as a comparison of the probabilitydistributions or a maximin approach, but these are likely to be too time-consuming given that only six marks are allocated to this part of the question.

(b) The relevant cost of hotel accommodation is £4 variable cost, but a contribution of £3 is obtained from the restaurant. Hence the net marginal cost is £1 per night.Therefore the minimum price per guest night for accommodation (and assumingeach guest takes a meal in the restaurant) is £1. If meals are not taken, theminimum price is £4 per night. A price in excess of these amounts will result in acontribution towards fixed costs which would otherwise not be obtained. It isassumed that there will be no effect on occupancy from normal business. Themaximum number of guest nights that it would be worthwhile contracting for(assuming a charge slightly in excess of £1 per night for accommodation) wouldbe 480 (2400 – 1920).

(c) The monthly fixed costs for each alternative are:

Close Stay open(£) (£) Staff wages and general overheads 3 500 20 500 Other fixed costs 7 500 7 500 ––––– ––––– 11 000 28 000 ––––– ––––– The increase in monthly fixed costs from staying open is £17 000.

(i) Contribution from basic winter trade and conferences Total guest nights Contribution Totalfor three months per night contribution (£) (£) Basic winter trade 1080 (12 90 days) 15 (19 4) 16 200 Conferences 2700 (30 90 days) 13 (17 4) 35 100 –––––– 51 300 Less additional fixed costs (£17 000 3) 51 000 –––––– Profit 300 –––––– (ii) Contribution from language courses Contribution Fixed costs Profit / Occupancy (£21 per night) ( W1) (loss) Probability EV (£) (£) (£) (£) 2160 45 360 67 500 (22 140) 0.3 (6 642) 4320 90 720 67 500 23 220 0.4 9 288 6480 136 080 67 500 68 580 0.3 20 574 –––––– 23 220 –––––– –––––– Working ( W1 ) Additional fixed costs in (i) of £51 000 + £15 000 tutor fees + £1500 advertising. On the basis of the above information, language courses should be offered.

The reservations include:

1. The owner’s attitude to risk. There is a 0.3 probability that a loss of £22 140 will occur. 112DECISION-MAKING UNDER CONDITIONS OF RISK AND UNCERTAINTY 2. The reliability of the estimates used in terms of occupancy levels and the probabilities attached to them.

3. The validity of the assumption that monthly general overheads (which include electricity) will be £8000 in the winter.

4. The effect on wear and tear and summer sales from the hotel being used as a language school in winter.

(d) The criterion for identifying costs in (a)–(c) is whether or not costs will change for the alternative under consideration. In other words, a relevant cost approach has been used, and sunk costs (i.e. committed fixed costs) have been ignored. Onlyincremental fixed costs are included in the analysis. Alternatives have beencompared using the expected value method. Expected values represent long-runaverage costs and suffer from the disadvantage that they ignore the decision-maker’s attitude to risk.

(a) There are two possible selling prices and three possible direct material costs for each selling price. The contributions per unit before deducting direct materialcosts are £12 (£15 £3) for a £15 selling price and £17 for a £20 selling price.

The purchase costs per unit of output are £9 (3 kg £3), £8.25 (3 kg £2.75) and £7.50. Where the firm contracts to purchase a minimum quantity any surplusmaterials are sold at £1 per kg.

Statement of outcomes Net Sales Gross purchase Fixed Profit /Expected quantities contribution cost costs (loss) Probability value (000) (£000) (£000) (£000) (£000) (£000) £15 selling price (£3 purchase price) 36 432 324 65 43 0.3 12.9 28 336 252 65 19 0.5 9.5 18 216 162 65 (11) 0.2 (2.2) –––– 20.2 –––– £15 selling price (£2.75 purchase price) 36 432 297 65 70 0.3 21.0 28 336 231 65 40 0.5 20.0 18 216 148.5 65 2.5 0.2 0.5 –––– 41.5 –––– £15 selling price (£2.50 purchase price) 36 432 270 65 97 0.3 29.1 28 336 210 65 61 0.5 30.5 18 216 a159 a 65 (8) 0.2 (1.6) –––– 58.0 –––– £20 selling price (£3 purchase price) 28 476 252 136 88 0.3 26.4 23 391 207 136 48 0.5 24.0 13 221 117 136 (32) 0.2 (6.4) –––– 44.0 –––– Solution IM 12.5 £20 selling price (£2.75 purchase price) 28 476 231 136 109 0.3 32.7 23 391 189.75 136 65.25 0.5 32.625 13 221 b 126.5b 136 (41.5) 0.2 (8.3) –––––– 57.025 –––––– £20 selling price (£2.50 purchase price) 28 476 210 136 130 0.3 39.0 23 391 c174 c 136 81 0.5 40.5 13 221 144 d 136 (59) (0.2) (11.8) –––– 67.7 –––– Notes a 170 000 kg minimum purchases at £2.50 per kg less 16 000 kg [70 000 (3 kg 18 000) at £1 per kg].

b 50 000 kg minimum purchases at £2.75 per kg less 11 000 kg [50 000 (3 kg 13 000) at £1 per kg].

c 70 000 kg minimum purchases at £2.50 per kg less 1000 kg [70 000 (3 kg 23 000) at £1 per kg].

d 70 000 kg minimum purchases at £2.50 per kg less 31 000 kg [70 000 – (3 kg 13 000) at £1 per kg].

If the objective is to maximize expected profits then the £20 selling price combined with purchasing option (iii) is recommended. On the other hand, if the maximincriterion is adopted then the £15 selling price combined with purchasing option (ii)is recommended. An alternative approach is to examine the probability distributions(final column of the statement) and adopt a combination which best satisfies thedecision-maker’s risk /return preferences.

(b) If demand is predicted to be optimistic, the highest payoff of £130 000 (£20 selling price and £2.50 purchase price) for the most optimistic demand level would be chosen. If the most likely demand is predicted, the highest payoff is £81000 (£20 selling price and £2.50 purchase price). If the pessimistic demand level ispredicted, the highest payoff is £2500. The expected value of profits assuming it ispossible to obtain perfect information is:

(£) £130 000 0.3 = 39 000 £81 000 0.5 = 40 500 £2 500 0.2 = 500 –––––– 80 000 –––––– The highest expected profit without perfect information in (a) is £67 700. Thereforethe maximum price payable for perfect information is £12 300 (£80 000 £67 700). DECISION-MAKING UNDER CONDITIONS OF RISK AND UNCERTAINTY 113 114DECISION-MAKING UNDER CONDITIONS OF RISK AND UNCERTAINTY (a) The relevant costs per unit are as follows:

1–2000 2001–4000 4001–8000 Over 8000units units units units(£) (£) (£) (£) Labour: Grade 1 a —444 Grade 2 a —— 3 3 Material: Xb 9999 Y c (4) (4) (4) 8 Variable overhead d 6666 –– –– –– –– Total relevant cost per unit 11 15 18 30 –– –– –– –– Notes a Labour costs are only relevant when idle time has been exhausted. This occurs at 2000 units for grade 1 labour (2000 units 2 hours) and 4000 units for grade 2 labour (4000 units 1 hour). It is assumed that beyond these output levels incremental labour costs of £2 per hour for grade 1 and £3 per hour for grade 2 will be incurred. b Replacement cost of £9 per unit.

c Each unit of Y used saves the company £2 disposal costs. The product requires 2 units of Y, thus saving £4 disposal costs. When the stock of 16 000 units has beenused (8000 units produced) additional supplies will be purchased at £4 per unit. d Variable overheads are assumed to vary with hours of input.

The relevant production costs for various output levels are as follows: Output Total cost (000 units) (£000) 22 2 3 37 (£22 + 1 £15) 4 52 (£37 + 1 £15) 5 70 (£52 + 1 £18) 6 88 (£70 + 1 £18) 8 124 (£88 + 2 £18) 10 184 (£124 + 2 £30) 15 334 (£184 + 5 £30) The outcomes and expected values for each selling price are presented in the following schedule: Outcomes and expected values Sales Production Advertising Expected Volume revenues costs costs Profit value (£000) (£000) (£000) (£000) (£000) Probability (£000)Selling price £20 4 80 52 20 8 0.1 0.8 6 120 88 20 12 0.4 4.8 8 160 124 20 16 0.5 8.0 –––– 13.6 –––– –––– Solution IM 12.6 DECISION-MAKING UNDER CONDITIONS OF RISK AND UNCERTAINTY115 Selling price £25 2 50 22 50 (22) 0.1 (2.2) 5 125 70 50 5 0.2 1.0 6 150 88 50 12 0.2 23.4 8 200 124 50 26 0.5 13.0 –––– 14.2 –––– –––– Selling price £40 0 0 0 100 (100) 0.2 (20.0) 3 120 37 100 (17) 0.5 (8.5) 10 400 184 100 116 0.2 23.2 15 600 334 100 166 0.1 16.6 –––– 11.3 –––– –––– (b) On the basis of the expected value decision rule, a selling price of £25 should be selected. Management might use criteria other than maximizing expected value. For example the decision might be based on the minimization of risk. The aboveprobability distributions indicate that £20 is the only selling price at which a losswill not arise. The final decision should be based on an examination of each ofthe above probability distributions and management’s attitude towards risk.

(c) Assuming that management is proposing a selling price of £40, if the information indicated that demand would be zero or 3000 units then Warren should cancel the advertising at a cost of £10 000. This would give the following expectedvalue:

Volume Gross Cost of Net Expected demanded Action profit information profit Probability value (000) (£000) (£000) (£000)0 Cancel advertising (10) 5 (15) 0.2 (3.0) 3 Cancel advertising (10) 5 (15) 0.5 (7.5) 10 Continue 116 5 111 0.2 22.2 15 Continue 166 5 161 0.1 16.1 –––– 27.8 –––– It is worthwhile obtaining the information, since the expected value increasesfrom £11 300 to £27 800. The £40 selling price now yields the highest expectedvalue, and this selling price should be selected if decisions are based onmaximizing expected values. Nevertheless, management might select anotherselling price, since the £40 selling price still has a 0.7 probability of making a loss.

(a) Sales Possible at £40 Total Expected demand per unit costs a Profit Probability value (000) (£000) (£000) (£000) (£000) Machine A 10 400 435 (35) 0.5 (17.5) 14 560 571 (11) 0.3 (3.3) 16 640 649 (9) 0.2 (1.8) –––– (22.6) –––– –––– Solution IM 12.7 116DECISION-MAKING UNDER CONDITIONS OF RISK AND UNCERTAINTY Machine B 10 400 460 (60) 0.5 (30.0) 14 560 548 12 0.3 3.6 16 640 616 24 0.2 4.8 –––– (21.6) –––– –––– Machine C 10 400 500 (100) 0.5 (50.0) 14 560 536 24 0.3 7.2 16 640 554 86 0.2 17.2 –––– (25.6) –––– –––– Note a The calculations of total costs are as follows:

Demand 10 000 units 14 000 units 16 000 units (£000) (£000) (£000) Machine A (maximum capacity of 10 000 units) Variable costs at £6.50 per unit a 65 65 65 Fixed costs 320 320 320 Material costs b 50 66 74 Subcontracting costs c — 120 190 Total costs 435 571 649 Machine B (maximum capacity of 12 000 units) Variable costs at £6 per unit a 60 72 72 Fixed costs 350 350 350 Material costs b 50 66 74 Subcontracting costs c — 60 120 Total costs 460 548 616 Machine C (maximum capacity of 16 000 units) Variable costs at £5 per unit a 50 70 80 Fixed costs 400 400 400 Material costs b 50 66 74 Subcontracting costs c ——— Total costs 500 536 554 Notes a Variable cost per unit demanded up to maximum capacity level for each machine. b £5 per unit for first 10 000 units plus £4 per unit for demand in excess of 10 000 units.

c Demand in excess of machine capacity £30 per unit (up to 4000 units subcontracted) plus £35 per unit for any subcontracting in excess of 4000 units. Recommendation Machine B yields the lowest expected loss, and should be chosen if decisions aremade on the basis of expected values. With machine C, there is a probability of 0.2of obtaining a profit of £86 000, but there is also a possibility of a large loss. Arisk-taker might prefer machine C to machine B. DECISION-MAKING UNDER CONDITIONS OF RISK AND UNCERTAINTY117 (b) (i) With certain information, the following decisions will be made:

Certain demand of 10 000 units:Purchase machine A which yields a minimum loss of £35 000.

Certain demand of 14 000 units: Purchase machine C which yields a maximum profit of £24 000.

Certain demand of 16 000 units: Purchase machine C which yields a maximum profit of £86 000.

Prior to purchasing the information, the probability that the market researchers will predict each demand level is as follows: 0.5 for a demand level of 10 000 units 0.3 for a demand level of 14 000 units0.2 for a demand level of 16 000 units With perfect information, the revised expected value will be as follows: Demand Expected units Machine Profit Probability value (000) (£000) (£000) 10 A (35) 0.5 (17.5) 14 C 24 0.3 7.2 16 C 86 0.2 17.2 –––– 6.9 Value of best decision using imperfect information (21.6) –––– Difference 28.5 –––– –––– Therefore the maximum which it is worthwhile to pay for perfect information is £28 500. For an explanation of this see ‘Buying perfect and imperfectinformation’ in Chapter 12.

(ii) The expected value of perfect information gives an approximation of the upper limit on the value of information. Any information which costs morethan this upper limit is not worth obtaining. The model can be adapted toindicate the expected value of imperfect information.

(a) (1) (2) (3) Contribution Probability Weighted amount, (1) (2) (£) (£) 1 000 000 0.75 750 000 (400 000) 0.25 (100 000) ––––––– Expected value 650 000 ––––––– The expected contribution is £650 000. Using the expected value criteria, BEMshould be given further consideration.

(b) Expected reduction on contribution of LOG (i) BEM’s sales = £3 200 000 Decline in sales Contribution Probability Weighted average (£) (£) (£) 1 600 000 400 000 0.5 200 000 800 000 200 000 0.25 50 000 2 400 000 600 000 0.25 150 000 ––––––– Expected reduction in contribution 400 000 ––––––– Solution IM 12.8 (ii)BEM’s sales = £800 000 400 000 100 000 0.5 50 000 200 000 50 000 0.25 12 500 600 000 150 000 0.25 37 500 ––––––– Expected reduction in contribution 100 000 ––––––– Expected reduction in total contribution = £325 000 [(0.75 400 000) + (0.25 100 000)] Revised expected contribution if BEM is launched = £325 000 (£650 000 £325 000) Using the expected value criteria, BEM should still be given further consideration.

(c) The expected value if the survey is commissioned is calculated as follows: Contribution Probability Weighted amount(£) (£) Survey predicts BEM’s acceptance 600 000 (£1 000 000 £400 000) 0.75 450 000 Survey does not predictBEM’s acceptance 0 0.25 0 ––––––– Expected value 450 000 ––––––– If the survey is commissioned, expected value increases by £125 000 (£450 000 £325 000). Since this is in excess of the survey cost of £100 000, the survey is justified.

(d) The expected value if the report indicates that BEM will gain acceptance is calculated as follows:

Contribution Probability Weighted amount(£) (£) Report correct 600 000 (£1 000 000 £400 000) 0.9 540 000 Report incorrect a (500 000) 0.1 (50 000) ––––––– Expected value 490 000 ––––––– Note a If the report is incorrect and the product is not accepted, there will be a negative contribution from BEM’s sales of £400 000 [see part (a)]. In addition the reduction in the contribution from LOG is expected to be £100 000 [see part (b)].Therefore the expected negative contribution if the product is not accepted is£500 000. If the report indicates that BEM will not gain acceptance, BEM will not be launched and the expected value will be zero. There is a 75% chance that Delphiwill indicate acceptance. Therefore the expected value of the report is as follows:

Contribution Probability Weighted amount(£) (£) Report indicates acceptance 490 000 0.75 367 500 Report indicates non-acceptance 0 0.25 0 ––––––– Expected value 367 500 ––––––– 118 DECISION-MAKING UNDER CONDITIONS OF RISK AND UNCERTAINTY Without the report the expected value is £325 000. Therefore the maximum sum payable is £42 500 (£367 500 £325 000).

(e) The strengths of the expected value (EV) approach are as follows: (i) EV forces management to recognize different possible outcomes and quantifythem.

(ii) EV attempts to measure expectations systematically.

(iii) EV forces management to consider probabilities of possible outcomes and to quantify them.

The weaknesses of the EV approach are as follows: (i) The method of assigning probabilities is subjective.

(ii) EV ignores risk since it fails to consider the dispersion of the possible outcom- es.

(iii) Only a few discrete estimates are used. The actual estimate represents the midpoint of a range of possible outcomes rather than a single estimate.

(iv) The expected value is an average outcome. Therefore it is best suited to repetitive decisions. This is not the case in this question.

(v) EV is best suited to situations where the risk of negative outcomes will not have a dramatic effect on the ability of a firm to survive. DECISION-MAKING UNDER CONDITIONS OF RISK AND UNCERTAINTY 119 120CAPITAL INVESTMENT DECISIONS: APPRAISAL METHODS Solution IM 13.1 Solution IM 13.2 (a) The answer should include a discussion of the following points:

(i) In theory, the acceptance of projects with positive NPVs (when discountedat the required rate of return, which is related to the project’s risk) should result in an increase in the share price.

(ii) The NPV method is superior to non-discounting methods because it takesinto account the time value of money. Also, by adding a risk premium, it ispossible to relate the project to the opportunity cost of investors in terms ofthe returns forgone from an investment of equivalent risk.

(iii) The NPV method is superior to IRR method because: 1. The reinvestment assumptions of NPV; 2. IRR is unsatisfactory because it focuses on the return itself rather than themagnitude of the earnings; 3. IRR method can give more than one IRR calculation when unconventional cash flows occur, and this might lead to decisions whichdo not maximize NPV; 4. IRR can incorrectly rank mutually exclusive projects.

(b) The answer should include a discussion of the following points: (i) An awareness of the surveys by Pike (1996) and Drury et al.(1993). (See Bibliography in main text for details.) (ii) Reasons why the payback method is widely used (avoids long-term forecasts of future cash flows, reduces risk, etc.) (iii) A discussion of why the accounting rate of return is widely used. It may be that managers select those projects which will have the greatest impact onprofitability when the annual accounts are published. For a discussion of thispoint see ‘The effect of performance measurement on capital investmentdecisions’ in Chapter 13.

(iv) A discussion as to why managers might prefer IRR to NPV methods: 1. It is claimed that with the IRR method it is unnecessary to explicitlyformulate the cost of capital.

2. Managers prefer to evaluate projects in percentage terms.

(a) Cumulative cash flows AB C (£) (£) (£) Year 1 80 000 100 000 55 000 2 150 000 170 000 120 000 3 215 000 220 000 215 000 4 270 000 Payback periods Project A = 2 years + (200 150) /65 = 2.77 years Project B = 3 years + (230 220) /50 = 3.2 years Project C = 2 years + (180 120) /95 = 2.63 years Capital investment decisions: appraisal methods Solutions to Chapter 13 questions (b) Accounting rate of return =average profits average investment Average profits = total net annual cash inflows /asset life A: (330 + 10 200) /5 = £28 000 B: (320 + 15 230) /5 = £21 000 C: (315 + 8 180) /4 = £35 750 Assuming that depreciation is charged on the straight line basis: Average investment = (initial investment + scrap value) /2 A: 210 /2 = £105 000 B: 245 /2 = £122 500 C: 188 /2 = £94 000 Accounting rate of return: A: £28 000/£105 000 = 26.67% B: £21 000 /£122 500 = 17.14% C: £35 750 /£94 000 = 38.03% (c) Outflow Inflows Discount factor Present value (£) (£) (£) Project A Year 0 200 000 — 1.00 200 000 1 +80 000 0.8475 +67 800 2 +70 000 0.7182 +50 274 3 +65 000 0.6086 +39 559 4 +60 000 0.5158 +30 948 5 +65 000 0.4371 +28 411 ––––––– +16 992 ––––––– Project B Year 0 230 000 1.00 230 000 1 +100 000 0.8475 +84 750 2 +70 000 0.7182 +50 274 3 +50 000 0.6086 +30 430 4 +50 000 0.5158 +25 790 5 +65 000 0.4371 +28 411 ––––––– 10 345 ––––––– Project C Year 0 180 000 1.00 180 000 1 +55 000 0.8475 +46 613 2 +65 000 0.7182 +46 683 3 +95 000 0.6086 +57 817 4 +108 000 0.5158 +55 706 ––––––– +26 819 ––––––– (d) The NPV method of evaluation is superior to the other methods, and the project with the largest NPV ought to be selected: project C. It should be noted thatproject C is also preferred to A and B when the payback and accounting rate ofreturn methods are used.

(e) Other factors which should be considered are qualitative factors such as the impact on existing sales, the effect on employees and the effect on the CAPITAL INVESTMENT DECISIONS: APPRAISAL METHODS 121 environment from each of the three projects. In addition the risk and reliability of the cash flows for each project should be considered.

(a) Cash flow Year 1 2345 (£) (£) (£) (£) (£) Saving in fleet costs 250 000 275 000 302 500 332 750 366 025 Less driver’s costs 33 000 35 000 36 000 38 000 40 000 Repairs and maintenance 8 000 13 000 15 000 16 000 18 000 Other costs 10 000 15 000 20 000 16 000 22 000 –––––– –––––– –––––– –––––– –––––– 51 000 63 000 71 000 70 000 80 000 Net savings 199 000 212 000 231 500 262 750 286 025 Depreciation of £120 000 per annum (£750 000 less £150 000 scrap value depreciated over 5 years) has been deducted from other costs since it is not a cashexpense.

(b) (i) Payback = 3 + (£750 000 £642 500) /£262 750 years = 3.41 years (ii) Accounting rate of return = average profit (£118 255) average investment (£450 000) = 26.3% Average profit = savings over 5 years depreciation 5 years = (£1 191 275 £600 000) /5 years = £118 255 per year Average investment = 1 2 initial outlay + 1 2 scrap value = 1 2 (£750 00) + 12 (£150 000) = £450 000 (iii) Net present value Cost Discount factor(£) (£) Year 0 (750 000) 1 Saving 199 000 0.893 177 707 2 Saving 212 000 0.797 168 964 3 Saving 231 500 0.712 164 828 4 Saving 262 750 0.636 167 109 5 Saving 286 025 0.567 162 176 5 Sale of proceeds 150 000 0.567 85 050 ––––––– Net present value 175 834 ––––––– (c) The answer should draw attention to the fact that the transport fleet investment has a higher NPV but a longer payback and lower accounting rate of return than the alternative. The decision should be based on the NPV rule and it isrecommended that the company invests in the new transport fleet. The answershould also explain the superiority of the NPV technique over the accounting rate Solution IM 13.3 122 CAPITAL INVESTMENT DECISIONS: APPRAISAL METHODS of return and payback methods (see ‘The concept of NPV’, ‘Payback method’ and ‘Accounting rate of return’ in Chapter 13).

Task 1:

(a) Year Cash flow Discount factor Present value (£) (£) 1 18 000 0.926 16 668 2 29 000 0.857 24 853 3 31 000 0.794 24 614 –––––– 66 135 Less investment outlay 55 000–––––– 11 135 –––––– (b) Payback occurs during the third year. Assuming even cash flows throughout the year the payback period is:

2 years + (£55 0£0 30 1 – 0 £ 0 4 0 7 000) = Approximately 2.3 years Task 2:

(a) The proposal should be accepted because it has a positive net present value.

(b) See the sections on the concept of net present value and payback method in Chapter 13 for the answer to this question.

(c) The answer should draw attention to the following points: (i) Incremental profits arising from a project are taxable. The tax is normallypayable approximately 12 months after the receipt of the associated inflowsand taxation should therefore be recorded as a cashflow in the appraisal witha time lag of 12 months.

(ii) Depreciation is not an allowable expense for taxation purposes. Instead, theInland Revenue specifies depreciation schedules (known as capital allowancesor writing down allowances) that must be used to compute taxable profits.Incremental taxation on project cash flows are therefore normallydetermined by multiplying the incremental profits arising from a project(cash inflows less cash outflows (excluding depreciation) less capitalallowances) by the company’s taxation rate. The impact of taxation oncapital investment appraisal is discussed in Chapter 14.

(a) Machine A End of Variable Fixed Cash Discount Presentyear Volume costs (£) costs (£) flow (£) factors value(£) 1 145 200(1) 726 000 20 000 746 000 0.870 649 020 2 159 720 798 600 20 000 818 600 0.756 618 862 3 175 692 878 460 20 000 898 460 0.658 591 187 –––––––– 1 859 069 Capital cost 60 000 –––––––– 1 919 069 –––––––– Solution IM 13.4 Solution IM 13.5 CAPITAL INVESTMENT DECISIONS: APPRAISAL METHODS 123 Machine BEnd of Variable Fixed Cash Discount Present year Volume cost (£) cost (£) flow (£) factors value (£) 1 145 200 755 040 38 000 793 040 0.870 689 945 2 159 720 830 544 38 000 868 544 0.756 656 619 3 170 000 884 000 38 000 922 000 0.658 606 676 3 5 692 56 920 56 920 0.658 37 453 –––––––– 1 990 693 –––––––– Note:

(1) Annual growth rate = 12 000/120 000 = 10%.

(b) Machine A should be purchased because it has the lowest present value of cash outflows. Sales revenues are irrelevant because the cash inflows are indentical forboth machines. A benefit that has not been quantified in the above analysis isMachine A’s surplus capacity which provides a safeguard should demand beunder-estimated.

(c) Because the machine must be replaced the £10 000 sale proceeds will occur whichever alternative the company chooses. Therefore the sale proceeds are notrelevant for decision-making.

(d) See the sections on compounding and discounting and the concept of net present value in Chapter 13 for the answer to this question.

The present values (discounted at 10%) for each of the projects are as follows: Project A Project B Project B A (£) (£) (£) Year 0 1000 10 000 9000 1 240 2 300 2060 2 288 2 640 2352 3 346 3 040 2694 4 414 3 500 3086 5 498 4 020 3522 ––– –––– –––– NPV 309 1 441 1132 ––– –––– –––– IRR 20% 15% 14% The IRR method ranks project A in preference to project B, whereas the NPV method ranks B in preference to A. The IRR method is misleading because it expresses the resultas a percentage rather than in monetary terms. This can result in incorrect decisionswhen projects with differing investments are compared. If projects A and B weremutually exclusive then project A would be selected using the IRR method and NPVwould not be maximized. In order to compare projects with unequal investments, it is necessary to consider what use will be made of the funds as represented by the difference between the investment costs between the two projects. A correct comparison between projects Aand B requires that we ascertain how the £9000 (difference between the investments)will be invested. If the company is not in a capital rationing situation then otherinvestment opportunities will not be available which will yield positive NPVs.Therefore the £9000 will be invested at the cost of capital and NPV will be zero.

Hence the total NPV for an investment of £10 000 when project A is selected will be£309 compared with £1441 when project B is selected. If a capital rationing situation exists then the acceptance of project A will enable £9000 to be invested in other profitable projects. Project A should be selected if the£9000 will yield an NPV in excess of £1132 (project B project A) or an IRR of Solution IM 13.6 124 CAPITAL INVESTMENT DECISIONS: APPRAISAL METHODS 14%. If this is not possible then project B should be selected. The objective is to maximize NPV; but when projects are ranked in terms of IRR, there is no guaranteethat NPV will be maximized. When capital rationing applies, NPV is maximized byranking projects in terms of the NPV per £1 of investment (i.e. the profitability index).For a discussion of the superiority of the NPV method over the IRR method see‘Comparison of the NPV and IRR’ in Chapter 13. (a)Preliminary workings The cash flow savings are calculated as follows: Year 2 Year 3 Years 4–8 (£) (£) (£) Maintenance cost (75 per house): Contractor A 6 750 (90 £75) 13 500 (180 £75) 22 500 (300 £75) Contractor B 11 250 (150 £75) 18 000 (240 £75) 22 500 (300 £75) Heating cost (£150 per house): Contractor A 13 500 (90 £150) 27 000 (180 £150) 45 000 (300 £150) Contractor B 22 500 (150 £150) 36 000 (240 £150) 45 000 (300 £150) Rental income increase (£315 per house): Contractor A 28 350 (90 £315) 56 700 (180 £315) 94 500 (300 £315) Contractor B 47 250 (150 £315) 75 600 (240 £315) 94 500 (300 £315) The payments to the contractors would be £600 000 (300 £2000), allocated as follows:

Contractor A Contractor B(£) (£) Year 0 100 000 300 000 1 150 000 (90 /300 £500 000) 150 000 (150 /300 £300 000) 2 150 000 (90 /300 £500 000) 90 000 (90 /300 £300 000) 3 200 000 (120 /300 £500 000) 60 000 (60 /300 £300 000) –––––– –––––– 600 000 600 000 –––––– –––––– The cash flow schedules (in £000) and DCF calculations are as follows:

Year 0 1 2 3 45678 Total Contractor A Maintenance cost reduction 6.75 13.5 22.5 22.5 22.5 22.5 22.5 132.75 Heating cost reduction 13.50 27.0 45.0 45.0 45.0 45.0 45.0 265.50 Rental income increase 28.35 56.7 94.5 94.5 94.5 94.5 94.5 557.55 Payments to contractor (100) (150) (150) (200) (600) – – – – – – ––––– ––––– ––––– ––––– ––––– ––––– ––––– ––––– Net cash flow (100) (150) (101.4) (102.8) 162.0 162.0 162.0 162.0 162.0 355.8 ––––– ––––– Discount factor at 14% 1.000 00.877 0.769 0.675 0.592 0.519 0.456 0.400 0.351 Net present value (100) (131.6) (78.0) (69.4) 95.9 84.1 73.9 64.8 56.9 (3.4) ––––– ––––– Solution IM 13.7 CAPITAL INVESTMENT DECISIONS: APPRAISAL METHODS 125 126CAPITAL INVESTMENT DECISIONS: APPRAISAL METHODS Contractor B Maintenance cost reduction 11.25 18.0 22.5 22.5 22.5 22.5 22.5 141.75 Heating cost reduction 22.50 36.0 45.0 45.0 45.0 45.0 45.0 283.50 Rental income increase 47.25 75.6 94.5 94.5 94.5 94.5 94.5 595.35 Payments to contractor (300) (150) (90) (60) (600) ––– ––– ––––– ––––– ––––– ––––– ––––– ––––– ––––– ––––– Net cash flow (300) (150) (9.0) 69.6 162.0 162.0 162.0 162.0 162.0 420.6 ––––– ––––– Discount factor at 14% 1.000 00.877 0.769 0.675 0.592 0.519 0.456 0.400 0.351 Net present value (300)(131.6) (6.9) 47.0 95.9 84.1 73.9 64.8 56.9 (15.9) ––––– ––––– The proposal for Contractor B gives the greater net cash inflow of £420 600 where the time value of money is ignored. The NPV calculations indicate that both projects yield a negative NPV. If non-financial factors demand that one of the quotations must be accepted then the above analysis suggests that on purely finan-cial grounds the quotation from Contractor A should be accepted.

(b) Let x= additional annual cash inflow required to yield a zero NPV. Then xcan be found by solving the following equation: a 0.3 x(0.877) + 0.3 x(0.769) + 0.4 x(0.675) + 3400 = 0 0.7638x= 3400 x = £4451 In other words, additional annual cash inflows of £4451 per annum are required in order to yield a zero NPV. Therefore a reduction in cash outflow per house of£14.84 (£4451 /300 houses) is required. Hence the maximum refurbishment price per house is £1985.16 (£2000 £14.84).

Note a The figure of 0.3 refers to the proportions paid in years 1 and 2 (90 houses completed out of a total of 300), and 0.4 refers to the proportion paid in year 3(120 /300). The figures in parentheses refer to the discount factors for years 1, 2 and 3, and £3400 represents the negative NPV in (a) which must be recovered forNPV to be zero.

(c) The maintenance and heating cost savings have not been adjusted for inflation. A discount rate of 14% suggests that a nominal discount rate has been applied. Thepayments to the contractor are fixed and not subject to inflation. If the cash flows are adjusted for inflation, it is possible that the project will yield a positive NPV.If the cash flows are uncertain, there might be a case for presenting a range of possible outcomes and applying probabilities. Expected values of NPVs orprobability distributions could then be presented. (a)Evaluation of machine, ignoring the time value of money (£) Labour savings ( 3 5 200 000 £0.25 for 3 years) 90 000 ) Extra labour cost for transferred workers (20% 3 5 £50 000 3 years) (18 000) Material saving a 2 000 ) Power saving 0.4 200 000 kW £0.05 for 3 years 12 000 ) Scrap value of new machine 10 000 ) Sale of old machine40 000 ) Savings in supervision costs ( 3 5 £10 000 3 years) 18 000 ) ––––––– Total savings over 3 years 154 000 ) Cost of new machine130 000 ) ––––––– Net savings 24 000 ) ––––––– Note a If the new machine is purchased, the material costs will be (£) (200 000 2 kg £70 /1000 3 years) 84 000 ) Less sale of old material (40 000 2 £25 /1000) (2 000) –––––– Net cost 82 000 ) –––––– If the new machine is not purchased, the stock of 80 000 kg can be used. Total purchases over 3 years will be(200 000 2 kg 3 years 80 000 kg) £75 /1000 84 000 Cash flow savings if the new machine is purchased 2 000 (b) Departmental profit and loss accounts (old machine) (£000) (£000) (£000) Sale of brushes 200 ) 200 ) 200 ) Variable production costs (200 000 £0.45 a ) (90) (90) (90) Overheads (60) (60) (60) Depreciation (£210 000 /7) (30) (30) (30) ––– ) ––– ) ––– ) Profit 20 ) 20 ) 20 ) Note a Variable cost per unit = labour (£0.25) + materials (2 £75 /1000) + electricity (£0.05). Departmental profit and loss accounts (new machine) (£000) (£000) (£000) Sale of brushes 200 ) 200 ) 200 ) Variable production costs (200 000 £0.27 a ) (54) (54) (54) Overhead: Supervision (4) (4) (4) Other (50) (50) (50) Depreciation (130 – 10) /3 years (40) (40) (40) Loss on sale of old machine b (50) Loss on sale of stocks c (4) ––– ) ––– ) ––– ) (2) 52 ) 52 ) ––– ) ––– ) ––– ) Solution IM 13.8 CAPITAL INVESTMENT DECISIONS: APPRAISAL METHODS 127 2013 2014 2015 2013 2014 2015 Solution IM 13.9 128CAPITAL INVESTMENT DECISIONS: APPRAISAL METHODS Notes a Variable cost per unit = labour ( 2 5 £0.25) + materials (2 £70 /1000) + electricity (0.6 £0.05) = £0.27 b ( 3 7 £210 000) sale proceeds (£40 000).

c 80 000 (£75 £25) /1000.

In 2013 there will be a loss of £2000 if the new machine is purchased. If the old machine is retained, the profit in 2013 will be £20 000. The manager may choose not to replace the machine if he or she focuses mainly on the impact ofthe decision on short-term performance. There is a conflict between the decision-making model and the performance evaluation model. For a more detaileddiscussion of this topic see ‘The effect of performance measurement on capitalinvestment decisions’ in Chapter 13.

(c) When the time value of money is incorporated into the analysis, the cash flow savings in the later years have a lower present value, and this will make theproject less attractive. If the machine’s life is extended, the benefits will accrue fora longer period and any replacement will be delayed. Consequently the machinewill yield a higher NPV.Details of the cost of capital are not given in the question. The effect of incor- porating the time value of money can be illustrated by selecting any discount rateand showing that the present value of the net savings will be less than £24 000.The higher the discount, the lower the benefit. At very high discount rates, theproject will have a negative NPV. The discounting process can also be used toillustrate that NPV is increased if project life is extended and cash flow savingsare maintained. Note that where machines are being compared which have different economic lives, it would be appropriate to use the equivalent annual cost method illustratedin Chapter 14.

(a) Present value of costs Discount Presentfactor value (£) (£) Raw material 7 000 21.243 a 148 701 Labour 5 000 21.243 a 106 215 Rental: Instalment 1 15 000 1.000 15 000 Instalment 2 15 000 0.942 b 14 130 Plant cost 32 400 1.000 32 400 Plant realizable value (14 000) 0.7876 c (11 026) ––––––– 305 420 ––––––– Notes a £7000 and £5000 are received each month from months 1 to 24. The discount factor is obtained from the cumulative discount tables for the 24-period row.

b One instalment in month 6 obtained from Appendix A of the main text.

c £14 000 is received in month 24. Present value of receiptsDiscount Month Receipt factor Present value (£) (£) 6 92 500 0.942 87 135 12 92 500 0.8874 82 084 18 92 500 0.836 77 330 24 92 500 0.7876 72 853 ––––––– 319 402 ––––––– NPV = £13 982 (£319 402 £305 420) (b) The PV of the receipts must be £319 402. Let X= each instalment. Then X+ 0.942 X+ 0.8874 X+ 0.836 X= £319 402 3.6654 X= £319 402 X = £87 140 Contract price = £348 560 (£87 140 4) The total mark-up is £12 160 (£348 560 £336 400) Percentage mark-up = (£12 160 /£336 400) 100 = 3.61% (c) The cash outflows in (a) and (b) are identical. However, there is a difference in the contract price and the timing of the instalments. Consequently the interestresulting from the costs is identical for both alternatives. The analysis willtherefore concentrate on the interest difference between the cash receipts.

Interest on Interest on original cash receipts revised cash receipts (£) (£) t 0 23 502 (£87 140 for 24 months) t 1 18 139 (£92 500 for 18 months) 17 088 (£87 140 for 18 months) t 2 11 729 (£92 500 for 12 months) 11 049 (£87 140 for 12 months) t 3 5 689 (£92 599 for 6 months) 5 359 (£87 140 for 6 months) t 4 0 –––––– –––––– 35 557 56 998 –––––– –––––– Note that the above interest calculations are done using the future value tables. For example, £23 502 is calculated as follows: £87 140 1.2697 (obtained for period 24) £87 140 = £23 502 The cash surpluses for each alternative (but ignoring interest on costs) are:

Original Proposed(£) (£) Revenues 370 000 348 560 Interest on receipts 35 557 56 998 Materials (168 000) (168 000) Labour (120 000) (120 000) Plant (cost – sale proceeds) (18 400) (18 400) Rental (30 000) (30 000) –––––– –––––– 69 157 69 158 –––––– –––––– CAPITAL INVESTMENT DECISIONS: APPRAISAL METHODS 129 (d) Several factors will influence the tender price. The relevant cost (avoidable costplus opportunity cost) will determine the minimum price below which it is not worth undertaking the contract. However, the question refers to long-termcontracts, and there is a strong argument for incorporating a provision for therecovery of a contribution to general fixed overheads when determining therelevant costs of the contract.The optimum price is the highest figure above the relevant cost (i.e. the minimum price) that the market will bear. It is unlikely that optimal prices can bedetermined, but a knowledge of the market, competitors’ prices, the existing stateof their order books and other potential orders is necessary for management to beable to make a sensible guess at a suitable selling price. It can be difficult accurately to predict future costs for long-term contracts.

Once the contract price has been agreed, it will be fixed. If the cost estimatesprove to be inaccurate, it is possible that the costs of the contract will exceed thetender price. The accuracy of the estimates will depend on the extent to which thecompany has undertaken similar contracts in the past, the length of the contractand the rate of inflation. The greater the uncertainty in the cost estimates, thegreater will be the need to increase the tender price to compensate for the extrarisk. It might be possible to mitigate the effects of inflation by agreeing to fix thetender price to some agreed price index and thus pass the risk of inflation on tothe customer. It is also important to consider the timing of the cash inflows and outflows when setting the tender price. The present value of the future outflows shouldrepresent the minimum price. The final tender price will be influenced by thetiming of the cash inflows. If the majority of the cash inflows are received towardsthe end of the contract, it will be necessary to tender a higher price in order tocompensate for the time value of money. 130 CAPITAL INVESTMENT DECISIONS: APPRAISAL METHODS CAPITAL INVESTMENT DECISIONS: THE IMPACT OF CAPITAL RATIONING, TAXATION, INFLATION AND RISK131 Solution IM 14.1 Solution IM 14.2 (a) A positive net present value indicates the potential increase in consumption which the project makes available after any funds have been repaid with interest. For a more detailed description see ‘The concept of NPV’ and ‘Calculating NPV’ inChapter 13.

(b) It is incorrect to use the borrowing rate as the discount rate. Presumably the firm is using up borrowing capacity by financing the project with 100% debtcapital. The implication of this is that it will be necessary to use less debt capitalin the future in order for the firm to maintain its target capital structure. Forexample, if the firm has a target 50% debt /equity ratio then it will be necessary to raise more equity capital in the future in order to maintain the target debt /equity ratio. For projects which are equivalent to the average risk of the firm’s existingassets the financing aspects should be incorporated into the analysis bydiscounting a project at the weighted average cost of capital based on thecompany’s target debt /equity ratio. See ‘Weighted average cost of capital’ in Chapter 14 for a more detailed description of the appropriate discount rate.

(c) For the answer to this question see ‘The effect of inflation on capital investment appraisal’ in Chapter 14.

(d) See ‘The opportunity cost of an investment’ in Chapter 13 and ‘Calculating risk- adjusted discount rates’ in Chapter 14 for the answer to this question.

(a) Computation of tax payable and capital allowances Year 1 2 3 4 (£000) (£000) (£000) (£000) Capital Allowances Opening WDV 10 000 7 500 5 625 4 219 Writing down allowances (25%) 2 500 1 875 1 406 4 219 (Balancing Allowance) Corporation Tax payable Sales 8 750 12 250 13 300 14 350Less: Materials 1 340 1 875 2 250 2 625 Labour 2 675 3 750 4 500 5 250 Overheads 185 250 250 250 ––––– ––––– ––––– ––––– Profit before depreciation 4 550 6 375 6 300 6 225 Capital allowance 2 500 1 875 1 406 4 219 ––––– ––––– ––––– ––––– Taxable profit 2 050 4 500 4 894 2 006 Tax payable at 30% 615 1 350 1 468 602 Payable one year later (year) 2 3 4 5 Capital investment decisions: the impact of capital rationing, taxation,inflation and risk Solutions to Chapter 14 questions 132CAPITAL INVESTMENT DECISIONS: THE IMPACT OF CAPITAL RATIONING, TAXATION, INFLATION AND RISK Computation of NPV Year 1 2 3 4 5 (£000) (£000) (£000) (£000) (£000) Sales 8 750 12 250 13 300 14 350 Outflows: Materials 1 340 1 875 2 250 2 625 Labour 2 675 3 750 4 500 5 250 Overheads 185 250 250 250 Working Capital Recovered (1000) Corporation Tax 0 615 1 350 1 468 602 ––––– ––––– ––––– ––––– ––––– Net Cash Flow 4 550 5 760 4 950 5 757 (602) Discount Factors at 17% 0.855 0.731 0.624 0.534 0.456 DCF 3 890 4 211 3 089 3 074 (275) (£000) Cumulative DCF 13 989 Capital expenditure and working capital 11 000 ––––– NPV 2 989 ––––– (b) The project should be accepted because it has a positive NPV.

(c) The report should include the following points: (i) The taxable profits are based on operating cash flows before depreciation.Capital allowances of 25% per annum on a reducing balance basis are available instead of depreciation for taxation purposes.

(ii) At the end of the project’s life a balancing allowance is available to ensure that the net cost of the asset has been allowed as a taxable expense over the life ofthe project.

(iii) Tax is assumed to be payable one year after the year end.

(d) The report should include the following points: (i) The NPV appraisal has been based on cash flows whereas the analysis in thequestion is based on profits using the accruals basis. This approach results intiming differences in the analyses relating to the payment of corporation taxand the incorporation of the capital cost of the asset.

(ii) The analysis in the question ignores the time value of money whereas it isincorporated in the NPV appraisal.

(iii) Interest payments are included in the analysis in the question whereas interest payments are not included in the NPV appraisal. This is because interestpayments are incorporated into the NPV appraisal within the discountingprocess which takes into account the cost of capital. Including interestpayments in the NPV appraisal will lead to double counting.

(a) If the Reclo machine is purchased there will be no incremental cash flows (or opportunity costs) for operating space since the company has adequate sparespace that has no alternative use. The feasibility survey is a sunk cost and theallocated overheads do not represent incremental cash flows. The charge from themarketing department is an internal charge and is not an incremental cash flow tothe company. Only the cost of the salesmen is a relevant incremental cash flow. Solution IM 14.3 Reclo cash flowsYear Year 012345 (£000) (£000) (£000) (£000) (£000) (£000) Sales at £3.50 per unit 455 478 502 527 ––– ––– ––– ––– Materials at £0.80 per unit 104 109 115 120 Labour at £1.30 per unit 169 177 186 196 Supervisor 20 21 22 23 Maintenance 20 42 44 46 Salesmen 45 47 50 52 ––– ––– ––– ––– 358 396 417 437 ––– ––– ––– ––– Net taxable operating cash flows 97 82 85 90 Tax at 25% with a one-year delay (24) (21) (21) (23) Investment outlay (175)Scrap value a 10 Tax saved on WDAs b 11 8 6 16 Working capital c (40) (2) (2) (2) (3) 49 –––– ––– ––– ––– ––– ––– Net cash flow (215) 95 67 70 82 42 –––– ––– ––– ––– ––– ––– NPV at 15% = +£32.1 NPV at 25% = £12.8 Using the interpolation formula shown in Chapter 13: IRR = 15% + 32.1 (35% 25%) = 22.2% 32.1 + (12.8) Notes a It is assumed that the scrap value has already been expressed in year 5 purchasing power.

b Year WDV Writing down allowance (WDA) Tax saving (25%) (£000) 1 175 44 11 2 131 33 839 8 2 5 6 47 3 1 8 5 5 55 45 (55 10) 11 In year 4 the balancing allowance is the WDV less the sale proceeds.

c It is assumed that the working capital in year 4 is released in year 5.

Bunger cash flows Year 012345 (£000) (£000) (£000) (£000) (£000) (£000) Taxable operating cash flows 50 53 55 59 Taxation at 25% (13) (13) (14) (15) Investment outlay (90)Scrap value 9 Tax savings on WDAs a 6437 Working capital (40) (2) (2) (2) (3) 49 –––– ––– ––– ––– ––– ––– (130) 48 44 44 54 41 –––– ––– ––– ––– ––– ––– CAPITAL INVESTMENT DECISIONS: THE IMPACT OF CAPITAL RATIONING, TAXATION, INFLATION AND RISK 133 134CAPITAL INVESTMENT DECISIONS: THE IMPACT OF CAPITAL RATIONING, TAXATION, INFLATION AND RISK Solution IM 14.4 NPV at 15% = +£25.2 NPV at 25% = –£5.3 IRR = 15% +25.2 (35% 25%) = 23.3% 25.2 + (5.3) Notes a Year WDV Writing down allowance (WDA) Tax saving (25%) (£000) 19 0 2 3 6 26 7 1 7 4 35 0 1 3 3 43 7 9 2 5 28 19 (28 9) 5 In year 4 the balancing allowance is the WDV less the sale proceeds.

(b) The incremental yield is calculated by considering the increments of cash flows of Reclo less Bunger. The incremental cash flows are:

Year 012345 (£000) (£000) (£000) (£000) (£000) (£000) Cash flows: Reclo (215) 95 67 70 82 42 Bunger (130) 48 44 44 54 41 Incremental (85) 47 23 26 28 1 The IRR on the incremental project is approximately 19.7%. The incremental project should be accepted only if the cost of capital is less than 19.7%. Acceptance of the incremental project means that having initially chosen the project with thehigher IRR (Bunger) we should move from Bunger to Reclo. This implies thatReclo should be purchased as long as the cost of capital is less than 19.7%. If thecost of capital exceeds 19.7% Bunger should be purchased but neither machineshould be purchased if the cost of capital exceeds 23.3% (i.e. Bunger’s IRR). Theabove comments are consistent with the NPVs that have been calculated with Reclohaving a higher NPV at 15%.

(c) For a discussion of the limitations of the IRR method see ‘Comparison of net present value and internal rate of return’ in Chapter 13.

(a) (£000) t 0 t 1 t 2 t 3 t 4 t 5 Year ending 2001 2002 2003 2004 2005 Initial outlay (256)Tax on WDAs a 22.40 16.80 12.60 Savings 60 66.00 72.60 79.86 Tax on savings (21.10) (23.10) (25.41) (27.95)Sale of new machine 108.00 Sale of old machine 40 Balancing charge (14.00) Net cash flow (216) 60 53.30 66.30 175.05 (27.95) NPV at 15% = £6334 CAPITAL INVESTMENT DECISIONS: THE IMPACT OF CAPITAL RATIONING, TAXATION, INFLATION AND RISK135 Note a Calculation of tax on writing down allowances (WDAs):

(£000) 2013 2014 2015 2016 Opening WDV 256 192 144 108 Sale proceeds (108) WDA (25%) (64) (48) (36) Closing WDV 192 144 108 Nil Tax on WDAs (35%) 22.40 16.80 12.60Timing t 2 t 3 t 4 (b) The answer to this question requires a calculation of the incremental profits and the incremental investment from replacing the machine for 2013 and 2014.

Incremental profits (2013) (£000) Cost savings 60.00 ) Depreciation on new machine (256 108) /4 (37.00) Savings in depreciation of old machine (50 /4) 12.50 ) Loss on sale of old machine (10.00) Additional taxes a (12.60) ––––– ) 12.90 ) ––––– ) Incremental profits ( ) (£000) Cost savings 66.00 ) Depreciation on new machine (37.00) Savings in depreciation of old machine 12.50 ) Additional taxesa (6.30) ––––– ) 35.20 ) ––––– ) Incremental capital employed (2013) (£000) Closing WDV of new machine (256 37) 219.00 ) Closing WDV of old machine retained (50 12.5) 37.50 ) ––––– ) 181.50 ) ––––– ) Incremental capital employed ( ) (£000) Closing WDV of new machine (256 74) 182 ) Closing WDV of old machine retained (50 25) 25 ) ––– ) 157 ) ––– ) Return on incremental investment 2013 = 7.1% (12.90 /181.50) 2014 = 22.4% (35.20 /157) In both years replacing the equipment will result in a decline in ROI. 2014 2014 136CAPITAL INVESTMENT DECISIONS: THE IMPACT OF CAPITAL RATIONING, TAXATION, INFLATION AND RISK Note a Additional taxes arising from the investment are calculated as follows:

2013 2014 (£000) (£000) Cost savings 60 66 WDA (64) (48) Balancing charge 40 ––– ––– Increase in taxable profits 36 18 ––– ––– Tax at 35% 12.6 6.3 (c) The report should include the following points: (i) A recommendation that the project should be accepted is justified on thebasis of the NPV rule.

(ii) An explanation that NPV is based on the assumption that the share price is the discounted present value of the future dividend stream and the market isaware of the effect on future cash flows arising from an investment decision.NPV takes no account of the effects of investment decisions on short-runreported profits. It is assumed that share price is based on future cash flowsarising from an investment.

(iii) Acceptance of the project will lead to a decline in ROI in 2001 and 2002, but ROI is likely to increase in later years. It is assumed that the lower ROI in theearly years will not adversely affect the share price.

(iv) The NPV calculation was based on the company’s overall cost of capital of15%. This rate would be appropriate only if the project’s risk is equivalent tothe average risk of the firm’s existing assets.

(v) The conflict between the performance measurement system and the NPV decision-making model (see ‘The effect of performance measurement oncapital investment decisions’ in Chapter 13 for a detailed discussion of thispoint). The report should draw attention to the conflict arising with thereplacement decision faced by the Towelling division (the project has apositive NPV, but ROI declines in the short run). Managers will tend toselect the alternatives which have the most beneficial effect on the perfor-mance measure against which they are judged. It is therefore important that aperformance measurement system is implemented which encouragesmanagers to take decisions which are in the best interests of the company as awhole (in other words, to achieve goal congruence). If top managementplaces too much emphasis on short-term performance then managers willtend to select those projects which have the most favourable impact in theshort-term even if such decisions are at the expense of projects which aremore beneficial in the long term. It is therefore important that performanceis measured in accordance with criteria which will encourage managers topursue a company’s long-term objectives. (a) The present values for the various replacement periods are as follows:Present value of cash outflows if the fleet is replacedat the end of year 123 4 5 (£) (£) (£) (£) (£) Cash flows 1. Costs 29 800 0.885 26 373 26 373 26 373 26 373 26 373 Resale (35 000) 0.885 (30 975) Purchase 55 000 0.885 48 675 2. Costs 33 700 0.783 26 387 26 387 26 387 26 387 Resale (24 000) 0.783 (18 792) Purchase 55 000 0.783 43 065 3. Costs 39 000 0.693 27 027 27 027 27 027 Resale (12 000) 0.693 (8 316) Purchase 55 000 0.693 38 115 4. Costs 45 100 0.613 27 646 27 646 Resale (2000) 0.613 (1 226) Purchase 55 000 0.613 33 715 5. Costs 72 000 0.543 39 096 Resale (200) 0.543 (109) Purchase 55 000 0.543 29 865 ––––––– ––––––– ––––––– ––––––– ––––––– Present values 44 073 77 033 109 586 139 922 176 285 Note that if a replacement period of one year is selected, the cash flows will be repeated in years 2, 3, 4 and so on. If the two-year period is selected, purchasesand resale will take place at the end of year 2, year 4 and so on. With a three-yearreplacement chain, purchase and resale will take place in years 3, 6, 9 and so on. Inorder to recognize these differences in cash flows, the present values should be calculated over a common time horizon for the various replacement periods (1, 2, 3, 4 and 5 years). Therefore the lowest common multiple will result in a commontime horizon of 60 years.

An alternative approach, which is equivalent to establishing the lowest common time horizon (see Learning Note 14.1 on the website ) and which recognizes the Replacement period (years) 1 2 3 4 5 (£) (£) (£) (£) (£) Present value 44 073 77 033 109 586 139 922 176 285 Annual equivalent factor at 13% 0.885 1.668 2.361 2.974 3.517 Annual equivalent annuity 49 300 46 183 46 415 47 017 50 114 The minimum equivalent annual cost is for a two-year replacement cycle. Therefore a two-year replacement cycle period should be selected.

(b) The main problem with this type of analysis is that it is assumed that the replacements will be identical taxis with the same cash flows as the old taxi fleetuntil the lowest common time horizon is reached. It is unlikely that costs, capitalallowances and taxation rates will remain unchanged over this time horizon. Inaddition, the cash flows have not been adjusted for inflation. Because of thesedifficulties, there might be a case for evaluating the alternatives over a selectedtime horizon which is sufficiently short to enable reasonable estimates to be madeand estimate the terminal values for each alternative at the end of the timehorizon. This approach is illustrated in Chapter 14.

CAPITAL INVESTMENT DECISIONS: THE IMPACT OF CAPITAL RATIONING, TAXATION, INFLATION AND RISK 137 Solution IM 14.5 potential replacement chains, is to use the equivalent annual cost method. In this approach, the annual equivalent annuity is estimated. The calculations are as follows: 138CAPITAL INVESTMENT DECISIONS: THE IMPACT OF CAPITAL RATIONING, TAXATION, INFLATION AND RISK (a) The calculation of the incremental cash flows and NPVs for projects 1 and 2 are shown below: Estimate of tax liability, Project 1 Year 123 (£000) (£000) (£000) Incremental sales 840 1840 2176 Incremental operating costs 569 970 1315 ––– ––– –––– Incremental operating profits 271 870 861Tax (35%) 95 304 301 Tax benefit from incremental depreciation 175 131 98 ––– ––– –––– Tax payable (80) 173 203 ––– ––– –––– Note that interest is not included in the above calculations because the tax effect isalready reflected within the discount rate. Cash flows, Project 1 Year 12 3 4 (£000) (£000) (£000) (£000) Sales 840 1840 2176 Operating costs 569 970 1315 ––– ––– –––– 271 870 861 Taxation (payable) recoverable 0 80 (173) (203) Salvage value 750 Tax effect of balancing allowance a 33 ––– ––– –––– ––– Net cash flow 271 950 1438 (170) Discount factor at 8% 0.926 0.857 0.794 0.735 Present value 251 814 1142 (125) Present value at 8% 2082 Investment outlay 2000 –––– NPV 82 –––– Note a Balancing allowance = [750 (2000 1156)] 0.35.

Estimate of tax liability, Project 2 Year 123 (£000) (£000) (£000) Incremental sales 1930 2876 3854 Incremental operating costs 1380 1820 2160 –––– –––– –––– Incremental taxable profit 550 1056 1694 Tax (35%) 192 370 593 Tax benefit from incremental depreciation 306 230 172 –––– –––– –––– Tax payable (recoverable) (114) 140 421 Solution IM 14.6 Cash flows, Project 2Year 1234 (£000) (£000) (£000) (£000) Sales 1930 2876 3854 Operating costs 1380 1820 2160 –––– –––– –––– 550 1056 1694 Taxation 114 (140) (421)Salvage value 1500 Tax effect of balancing charge a (8) ––– –––– –––– ––––– 550 1170 3054 (429) Discount factor at 8% 0.926 0.857 0.794 0.735 Present value 509 1003 2425 (315) (£000) Present value at 8% = 3622 Investment outlay = 3500 –––– NPV = 122 –––– Note a Balancing charge = [1500 (3500 2023)] 0.35 Project 2 should be accepted, since it has the higher NPV.

(b) Additional factors to be considered include: (i) Have all alternative projects been considered?

(ii) Are the projects of similar risk? Is the riskiness of the projects similar to the average risk of the current projects? If the projects are not of risk equal orsimilar to the risk of the existing assets then it is inappropriate to use thecompany’s existing weighted average cost of capital as the discount rate?

(iii) Are there any important qualitative factors which have not been consideredin the analysis in (a)?

(c) The projects will now have unequal lives. In order to take this into account, the equivalent annual value method can be used. The calculations are as follows: Project 1 Year 12345 (£000) (£000) (£000) (£000) (£000) Cash flow 271 950 1438 77 (188) Discount factor at 8% 0.926 0.857 0.794 0.735 0.681 Present value 251 814 1142 57 (128) NPV = £136 000 (2136 2000) Annual equivalent values: Project 1 = £34 060 (£136 000 /3.993) Project 2 = £36 836 (£122 000 /3.312) Note that 3.993 and 3.312 represent the annuity factors for four and five years respectively. Project 2 should still be undertaken, since it has the highest equivalent value. It is assumed that the cash flow patterns will be repeated until a common time horizon is reached.

(d) For the answer to this question see ‘Comparison of net present value and internal rate of return’ and ‘Payback method’ in Chapter 13. CAPITAL INVESTMENT DECISIONS: THE IMPACT OF CAPITAL RATIONING, TAXATION, INFLATION AND RISK 139 140CAPITAL INVESTMENT DECISIONS: THE IMPACT OF CAPITAL RATIONING, TAXATION, INFLATION AND RISK Calculation of return on average investment Year 12345 ($000) ($000) ($000) ($000) ($000) Sales: Parcels a 682 1075 1129 1185 1244 Sales: Lettersb 2048 2867 3010 3160 3318 –––– –––– –––– –––– –––– 2730 3942 4139 4345 4562 –––– –––– –––– –––– –––– Wages c 2457 2580 2709 2844 2986 Premises d 158 165 174 182 191 Running and maintenance: Vans e 210 265 333 420 529 Trucks e 84 106 133 168 212 Advertising 525 276 –––– –––– –––– –––– –––– Cash expenses 3434 3392 3349 3614 3918 Depreciation f 232 232 232 232 232 –––– –––– –––– –––– –––– 3666 3624 3581 3846 4150 –––– –––– –––– –––– –––– Taxable profit (936) 318 558 499 412Taxation g (374) 127 223 200 165 –––– –––– –––– –––– –––– Profit after tax (562) 191 335 299 247 Average investment is $1 160 000 h = $580 000 2 Average annual after tax return is [( 562) + 191 + 335 + 299 + 347] = $102 000 5 Annual after tax return on investment = 102 000 = 17.6% 580 000 Net present value calculation Year 0123456 ($000) ($000) ($000) ($000) ($000) ($000) ($000) Sales 2730 3942 4139 4345 4562 Cash expenses 3434 3392 3349 3614 3918 Taxation (374) 127 223 200 165Initial investment h 1160 –––– ––– ––– ––– ––– ––– ––– (1160) (704) 924 663 508 444 (165) Discount factor (14%) 0.877 0.769 0.675 0.592 0.519 0.456 Present value (1160) (617) 711 448 301 230 (75) Net present value = ($162 000) Notes and assumptions a Year 1 = 500 parcels $5.25 5 days 52 weeks, year 2 = 750 parcels $5.25 (1.05) 5 days 52 weeks, year 3 = year 2 1.05, year 4 = year 3 1.05, year 5 = year 4 1.05.

b Year 1 = 15 000 $0.525 5 days 52 weeks, year 2 = 20 000 $0.525 (1.05) 5 days 52 weeks. From year 3 onwards, prices are assumed to increase at 5% per annum.

c Year 1 = 180 $13 000 (1.05). It is assumed that the salaries of the five managers are payable whether or not the new service is introduced, and are not Solution IM 14.7 CAPITAL INVESTMENT DECISIONS: THE IMPACT OF CAPITAL RATIONING, TAXATION, INFLATION AND RISK141 relevant cash flows. Other assumptions could be made. For example, if it is planned to make the managers redundant, the salaries would be relevant from theplanned date of redundancy. Outflows from year 2 onwards have been increasedby 5% for inflation. d Year 1 = $150 000 (1.05). Cash flows are assumed to increase at 5% per annum from year 2 to year 5. e Vans: 100 $2000 1.05 (year 1), year 2 = 100 $2000 (1.20) (1.05) 2 .

Trucks: 20 $4000 1.05 (year 1), year 2 = 20 $4000 (1.20) (1.05) 2 , year 3 = year 2 1.20 1.05, year 4 = year 3 1.20 1.05, year 5 = year 4 1.20 1.05.

f $1 160 000 /5 years.

g It is assumed that the estimated annual profits of the postal service are in excess of $500 000 per annum and that incremental income will be subject to taxation at a rate of 40%.

h Initial investment = (100 $8000) + (20 $18 000).

Note that market research is a sunk cost.

The report should include the following comments: (i) The proposed new investment satisfies the return on investment criterion of 5% per annum (excluding financing costs), but has a negative expected NPV.

(ii) The government criteria relate to the overall performance of the service as a whole and not individual projects. It might be possible that the service as awhole satisfies the criteria, even though the proposed new service does not.

(iii) Qualitative factors have not been taken into account. There might beadditional financial advantages to the economy, arising from the introductionof a postal service, which have not been included in the financial appraisal.

(iv) The discount rate used in the NPV calculation assumes that the risk of thenew service is the same as the postal service as a whole. If this is not the case,the cash flows should be discounted at the revised risk adjusted discount rate.

(v) The estimates are based on constant demand after the first year. Is this correct? The possibility of demand increasing after the first year should beinvestigated. Other possibilities for increasing net cash flows should also beinvestigated. For example, can vehicle costs and wages be reduced?

(vi) Consideration should be given to evaluating the project over a longer timehorizon than five years. The vehicles would need replacing after five years,but it is unlikely that the advertising costs (which are significantly in excess ofthe negative NPV) will be repeated.

(vii) Conclusion: the project has a negative NPV and the financial evaluationsuggests that it should not be accepted. However, attention should bedirected to the factors specified above and the project should be re-evaluated over a 10-year time horizon. If the cash flows are repeated over a10-year horizon (without the advertising costs) it is likely that it will yield apositive NPV.

(a) Average profits do not incorporate the time value of money or incremental cash flows. Profits represent a periodic performance measure. Capital investmentdecisions should be based on cash flows and not accounting profits.Payback is a widely used appraisal method. It is a particularly useful method where a firm faces liquidity constraints and requires a fast repayment ofinvestments. The payback method may also be appropriate in situations whererisky investments are made in uncertain markets that are subject to fast design andproduct changes or where future cash flows are extremely difficult to predict. Itsmajor weakness is that it ignores the time value of money and cash flows after thepayback period is complete. Solution IM 14.8 Discounted payback does take into account the time value of money but it ignores cash flows after the payback period. It may also lead to the rejection of positive NPV projects if they do not recoup the investment within the paybackperiod set by management. Alternatively, because the cash flows are discountedprojects will not be accepted that have negative NPVs. Director C is focusing on profits rather than NPVs. Cost of capital has been ignored. If the risk-adjusted cost of capital is also 10% then the project will have azero NPV. It is extremely unlikely that the risk-adjusted cost of capital will be lessthan the returns available from investing in financial markets.

(b) Investment 1: cash flows Year 0123456 (£000) (£000) (£000) (£000) (£000) (£000) (£000) Initial cost 500 Sales a 400 491 594 712 847 Production costs b 260 327 416 583 706 ––– ––– ––– ––– ––– Taxable cash flow 140 164 178 129 141Tax at 25% b (35) (41) (45) (32) (35) Taxed saved by depreciation 31 24 18 13 10 Balancing allowance saving c 30 ––– ––– ––– ––– ––– ––– –– Net cash flow (500) 140 160 161 102 122 5Discount factor d 1 0.865 0.749 0.648 0.561 0.485 0.420 Present value e (500) 121 120 104 57 59 2 Payback period: noneExpected NPV = (£37 000) Investment 2: cash flows Year 0123456 (£000) (£000) (£000) (£000) (£000) (£000) (£000) Initial cost (175) Sales a 500 654 760 829 988 Production costs b 460 567 653 764 889 ––– ––– ––– ––– ––– ––– Taxable cash flow 40 87 107 65 99 Tax at 25% (10) (22) (27) (16) (25) Tax saved by depreciation 11 8 6 5 4Balancing allowance saving c 10 ––– ––– ––– ––– ––– ––– –– Net cash flow (175) 40 88 93 44 88 (11) Discount factor d 1 0.865 0.749 0.648 0.561 0.485 0.420 Present value e (175) 35 66 60 25 43 (5) Discount payback period: approximately 3–5 years Expected NPV = £49 000 Notes a The cash flows have been expressed as nominal /money cash flows. It is assumed that cash flows have been expressed in year 1 purchasing power. Therefore year 2 cash flows have been increased by 9%, year 3 by (1.09) 2 , year 4 by (1.09) 3 and so on. Alternatively, cash flows can be expressed in real terms and discounted at thereal discount rate. If this approach is used the depreciation tax shields must bedeflated by the inflation rate because they do not rise in line with the general rateof inflation.

b (T 1) cash flows 25%. 142 CAPITAL INVESTMENT DECISIONS: THE IMPACT OF CAPITAL RATIONING, TAXATION, INFLATION AND RISK CAPITAL INVESTMENT DECISIONS: THE IMPACT OF CAPITAL RATIONING, TAXATION, INFLATION AND RISK143 c The WDV of investment 1 at the end of year 5 is £118 000. Therefore the balancing allowance at the end of the project’s life is £118 000 25% tax rate = £29 500. Investment 2 has a WDV at the end of year 5 of £41 000 resulting in a balancing allowance of £10 250 (£41 000 25%).

d The cash flows have been expressed in nominal /money terms. Therefore the nominal /money discount rate has been used. It is calculated by multiplying the real discount rate (1.07) by [1 + the expected general rate of inflation (8%)] giving adiscount rate of 15.56%. The discount factors are 1 /1.1556 for year 1, 1 /(1.1556) 2 for year 2, and so on.

e The financing costs of the investment have not been included in the cash flows because the financing cost is already incorporated in the discount rate. Internalfunds do not represent a zero cost of financing since they have an opportunitycost in terms of the returns that could have been earned from investing the fundselsewhere.

(c) Non-financial factors that might influence the investment include the following. (i) Investment 2 is more labour-intensive and creates more jobs.

(ii) Investment 2 is dependent on the availability of appropriate skilled labour.

(iii) The impact of any environmental factors should be taken into account. (iv) The reliability of both items of equipment should be considered.

(a) The annual net savings are: (£) Data processing costs saved 46 000 Less: Maintenance costs (2 000) Less: Staff costs (15 000) Less: Stationery and related costs (4 000) –––––– 25 000 (annual saving discount factor) investment cost = NPV The discount factor at which NPV is zero is: (£25 000 DF) £161 500 = 0 DF = £161 500 = 6.46 £25 000 By inspecting the discount tables for the 5% column, it can be seen that 5% and eight years yields a discount factor of 6.46. Therefore the life which produces a zeroNPV is eight years.

(b) (i) Six-year life: NPV at 5% = (£25 000 5.0757) £161 500 = £34 607 NPV at 0% = (£25 000 1.00 6 years) £161 500 = £11 500 The IRR is negative, and a precise calculation is unlikely to provide any meaningful information.

(ii) Indefinite life: £25 000 DF £161 500 = 0 DF = 6.46 An indefinite life implies infinity. However, the discount factorsfor 50 years will provide a close approximation to the discountfactor when discounting to infinity. The discount rate for 50years with a discount factor of 6.46 is between 15 and 16%.Therefore IRR is appropriately 15.5%. Alternatively the per-petuity formula can be used: Solution IM 14.9 £25 000= £161 500 discount rate Discount rate = 15.5% (c) Let X= annual running costs. Then (£46 000 7.722) 7.722 X £161 500 = 0 7.722 X= £193 712 X = £25 086 (d) The first stage should be to calculate the NPV using the expected value of the relevant variables. A risk-adjusted discount rate should be used to discount the cash flows. The viability of the project can then be examined by testing itssensitivity to changes in the values of the crucial variables. Sensitivity analysistakes each variable in turn and calculates the critical value which will result in theproject having a zero NPV, assuming that the estimated values of all the othervariables are correct.The critical life of the project is eight years, and, assuming an indefinite life, the project will have a positive NPV as long as the cost of capital is less than 15.5%.Alternatively if the life of the computer is only six years, the project is onlyacceptable if the company has a negative cost of capital in real terms (i.e. the costof capital is lower than the level of inflation). In part (c) it was shown that if anoptimistic estimate of project life is taken, annual running costs can increase to£25 086 before the NPV becomes negative. The accountant should present the estimated NPV and provide details of the values of the relevant variables on which the NPV calculations are based. The critical values of these variables based on varying assumptions should then betabulated to give the decision-maker an indication of the risk associated with theproject.

(e) Sensitivity analysis is a crude method of analysing risk, because the critical variable which is calculated is based on the assumption that the estimates of the othervariables are correct. Risk analysis could be improved by establishing probabilitydistributions for each variable. Simulation techniques can then be used to estimate aprobability distribution of the possible net present values from the project.Better estimates of the uncertain variables might be obtained by discussing with users of similar systems their experiences from implementing and running the newsystem. The question does not provide any information on how the 5% cost of capital is determined. Is it a risk-adjusted rate or the company’s overall cost of capital? Theoverall cost of capital should be used only to evaluate projects of similar risk toexisting projects. It is quite likely that the computer project is not of similar risk to existing projects. The project should therefore be discounted at a lower rate if it is below-average risk and at a higher rate if it is above-average risk. The precise rate is difficult to specify and this is the one variable where it might be appropriate toascertain how sensitive the NPV is when different discount rates are used. Inflation can be dealt with by discounting real cash flows at the real discount rate or discounting cash flows which are adjusted for inflation at a discount ratewhich incorporates a premium for inflation. The accountant has used cash flowswhich are expressed in current prices and discounted at a real rate. Estimatingcash flows expressed in terms of current prices is only appropriate when all cashflows increase at the average rate of inflation. If the cash flows are subject todifferent rates of inflation then it is preferable to adjust each component by thespecific rate of inflation and discount the inflation-adjusted cash flows at a moneyrate cost of capital (i.e. a rate which incorporates inflation). 144 CAPITAL INVESTMENT DECISIONS: THE IMPACT OF CAPITAL RATIONING, TAXATION, INFLATION AND RISK CAPITAL INVESTMENT DECISIONS: THE IMPACT OF CAPITAL RATIONING, TAXATION, INFLATION AND RISK145 (a)Workings Year 1 Year 2 Year 3(£) (£) (£) Contribution (internal manufacture) 10.50 (£10 1.05) 11.03 (£10 1.05 2 ) 11.58 External purchases: Selling price 52.50 (£50 1.05) 55.13 57.88 Internal costs 26.25 (£25 1.05) 27.56 28.94 Contribution before purchase cost 26.25 27.57 28.94 Purchase cost 20.00 20.00 20.00 Note that external purchase costs are paid in advance. Therefore payments occur at t 0 , t 1 and t 2 .

Present value of fixed costs: £10 000/1.15 + £12 500 /(1.15) 2 + £15 000 /(1.15) 3 = £28 021 Economic condition A Year 1 Year 2 Year 3 Contribution per unit (£) 10.50 11.03 11.58 Demand 10 000 12 000 14 400 Total contribution (£) 105 000 132 360 166 752 (£) PV of contribution 301 129 PV of fixed costs (28 021) Investment cost (375 + 25) (400 000) ––––––– NPV (126 892) ––––––– Economic condition B Contribution per unit (£) 10.50 11.03 11.58 Internal output 15 000 18 000 a 20 000 a Total contribution (£) 157 500 198 540 231 600 (£) (£) PV of contribution 439 362 PV of units bought in [1600 a £28.94 = £46 300 /(1.15) 3 ] 30 446 Less PV of purchase costs 1200 a 20 = £40 000 /(1.15) 2 ] 30 245 201 –––––– PV of fixed costs (28 021) Investment cost (400 000) ––––––– NPV 11 542 ––––––– Note a Demand in year 3 is 21 600 units. Therefore 1600 units demand must be met from external purchases. However, the contract requires that purchases must be in batches of 2000 units. It is assumed that the surplus purchases have norealizable value. Solution IM 14.10 146CAPITAL INVESTMENT DECISIONS: THE IMPACT OF CAPITAL RATIONING, TAXATION, INFLATION AND RISK Economic condition C Year 1 Year 2 Year 3 Contribution per unit (£) 10.50 11.03 11.58 Internal demand 20 000 20 000 20 000 Total contribution (£) 210 000 220 600 231 600 Sale of external production: Year 2: 4000 £27.57 110 280 Year 3: 8000 a £28.94 231 520 External purchase: Year 2: 4000 £20) (80 000) Year 3: 8000 £20) (160 000) Total contribution 130 000 170 880 463 120 (£) PV of total contribution 546 762 PV of fixed costs (28 021) Investment cost (400 000) ––––––– NPV (118 741) ––––––– Note a Total demand in year 3 is 28 800 units, but external purchases can only be obtained in batches of 2000 units. It is therefore economic to purchase 8000 units. The purchase of a final batch of 2000 units to meet the unfulfilled demandof 800 units cannot be justified.

Expected NPV= ( £126 892 0.25) + (£11 542 0.45) + (£118 741 0.30) = £9093 On the basis of the expected NPV decision rule, the refurbishment is justified.

(b) The expected value represents the weighted average of the possible outcomes. However, the expected value calculation will be flawed if biased estimates of the range of outcomes are presented. It should also be noted that the expected valuerepresents the average long-run outcome if a project were undertaken many times. Itis most unlikely that the actual outcome will equal the expected value for ‘one off’decisions. Care must therefore be taken when interpreting expected values.Expected values focus on averages and ignore the range of variations around the mean. Risk is therefore ignored when decisions are based on expected values.In part (a) the project has an expected NPV of £9093, but this does not drawattention to the fact that the NPVs can range from £126 892 to + £119 741.

In order to incorporate risk into the analysis, finance theory advocates that cash flows expressed in expected values should be discounted at a risk-adjusted costof capital. The risk-adjusted cost of capital can be determined by using the capitalasset pricing model. The NPV calculation in (a) is based on a cost of capital of 15%.It is assumed that this rate is the company’s risk-adjusted discount rate. This ratewould only reflect the risk-adjusted cost of capital for the refurbishment project if itsrisk is equivalent to average firm risk. A higher cost of capital should be used if theproject’s risk is greater than the average risk for the firm’s existing assets. To summarize, expected values ignore risk. The latter is incorporated into the analysis by discounting cash flows expressed in expected values at the risk-adjusted cost of capital. The resulting risk-adjusted expected NPV represents theaverage outcome. To assess how sensitive the expected NPV calculation is to thechanges in the variables which are used to calculate it, sensitivity analysis shouldbe employed. THE BUDGETING PROCESS147 Solution IM 15.1 Solution IM 15.2 Solution IM 15.3 Solution IM 15.4 Solution IM 15.5 (a) See ‘The multiple functions of budgets?’ in Chapter 15 for the answer to this question.

(b) See ‘Administration of the budget process’ and ‘Stages in the budget process’ in Chapter 15 for the answer to this question.

(a) See ‘Stages in the budget process’ in Chapter 15 for the answer to this question. (b) See ‘Computerized budgeting’ in Chapter 15 for the answer to this question. See ‘Zero-base budgeting’ in Chapter 15 for a description of zero-base budgeting and an explanation of how it differs from other more traditional forms of budgeting. In profit-orientated organizations those costs which are of a discretionary nature such as serviceand support activities are appropriate candidates for zero-base budgeting. Examples ofdepartments which fall into this category include personnel, research and development,accounts, and data processing. (a /b) See ‘Zero-base budgeting’ in Chapter 15 for the answer to these questions.

(c) It is preferable to introduce zero-base budgeting selectively rather than ‘across the board’. The approach should initially be applied to those activities where immediate benefits are likely. This might lead to a greater acceptance by itsusers. Care should be taken in selecting the activities to which zero-basebudgeting is to be applied. In Chapter 15 it will have been noted that it is bestsuited to non-manufacturing activities and non-profit making organizations.When the system is introduced, meetings and seminars should be arrangedexplaining the principles of zero-base budgeting. Because zero-base budgeting iscostly and time-consuming, there are strong arguments for selective ad hoc applications which are likely to yield benefits. It is unlikely that a universalapplication of zero-base budgeting in an organization can be justified.

(a /b) See ‘Zero-base budgeting’ in Chapter 15 for the answer to this question.

(c) The problems that might be met in introducing zero-base budgeting include: (i) The implementation of zero-base budgeting might be resisted by staff.Traditional incremental budgeting tends to protect the empire that amanager has built. Zero-base budgeting challenges this empire, and sothere is a strong possibility that managers might resist the introduction ofsuch a system.

(ii) There is a need to combat a feeling that current operations are efficient.

(iii) The introduction of zero-base budgeting is time-consuming. (iv) Top-management support may be lacking.

(d) See ‘Zero-base budgeting’ in Chapter 15 for the answer to this question.

The budgeting process Solutions to Chapter 15 questions 148THE BUDGETING PROCESS Solution IM 15.6 Solution IM 15.7 Solution IM 15.8 Solution IM 15.9 For the steps in the preparation of master budgets see ‘Stages in the budgeting process’ in Chapter 15.The main budgets that should normally be prepared are:

(i) sales budget; (ii) production budget; (iii) direct material usage budget; (iv) direct materials purchase budget; (v) direct labour budget; (vi) factory overhead budget; (vii) selling expenses budget; (viii) administration budget; (ix) cash budget;(x) budgeted balance sheet and profit and loss account.

For comments and illustrations of the above budgets see the detailed illustrationpresented in Chapter 15. (a /b) See ‘The budget period’ in Chapter 15 for a description of rolling budgets and an explanation of how a rolling budget system works. The ‘CIMA Terminology’ defines a rolling budget as ‘The continuous updating of a short-term budget byadding, say, a further month or quarter and deducting the earliest month orquarter so that the budget can reflect current conditions.’ (c) The following are some advantages of rolling budgets: (i) Actual performance is likely to be compared with a more realistic targetbecause budgets are being constantly reviewed and updated.

(ii) Planning is not something that takes place once per year when the budget is being formulated. With rolling budgets, budgeting is a continuous process,and managers are encouraged constantly to look ahead and review futureplans.

(iii) The work load of the budget staff is spread throughout the year rather than the whole budget process being concentrated into a few months.

(d) Problems that may be encountered include:

(i) The work load is increased in comparison with preparing annual budgetsonce per year.

(ii) Because budgets are reviewed and changed at the end of each quarter, there may be a danger when a new quarter’s budget is added that staff will notgive sufficient attention to preparing this budget because they know it islikely to be changed in the revision process.

(iii) Too much attention might be given to the continuous short-term aspects of budgets at the expense of long-term planning.

See ‘The multiple functions of budgets’ and ‘Conflicting roles of budgets’ in Chapter15 for the answer to this question.

(a) (i) Sales budget in quantity and value July August September Total Sales units 400 300 600 1 300 Sales value (£) 100 000 75 000 150 000 325 000 (ii) Production budget in units Sales 1300 Closing stock 225 –––– 1525 Opening stock (200) –––– Good output required 1325 Normal loss (1325 × 1/9) 147 –––– Production required 1472 –––– (iii)Raw material usage budget Production (units) 1472 (kg) Material A (at 3 kg per unit) 4416 Material B (at 2 kg per unit) 2944 Material C (at 4 kg per unit) 5888 (iv) Raw material purchases budget A B C Total (kgs) (kgs) (kgs) Kgs used 4 416 2 944 5 888 Stock increase (20%) 200 80 120 –––––– –––– –––––– Purchases in kgs 4 616 3 024 6 008 –––––– –––– –––––– Unit cost £3.50 £5.00 £4.50 Purchases cost £16 156 £15 120 £27 036 £58 312 (v) Labour requirements budget Production in units 1 472 Unit labour hours 10 Total hours 14 720 Cost per hour £8.00 Total cost £117 760 (b) The principal budget factor (also known as the limiting factor) is the factor that constrains or limits the activities of the organization during a budget period.During the budget process, the principal budget factor is the foundation uponwhich all of the budgets must be based and which constrains activity from beingexpanded. For example, if machine hours are the principal budget factor, theproduction budget, sales budget and all of the remaining budgets will be restrictedto the maximum output from the available machine hours. Prior to thepreparation of the budgets it is necessary for management to identify the principalbudget factor, since this factor will determine the point at which the annual budgeting process should begin.

(c) Labour requirements budget Product Z Production in units = D15 Labour hours per unit = A5 Total hours = D15*A5 Cost per hour = D5 Total cost = D5*E30 The labour requirements budget would be drawn from a spreadsheet containing the basic input information (such as cells A5, D6, etc) and a working area fromwhich information is derived and which then cascades throughout thespreadsheet. A change in input information, or any relationships within themodel, is immediately reflected in the output information. THE BUDGETING PROCESS 149 150THE BUDGETING PROCESS Solution IM 15.10 Solution IM 15.11 (a) (i)Sales budget Quarter 1 Quarter 2 Quarter 3 Quarter 4 Total Sales units 40 000 50 000 30 000 45 000 165 000 Unit price (£) 150 150 160 160 Revenue (£000) 6 000 7 500 4 800 7 200 25 500 –––––– –––––– –––––– –––––– –––––– (ii) Production budget (units) Opening stock 9 000 5 000 3 000 4 500 Production (difference) 36 000 48 000 31 500 44 500 160 000 –––––– –––––– –––––– –––––– –––––– 45 000 53 000 34 500 49 000 Closing stock a 5 000 3 000 4 500 4 000 –––––– –––––– –––––– –––––– Sales 40 000 50 000 30 000 45 000 –––––– –––––– –––––– –––––– Note a 10% of next quarter’s sales.

(iii) Material usage budget (units) Total (000) (000) (000) (000) (000) Component R 144 (36 000 4) 192 126 178 640 Component T 108 (36 000 3) 144 94.5 133.5 480 Shell S 36 (36 000 1) 48 31.5 44.5 160 (iv) Production cost budget Total (000) (000) (000) (000) (000) Materials: Component R 1 152 1 689.60 1 108.80 1 566.40 5 516.80 Component T 540 792.00 519.75 734.25 2 586.00 Shell S 1 080 1 440.00 945.00 1 335.00 4 800.00 ––––– ––––––– ––––––– ––––––– –––––––– 2 772 3 921.60 2 573.55 3 635.65 12 902.80 Labour (at £30 per unit) 1 080 1 440.00 945.00 1 388.40 4 853.40 Variable overhead 360 480.00 315.00 445.00 1 600.00Fixed overhead a 54 72.00 47.25 66.75 240.00 ––––– ––––––– ––––––– ––––––– –––––––– Total production cost 4 266 5 913.60 3 880.80 5 535.80 19 596.20 ––––– ––––––– ––––––– ––––––– –––––––– Note a Charged out at £1.50 per unit of output (£240 000 /160 000 units).

(b) The principal budget factor is the factor which limits the organization’s ability to achieve increasing profits. In most organizations the principal budget factor issales. For a brief discussion of how sales may be forecast see ‘Sales budget’ inChapter 15.

(a) Cash budget Week 1 2 3456 (£000) (£000) (£000) (£000) (£000)(£000) Cash receipts from sales a 80 80 75 70 70 80 –– ––– –– –– –– –– –– ––– –– –– –– –– Cash payments:

Materials b 27 46 12 – – – Direct labour and variable overhead c 41 41 16 16 16 16 Fixed overhead d 16 16 12 12 12 12 –– ––– –– –– –– –– 84 103 40 28 28 28 –– ––– –– –– –– –– THE BUDGETING PROCESS151 Solution IM 15.12 Weekly surplus/(deficit) (4) (23) 35 42 42 52 Opening cash balance (39) (43) (66) (31) 11 53 Closing cash balance (43) (66) (31) 11 53 105 Notes a Week 1 2 3456 (£000) (£000) (£000) (£000) (£000)(£000) Opening debtors 80 40 Week 1 sales 40 40 23 535 33 535 43 535 54 5 –– –– –– –– –– –– 80 80 75 70 70 80 –– –– –– –– –– –– The above sales can be achieved because opening stocks of finished goods (2800units) + production in weeks 1 and 2 (2400 units) are greater than sales in weeks1–5 (3800 units) by 1400 units.

b Purchase of materials:

Week 1 Week 2(£) (£) Closing stock 40 000 10 000 + Production 42 000 42 000 (1200 £35) – Opening stock (36 000) (40 000) –––––– –––––– = Purchases 46 000 12 000 (paid for 1 week later) c (£) Weeks 1 and 2 = 1200 £30 = 36 000 + 5 000 (overtime premium)––––– 41 000 ––––– Weeks 3–6 = 800 £20 = 16 000 ––––– d Weeks 1 and 2 = 800 £25 = 20 000 – 4 000 (depreciation)––––– 16 000 ––––– Weeks 3–6 = £16 000 £4000= 12 000 ––––– (b) The matters which should be drawn to the attention of the management are: (i) The overdraft limit will be exceeded in week 2, and arrangements should bemade to increase this limit.

(ii) Excess funds will be available from weeks 4 to 6 and plans should be made to invest these funds on a short-term basis.

(iii) Funds will be required as soon as production recommences in order to re-establish stocks of raw materials and finished goods.

(a) The costs incurred over the three-year period are as follows: 2013 2014 2015(£) (£) (£) Direct material (270 houses p.a.) a 20 250 (270 £75) 21 263 (£20 250 1.05) 22 326 (£21 263 1.05) Direct labour 72 900 (270 £270) 78 003 (£72 900 1.07) 83 463 (£78 003 1.07) Variable overheads b 25 515 (270 £94.50) 27 046 (£25 515 1.06) 28 669 (£27 046 1.06) 152THE BUDGETING PROCESS Fixed overheads:c Avoidable 15 430 16 356 (£15 430 1.06) 17 337 (£16 356 1.06) Depreciation 10 287 10 287 10 287 Head office 25 718 27 261 (£25 718 1.06) 28 897 (£27 261 1.06) Notes a Number of houses maintained each year = (500 30%) + (600 20%) = 270 b Overhead cost per house: (£) Material related 15 (20% £75) Labour related 270 (100% £270) ––– 285 Variable overhead per house = £4.50 (30% £15) + £90 ( 1 3 £270) = £94.50 c Fixed overhead per house = £190.50 (£285 £94.50) Total fixed overheads for 2013 = £51 435 (£190.50 270 houses) Avoidable fixed overheads = £15 431 (30% £51 435) Depreciation = £10 287 (20% £51 435) Head office = £25 718 (50% £51 435) Painting and decorating cash budget 2013 2014 2015(£) (£) (£) Direct materials payments: a Previous year creditors 2 100 1 823 1 914 Current year 16 402 17 223 18 084 Cash purchases 2 025 2 126 2 233 Direct labour payments: b Previous year accruals 2 800 2 916 3 120 Current year 69 984 74 883 80 124 Variable overhead: c Previous year 600 851 902 Current year 24 664 26 144 27 713 Fixed overhead: d Avoidable 15 430 16 356 17 337 Head office 25 718 27 261 28 897 159 723 169 583 180 324 Notes a Current year purchases = 90% (90% direct material cost) a Cash purchases = 10% direct material costa Previous year creditors = 10% (90% direct material cost) b Current year labour cost = 96% direct labour cost a Previous year accrual = 4% direct labour cost c (Variable overhead incurred /12 months) 40%.

d Depreciation is a non-cash flow expense. (b) (i) The relevant cash flows (see part (a)) are:2013 2014 2015 Total(£) (£) (£) (£) Direct materials 20 250 21 263 22 326 Direct labour 72 900 78 003 83 463 Variable overhead 25 515 27 046 28 669 Avoidable fixed overhead 15 430 16 356 17 337 134 095 142 668 151 795 428 558 The quotation from the outside company is £405 000 (3 £135 000). On the basis of the information given in the question, it would be cheaper if the work were undertaken by the outside company.

(ii) Other factors which have not been taken into account in the financial analysis and which support the work being undertaken by the outside company include:1. There may be additional savings /cash inflows arising from closing down the painting and decorating department, such as the sale of stocks of paint,subletting the premises or benefits arising from the use of the premises forother activities.

2. The payments to the outside company may be payable quarterly in arrears. Thus when the time value of money is taken into account the benefits willbe greater than indicated in the analysis in (a).

Other factors not considered in (b) which do not support closing the department down include: 1. The housing association has less control over the quality of work and this could cause dissatisfaction amongst the tenants.

2. The closure of the department could lead to redundancy payments which are in excess of the savings made by the change.

3. What will happen when the contract is completed? If the market is not very competitive, the outside company will be in a dominant bargainingposition when the contract is re-negotiated if the housing associationcannot easily set up a painting and decorating function. This could leadto the housing association being ‘ripped off’ when the contract is renegotiated. THE BUDGETING PROCESS 153 154MANAGEMENT CONTROL SYSTEMS Solution IM 16.1 Solution IM 16.2 Solution IM 16.3 See Chapter 16 for an explanation of budgetary slack and fixed budgets and Chapter 15 for incremental budgets.

In particular, the answer should stress that slack budgets lead to an understatement of revenues and an overstatement of costs. This may result in the generation of misleading budgets and inappropriate decisions and may not reflect actual outcomes.See answer to Question IM 16.10 for a discussion of how budget slack might beeliminated. With regard to incremental budgets, past inefficiencies are unlikely to be eliminated and this will tend to increase budgeted cash outflows and expenses. The deficiencies ofincremental budgeting might be eliminated by implementing zero-base budgets. Fixed budgets will result in inaccurate cash and profit budgets if actual activity is significantly different from the fixed budget level of activity. The problem can bereduced by generating budgets for a range of activity levels using sensitivity analysis toascertain how sensitive the plans are to changes in activity levels. If outcomes areparticularly sensitive to changes in activity levels, consideration should be given toincluding a monetary provision for volume changes at the planning stage.

(a) See ‘Rolling budgets’ in Chapter 15, ‘Flexible budgets’ in Chapter 16 and ‘Planning and operational variances’ in Chapter 18 for the answer to this question.

(b) The continuous nature of rolling budgets and the fact that the budget will be reviewed at frequent intervals may reduce the need for budgetees to protectthemselves against the uncertainties inherent in the annual budgeting process.Alternatively, if rolling budgets seek to incorporate a continuous improvement, orif a good performance in the previous period is reflected by a more demandingbudget, then rolling budgets might be seen as an additional short-term threat andthus encourage the need to build in slack.Without flexible budgets managers might restrict activity in order to ensure that actual expenditure will be lower than budget (purely because of the lower level ofactivity). At the budget setting stage flexible budgets are unlikely to have muchimpact on budget slack. Planning and operational variances should reduce the incidence of budget slack at the budget setting stage if the targets are likely to be adjusted to reflect thechanging conditions that have occurred during the budget period.

A large proportion of non-manufacturing costs are of a discretionary nature. In respectof such costs, management has some significant range of discretion as to the amount itwill budget for the particular activity in question. Examples of discretionarycosts (sometimes called managed or programmed costs) include advertising, research anddevelopment and training costs. There is no optimum relationship between inputs (asmeasured by the costs) and outputs (as measured by revenues of some other objectivefunction) for these costs. Furthermore, they are not predetermined by some previouscommitment. In effect, management can determine what quantity of service it wishesto purchase. For example, it can choose to spend small or large amounts on research Management control systems Solutions to Chapter 16 questions MANAGEMENT CONTROL SYSTEMS155 and development or advertising. The great difficulty in controlling such costs is that there is no established method for determining the appropriate amount to be spent inparticular periods.

One approach to this problem is to compare amounts spent on the various discretionary items with those of similar organizations or with past periods. However,past periods may represent excessive or deficient budget allocations, and therefore are aweak base for comparison purposes. Another approach is to allow the spending of anamount that management believes it can afford. For example, some firms budgetdiscretionary expenses as a percentage of sales. The weakness of this approach is thatfuture sales may be determined by such items as research and development andadvertising expenditure, but when the sales revenue declines, the budgeted expenditureon research and development and advertising will be similarly reduced. This may be anincorrect approach, since it may be more appropriate in the circumstances to increaseexpenditure on research and development and advertising to stimulate future sales. The major argument for selecting sales as a basis for determining the amount of budgeted expenditure in discretionary items is not because there is any presumedcausal relationship with sales, but because sales represents a useful indication of howmuch the company can afford to spend. It is essential that fixed budgets be used for the control of discretionary expenses. At the budget stage management will have determined the amount to be spent. This willnormally be a policy decision to be implemented, and the costs will then be regardedas fixed for the appropriate budget period. Flexible budgets based on the adjustmentof expenditure because of changes in activity are therefore inappropriate for thecontrol of discretionary expenses. Note also that any underspending may notnecessarily be a good thing, since this may result in a lower level of service than thatoriginally planned by management. For example, underspending on research anddevelopment may indicate that the policy on the amount to be spent on research anddevelopment has not been followed.

(a) A description of each of the terms is presented in the text. See the index for the relevant pages.

(b) See ‘Aspiration levels’ and ‘Setting financial performance targets’ in Chapter 16 for the answer to this question.

These are open-ended questions that are intended to test independent thought and initiative in relating the literature to the questions asked. Therefore anwers are notprovided for these questions.

(a) Budgets may be imposed upon managers who are responsible for their implementation. Alternatively managers may participate in determining the budget for which they are responsible. For a discussion of the advantages anddisadvantages of allowing managers to participate in the budget process see‘Participation in the budget and target setting process’ in Chapter 16. Inparticular, the answer should stress the following advantages which have beenclaimed to have resulted from a participative budgeting process:(i) Participation increases the aspiration levels and motivation of the budgetees and increases the probability that the budget will be accepted as a legitimatetarget for which to aim.

(ii) Participation may lead to an increased level of efficiency.

(iii) P articipation improves communication between the budgetees and their superiors. The disadvantages of participative budgeting include:

(i) It may lead to creation of budget slack. Where managers are able to influence their budget standard, there is a possibility that they will bias the information in Solution IM 16.4 Solutions IM 16.5 –16.8 Solution IM 16.9 156MANAGEMENT CONTROL SYSTEMS order to gain the greatest possible benefit. This will apply particularly where the reward system places great stress on achieving the budget.

(ii) The personality traits of the budgetees may limit the benefits of participation. Individuals with certain personality traits may perform better when budgetsare imposed by a higher authority.

(iii) Participation may encourage managers to adopt a departmental self-centredapproach and concentrate solely on maximizing the benefits of their owndepartments at the expense of the benefits of the organization as a whole.

Some of the disadvantages which result from imposed budgets include:

(i) Non-acceptance of the budget as a target may result in the budgetees not attempting to achieve the target set.

(ii) The budget is likely to be viewed as a punitive device which managementuses in a recriminatory manner to evaluate subordinates. There is a dangerthat this might create hostility towards the budget system and a failure to usethe system as a planning and control device.

(iii) Pressure to achieve an imposed budget might result in the falsification of data or under performance in order to influence the setting of future budgettargets so that they are set at easily attainable levels.Problems are likely to apply whichever approach is used.

(b) The answer to this question should focus on describing incremental and zero-base budgeting. In particular the answer should stress that, with incremental budgeting,past inefficiencies and slack can perpetuate and be built into future budgets. It isclaimed that zero-base budgeting can overcome the problems of incremental bud-geting. For a more detailed explanation see ‘Zero-base budgeting’ in Chapter 15.

(a) The report should include the following items: (i) An indication that the budget holder will have a greater knowledge of his, orher, activities than the management accountant or senior management andthus may be in a position to obtain more resources (or an easier sales target)than is justifiable.

(ii) To reduce slack both the management accountants and senior management should seek to thoroughly understand the budget holder’s activities, pastbudget performance and any future changes in circumstances that mightapply.

(iii) Past trends should be reviewed in order to establish whether current budgetrequests appear to be realistic.

(iv) Wherever possible budgets should be compared with external referencepoints, such as similar departments within the group or with data obtainedfrom trade associations. Quotations might be obtained from potentialsuppliers relating to outsourcing the activity to compare the cost ofoutsourcing with the proposed budget.

(v) Budget holders should be required to make a presentation to senior managers to justify the reasonableness of their budgets.

(b) The answer could include the following points: (i) The financial markets expect profit forecasts to be achieved. Non-achievement can have an adverse effect on share prices. The budget is setsometime before the start of the budget year and the outcomes are subject tomuch uncertainty. The incorporation of some slack may therefore bejustifiable to cope with the uncertainty and to increase the probability that thebudget, and profit forecasts, for the organization as a whole will be achieved.

(ii) Failure to achieve the budget is de-motivating and can result in a loss ofrewards. Achieving the budget creates the feeling of achievement and successand avoids the dysfunctional consequences of failure. Budgets are more likelyto be achieved if some budget slack is accepted. Budget slack may reduce the Solution IM 16.10 negative consequences of budgets described in Chapter 16 by reducing the short-term pressure on managers. Budget slack also allows some flexibilitysince an overspend in one area might be compensated by reducingexpenditure in another area. This may only be possible if the budget holderhas some slack within his, or her, overall budget.

(iii) All of the activities of the organization are based on the budgets being achieved. For example, liquidity requirements are determined from theoutcomes of the budget process. Failure to achieve the budget can haveserious consequences if costs exceed budget and revenues are less than budget.By accepting some form of budget slack there is a greater guarantee that theplans reflected in the budget will be achieved and all activities within theorganization will be co-ordinated. Also by having some slack managers may beless tightly constrained and be more innovative. In addition, panic budgetreductions may be avoided when it becomes apparent that the budget may notbe achieved.

(iv) It is questionable whether the acceptance of budget slack should formally be incorporated into the budget process. This would diminish the role thatbudgets play in ensuring that resources are wisely managed and may result inexcessive slack. Budget slack might be recognized unofficially, possibly byadopting a flexible approach to budget approval within the budget settingprocess and ensuring that budgeting is accompanied by a profit-conscious styleof budget evaluation.

(a) Actual volume exceeds the budgeted volume by 12½% [(720 – 640)/640]. Therefore all of the variable costs are increased by 12½% and the fixed costsremain unchanged in the flexed operating statement reproduced below.

Flexed operating statement based on actual sales volume of 720 000 units: Budget Actual Variance(£000) (£000) (£000) Sales 1024 1071 47 –––– –––– –––– Cost of sales Materials 189 144 45 Labour 270 288 (18) Overheads (Variable) 36 36 Nil Labour (Fixed) 100 94 6 –––– –––– ––––595 562 33 –––– –––– –––– Selling and distribution costs Fixed 72 83 (11) Variable 162 153 9 –––– –––– ––––234 236 (2) –––– –––– –––– Administration Fixed 184 176 8Variable 54 54 Nil –––– –––– ––––238 230 8 –––– –––– –––– Net profit (43) 43 86 Possible reasons for variances:Actual sales volume exceeds budgeted sales volume thus generating revenues inexcess of budgets. However, actual selling price was less than budgeted sellingprice but the overall effect has been favourable in terms of sales revenues. MANAGEMENT CONTROL SYSTEMS 157 Solution IM 16.11 158MANAGEMENT CONTROL SYSTEMS The favourable material variance may be due to negotiating more favourable prices and/or more efficient usage of the materials. The adverse labour variance may have arisen because of the purchase of poor quality materials or more overtime being worked to meet the increased sales volume. The decline in the fixed labour cost may have been caused by employeesleaving and not being replaced immediately. The adverse fixed selling and distribution cost variance may be due to an increase in the cost of advertising or extra advertising. The variable element may be due to moreefficient distribution methods resulting in a reduction in delivery costs. The favourable fixed administration cost variance may be due to reduction in rentals of office machinery or office staff leaving and not being replacedimmediately.

(b) See ‘Flexible budgeting’ in Chapter 16 for the answer to this question.

(c) The answer should focus on the following points: (i) Difficulty in accurately dividing costs into fixed and variable elements. Pastcost and activity information is used to provide an estimate to predict future cost behaviour. Inaccurate estimates will result in the prediction ofinaccurate costs.

(ii) Past information is used to predict future costs. Past trends are normally used to predict price behaviour but what has happened in the past does not alwaysprovide a reliable guide for the future.

(iii) Step fixed costs may occur but it is difficult to predict the exact point wherethe step increases will occur.

(iv) Flexible budgeting normally assumes that variable costs are constant per unitbut this may be inappropriate if curvilinear cost–volume relationships exist.

Task 1(a) The existing statement suffers from the following weaknesses: (i) There are no actual or budgeted figures or variances for the most recentmonth.

(ii) The actual expenditure is based on cash payments and does not show committed expenditure. Cash expenditure can provide misleading information on the expenditure that will be incurred and it is preferable ifexpenditure is recorded on an accruals basis.

(iii) There is no attempt to distinguish between controllable and non-controllable expenses or break down the statement into meaningful sub-headings.

(iv) It is not very user-friendly. The term ‘Cr’ in the under/over spend is likely to be confusing to non-accountants.

(v) No attempt is made to forecast the year end result. It is useful to add expenses to date to estimated expenses to the end of the year so that the likely year endoutcome can be compared with the budget.

(vi) Capital expenditure is included rather than it being included in the capitalexpenditure budget and then depreciated over time. Solution IM 16.12 MANAGEMENT CONTROL SYSTEMS159 Task 1(b) Proposed statement format Monthly data for current Cumulative Year and forecast period variances to data Original revised variance Budget actual variance budget forecast Direct teaching Teachers – full-time Teachers – part-timeOther employee expensesResources Administration Administration staffStationery, postage and phone Property services Caretaker and cleanersLighting and heatingRepairs and maintenanceRates Other Miscellaneous expenses Total revenue expenditureFixed assetsTotal capital expenditure Task 1(c) Advantages of the proposed format include: (i) Identification of budget, actual and variance for the current month. Thisallows for speedy remedial action and provides early warning of potential problems.

(ii) The introdution of a forecast of the position at the end of the period whichcan provide an indication of the likely outcomes and used for feedforwardcontrol.

(iii) The grouping of expenditure by similar items which will enable managers tofocus on major areas of expenses and identify those areas that need attention.

(iv) The cumulative variances to date which will enable management to examinecurrent variances within the context of the performance throughout the wholebudget year.

Task 2(a) Calculation of number of year 1 pupils Junior School Number in Proportion choosing Number choosing final year Mayfield School Mayfield School Ranmoor 60 0.9 54 Hallamshire 120 0.8 96 Broomhill 140 0.9 126 Endcliffe 80 0.5 40 ––– Total choosing Mayfield School 316 ––– Forecast of pupil numbers Numbers as Year commencing Year Age range at 31 May August1 11–12 300 316 2 12–13 350 300 3 13–14 325 350 4 14–15 360 325 5 15–16 380 360 6 16–17 240 304 (80% × 380) 7 17–18 220 228 (95% × 240) –––– –––– 2175 2183 –––– –––– 160MANAGEMENT CONTROL SYSTEMS Solution IM 16.13 Note: Current years 1–4 pupils become years 2–5 pupils next year.80% of current year 5 pupils become year 6 pupils next year.95% of current year 6 pupils become year 7 pupils next year.

Forecasted income Pupil Annual Total Years numbers fee income1–5 1651 £1200 £1 981 2006–7 532 £1500 £798 000 –––– ––––––––– Totals 2183 £2 779 200 –––– ––––––––– Task 2 (b) Budgeted surplusIncome £2 779 200 Expenditure £2 581 296 × 1.05 £2 710 361 ––––––––– Budgeted surplus £68 839 –––––––––– (a) Budgeted outcomes for Strategic plan Budget Estimate prepared prepared prepared Ex-post budget Aug. 2012 Oct. 2012 Apr. 2013 DGM’s view GMD’s view Market size a 150 000 150 000 165 000 165 000 165 000 Sales volume a 35 000 36 000 35 800 38 500 38 500 Market share (%) 23.3 24 21.7 23.3 23.3 (£000) (£000) (£000) (£000) (£000) Sales revenue b 28 000 28 800 28 100 29 834 30 800 Marginal cost c 14 350 15 300 14 900 16 024 15 785 Contribution 13 650 13 500 13 200 13 810 15 015 Fixed cost 6 500 6 800 7 200 7 200 6 500Product development d 2 000 2 000 1 400 1 400 2 240 Marketing d 3 500 3 200 2 600 3 800 3 920 ––––– ––––– ––––– ––––– ––––– Profit 1 650 1 500 2 000 1 410 2 355 ––––– ––––– ––––– ––––– ––––– Notes a Ex-post budget = strategic plan + 10%.

b 35 000 £800; 36 000 £800; 35 800 £784.92; 38 500 £774.92; 38 500 £800.

c Strategic plan = 35 000 £410; April 2013 estimate = 35 800 £416.20; DGM ex-post budget = 38 500 £416.20; GMD ex-post budget = 38 500 £410.d DGM ex-post budget = strategic plan + £300 000 for marketing; April 2013 estimate for product development. GMD ex-post budget = sales revenue (£30 800) 20% = £6160, which is allocated between product development and marketing using the strategic planratio of 20 /55 for product development and 35 /55 for marketing.

Comments (i) The projected profit is £500 000 in excess of budget and the estimated bonus is 46.7% (20% + [100% 20% £0.5 m /£1.5 m]).

(ii) Projected product development costs have declined by approximately one-third and this suggests that the manager is seeking to improve short-termprofits by actions that will reduce long-term profits.

(iii) Projected marketing costs have also declined by approximately 25% and this may have contributed to the decline in market share and the failure to 2013 MANAGEMENT CONTROL SYSTEMS161 achieve the ex-post budgeted sales based on the group managing director’s view. The reduced marketing expenditure may also have a detrimentalimpact beyond the current year.

(iv) The divisional general manager (DGM)’s proposal to reduce selling pricesand not maintain marketing expenditure specified in the strategic plan hasresulted in a reduced profit when compared with the group managingdirector (GMD)’s ex-post budget.

(v) Fixed costs have increased significantly over budget and strategic plan whereas average unit variable cost is less than budget but above strategicplan. Further investigation is required to ascertain the reasons for thesechanges.

(vi) It seems that the manager has attempted to obtain the bonus by making short-term savings that may produce significant reductions in long-termprofit.

(b) The existing bonus scheme focuses entirely on profit as the single performance measure. The main advantage of the current bonus scheme is that it is easy tounderstand and encourages managers to focus on the same measure that is used bythe external financial markets to evaluate the performance of the company as awhole.The current system encourages the DGM to try to negotiate a budget that understates potential profit by overstating costs and understating sales. This mayhave a detrimental impact on group planning. The profit calculation includes a large proportion of discretionary expenses.

The current scheme encourages managers to spend less than budget on those itemsthat are unlikely to have a short-term impact, e.g. product developmentexpenditure. However, the short-term reduction in costs may result in a muchhigher reduction in long-term profits. The bonus scheme gives no bonus for a failure to meet budgeted profit by only a small amount whereas a 20% bonus is given if the budget is just achieved. Also,if profit is greater than the maximum there is no incentive to increase profits anyfurther. There is also no attempt to distinguish between controllable and non-controllable profit or provide an incentive to achieve other important goals, e.g.quality, market share, flexibility, innovation etc.

(c) The revised bonus scheme should be based on controllable profit defined as follows: Contribution Less: Controllable fixed costs Planned product development costsPlanned advertising costs Note that the use of planned discretionary costs will reduce the incentive for themanager to undertake unnecessary cost cutting. Using planned discretionary spend-ing motivates DGMs to spend the amount agreed in the strategic plan. Ideally, additional qualitative and non-financial performance measures should be included in the bonus scheme. However, this would involve some form ofweighting system to determine the contribution of each measure to the overallbonus. Without additional information it is difficult to make specific recommendations and there is always the danger that the proposed solution willbe too complex. Alternatively, the bonus might be reduced by specific amountsbecause of a failure to achieve other important group goals. Finally, attention should be given to removing the fixed bonus of 20% and the maximum of 100%. If the bonus continues to be based on profits then it would bepreferable to fix it at a specific percentage of the amounts by which they exceedthe targets. 162MANAGEMENT CONTROL SYSTEMS (d) Extending the bonus scheme throughout the organization ought to increase motivation. However, bonuses based on total company profits are less suited to lower management levels because individuals are likely to consider that theycannot significantly influence total company profits. A further disadvantage is thatthose who contribute little are awarded the same bonus as those that contribute agreat deal. A possible solution is to introduce differential bonuses but suchschemes are more complex and may cause conflict as some individuals will beperceived as receiving more favourable treatment.

(a) The answer should highlight the following factors in terms of budget preparation and form and content of the performance report.(i) There was a lack of participation in the preparation of the budget.

(ii) There was failure to distinguish between controllable and non-controllablecosts. For example, the manager is presently accountable for allocatedadministration costs.

(iii) There was failure to flex the budget. (iv) The memorandum has been written in a very authoritarian style. (v) The investigation of variances with a variation in excess of a fixed percentage is questionable.

The above factors might have the following effects on the behaviour of thesupervisor. (i) The lack of participation might result in the budgetees not accepting the budget as being a legitimate target. Consequently the budget will fail tomotivate the budgetees to keep within the budgeted expenditure.

(ii) There might be creation of negative attitudes, resulting in low morale,increased tension and the creation of anti-management groups.

(iii) Management is adopting a budget-constrained style of evaluation. (iv) The budgetees might reduce performance and put more effort into ensuring that the budget is just achieved rather than attempting to minimize costs.

(v) There may be over emphasis on just meeting the budget (possibly through the falsification of data) and a failure to consider other important organizationalobjectives (such as a speedy turnround period and production of clean linen)because they are not included in the performance evaluation.

The answer could also incorporate published research findings which relate to the above comments. For example, participation (Coch and French), styles ofperformance evaluation (Hopwood), imposed standards compared withacceptance of budgets (Stedry), budget pressure (Argyris).

(b) The re-drafted report should include an introductory section explaining the purpose of the new system and emphasizing that the present report is a trial run.In other words, the report should be written in more personal terms andencourage the cooperation of the budgetees in running the new system. Inaddition, it should indicate that a meeting will be held in a few days’ time toexplain the purpose of the performance reporting system. The administratorshould also stress that he or she will be pleased to arrange appointments to discussindividual problems.The performance report should be re-drafted, distinguishing between controllable and non-controllable costs (allocated administration costs andequipment depreciation). The re-drafted budget should be flexed using eitherweight-processed or patient days, but from the information given it is difficultto estimate cost behaviour. Consequently the answer should illustrate theflexible budget approach rather than concentrating on accurate calculations.The report should conclude by congratulating the manager on exceeding Solution IM 16.14 budgeted activity. In addition, it should highlight the need to incorporate non- financial measures such as average turnround period, number of days’ absenteeism,and quantity of linen returned because of inferior cleaning quality.

(a) See ‘Participation in the budget and target setting process’ in Chapter 16 for a discussion of the advantages and disadvantages of allowing managers toparticipate in budget setting. With regard to the changes in the current system, theanswer should include a discussion of the following factors.(i) Head office does not appear to provide any guidelines or policy to those who are responsible for preparing the budgets. Steps should be taken by seniormanagement at head office to communicate the policy effects of the long-term plans and objectives of the company and provide appropriate guidelineswhich should govern the preparation of the budgets.

(ii) The present system is based on pseudoparticipation, and there is a lack ofnegotiation in the budget setting process. Area managers should work withbranch managers at the budget setting stage and negotiate a challengingbudget which the branch managers perceive that they have influenced. Thearea managers should combine the agreed branch budgets into an area budgetand negotiate this budget with head office. There should be a formalopportunity for the area managers to justify their budgets at head office level,and head office senior management should justify to area managers anychanges which are made to the budgets. Head office should consider settingup a budget committee which provides the formal mechanism for negotiatingand approving area budgets. For a discussion of a procedure for negotiatingand approving budgets see ‘Negotiation of budgets’ and ‘Coordination andreview of budgets’ in Chapter 15. Where budget changes are made, reasonsfor the changes should be explained to all parties involved in the preparationof budgets. At present there appears to be a lack of budget communicationfrom head office to area managers and from area managers to branchmanagers.

(iii) The bonus system is currently directly linked to the budgetary controlsystem. This can lead to dysfunctional behaviour and encourage managers tobias the budget estimates. Consideration should be given to developing analternative to the present bonus system where rewards are linked to widerquantitative and qualitative targets rather than the ability to ‘meet thebudget’.

(b) The main advantage of using the net margin target as a single performance measure is simplicity. Where multi-performance measures are used, the problem arises as to howmuch emphasis should be placed on the individual performance measures and how torespond when one measure can be improved at the expense of another. The netmargin figure is easy to understand and interpret, and represents the overall measureupon which the survival of the business depends.The use of net margin as the only target has a number of limitations. Managers may be encouraged to focus on improving this measure in the short term, evenwhen their actions have adverse long-term consequences. For example, short-termnet margins may be pursued at the expense of product quality and developinglong-term customer goodwill and future growth. A performance evaluation based on net margin would result in managers being evaluated on a measure which is based on items which are beyond their control. Acontrollable profit measure which excluded items beyond a manager’s controlwould be more appropriate. Evaluation of managerial performance is a complex area, and one summary financial measure cannot capture all of the variables which influence managerialperformance. The net margin target is a short-run measure which deals only with MANAGEMENT CONTROL SYSTEMS 163 Solution IM 16.15 the past period, whereas performance measures should attempt to assess future results that can be expected because of present actions. Multi-performance measures are better than a single-performance measure in assessing likely futureresults from current actions, and they also reduce the potential dysfunctionalconsequences arising from concentration on a single performance measure.Appropriate multi-performance measures should be developed. Possible measuresinclude the value of new loans, margin percentages, percentage of bad debts,development of new products, time taken to process applications, ability of clients to meet repayment schedules, and customer quality analysed by credit risk. 164 MANAGEMENT CONTROL SYSTEMS Solution IM 17.1 Solution IM 17.2 STANDARD COSTING AND VARIANCE ANALYSIS 1165 (a) (i)Flexed budget for month 6 Original Flexed Actual Totalbudget budget cost variance Units of J 20 000 18 500 18 500 (£) (£) (£) (£) Direct materials 480 000 444 000 442 650 1 350F Direct labour 140 000 129 500 129 940 440A Variable overhead 60 000 55 500 58 800 3 300A Fixed overhead 100 000 100 000 104 000 4 000A –––––– –––––––––––– –––––– 780 000 729 000 735 390 6 390A –––––– –––––– –––––– –––––– (ii) Material price variance = (standard price actual price) actual quantity = (AQ SP) (AQ AP) = (113 500 £4) £442 650 actual cost = £11 350F Material usage variance = (standard quantity actual quantity) standard price = ((18 500 6) 113 500) £4 = £10 000A Wage rate variance = (standard rate actual rate) actual hours = (SR AH) (AR AH) = (£7 17 800) £129 940 = £5340A Labour efficiency = (standard hours actual hours) standard rate variance = (18 500 1 hr 17 800) £7 = £4900F (b) See ‘The budget period’ in Chapter 15 for a description of rolling budgeting (i.e. rolling forecasts).

Task 1(a) Preliminary workings: Standard Actual Metres per Alpha 36 000/12 000= 3 32 000/10 000= 3.2 Cost per metre £432 000/36 000= £12.00 £377 600/32 000= £11.80 Labour hours per Alpha 72 000/12 000= 6 70 000/10 000= 7 Cost per hour £900 000/72 000= £12.50 £845 600/70 000= £12.08 The standard marginal cost per unit of Alpha is: (£) Materials (3 metres at £12 per metre) 36.00 Labour (6 hours at £12.50 per hour) 75.00 ––––– ––––– The standard cost of the actual production is: (£) Materials and labour (10 000 units at £111)Fixed overheads 396 000 –––––––– 1 506 000 –––––––– Standard costing and variance analysis 1 Solutions to Chapter 17 questions 111.00 1 110 000 Task 1(b)(£) Price variances = (Standard price – Actual price) Actual Quantity = (Standard price × Actual Quantity) – Actual cost Materials price = (£12 × 32 000 metres) – £377 600 6 400F Labour rate = (£12.50 × 70 000 hours) – £845 600 Quantity variances = ((Standard quantity for actual production) – Actual Quantity) Standard rate Material usage = (10 000 × 3 = 30 000 – 32 000) £12 24 000A Labour efficiency = (10 000 × 6 = 60 000 – 70 000) £12.50 Fixed overhead expenditure variance = Budgeted fixed overhead – Actual cost Fixed overhead expenditure variance = £396 000 – £405 000 9 000A Task 1(c)(i) Reconciliation statement for 3 months ending 31 May Standard cost of actual production 1 506 000 Materials price variance 6 400F Material usage variance 24 000A Labour rate variance Labour efficiency varianceFixed overhead expenditure variance 9 000A –––––––– Actual cost of production 1 628 200 –––––––– Task 1(c) (ii) The report should indicate that: (i) The original variances were based on a comparison of the costs of 12 000units actual output with the costs for a fixed budget output of 10 000 units. Therefore like has not been compared with like. The revised analysis has beenbased on a flexible budget comparison with the actual costs being comparedwith the standard cost for an output of 12 000 units.

(ii) The revised statement analyses variances by price and quantity whereas theoriginal statement only reports total variances.

Task 1(c) (iii) The revised statement provides more meaningful information because: (i) It provides a different message. The original statement implied an overallfavourable situation in terms of the variances whereas the revised statement indicates that overall the variances are adverse.

(ii) It highlights the major areas where investigations are required based on a management by exception approach.

(iii) It reports only an expenditure variance for fixed overheads rather than unitising fixed overheads (see ‘Standard absorption costing’ in Chapter 17 foran explanation of this point).

Task 2 A separate idle time variance of £150 000 adverse ( 12 000 hours at £12.50) arising from the machine breakdown of 12 000 hours should be reported. Note that the standard wage rate should be used to calculate the variance. The following revised labourefficiency variance should be reported that recognizes that the actual labour hoursengaged on production were 58 000 and not 70 000 as originally reported. Therevised variance is:

(10 000 × 6 hours = 60 000 – (70 000 – 12 000)) £12.50 = £25 000F 166 STANDARD COSTING AND VARIANCE ANALYSIS 129 400F 125 000A 29 400F 125 000A The material price variance should be divided into a material price purchasing efficiency variance and a material price planning variance as described in Chapter 18. The change in the price index is 10% (420.03/466.70 – 1) so the revised standard price is 90% of £12 = £10.80. The price variance is divided as follows:

Material price planning variance = (£12 – £10.80) 32 000 metres = £38 400F Material price purchasing efficiency variance = (£10.80 × 32 000 metres) – £377 600 = £32 000A Revised Reconciliation Statement (£) (£) Standard cost of production 1 506 000 Variances arising from normal production Material price variance £32 000 (A) Material usage variance £24 000 (A) Labour rate variance 29 400 (F) Labour efficiency variance £25 000 (F) Fixed overhead expenditure variance £9000 (A) 10 600 (A) ––––––– Variance arising from the machine breakdown Labour efficiency variance £150 000 (A) £150 000 (A) ––––––– Variance arising from the change in material prices Material price variance £38 400 (F) –––––––– Actual cost of production 1 628 200 –––––––– Tasks 3 (a) and 3(b) See ‘Cost of quality report’ in Chapter 21 for the answer to this question. Task 3(c) (i) In the new production environment there are fixed price contracts with guaranteed levels of quality. This suggests that there will be few material price variances. Also thecost of labour has now become a short-term fixed cost so labour efficiency variancesare unlikely to reflect the cost of either the resources saved or the extra costs that willbe incurred in the short-term. Wage rate variances are also likely to be uncontrollable.It is therefore questionable whether a standard marginal costing system will continueto provide meaningful information for cost control. For a more detailed discussion ofthese issues see ‘Criticisms of standard costing’ in Learning Note 18.4 on the openaccess website. Task 3(c) (ii) With flexible working practices it can become extremely difficult to capture actual labour costs by individual jobs. If most of the overhead costs are common andunavoidable to all alternatives (i.e. facility or business-sustaining) only material costswill be easily traceable to jobs. If overhead costs are only a small proportion of totalcosts then accumulating the full marginal cost of individual jobs will becomequestionable. Task 3(d) With the introduction of just-in-time techniques inventory levels will be substantially reduced, thus resulting in a saving in the interest cost of money tied up in inventories.This information will not be recorded in the costing system.

STANDARD COSTING AND VARIANCE ANALYSIS 1 167 –– (a) The standard cost details are as follows:(£) Selling price 14 Materials (10 000kgs/5 000 units = 2kgs per unit at £0.50) 1 Labour (0.5 hours at £ ) Fixed production overhead (£10 000/5000 units 2 Standard profit 5 The price variances are calculated as follows: (Standard price – Actual price)Actual quantity Material price = (£0.50 – £0.60)10 600kgs 1 060A Wage rate = (£12 – £11.40)2970 Sales price = (£14 – £15)49004 900F Note that actual hours worked are 5400 units × 0.55 = 2970 The usage variances are calculated as follows:((Standard quantity for actual production) – Actual quantity)Standard rate Material usage = (5400 × 2kgs = 10 800 10 600)£0.50 100A Labour efficiency = (5400 × 0.5 hours = 2700 – 2970)£12 Fixed production overhead expenditure: (Budgeted cost) – (Actual cost) £10 000 – £10 300 300A Administration overhead expenditure: (Budgeted cost) – (Actual cost) £3000 – £3100 100A Fixed production volume (Actual production – Budgeted production)Fixed overhead rate (5400 – 5000)£2 800F Sales volume: (Actual sales volume – Budgeted sales volume)Standard profit margin (4900 – 5000) £5 500A Budget/actual reconciliation statement – April (£) Budgeted profit (5000 × £5 – £3000 administration cost) 22 000 Sales price variance 4 900 (F) Sales volume profit variance (100 × £5) 500 (A) –––––– Budgeted profit on actual sales 26 400 Variances: (£)(F) (£)(A) Direct material:Price 1060 Usage 100 Direct labour: RateEfficiency Fixed production overhead: Expenditure 300 Volume 800 Administrative cost expenditure 100 variance –––– –––– (A) –––– –––– ––––– Actual profit 24 382 ––––– Solution IM 17.3 168 STANDARD COSTING AND VARIANCE ANALYSIS 1 12 6 9 1 782F 3 240A 1782 3240 2682 4700 2018 –– Calculation of actual profit:(£) (£) Actual sales revenue Actual costs: Material 6 360 Labour (2970 × £11.40) Production overhead 10 300 –––––– Stock c/fwd (500 units at –––––– –––––– 27 482 Fixed administration 3 100 –––––– 24 382 –––––– (b) See relevant variances in Chapter 17 for the answer to this.

(c) Interdependence occurs when an event has a favourable impact on one variance but an adverse impact on another variance. For example, the purchase of inferiorquality materials may account for a favourable material price variance but it mayalso have a negative impact on the material usage and labour efficiency variancesdue to the poorer quality causing an increase in usage.

(a) Budgeted fixed overhead rate = = £2.65 Standard hours per unit of output = 8400 hours/1200 units = 7 hours Actual production in standard hours = 1100 × 7 hours = 7700 hours Fixed overhead variance = Standard cost for actual production – Actual cost = 7700 × £2.65 = £20 405 – £25 536 = £5131 Adverse Fixed overhead expenditure variance = Budgeted cost – Actual cost = £22 260 – £25 536 = £3276A Fixed overhead efficiency = (Standard hours – Actual hours) Standard rate = (7700 – 7980) × £2.65 = 742A Fixed overhead capacity = (Actual hours – Budgeted hours) Standard rate = (7980 – 8400) × £2.65 = £1113A Variance summary: (£) Fixed overhead expenditure variance = 3276A Fixed overhead efficiency variance = 742A Fixed overhead capacity variance = 1113A –––––– Total fixed overhead variance 5131A –––––– (b) See the section on fixed overhead expenditure variance, volume efficiency variance and volume capacity variance in Chapter 17 for the answer to thisquestion.

(c) The purchase of cheaper, poor quality materials may result in a favourable material price variance but may also result in adverse material usage, labourefficiency and overhead efficiency variances. Fixed overheads (£22 260) Direct labour hours (8400) Solution IM 17.4 STANDARD COSTING AND VARIANCE ANALYSIS 1 169 33 858 73 500 £9) 50 518 4 500 46 018 Replacing skilled labour with unskilled labour will tend to result in a favourable wage rate variance and also adverse labour efficiency, material usage and overhead efficiency variances.

Task 1(a) (£) Labour rate = (Standard price – Actual price)Actual Quantity = (Standard price × Actual Quantity) – Actual cost = £12 × 11 440 = £137 280 – £136 708 572F Labour efficiency = ((Standard quantity for actual production) – Actual Quantity) Standard rate = (1040 × 10 hours = 10 400 hours – 11 440)£12 Fixed overhead expenditure = (Budgeted cost) – (Actual cost) = (1200 × £157.50 = £189 000) – (£207 000)18 000A Fixed overhead volume = (Actual production – Budgeted production) Fixed overhead rate = (1040 × 10 hours = 10 400 stand. hours – (1200 × 10 hours)) £15.75 25 200A or (1040 units – 1200 units)£157.50 per unit giving £25 200A Fixed overhead capacity = (Actual hours – Budgeted hours) Fixed overhead hourly rate = (11 440 – (1200 × 10)) £15.75 8 820A Fixed overhead efficiency = ((Standard hours for actual production) – Actual hours)× Fixed overhead hourly rate = (1040 × 10 = 10 400 – 11 440) £15.75 16 380A Task 1 (b) Reconciliation of standard and actual cost £ Standard cost of production (1040 × £637.50)Labour rate variance 572F Labour efficiency varianceFixed overhead expenditure variance 18 000A Fixed overhead capacity variance 8 820A Fixed overhead efficiency variance 16 380A ––––––– Actual cost of production ––––––– Task 2 (a) The original labour rate before allowing for the 5% increase was £11.43 (£12/1.05) (b) Revised labour rate = £11.43 × (104.04/102.00) = £11.66 (c) The labour rate can be analysed as follows: Planning variance due to error in estimating wage rates: (Original standard rate – Revised standard rate ) × Actual hours(£12 – £11.66) × 11 440 hours £3 890F Operational wage rate variance(Revised standard rate – Actual rate) × Actual hours= (Revised standard rate × Actual hours) × Actual wages cost(£11.66 × 11 440 hours = £133 390 – £136 708 ––––– Original wage rate variance 572F ––––– Solution IM 17.5 170 STANDARD COSTING AND VARIANCE ANALYSIS 112 480A 663 000 12 480A 718 108 3 318A (d) The initial analysis suggests a favourable variance but the revised analysis indicatesthat this was due to an incorrect estimate of the wage rate. After allowing for an ex-post adjustment of the standard an adverse variance of £1144 is reported. Thisprovides a different message from the initial analysis and the reasons for theadverse variance should be investigated. The revised analysis provides usefulfeedback information that will help management to improve the future estimatesof wage rates.

(e) The index may not be valid because of the following reasons: (i) The rate is an average and may incorporate many different skill levels. Theaverage may not be applicable to Eastern Division.

(ii) The index applies to the whole country but regional variations may apply.

(iii) The company may have a policy of offering higher wage rates to attract high calibre personnel. Alternatively, there may be a shortage of labour in the arearesulting in the need to offer higher wage rates to attract the requisite amountof labour.

(f) See relevant variances within Chapter 17 for the answer to this question.

(a) (i) Sales margin (profit) volume variance: (Actual volume – Budgeted volume) × Standard margin (£3) = £5250 Adverse(Actual volume × Standard margin) – (Budgeted volume × Standard margin)= £5250A(Actual volume × Standard margin) – £30 000 = –£5250(Actual volume × Standard margin) = £24 750Actual volume = £24 750/£3 = 8250 units (ii) Labour efficiency variance: (Standard hours – Actual hours) × Standard rate = £12000 Adverse(Standard hours × Standard rate) – (Actual hours × Standard rate) = –£12000(8250 units × 4 hours =33 000 × £12) – (Actual hours × £12) = –12 000£396 000 – (Actual hours × £12) = –12 000Actual hours × £4 = £408 000Actual hours = £408 000/£12 = 34 000 hours (iii) Material usage variance: (Standard quantity – Actual quantity) × Standard rate = £400F(Standard quantity × Standard rate) – (Actual quantity × Standard rate) =£400(8250 × 5 litres = 41 250 litres × £0.20) – (Actual quantity × £0.20) =£400£8250 – (Actual quantity × £0.20) = £400Actual quantity × £0.20 = £7850Actual quantity used = 39 250 litresActual quantity purchased = 39 250 – stock decrease (800) = 38 450 litres (iv) Total variable overhead variance: Standard variable overhead cost – Actual cost = £500 Adverse(8250 × £6 = £49 500) – Actual cost = £500 Actual cost = £50 000 (v) Fixed overhead expenditure variance: Budgeted cost – Actual cost = £500 Favourable10 000 units × £14 = £140 000 – Actual cost = £500Actual cost = £139 500 Note that budgeted output = Budgeted profit (£30 000) Standard profit margin (£3) Solution IM 17.6 STANDARD COSTING AND VARIANCE ANALYSIS 1 171 (b) The answer should draw attention to the fact that standard costing is most suited to an organization whose activities consist of a series of common or repetitive operations. Standard costing procedures cannot easily be applied tonon-manufacturing activities where the operations are of a non-repetitive nature,since there is no basis for observing repetitive operations and consequentlystandards cannot be set.In those non-manufacturing organizations where routine operations do not exist, standard costing cannot easily be applied. Instead, budgetary control is usedto control costs. A budget relates to an entire activity or operation whereasstandards can be applied to the units of output and thus provide a basis for thedetailed analysis of variances. Therefore budgeting focuses on controlling costs atthe aggregate level and does not analyse the difference between actual andbudgeted expenditure by price and quantity variances.

(a) Statement of total standard costs for product EM Actual cost Total variance Standard cost(£) (£) (£) Direct material: E 6 270 270A 6 000 M 650 50A 600 Direct labour 23 200 2 200A 21 000 Variable overhead 6 720 720A 6 000 Fixed overhead 27 000 3 000F 30 000 (b) Standard product cost (£) Direct material E (1 metre at £10 per metre) 10.00 a Direct material M (0.333 metres at £3) 1.00 b Direct labour (5 hours at £7) 35.00c Variable overhead (5 hours at £2) 10.00d Fixed overhead (5 hours at £10) 50.00e –––––– 106.00 –––––– Notes a Standard direct material cost per unit = £6000 /600 units = £10 Actual quantity standard price = £6600 (£6270 + £330) Standard price per metre = £10 (£6600 /660 metres) Standard quantity = 1 metre (£10 standard cost /£10 per metre standard price) b Standard direct material cost per unit = £1 (£600 /600 units) Actual quantity standard price = £600 (£650 £50) Standard price = £3 (£600 /200 metres) Standard quantity = 0.333 metres (£1 /£3 metres) c Standard direct labour cost per unit = £35 (£21 000 /600 units) Actual hours standard price = £22 400 (£23 200 £800) Standard rate = £7 (£22 400 /3200 hours) Standard quantity = 5 hours (£35 /£7 per hour) d Standard variable overhead rate per unit = £10 (£6000 /600 units) Standard hours calculated in note c= 5 hours Standard rate = £2 (£10 /5 hours) e Standard fixed overhead rate per unit = £50 (£30 000 /600 units) Standard hours calculated in note c= 5 hours Standard fixed overhead rate = £10 (£50 /5 hours) (c) Actual fixed overheads + expenditure variance = budgeted fixed overheads Budgeted fixed overheads = £27 000 + £500 = £27 500 Solution IM 17.7 172 STANDARD COSTING AND VARIANCE ANALYSIS 1 Budgeted production = budgeted fixed overheads/standard cost = £27 500 /£50 = 550 units (d) See ‘Establishing cost standards’ in Chapter 17 for the answer to this question. (a) Standard product cost (£) (£) Direct materials: WALS (15 £60) 900 LOPS (8 £75) 600 ––– 1500 Direct labour (60 hours at £10.50 per hour) 630 Production overheads (£504 000 /2400 units) 210 –––– Standard product cost 2340 –––– (b) (£) Direct material usage variance = (standard quantity actual quantity) standard price WALS = [(180 15 2850 a ) £60] 9 000A LOPS = [(180 8 1470 a ) £75] 2 250A Direct material price variance = (standard price actual price) actual quantity WALS = [(£60 £57) 3000 b ] 9 000F LOPS = [(£75 £81) 1000 b ] 6 000A Labour efficiency variance = (standard hours actual hours) standard rate [(180 60 hours – 11 700 hours) £10.50] 9 450A Wage rate variance = (standard rate actual rate) actual hours [(£10.50 £112 320 /11 700) 11 700] 10 530F Fixed production overhead expenditure = budgeted fixed overhead actual fixed overhead (£504 000 /12 £42 600) 600A Fixed production volume = (actual production – budgeted production) fixed overhead rate [(180 2400 /12) £210] 4 200A Notes a Actual usage of components is calculated as follows:

WALS LOPS Opening stock 600 920 Purchases 3000 (£171 000 /£57) 1000 –––– –––– 3600 1920 Less closing stock 750 450 –––– –––– Components used 2850 1470 –––– –––– b Material usage variances can be calculated by defining actual quantity as either ‘material purchases’ or ‘material usage’. In the above answer the variances have beencalculated on the basis of material purchases. For cost control purposes it is prefer-able to report price variances in the period in which they arise rather than delaying the reporting of the variances until the period when the materials are used. Solution IM 17.8 STANDARD COSTING AND VARIANCE ANALYSIS 1 173 (c)Reconciliation of standard and actual gross profit (£) Sales 504 000 Standard cost of sales (180 £2340) 421 200 –––––– Standard gross profit 82 800 Favourable Adverse (£) (£) Material usage: WALS 9 000 LOPS 2 250 Material price: a WALS 8 550 LOPS 8 820 Direct wage rate 10 530Labour efficiency 9 450 Fixed expenditure 600 Fixed volume 4 200 –––––– –––––– 19 080 34 320 A 15 240A ––––– Actual gross profit 67 560 Note a The direct materials consumed of £281 520 given in the question has been calculated on the basis that raw material stocks are valued at actual cost and not standard cost. This implies that price variances are included in the stockvaluations and not written off as an expense until the period in which they areused. In order to reconcile the profits, it is necessary to calculate material pricevariances on the basis of ‘quantity used’ rather than quantity purchased. Therevised calculations are as follows:

WALS: (£60 £57) 2850 = £8550F LOPS: (£75 £81) 1470 = £8820A (d) The report should emphasize that the statement in (c) above provides manage- ment with an explanation of why actual profit differs from budget profit. It isimportant that the report be used to assist in ascertaining the reasons for thevariances and taking appropriate remedial action to eliminate future inefficiencies,or altering future plans to reflect changing circumstances. Preferably the reportought to be supplemented with an explanation of the causes of the variances ofsignificant amounts. It is possible that the price variances reflect price changeswhich are beyond the control of management. However, usage variances are likelyto be controllable, and it is important that these variances be investigated andappropriate remedial action taken to eliminate any inefficiencies.

(a) Budgeted profit and loss account (£) Income from fares (40 000 £l) 40 000 Variable costs: Fuel (40 000 2.5 £0.08) (8 000) Overheads (40 000 2.5 £0.05) (5 000) Fixed costs: Employment (10 drivers) (10 000) Other (9 000) ––––– Profit 8 000 ––––– Actual profit and loss account (£) Income from fares (38 000 £0.95) 36 100 Variable costs: Fuel (105 000 £0.084) (8 820) Overheads (105 000 £0.048) (5 040) Solution IM 17.9 174 STANDARD COSTING AND VARIANCE ANALYSIS 1 Fixed costs: Employment(9 600) Other (9 300) –––– Profit 3 340 –––– Profit variance A 4 660A –––– (b) Variance analysis Sales margin volume {2000 [£1 – 2.5 (£0.08 + £0.05)]} A 1 350A Sales margin price [38 000 (£0.95 £l)] A 1 900A Variable cost efficiency variances: Fuel {[(38 000 2.5) 105 000] £0.08} A 800A Overheads {[(38 000 2.5) 105 000] £0.05} A 500A Variable cost spending variances: Fuel [(£0.08 £0.084) 105 000] A 420A Overhead [(£0.05 £0.048) 105 000] A 210F Fixed cost variances: Employment A 400F Other A 300A –––– A 4 660A –––– The report should contain an explanation of the major variances. There was a 5% reduction in fare-paying miles (2000 miles) and a 5% increase in driven miles (5000miles). The reduction in fare-paying miles resulted in a decline in profits of £1350,and the increase in driven miles caused variable costs to increase by £1300. Theaverage fare income per mile was 5p less than budget, and this resulted in actual rev-enue being less than budgeted revenue by £1900. Fuel costs per mile exceeded the budgeted rate by £0.04, causing an adverse spending variance of £420. This was compensated by variable overhead spendingbeing £210 less than budget. Employment costs were £400 less than budget. The failure to immediately replace the driver had a significant impact on the profit variance. The unavailability of taxis at peak times may account for the adverse salesvolume variance. With one car fewer operating during the period, it may have beenmore difficult to minimize mileage. Consequently adverse mileage efficiencyvariances are reported. The adverse sales margin price variance may have resultedfrom ‘off-peak’ business increasing at the expense of peak business because of theunavailability of taxis at peak times. The saving in fuel costs may be due to areduction in the price of petrol or a greater proportion of off-peak longer-journeybusiness which requires less petrol consumption per mile. The savings in employment costs are likely to result directly from the driver leaving during the month. Alternatively the driver may have left early in themonth, and the variance is a combination of savings in three weeks’ wages and theextra cost of overtime paid.

(c) The following additional information and variances would be useful: (i) Efficiency variances analysed by cars to pinpoint where the variances occur.

(ii) Analysis of sales variances by business segments (e.g. late evening peak ordaytime off-peak).

(iii) Separate planning and operating variances to ascertain how much of thepetrol price variance is due to price changes and how much is due to efficientdriving.

(iv) An analysis of variable and fixed overheads by categories and employment costs by fixed salaries, overtime etc.

The above recommendations can only be justified if the additional costs of operating the control system do not exceed the benefits from the recommendedchanges. STANDARD COSTING AND VARIANCE ANALYSIS 1 175 176STANDARD COSTING AND VARIANCE ANALYSIS 2: FURTHER ASPECTS Solution IM 18.1 Solution IM 18.2 (a) For the answer to this question you should refer to ‘The future role of standard costing’ in Learning Note 18.5 on the open access website.

(b) See ‘Target costing’ in Chapter 21 for the answer to this question. In addition, the answer should stress that the target cost should be analysed by the different elements of cost for cost management. Actual costs for each cost element should bereported on a regular basis and the variances represent feedback information in thequest to drive actual costs down to target costs. Target costs are viewed as a toolfor cost management and reduction rather than short-term operational costcontrol. They represent a strategic and marketing approach rather than an internalfocus.

(c) Standard costs are derived from a study of internal operations whereas target costs are market-driven, based on market information and target profit margins.Standard costs are internally focused and established after production has begunwith the emphasis being on cost control. In contrast, target costs are externallyfocused and are established before production commences. The emphasis is oncost reduction rather than seeking to ensure that costs adhere to somepredetermined standard.

(a) The cost of investigating and correcting a variance is £1800 and the probability of this event occurring is 0.25. The cost of investigating a variance where acorrectable cause is not found is £1400. The probability of this event is 0.75.Therefore the expected value of the cost of investigation is (£1800 × 0.25 ) + (£1400 × 0.75) = £1500. The expected value of the benefits from investigation is 75% of the size of the variance and the probability of a correctable cause is 25%. Therefore the expectedvalue of the benefits is 0.1875 of the amount of the variance (0.75 × 0.25 × theamount of the variance). The indifference point is where 0.1875 × Benefit = £1500 expected cost of investigation so that the benefit (i.e. the amount of the variance ) = £1500/0.1875= £8000 Thus variances in excess of £8000 should be investigated.

(b) (i) For the answer to this question see ‘The investigation of variances’ in Chapter 18 and Learning Note 18.3 on the open access website. In particular, theanswer should point out the difficulty in estimating the cost and benefits ofinvestigation and the fact that past observations of when the operation isunder control should be observable. This information may not be available fornew operations.

(ii) See ‘The investigation of variances’ in Chapter 18 for the answer to thisquestion.

Standard costing and variance analysis 2: further aspects Solutions to Chapter 18 questions Workings Parts (a) and (b) require a detailed analysis of the variances. The variance calculationsare as follows.(£) Material price: (standard price actual price) actual quantity purchased Plaster of Paris [£8 (£43 200 /5400)] 5400 0 Paint [£30 (£5800 /173)] 173 A 610A Material usage: (standard quantity actual quantity a ) standard price Plaster of Paris (286 b 20 5420) £8 A2400F Paint (286 143) £30 0 Wage rate: (standard rate actual rate) actual hours (£10 £11) 730 A 730A Labour efficiency: (standard hours actual hours) standard rate (286 2.5 730) £10 A 150A Fixed overhead expenditure (budgeted fixed overheads actual fixed overheads) (300 £100 £34 120) A4120A Volume efficiency: (standard hours actual hours) fixed overhead rate c (715 730) £40 A 600A Volume capacity: (actual hours budgeted hours) fixed overhead rate c (730 300 2.5) £40 A 800A Sales margin price: (actual selling price budgeted selling price) actual sales volume (£380 £380) 284 0 Sales margin volume: (actual sales quantity d budgeted sales quantity) standard margin (284 300) £80 A1280A (a) Stores ledger control account (plaster of Paris) (kg) (£) (kg) (£) Balance b /f 2800 22 400 WIP (SQ SP) 5720 45 760 Creditors 5400 43 200 Balance c /f Material usage variance 300 2 400 (closing stock) 2780 22 240 –––– –––––– –––– –––––– 8500 68 000 8500 68 000 –––– –––––– –––– –––––– Stores ledger control account (paint) (litres) (£) (litres) (£) Balance c /f 140 4200 WIP a /c (SQ SP) 143 4290 Creditors 173 5190 Balance c /f (closing stock) 170 5100 ––– –––– ––– –––– 313 9390 313 9390 ––– –––– ––– –––– WIP account (£) (£) Stores ledger control account: Finished goods stock a /c 85 800 Plaster 45 760 Paint 4 290 Wages control account (SQ SP) 7 150 Fixed overhead account 28 600 ––––– ––––– 85 800 85 800 ––––– ––––– Solution IM 18.3 STANDARD COSTING AND VARIANCE ANALYSIS 2: FURTHER ASPECTS 177 178STANDARD COSTING AND VARIANCE ANALYSIS 2: FURTHER ASPECTS Finished goods stock account (£) (£) Opening balance (9 £300) 2 700 Cost of sales (284 £300) 85 200 WIP a /c 85 800 Closing stock c /f 3 300 –––––– –––––– 88 500 88 500 –––––– –––––– The entries in the creditors, wages and fixed overhead control accounts are shown below: Creditors (£) Stores ledger (plaster) 43 200 Stores ledger (paint) 5 190Material price variance a /c 610 Wages control (£) (£) Wages accrued a /c 8030 WIP 7150 Wage rate variance a/c 730 Labour efficiency variance a /c 150 ––––– ––––– 8030 8030 ––––– ––––– Fixed overhead control (£) (£) Expense creditors 34 120 Overhead expenditure variance 4 120 Volume efficiency 600 Volume capacity 800WIP a/c 28 600 –––––– –––––– 34 120 34 120 –––––– –––––– (b) It is assumed that (ii) refers to a statement showing standard profit on actual sales and (iii) refers to a statement showing actual profit.

(i) Budget trading statement (£) (£) Sales revenue (300 £380) d 114 000 Cost of sales: Materials plaster (300 £160) 48 000 paint (300 £15) 4 500 Direct wages (300 £25) 7 500 Fixed production overheads (300 £100) 30 000 –––––– 90 000 –––––– Budgeted profit 24 000 –––––– (ii) Standard cost trading statement (£) Actual sales (284 £380) 107 920 Standard cost of sales (284 £300) 85 200 –––––– Standard profit on actual sales 22 720 –––––– (iii)Financial trading statement (£) (£) Actual sales 107 920 Opening stock e (£22 400 + £4200 + £2700) 29 300 Materials (£43 200 + £5800) 49 000 Labour 8 030 Fixed overhead 34 120 –––––– 20 450 Less closing stock e (£22 240 + £5100 + £3300) 30 640 89 810 –––––– –––––– Actual profit 18 110 –––––– (iv) Reconciliation (£) Budgeted profit (i) 24 000 Less sales margin volume variance 1 280 –– ––––– Standard profit on actual sales (ii) 22 720 Cost variances Favourable Adverse(£) (£) Paint price 610 Plaster usage 2400 Wage rate 730 Labour efficiency 150 Fixed overhead expenditure 4120 Volume efficiency 600Volume capacity 800 –––– –––– 2400 7010 4 610A –––– –––– ––––––– Actual profit (iii) 18 110 ––––––– Notes a Note that actual material usage is calculated as follows:

opening stock + purchases closing stock b Throughout the answer, actual production and sales are expressed in 100 sets.

c The fixed overhead rate is expressed as a rate per standard hour (i.e. 1 hour £10 400%).

d Note that budgeted production and sales are expressed in 100 sets.

e Note that opening and closing stocks are valued at standard cost. The variances are written off as period costs.

(a) Sales mix variance Actual sales Actual sales volume in Difference Standard Sales marginvolume budgeted proportions contribution margin mix variance Male 2000 3200 (80%) 1200 £4.50 £5400 Female 2000 800 (20%) + 1200 £8.00 + £9600 ––––––– + £4200F ––––––– Sales quantity variance Solution IM 18.4 STANDARD COSTING AND VARIANCE ANALYSIS 2: FURTHER ASPECTS 179 Actual sales volume in Budgeted Difference Standard Sales marginbudgeted proportions sales quantity contribution margin quantity variance Male 3200 (80%) 4000 800 £4.50 £3600 Female 800 (20%) 1000 200 £8.00 £1600 ––––––– £5200 ––––––– Comparison of budgeted and actual performance ££ Budget Actual Sales – Male 30 000 16 000 Female 18 000 40 000 Commissions – Male 12 000 7 000 Female 10 000 22 000 Fixed costs 20 000 24 000 –––––– –––––– Profit 6 000 3 000 –––––– –––––– Analysis of profit variance Sales price variances – Male (£8 – £7.50)2000 1 000F Female (£20 – £18)2000 4 000F Sales mix variance 4 200F Sales quantity variance 5 200A Fixed overhead expenditure variance (£20 000 – £24 000) 4 000A Labour rate variances – Male (£3 – £3.50)2000 1 000A Female (£10 – £11)2000 2 000A –––––– Profit variance 3 000A –––––– (b) The report should include the following points: (i) The favourable sales price variances suggest that selling prices may haveincreased or that the clients may have required different treatments.

(ii) Compared with the budget the sales volume has declined resulting in an overall sales volume variance of £1000A (£4200 – £5200). This has beenoffset by the favourable mix variance with sales consisting of a greaterproportion of the higher margin female clients. Overall the sales variances forthe period were £4000 favourable.

(iii) The d ecline in profit, compared to budget, was due to an increase in fixed overhead expenditure and higher than planned commission rates. The lattermay be due to commission rates being linked to selling prices. To ascertain thereasons for the adverse fixed overhead expenditure variance the individualfixed overhead expense categories should be examined.

(c) For the answer to this question see ‘Difficulties in interpreting sales margin variances’ in Chapter 17 and ‘Criticisms of sales margin variances’ in LearningNote 18.1 on the website. In addition, the answer should stress the benefits fromadopting an ex postvariance analysis approach as described in Chapter 18.

(a) Material usage revision variance(Original standard usage ex post usage) original standard price [(4000 1.5 kg = 6000) (4000 1.8 kg = 7200)] £8 = £9600A Material price revision variance(Original standard price ex post standard price) ex post budgeted quantity (£8 £7.50) 7200 = £3600F Wage rate revision variance Solution 18.5 180 STANDARD COSTING AND VARIANCE ANALYSIS 2: FURTHER ASPECTS STANDARD COSTING AND VARIANCE ANALYSIS 2: FURTHER ASPECTS181 (Original standard price ex post standard price) ex post budgeted quantity (£12 £11.80) 8000 hours = £1600F Other variances Material usage = (standard quantity actual quantity) standard price = [(4400 1.8 kg) 7800 kg] £7.50 = £900F Material price = (standard price actual price) actual quantity = (£7.50 £7.90) 7800 = £3120A Labour efficiency = (standard quantity actual quantity) standard price = [(4400 2 hrs = 8800) (9200 150)] £11.80 = £2950A Labour idle time = 150 hours at £11.80 = £1770A Wage rate = (standard rate actual rate) actual hours (£11.8 £12.10) 9200 = £2760A (b) Revised standard contribution per unit (£) (£) Selling price 45.00 Direct materials (1.8 kg £7.50) 13.50 Direct labour (2 kg £11.80) 23.60 37.10 –––– –––– Contribution 7.90 –––– The sales volume variance has been calculated as follows: (Budgeted sales volume actual sales volume) standard contribution per unit (4000 4100) £7.90 = £790F The calculations for the breakdown of the sales volume variance are as follows:

Extra capacity = ((9200 labour hours /2) – 4000 units) £7.90 = £4740F Productivity drop = lost production arising from labour efficiency of 125 units(250 hours/2 hours) at £7.90 = £987.50A Idle time = 75 lost units (150 hours /2) at £7.90 = £592.50A Stock increase = 300 units at £7.90 = £2370A The net effect of adding the above variances is 100 units with a value of £790.

(c) The report should indicate that the original budgeted contribution of £36 000 has been adjusted in order to reflect the permanent changes which have arisen since the original budgets and standards were set. The revised budgeted contribution of £31 600 represents the revised target against which performance will beevaluated.A favourable sales volume variance of £790 has been reported, and the operating statement analyses this variance by the following causal factors: (i) Extra capacity : The 1200 extra labour hours which have been made available have created the potential for 600 units additional sales generating an extracontribution of £4740. Given that the additional sales did not materialize, itis questionable with hindsight whether it was appropriate to increasecapacity. This decision can only be justified if demand in future periods islikely to exceed productive capacity.

(ii) Productivity drop : The decline in labour efficiency of 250 hours has resulted in a lost output of 125 units with a potential additional contribution of£987.50. If this will (say in the next period) result in future lost sales demandthen the variance represents lost contribution arising from labour efficiency.On the other hand, if the decline in production will not lead to reducedfuture sales volume then the monetary value of this variance has littleeconomic significance.

(iii) Idle time : An idle time of 150 hours has resulted in a lost output of 75 units – – – – – – with a potential contribution of £592.50. Comments similar to those outlined in (ii) apply. The causes of the idle time should be established andappropriate remedial action taken.

(iv) Stock increase : The variance relating to the stock increase of 300 units is intended to represent the potential loss in contribution of £2370 if the stocksdeteriorate and cannot be sold in the future. The reasons for the stockincrease should be established. If the stocks on hand were a result of a failureby sales management to dispose of them then sales management should beheld accountable for the variance. On the other hand, if the stock increasewas a result of over production by the production staff then productionshould be held accountable for the variance. The remaining variances relate to production operating variances and require explanations relating to possible causes. Material usage : The favourable variance suggests efficient usage in materials, although the 20% increase in the standard might have been an over estimate of the target material usage. Material price : The adverse variance indicates that the company is paying in excess of the current target market price of £7.50. This might reflect a failure to change the sources of supply or contracts entered into when the standardprice was £8. It could also be due to the purchase of higher-quality materials asreflected in the previous standard. This might also explain the favourable usagevariance. It is important that the variance be investigated and appropriateremedial action taken to avoid future adverse variances.

(a) Variance report for quarter ending 30 November (£000) Budgeted profit 111 Sales volume planning variance a 168A ––––– Revised ex postbudget (57) Sales variances: Operating volume (market share) b 126F Mix c 10F Price d 5F 141F ––– ––– 84F Material cost e 6.25F Sales commission price f 0.25A 6F ––––– Fixed overhead g 6A Selling and administration 5A ––––– Actual net profit 79A ––––– A contribution approach has been adopted since it is considered that this approach will provide more meaningful information. The budgeted contributions per squaremetre for each product are: Plastic Mahogany(£) (£) Selling price 220 340 Materials (49) (131) Commissions (11) (17) ––– ––– 160 192 ––– ––– Note that labour is a fixed cost.The average contribution per unit sold is: Solution IM 18.6 182 STANDARD COSTING AND VARIANCE ANALYSIS 2: FURTHER ASPECTS £1 000 000 (£278 000 + £50 000) = £168 4000 units Notes Variance analysis (£) a Sales planning volume variance (market volume variance) (3000 4000) £168 168 000A b Sales operating volume variance (market share) (3750 3000) £168 126 000F c Sales mix variance:

(actual sales volume actual sales in standard mix) standard margin Plastic (2500 3750) £160 = 50 000 Mahogany (1250 3750) £192 = + 60 000 10 000F d Sales price variances: (actual price standard price) AQ Plastic (£208 £220) 2500 = 30 000A Mahogany (£368 £340) 1250 = 35 000F 5 000F e Material cost variances:

Plastic 2500 £49 £120 000 = 2500F Mahogany 1250 £131 £160 000 = 3750F 6 250F f Sales commissions price:

Plastic (2500 £11) £26 000 = £1500F Mahogany (1250 £17) £23 000 = £1750A 250A g Fixed overhead variances:

Mahogany Plastic Labour 108 105 = £3000F 84 85 = £1000A 2 000F Production overheads 162 166 = £4000A 79 83 = £4000A 8 000A ––– ––– A 6 000A––– ––– A (b) The answer should emphasize the favourable performance by the firm during a period in which the regional market has declined by 25%. The difference between the actual profit and the original budget has arisen because of the change in themarket conditions with an adverse planning variance of £168 000. Given the benefit of hindsight, the firm would have budgeted for a £57 000 loss.

The favourable performance was due to a favourable sales mix variance of £126 000. The planned market share was 12% whereas the actual market sharewas 15%. Attention should also be drawn to the favourable sales mix and pricevariances. Overall, there was a net adverse selling cost variance of £5000.

(c) The answer should include a discussion of the following points: (i) The shop-floor employees may consider that there is little relationshipbetween their efforts and net profit. Therefore it may not motivate theemployees to improve their productivity.

(ii) The sales force is currently provided with an incentive via sales commission.

They are likely to be more motivated by a direct incentive scheme rather thanan indirect scheme where the rewards are shared equally amongst all the staff.

(iii) The guarantee of 90% of earnings and a possible loss of earnings may cause suspicion and create hostility to the new scheme.

(iv) There is a danger that a reward system based on net profits may encouragedysfunctional behaviour which focuses entirely on short-term profits andignores long-run profits.

(v) Production managers may feel that they have ‘lost out’ at the expense of the factory employees and no longer have a status symbol.

STANDARD COSTING AND VARIANCE ANALYSIS 2: FURTHER ASPECTS 183 184STANDARD COSTING AND VARIANCE ANALYSIS 2: FURTHER ASPECTS The question does not indicate whether a standard variable costing or a standard absorption costing system should be used. It is considered that a standard variablecosting system provides more useful information. Sales variances are therefore expressedin the terms of contribution margins, and a fixed overhead volume variance will notarise. The calculations are as follows. 1.Contribution per unit Quicut Powacut(£) (£) Selling price 120 (£28 800 /240) 200 (£24 000 /120) Variable cost 40 (£9600 /240) 60 (£7200 /120) ––– ––– Contribution 80 140 ––– ––– 2. Analysis of sales volume variances (1) (2) (3) (4) Budgeted sales Revised sales Actual sales Actual sales volume in target in volume in volume in standard mix standard mix a standard mix actual mix (000) (000) (000) (000) Q 240 312 260 280 P 120 156 130 110 Note a Revised forecast increased by 30% because the total market sales volume was 30% greater than the original forecast. Sales volume variance, (1)–(4):

(£000) Q40 £80 unit contribution 3200F P1 0 £140 unit contribution 1400A –––– 0 1800F–––– 0 Volume variance can be analysed as follows. Planning variance, (1)–(2):

(£000) Q72 £80 unit contribution 5 760F P3 6 £140 unit contribution 5 040F ––––– 0 10 800F––––– 0 Marketing share variance (controllable sales volume variance, (2)–(4)) (£000) Q32 £80 unit contribution 2560A P4 6 £140 unit contribution 6440A –––– A 9000A–––– A It is possible to extract a sales mix variance to ascertain how much of the £9000 con- trollable sales volume variance is accounted for by a change in the sales mix. Thesales mix variance is the difference between columns (3) and (4):

(£000) Q20 £80 unit contributions 1600F P2 0 £140 unit contributions 2800A –––– A 1200A–––– A Solution IM 18.7 In other words, if the actual sales mix had been in accordance with the budgeted sales mix, the controllable sales volume variance would have been £7.8m.

3. Sales price variances(Actual selling price budgeted selling price) actual quantity:

(£000) Q [(£32 200 /280) £120] 280 1400A P [(£24 200 /110) £200] 110 2200F –––– 800F –––– 4. Variable cost variancesFlexed budget actual cost:

(£000) Q (280 40 = £11 200) £11 480 280A P (110 60 = £6600) £6820 220A ––– A 500A––– A 5. Fixed costs (1) (2) (3) Original budget Revised budget (350 000 units) (360 000 units) Actual (£000) (£000) (£000) Traceable manufacturing: Q 8200 9200 a 7600 P 6800 6800 a 6800 Manufacturing period costs 5700 6000 6000 Administration and selling period costs 4300 4500 4500 Note a The question does not indicate how changes of output levels affect the fixed costs of individual departments. It is assumed that the increase in fixed costs is attributable purely to Quicut, where the output has increased.

(£000) Traceable fixed costs: Activity /planning variances, (l)–(2) Q 1000A P0 Expenditure, (2)–(3) Q 1600F P0 Manufacturing period costs: Activity /planning variances, (1)–(2) 300A Expenditure, (2)–(3) 0 Administration and selling costs: Activity /planning variances, (1)–(2) 200A Expenditure, (2)–(3) 0 (a) (i) Analysis for sales director Q P Total (£000) (£000) (£000) Budgeted contribution ( W1) 19 200 16 800 36 000 ––––– ––––– ––––– Planning /forecasting volume variance (uncontrollable) 5 760F 5 040F 10 800F Controllable market share variance (of which £1200 is accounted for by a change in sales mix) 2 560A 6 440A 9 000A Sales price variance 1 400A 2 200F 800F ––––– ––––– ––––– STANDARD COSTING AND VARIANCE ANALYSIS 2: FURTHER ASPECTS 185 Increase in contribution due to salesperformance 1 800F 800F 2 600F Administration and selling cost variances: Period costs planning /activity variance 200A Period costs expenditure — –––––– Increase in profit due to sales performance 2 400A –––––– (ii) Analysis for product managers Quicut Powacut (£000) (£000) (£000) (£000) Budgeted departmental profit 11 000 10 000 Planning /forecasting sales volume variance 5760F 5040F Market share variance 2560A 6440A Sales price variance 1400A 1 800F 2200F 800F –––– –––– Variable cost variance 280A 220A ––––– ––––– Actual departmental contribution 12 520 10 580Less traceable fixed manufacturing costs:

Planning /activity variance 1000A — — Expenditure variance 1600F 600F — — –––– ––––– –––– ––––– Actual departmental profit 13 120 10 580 ––––– ––––– Working (£000) ( W1 ) Budgeted contribution: Q 19 200 (£28 800 £9600) P 16 800 (£24 000 £7200) ––––– 36 000 ––––– (b) The initial impression is that the company has done well, with actual profits in excess of budgeted profits. The selling price of Powacut has been increased and sales volume has declined, whereas the selling price of Quicut has decreased andsales volume has increased. The net result has been an overall improvement overbudget in sales performance for both products. The adverse sales mix variance,however, indicates that it might have been better to increase the sales volume ofPowacut since this is the most profitable product. Cost variances are small, butthey do require further investigation.The variances are less impressive when the increase in the total sales volume for the industry is considered. The comparison with the original budget indicates afavourable volume variance of £1.8 m, but in view of the increase in the marketone would have expected a volume variance of £10.8 m. Consequently thefavourable volume variance can be attributed to an increase in the total marketrather than an improvement by the company. The company has not performed aswell as it should have done considering the change in the environment. The variances resulting from a change in the total market represents the planning variances. The planning variances consist of the following:

(£000) Sales volume planning F10 800F Traceable fixed costs A1 000A Manufacturing fixed costs A 300A Administration and selling A 200A ––––––– A9 300F ––––––– The remaining variances of £7.1 m represent adverse operating variances. The company should take steps to improve sales forecasts and consider fully theconsequences of adjusting selling prices to influence sales volume. The reduction in 186 STANDARD COSTING AND VARIANCE ANALYSIS 2: FURTHER ASPECTS Quicut’s selling price might have had an adverse effect in view of the £1.5 m increase in fixed costs.

(a) See ‘Statistical control charts’ in Chapter 18 for the answer to this question.

(b) The costs incurred for each decision for each potential state of nature will be as follows:

Potential states of nature Process in control Process out of control (£) (£) Decision :

Investigate the variance 1000 1000 + 2000 Do not investigate the variance Nil 10 000 The total variance is £7000 and the question indicates that there is a 0.80probability that the process is in control. The probability that the process is out ofcontrol is 0.20 (1 0.80). The expected value of the costs for each alternative are:

(£) Investigate the variance [(0.8 £1000) + (0.2 £3000)] 1400 Do not investigate the variance (0.20 £10 000) 2000 The variance should be investigated since the expected cost of investigating thevariance is lower than not investigating.

(c) The indifference point will occur when the expected cost of investigating and correcting the variance is equal to the benefits arising from investigating andcorrecting the variance (i.e. the cost of allowing the variance to continue). Letx= probability that the variance is out of control.

The indifference point will occur where:

1000 + 2000x= 10 000 x 8000 x= 1000 x = 0.125 Thus the variance should be investigated if the probability that the process is out of control exceeds 0.125 or if the probability that the process is in control is less than0.875 (1 0.125).

(d) The answer should draw attention to the difficulty in determining the costs and benefits of investigation (see ‘Decision models with costs and benefits of investigation’ in Learning Note 18.3 on the open access website for an explanation).In addition the answer should include a discussion of the following points.(i) Developing a model provides a conceptual understanding of the factors influencing the variance investigation decision.

(ii) The model identifies the most important elements influencing the decisionand specifies them in a predetermined mathematical form.

(iii) Because the model is specified in mathematical terms there is a danger that it may oversimplify the variance investigation decision.

(iv) There is a danger that decisions may become too mechanistic. It may bepreferable to rely on human judgement. Solution IM 18.8 STANDARD COSTING AND VARIANCE ANALYSIS 2: FURTHER ASPECTS 187 Solution IM 19.1 Solution IM 19.2 Solution IM 19.3 Solution IM 19.4 188DIVISIONAL FINANCIAL PERFORMANCE MEASURES (a) See ‘Profit centres and investment centres’ in Chapter 19 for the answer to this question.

(b) See ‘Pre-requisites for successful divisionalization’ in Chapter 19 for the answer to this question.

(c) The main behavioural and control consequences which may arise if profit or investment centres are introduced relate to designing performance measures that encourage goal congruence and avoid dysfunctional behaviour. This situation mayoccur when divisional managers make decisions to increase their performance atthe expense of the company as a whole. Friction may also arise with transferpricing where this leads to incorrect decisions or fails to provide a reasonablemeasure of divisional performance.

(d) See ‘Return on investment’, ‘Residual income’ and ‘Economic value added’ in Chapter 19 for the answer to this question.

See Chapter 19 for the possible answer to this question.

(a) See the introduction and ‘Advantages of divisionalization’ in Chapter 19 for the answer to this question.

(b) See ‘Disadvantages of divisionalization’ and ‘Pre-requisites for successful divisionalization’ for the answer to this question. In addition, the answer should discuss the difficulty of establishing performance measures that encourage goalcongruence and avoid the dysfunctional consequences described in Chapters 16and 19.

(c) See the answer to Question IM 19.10 (part 2c) for the answer to this question. In addition the answer should point out that group management will need to placegreater emphasis on co-ordinating the activities of the divisions, includingmanaging the transfer pricing system, and implementing and controlling thedivisional reward structures.

(a) The answer should stress the need for divisional measures to focus on performance measures that are more directly related to the strategic objectives and the strategies of the organization. At the operational level these are cascaded downinto operational measures that are more related to specific operational activities.In particular at the divisional level a balanced scorecard approach should beadopted. The answer should draw off ‘The balanced scorecard as a strategicmanagement system’ in Chapter 22 whereas for operational measures thediscussion should draw off ‘Operational measures’ in Chapter 22.

(b) The answer could draw off the section titled ‘Results or output controls’ in Chapter 16. In addition, the answer should point out the difficulties of measuringperformance in non-profit organizations because output is often difficult tomeasure. The following issues should also be discussed:

Divisional financial performance measures Solutions to Chapter 19 questions (i) goal congruence; (ii) establishing measurable objectives; (iii) cultural factors.

It is important that the employees identify with the goals and objectives that are set and accept their performance being measured on the basis of these factors.Participation has a significant role to play in ensuring that the goals and objectivesand the resulting performance measures are accepted and will act as a motivatingforce (see Chapter 16 for a discussion of the role of participation in performanceevaluation). Particular care must be taken in developing performance measures sothat they will encourage goal congruence and minimize the dysfunctionalconsequences. Here the answer could draw off the discussion in Chapter 16relating to the harmful side-effects of controls. Control in non-profit organizations is particularly difficult, because it is not always possible to state the objectives in quantitative terms or to measure theoutput of services. If it is not possible to produce a statement of a particularobjective in measurable terms, the objective should be stated with sufficient clarityfor there to be some way of judging whether or not it has been achieved. In a non-profit organization performance measures should attempt to measure both the quantityand the qualityof outputs. It is usually much easier to measure quantity than quality. For example, in an educational establishment the quantitymeasure of the number of students who graduated in the previous year is mucheasier to measure than the quality measure of how well the students wereeducated. Nevertheless, the quality measure should not be overlooked. In somecases the quantity indicator may provide an approximate measure of quality. Forexample, the number of students who have graduated in the previous year,analysed according to degree classification, may provide an approximation of thequality of the education. Frequently in non-profit organizations input measures are used as proxy measures for output. If no satisfactory output measures can be formulated, inputmeasures are a better measure of output than no measure at all. For example, itmay not be feasible to construct output measures reflecting the quality of healthcare. In the absence of such measures, the amount spent on salaries and medicinesmay provide a useful clue to output. If, in the extreme, nothing was spent, we canconclude that nothing was accomplished. When inputs are used as proxy outputmeasures, care must be exercised to avoid undue reliance on them. For example,the amount spent on wages and medicines may not represent an improved serviceto the users because the resources may not have been used effectively. Attemptsshould be made to develop useful measures of output so that efficiency andeffectiveness can be measured. It is important that financial measures are notoveremphasized and that a balanced scorecard approach (see Chapter 22) isadopted using realistic targets that relate the performance measures to theobjectives of the organization. It is important that management are aware of cultural issues in designing a performance measurement and evaluation system. Any changes should be handledcarefully and thoroughly explained. Staff should be fully involved in order tosecure their support. If staff are alienated the system will not be successful.

(a) The economic evaluation of the three projects using the NPV decision rule is as follows:

Project A: (£21 000 2.855) £60 000 = £45 Project B: [£25 000) /1.15 + £20 000 /(1.15) 2 + £20 000 /(1.15) 3 + £15 000 /(1. 15) 4 ] £60 000 = £1412 Project C: [£10 000 /1.15 + £20 000 /(1.15) 2 + £30 000 /(1.15) 3 + £40 000 /(1.15) 4 ] £60 000 = + £6414 Solution IM 19.5 DIVISIONAL FINANCIAL PERFORMANCE MEASURES 189 Consequently, from the company’s point of view, project C should be accepted, pro- ject A is marginal and project B should be rejected. The following ROI and residualincome (RI) measures in respect of each project over the four-year period would bereported:Year 123 4 (£) (£) (£) (£) Project A Net asset value at beginning of year 60 45 30 15 –––– –––––– ––– –––– Net cash flow 21 21 21 21 Depreciation 15 15 15 15 –––– –––––– ––– –––– Net profit 6 6 6 6 Cost of capital (15% of NAV) 9 6.75 4.5 2.25 –––– –––––– ––– –––– Residual income (3) (0.75) 1.5 3.75 –––– –––––– ––– –––– –––– –––––– ––– –––– ROI 10% 13.33% 20% 40% Project B Net asset value at beginning of year 60 45 30 15 –––– –––––– ––– –––– Net cash flow 25 20 20 15 Depreciation 15 15 15 15 –––– –––––– ––– –––– Net profit 10 5 5 0 Cost of capital (15% of NAV) 9 6.75 4.5 2.25 –––– –––––– ––– –––– RI 1 (1.75) 0.5 (2.25) –––– –––––– ––– –––– –––– –––––– ––– –––– ROI 16.67% 11.1% 16.67% – Project C Net asset value at beginning of year 60 45 30 15 –––– –––––– ––– –––– Net cash flow 10 20 30 40 Depreciation 15 15 15 15 –––– –––––– ––– –––– Net profit (5) 5 15 25 Cost of capital (15% of NAV) 9 6.75 4.5 2.25 –––– –––––– ––– ––––– RI (14) (1.75) 10.5 22.75 –––– –––––– ––– ––––– –––– –––––– ––– ––––– ROI (8.3%) 11.1% 50% 166.7% Divisional managers are rewarded and evaluated on the basis of ROI. If the divisional manager places a great emphasis on the short-term performance measure, it is unlikely that he or she would consider project C, since this yields anegative ROI in years 1 and 2. It is likely that the manager would opt for project B,since this yields the highest ROI in the first year. If the divisional manager adopts alonger-term perspective, he or she may opt for project C, since this yields thehighest average yearly ROI over the four-year period. If divisional managers wereevaluated on the basis of RI, it is likely that the manager would again chooseproject B if a short-term perspective is adopted and project C if a long-termperspective is adopted. Note that project C has the largest average annual RI.

From the company’s point of view, decisions ought to be made based on the NPV rule. This would lead to the acceptance of project C and the rejection of projects A and B. Thus there is a possibility that there will be a divergence of viewsbetween the company and the division regarding which project should beaccepted.

(b) For the answer to this question see ‘The effect of performance measurement on capital investment decisions’ in Chapter 19 and ‘Reconciling short- and long-termresidual income measures’ (Learning Note 19.1 on the open access website). 190 DIVISIONAL FINANCIAL PERFORMANCE MEASURES (a)Grain Bakery Return on capital 23.34% £44 000 £40 300 21%£25 900 £23 800 employed £15 850 £10 000 Residual income £1322.5 [£3700 (15% £15 850)] £600 [£2100 (15% £10 000)] (£000) Controllable profit £4400 (£3700 + £700) £3200 (£2100 +£1100) (£000) The gain on the sale of plant of the Bakery division has been excluded from the above figures, since this is assumed to refer to a decision taken by central management. Theobjective is to measure managerial performance. Therefore allocated head office costsare excluded from the above calculations. With the ROCE and residual income (RI) calculations, depreciation has been deducted to calculate the divisional profits.However, for the purpose of measuring managerial performance the majority of the depreciation charge will be non-controllable because central management controlsthe majority of investment decisions. Consequently the ROCE and RI calculationsshould only include depreciation on controllable investment. The calculation of con-trollable profit excludes all of the depreciation charges, but in practice shouldinclude a charge for depreciation on controllable investment. The ROCE and RI calculations are based on written down values for the year ended 30 November. It would be preferable to base the calculations on theaverage value for the year rather than the year-end value. When written downvalues are used, the asset valuation declines each year, and this can cause ROCEand RI to increase even though profits have not increased. An alternative is to usegross book values, but this can also distort the performance measure. Preferablyassets should be valued at market values or replacement cost when calculating RIand ROCE (see ‘Impact of depreciation’ in Chapter 19). The overall company cost of capital has been used to calculate RI. An overall cost of capital charge is appropriate only when divisional projects are equal to theaverage risk of the company as a whole. In other words, the cost of capital chargeshould depend on the risk of divisional investments (see ‘Determining thedivisional cost of capital charge’ in Learning Note 19.2 on the open access websitefor a more detailed discussion). Finally, only controllable divisional overheads should be included in divisional profit calculations. If divisions cannot acquire supplies from outside the group thenthey should be charged for actual quantities at an agreed standard price or marketprice. Care must be taken to ensure that the profit calculations are not distorted byusing transfer prices which are inappropriate for performance evaluation.

(b) See ‘Distinguishing between the managerial and economic performance of the division’, ‘Return on investment’, ‘Residual income’ and ‘Economic value added’ inChapter 19 for the answer to this question. In particular, answers should indicatethat the managers have minimal control over investment decisions and are beingincorrectly treated as investment centres. Controllable profit attempts to excludeitems which are beyond the control of divisional managers, and is thereforepreferable to methods which do not distinguish between controllable andnoncontrollable items. The weakness of controllable profit is that it fails to motivatemanagers to control the investment in working capital. It is also an absolutemeasure, thus making interdivisional or company comparisons inappropriate whencapital employed differs significantly. The determination of performance levelswould have to be based on a comparison of actual and budgeted divisional profitssupplemented by a standard costing and budgetary control system. DIVISIONAL FINANCIAL PERFORMANCE MEASURES 191 Solution IM 19.6 RI is appropriate where managers have a significant influence over their invest- ment decisions. Managers are thus encouraged to improve their performance rating by seeking investment opportunities which earn a return in excess of cost ofcapital. Divisional independence is maximized and goal congruence is encouraged.Managers are not motivated to accept only projects which are in excess of theircurrent ROCE. RI is consistent with maximizing the present value of future cashflows in the long run if assets are valued at their economic values and annuitydepreciation is used. If these conditions do not hold, there is no guarantee that theshort-run RI will be consistent with maximizing the present value of future cashflows. If Sliced Bread were to adopt the RI measure, it would be essential thatdepreciation and interest charges be based on controllable assets valued atreplacement cost or market values. The resulting RI calculation should becompared with a budget based on previous years’ performance and anticipatedfuture changes. In addition, the performance measures should be supplemented bya system of standard costing and budgetary control. ROCE is widely used for measuring divisional performance. This is because it is a relative measure which is widely understood by managers and which is capableof being analysed in a pyramid of sub-ratios. The weakness of ROCE is that itdoes not motivate managers of investment centres to invest in projects which areless than the existing ROCE but above the cost of capital. Consequently it may notencourage goal congruence and is not consistent with a DCF appraisal. If ROCE isused, it is preferable to value the investment at replacement cost or market values.Care should be taken when comparing divisional ROCE with other divisions andcompanies, because different accounting policies and asset valuations might beused. ROCE is most suited to measuring the performance of profit centres.

(c) See ‘Addressing the dysfunctional consequences of short-term financial performance measures’ in Chapter 19 for the answer to this question. Inparticular, the answer should stress that information on market share, productdiversification and product quality should be included as further measures ofdivisional performance.

(a) Return on investment ABCD Profit (£m) 4.0 1.1 1.2 0.5 Net assets (£m) 23.5 9.5 4.0 1.8 Return on investment 17.02% 11.58% 30% 27.78% Residual income Profit (£m) 4.0 1.1 1.2 0.5 Interest charge (16% on net assets) (£m) 3.76 1.52 0.64 0.29 Residual income (£m) 0.24 (0.42) 0.56 0.21 Assumptions The divisions are investment centres, and it is therefore appropriate to chargemanagers an imputed interest charge on divisional assets. The interest /cost of capital charge is based on the average cost of capital for the company (0.4 10% + 0.6 20% = 16%). It is assumed that the risk attaching to the activities of each division is equivalent to the average overall risk on the company’s assets. If riskvaries from division to division, a different percentage cost of capital /interest charge should be applied to each division. The higher the risk, the higher shouldbe the interest charge. The group interest charge has been ignored, since it is apurely notional charge which bears no relation to the company’s cost of capital. The above calculations are after taking into account the exchange gain by division A. It is assumed that managers are accountable for foreign exchangemanagement where overseas transactions occur. However, the exceptional charge Solution IM 19.7 192 DIVISIONAL FINANCIAL PERFORMANCE MEASURES to division C has not been included in the above calculations, since it is assumed to be an exceptional item and results from a decision taken at head office level.The profits are after charging depreciation, since this reflects a charge for the useof divisional assets. It would be preferable to base the depreciation charge onreplacement cost rather than historical cost.For a detailed discussion of the usefulness of residual income (RI) and return of investment (ROI) see Chapter 19. The answer should stress that ROI is a relativemeasure which gives an approximate indication of the return on a division’sinvestment. This can be compared with an appropriate cost of capital and thussignify whether or not divisional investments are obtaining adequate returns. Themeasure highlights those divisions where economic viability may need to bereviewed using appropriate relevant economic cost and revenue estimates. ROIcan also be used for comparing the returns between divisions of different sizes. Itis also widely used by financial analysts for making intercompany comparisons. RIis an absolute measure which in the long-run takes into account the opportunitycost of an investment and is equivalent to NPV. By making a risk-adjusted cost ofcapital charge, risk is incorporated into the performance measure. RI also encourages managers to invest in projects whose returns are in excess of the cost of capital. Possible standards for comparison include budgeted /target ROI or RI, comparisons with other divisions within the group, comparisons with previous periods andcomparisons with similar companies operating outside the group. However, care must be taken to ensure that one is ‘comparing like with like’ and that themeasurements are consistent and based on the same asset valuation and profitmeasurement principles.

(b) It is unclear whether the question relates to the evaluation of the division as an economic entity or the evaluation of the performance of the divisional managers.Where the economic performance of a division is being evaluated, all head officecosts should be allocated to divisions. Allocations should be based on benefitsreceived (e.g. sales values for the credit control department) using appropriate costallocation bases. Alternatively a transfer pricing system can be established forthose head office services where divisional usage can be measured. Head officecosts are joint costs, and it is inevitable that arbitrary allocations will be used totrace some costs to divisions. Care should therefore be taken when interpretingthe economic performance of a division, and the performance measures should beseen as a monitoring system which can be used to trigger off an economicinvestigation of the viability of a division.For evaluating managerial performance, only controllable head office expenses should be charged to divisional managers. For the answer to this part of thequestion see ‘Alternative divisional profit measures’ in Chapter 19. Arbitraryallocations should be avoided. It is preferable to use transfer prices based ondivisional usage when charging head office costs to divisional managers.

(c) The main problems are: (i) The initial high investment together with long paybacks may result in a lowROI or negative RI in the early years of a project’s life.

(ii) The cash flows are more uncertain in high-tech industries, and it is therefore difficult to set budgets against which to monitor actual performance.

(iii) Many of the benefits are of a qualitative nature and not easy to quantify. (iv) It is difficult to establish an appropriate cost of capital which takes into account risk when calculating RI. If ROI is used, the ROI should be higher to compensate for the increased risk. However, it is extremely difficult todetermine the additional return which is required to justify the additionalrisk.

(v) The RI and ROI measures are overstated if written down values are used in the calculations. Managers will be reluctant to replace old assets with newassets, because this will lead to a large increase in the investment base and anaccompanying decline in ROI and RI. DIVISIONAL FINANCIAL PERFORMANCE MEASURES 193 The following actions should be taken to improve these measures:(i) Value assets at replacement cost instead of historical cost. Depreciation charges should also be based on replacement costs (see ‘The impact of depreciation’ in Chapter 19).

(ii) Use other performance measures in addition to ROI and RI so that some ofthe dysfunctional consequences which arise from placing too much emphasison single financial measures can be avoided (see ‘Addressing thedysfunctional consequences of short-term financial measures’ in Chapter 19).

(iii) Set realistic budgets and accept that cash flows may decline in the short term. Compare actual results with realistic budgets and avoid placing too muchemphasis on short-term results.

(iv) Use risk-adjusted imputed interest charges using the capital asset pricingmodel (see Chapter 14). For a more detailed discussion of the conflictbetween short-run and long-run performance measures and alternativedepreciation methods see Learning Note 19.1 on the open access website.

(a) Performance statements similar to that illustrated in Exhibit 19.1 in the text should be presented in the answer to this question. In addition, the statementsshould contain columns for budgeted, actual and variances. If the statements areproduced at frequent intervals, a column for the cumulative variances for the yearto date should be included. Alternatively it might be preferable to showcomparisons with previous period or year figures.Managers should be held responsible for the controllableresidual income.

Where managers have no control over the investment in fixed assets or workingcapital, it is inappropriate to evaluate them on the basis of residual income.Instead, managers could be evaluated on the basis of budget and actualcontrollable contribution or controllable contribution as a percentage of assetsinvested in the division. Where the divisions (e.g. coal mines) sell mainly to otherdivisions within the group and have little influence over the level of total salesrevenue, it might be preferable to regard them as service cost centres. Performanceshould be evaluated based on a comparison of budget (target) and actual costs. In addition, the reports should be supplemented by appropriate non-financial measures such as physical output measures, output per employee, stock levels andlabour turnover.

(b) Key measurement issues to resolve include: (i) The basis for determining appropriate transfer prices based on the objectivesof a transfer pricing system specified in Chapter 20. Where possible, market-based transfer prices ought to be used. Otherwise a choice must be madebetween using negotiated or centrally determined transfer prices.

(ii) The basis for determining asset valuations for the purpose of calculating the residual income interest charge or return on capital employed. For thesecalculations a choice must be made between valuing assets at historical cost(gross or net book value) or some departure from historical cost. See ‘Theimpact of depreciation’ in Chapter 19 for a discussion of asset valuation for aresponsibility accounting system.

(iii) W here residual income or EVA is used, the basis for determining the percentage interest charge should be determined. Should this percentage beconstant or vary from division to division? See ‘Determining the divisionalcost of capital’ in Learning Note 19.2 on the open access website for adiscussion of this point.

(iv) The extent to w hich non-financial measures should be included in the performance measurement system and the weighting to be given to specificmeasures when multi-performance measures are used. Solution IM 19.8 194 DIVISIONAL FINANCIAL PERFORMANCE MEASURES (c) For tariff-setting purposes, all costs incurred will be allocated to the variousproducts /tariffs in order to calculate unit full costs. In addition, unit costs will be categorized into their fixed and variable elements in order to provide information for determining short- and long-run minimum prices and cost volume profit relationships. Estimates of demand functions will be required for the varioustariffs if optimal prices are to be set. For performance evaluation, costs are allocated to responsibility centres (instead of products), based on the principles outlined in Chapter 16. It is important that theperformance reporting system distinguish between controllable and non-controllablecosts. Consequently the problem of allocating joint costs to cost objects may notarise. Actual performance should be compared with an appropriate target such as aflexed budget, past results or other profit /investment centres. Responsibility accounting places more emphasis on the use of nonfinancial measures.

(a) (i) Exhibit 19.1 in the text provides an illustration of the calculation of alternative divisional profit measures. Controllable divisional profit beforetaxes is calculated as follows: (£) Sales to outside customers Transfers to other divisions ––––– Less: Variable costs (including goods purchased from other divisions) ––––– Variable Contribution margin Less: Controllable divisional fixed costs ––––– Controllable profit before tax ––––– (ii) The degree of divisional autonomy can influence controllable profits. Where central headquarters imposes a transfer pricing system, reported controllableprofit may be significantly influenced by the input and output prices set bycentral headquarters. Alternatively, where a competitive external marketexists market prices can be used for inter-divisional sales and purchases anddivisional profit is more likely to represent the real economic contribution ofthe division to total company profits. In these circumstances divisionalcontrollable profit is mainly subject to those factors that can be influenced bydivisional management.In some situations divisional managers are not allowed to purchase and sell goods outside the group. Therefore divisional managers do not have fullcontrol over input and output decisions. Where divisional managers have fullautonomy they can seek cheaper sources of supply and are thus able toincrease controllable profits. Divisional managers can also determine the mixof internal and external sales and purchases. Thus the degree of divisionalautonomy determines the extent to which divisions can influencecontrollable profit. If divisions are not investment centres they cannot influence divisional investment, and depreciation on divisional assets will be beyond the controlof divisional managers. However, where divisions are regarded as investmentcentres the accounting policy for depreciation may be determined at grouplevel. Group depreciation policy will therefore have a significant influence onreported controllable divisional profit.

(b) The investment should be undertaken because it has a positive NPV of £45 060 [(£380 000 2.487) £900 000)]. However, divisional management is likely to make the decision on the basis of the impact that acceptance of the investment willhave on the divisional performance measure. The residual income calculations areas follows: Solution IM 19.9 DIVISIONAL FINANCIAL PERFORMANCE MEASURES 195 (i)Residual income using straight line depreciation Year 1 Year 2 Year 3 (£000) (£000) (£000) WDV at start of year 900 600 300 ––– ––– ––– Net cash inflow 380 380 380 Less depreciation 300 300 300 ––– ––– ––– Net profit 80 80 80 Less interest on capital (10%) 90 60 30 ––– ––– ––– Residual income (10) 20 50 ––– ––– ––– (ii) Residual income using annuity depreciation Year 1 Year 2 Year 3 (£000) (£000) (£000) WDV at start of year a 900 .0 628.1 329 .0 Net cash inflow 380 .0 380 .0 380 .0 Less: Depreciationa (271.9) (299.1) (329) .0 Interest on capital (90.0) (62.8) (32.9) –––– –––– –––– Residual income 18.1 18.1 18.1 –––– –––– –––– Note a Calculation of annuity depreciation:

(1) (2) (3) = (1) (2) Annual 10% interest on Capital Capital Year repayment capital outstanding repayment outstanding (£000) (£000) (£000) (£000) 0 900 .0 1 361.9 90 .0 271.9 628.1 2 361.9 62.8 299.1 329.0 3 361.9 32.9 329.0 The annual repayment is calculated by dividing the investment outlay of £900 000 by the present value of an annuity for 3 years at 10% (2.487). If straight line depreciation is used general management may reject the investment if they adopt a short-term perspective because the residual incomeis negative in the first year. With annuity depreciation residual income ispositive and constant each year and management is motivated to accept theinvestment. The annuity method of depreciation will not necessarily beconstant and positive in all years for positive NPV projects where cash flowsvary from year to year. For a discussion of the impact of depreciationmethods on residual income where unequal cash flows occur see LearningNote 19.1 on the open access website.

Part One (a) The reported performance for 2012 and 2013 without any of the proposals is estimated to be as follows: ROCE: £450 000/£4 800 000 = 9.4% Average daily purchases: (£2 920 000/365) = £8 000Average daily sales: (£6 900 000/365) = £18 904.10Average daily cost of sales: (£6 900 000 – £450 000)/365 = £17 671 Cash conversion period: Number of days debtors (£1 035 000/£18 904) = +55 days Number of days stocks (£530 000/£17 671) = +30 days Number of days creditors (£320 000/£8000) = 40 days –––––––– 45 days–––––––– Solution IM 19.10 196 DIVISIONAL FINANCIAL PERFORMANCE MEASURES Number of innovations = 4 On the basis of the above information none of the divisional managers would receive an annual salary bonus. The office manager’s proposal This will cause stocks to be £160 000 lower for both years and creditors will be £180 000 more than predicted for 2012 and revert to the predicted level for2013.

ROCE for 2012: (£450 000 £2000) / (£4 800 000 £160 000 £180 000) = 10.04% ROCE for 2013: (£450 000 £16 500) / (£4 800 000 £160 000) = 9.3% Revised average sales per day: (£6 900 000 + £160 000)/365 = £19 342 Revised cash conversion period: Number of days debtors (2012) (£1 035 000/£19 342) = +54 days Number of days stocks (£530 000 – £160 000)/£17 671) = +21 days Number of days creditors (£320 000 + £180 000)/£8000) = 63 days –––––––– 12 days –––––––– Revised cash conversion period: Number of days debtors (2013) (£1 035 000/£18 904) = +55 days Number of days stocks (£530 000 – £160 000)/£17 671) = +21 days Number of days creditors (£320 000)/£8000) = 40 days –––––––– 36 days –––––––– The number of innovations remain unchanged at 4. For 2012 all of the divisional managers, with the exception of the chief executive and the design manager, will receive their bonuses. In 2013 only the accountantand office manager will receive their bonuses. Production manager’s proposal It is assumed that the increase in operating profit is after charging annualdepreciation on the new equipment of £45 000. In the first year of purchase theROCE would be: (£450 000 + £25 000) / (£4 800 000 + £400 000 £45 000) = 9.2% This will result in a decline in the ROCE, and since the other measures will remain unchanged, the proposal is unlikely to be accepted. Also in the secondyear of purchase the ROCE will still be less than the existing return of 9.4% so itis unlikely to be accepted if a longer time horizon is adopted. Design manager’s proposal In the first year of implementation profit will increase from £450 000 to £470 000. The change in net assets will be as follows: DIVISIONAL FINANCIAL PERFORMANCE MEASURES 197 Original estimate 4 800 000 Net cost of investment in the first year (£100 000 – £10 000depreciation) +90 000 Increase in stocks less creditors (£530 000 – £320 000) × £20 000/£450 000 +9 333 Increase in debtors from goods on sale or return (£6 900 000 × £20 000/£450 000 × 0.5) +153 333 –––––––– Estimated net assets 5 052 666 –––––––– Revised ROCE (£470 000 / £5 052 666) 9.3% The cash conversion period without considering the proposal is 45 days which is in excess of the target of 40 days. The proposal will increase the conversionperiod and a detailed calculation is unnecessary since it will be in excess of the 40days target required for the bonus. Presumably the proposal will be classed as being successfully brought to the market after it has overcome the initial market resistance. This will not occur until 2013. Theproposal would therefore generate bonuses for the chief executive and designmanager in 2013 but not for any of the remaining members of DE management.

(b) Office manager’s proposal It is assumed that the £16 500 per annum represents cash flows. The NPV of the proposal is as follows:

£ Annual 10 year cash flows (£16 500 × discount factor for 10 years of 6.710) 110 715 Assumed replacement of stock after 10 year time horizon (£160 000 × 0.4632) 74 112 Immediate penalty cost – 2 000 Proceeds from disposal of stock +160 000 –––––––– NPV 26 827 –––––––– Production manager’s proposal Annual cash flows (£25 000 + £45 000 depreciation) discounted for 8 years (£70 000 × 5.747) 402 290 Residual value (£40 000 × 0.5403 discount factor) 21 612 Initial outlay 400 000 –––––––– NPV 23 902 –––––––– Design managers’s proposal Investment outlay 100 000 Increase in working capital (£9 333 + £153 333 see part (a) ) 162 666 Annual incremental cash flows (£20 000 + £10 000 depreciation discounted for 10 years = £30 000 × 6.710) +201 300 Assumed residual value of incremental working capital in year 10 = £162 666 × 0.4632 +75 347 –––––––– NPV +13 981 ––––––– The design manager and the production manager’s proposal should be accepted and the office manager’s proposal should be rejected. 198 DIVISIONAL FINANCIAL PERFORMANCE MEASURES Part Two (a) The advantages are: (i) The consultants are likely to have greater experience of designing andimplementing new management accounting systems.

(ii) The consultants are likely to have a greater knowledge of new innovations.

(iii) The consultants have the resources to implement new systems whereas FPE’s staff are likely to be too busy with day to day activities and therefore unable to devote sufficient time to implementing new systems.

(iv) They can draw off staff who specialize in different areas or who have theexperience across a wide range of business functions.

The disadvantages are: (i) Lack of detailed knowledge of existing systems.

(ii) Lack of detailed knowledge of FPE’s business.

(iii) Consultants are costly to employ. (iv) Resistance to change by existing staff may be greater if they have not beeninvolved in designing and developing the new systems.

(b) See Chapter 19 for the answer to this question.

(c) The answer should explain that cost centres will be replaced by profit or investment centres and how top management will rely more heavily on usingresults controls, such as ROI or EVA, to monitor divisional performance. Inaddition the financial measures will be supplemented by non-financial measuresusing the balanced scorecard approach described in Chapter 22. The answershould include a discussion relating to the move from detailed controls to adelegation of authority and control by means of approval of the master budget(rather than the detailed functional budgets) and long-term plans by centralmanagement. Capital expenditure will be controlled by means of an overall ceilingwithin which divisionalized management can authorize. Beyond a certain limit andfor major strategic projects central management approval may be necessary.

Part Three (a) See ‘Return on investment,’ ‘Residual income’ and ‘Economic value added’ in Chapter 19 for the answer to this question.

(b) The answer should draw attention to the dysfuctional consequences that can arise by placing too much emphasis on performance measures. Such dysfunctional consequences are likely to be exacerbated by linking pay to the performancemeasures. See ‘Harmful side effects of controls’ in Chapter 16 for a discussion ofwhy the dysfunctional consequences are likely to arise. For the measures thatmight be taken to deal with the identified problems see ‘Addressing thedysfunctional consequences of short-term financial measures’ in Chapter 19.

(c) For an explanation of the JIT philosopy see ‘Just-in-time systems’ in Chapter 21. The answer should also draw attention to the fact that ROCE includes many itemsthat the production manager may not be able to influence. The cash conversionperiod performance measure will support the JIT philosophy by encouraging thereduction in stocks but it also includes debtors and creditors which are notdirectly related to the activities of the production manager. If top managementwant to motivate the production manager to follow a JIT philosophy they shouldadopt performance measures that support the JIT philosophy. Such measuresmight include a single throughput measure (see ‘Operation process measures’ inChapter 22 for an explanation) or a range of measures relating to set-up times,throughput cycle times, percentage defects, stock levels and percentage ofdeliveries that are on time.

DIVISIONAL FINANCIAL PERFORMANCE MEASURES 199 Solution IM 20.1 Solution IM 20.2 TRANSFER PRICING IN DIVISIONALIZED COMPANIES (a) For an explanation of why cost-plus transfer prices are unlikely to lead to themaximization of group profits see ‘Cost plus a mark up transfer prices’ in Chapter 20. If there is an external market for the intermediate product, the cost-plustransfer price would lead to maximization of group profits only if it was equal tothe external market price. If the company has no market for the intermediateproduct and the variable cost per unit of output of the supplying division isconstant, the transfer price which would lead to maximization of group profitswould be unit variable cost.If Exel Division transfers the products at actual cost plus 20% mark-up, the division will not be motivated to control its costs. Exel will obtain a greater mon-etary mark-up if actual costs are higher than they should be. Any inefficiencies willbe passed on to the receiving division. Thus actual costs are an inappropriate basisfor assessing divisional performance. Transfers should be at standardmarginal cost and not actual cost. Any difference between the transferred-out costs andactual costs incurred would then result in the supplying division being accountablefor adverse or favourable variances. Thus the supplying division is motivated tominimize its costs.

(b) Where there is a shortage of supply of the raw materials to produce the inter- mediate product, a linear programming model can be formulated whichincorporates all the relevant input, cost, revenue and output information relatingto the supplying and receiving divisions. The solution to the model indicates howmuch of the intermediate products should be produced, the quantity of theintermediate product which should be transferred to the receiving division, andthe quantity of the intermediate and final products which should be soldexternally in order to maximize group profit. A production programme derivedfrom the output of the linear programming model could be dictated to thedivisions by the management at central headquarters. Alternatively transfer pricescan be established from the output of a linear programming model which willmotivate the managers to produce the optimum output.

(c) Where the supplying division does not have sufficient capacity to meet the demands placed upon it, the transfer price derived from the linear programmingsolution will result in the supplying division being credited with all of the contri-bution arising from the transfers, and the receiving division reporting a zerocontribution. Therefore the performance measurement data will not provide anappropriate indication of the receiving division’s contribution to total groupprofit. In addition, imposing a transfer price will result in divisional autonomybeing undermined. For a discussion of how this problem might be resolved see‘Proposals for resolving transfer price conflicts’ in Chapter 20.

(a) Figure Q20.2 illustrates the situation faced by the group. Where there is a perfectly competitive market for the intermediate product the current market price is the most suitable basis for setting the transfer price. Thesupplying division (Fabri) should supply as much as the receiving division (Gini) Transfer pricing in divisionalized companies Solutions to Chapter 20 questions 200 requires at the current market price, so long as the incremental cost is lower than the transfer price. If this supply is insufficient to meet the receiving division’sdemand, it must obtain additional supplies by purchasing from an outside supplierat the current market price. Alternatively, if the supplying division produces moreof the intermediate product than the receiving division requires, the excess can besold on the outside market at the current market price.Applying the above principles, 50% of Fabri’s output would be transferred to Gini at the current market price and the remaining capacity of 50% sold on theexternal market. Alternatively, divisional profitability and overall group profit-ability would remain unchanged if 70% of Fabri’s capacity were sold in theexternal market and 30% transferred to Gini. Gini would then purchase a further20% in the external market. Where sales in the external intermediate product market result in selling costs additional to those incurred from internal sales, the market price transfer pricingrule should be modified by deducting the additional selling costs from the externalmarket price. If the market for the intermediate product is imperfect it is unlikely that market prices will represent the optimal transfer price. With imperfect markets, it isnecessary for central headquarters to intervene and examine the marginal cost,marginal revenue and net marginal revenue schedules of the supplying andreceiving division and set the transfer price at the point where the marginal cost ofthe supplying division is equal to the sum of the marginal revenue and netmarginal revenue schedules (i.e. the marginal cost of the supplying division at theoptimum output level for the group as a whole). If Fabri’s variable costs are constant and fixed costs remain unchanged through- out the potential output range for the period then variable cost per unit of outputis the optimal transfer price. In addition Gini division could pay Fabri division afixed payment for the period for the privilege of obtaining the intermediateproduct at marginal cost. For example, if 70% of Fabri’s output is allocated to theintermediate external market and the remaining 30% for transfers to Gini thenGini should negotiate a fixed payment equivalent to approximately 30% of Fabri’sfixed costs for the period. The aim should be to motivate Gini to reject anyexternal supplier quotes in excess of the marginal cost of Fabri division.

(b) If the market for the intermediate product is imperfect and divisional autonomy is limited then it is likely that central headquarters will intervene and set an imposedtransfer price as described in part (a) of the question. However, if the divisionshave full independence then the divisions are likely to negotiate a mutually TRANSFER PRICING IN DIVISIONALIZED COMPANIES 50% of capacity 70% of capacity Gini division Fabri division External final product market Intermediate external product market Figure Q20.2 201 acceptable transfer price. Negotiated transfer prices may not maximize group profits but this may be offset by the motivational advantages that arise fromgranting full independence.Divisional profitability measures will be affected by the transfer price used, since the transfer price represents revenue to the supplying division and an expense to the receiving division. Where a perfectly competitive market price exists, the divisionalprofitability measures are more likely to represent the real economic contribution ofthe divisions to total company profits. However, where an imperfect external marketexists, or is non-existent, there is a danger that the transfer price will not reflect adivision’s real contribution to group profits. Distortions are likely to be greater wheninternal purchases /sales represent a significant percentage of total divisional purchases /sales and where the percentage fluctuates from period to period. Thus the impact of the transfer price on the divisional performance measure is a factor thatmust be considered when setting transfer prices.

(a) (i) See Exhibit 19.1 in Chapter 19 for the answer to this question. (ii) It is assumed that the question relates to transfer pricing issues only. Where there is a perfect competitive market for the intermediate product, and fullautonomy is granted, it is likely that divisional managers will choose to tradeat the external market price. This should result in optimal decisions in mostcircumstances. However, if the supplying division cannot sell all of its outputexternally, to ensure that group profits are maximized, the receiving divisionmust be instructed to purchase from the supplying division the quantity it isprepared to supply at the market price. If full autonomy is given to divisionsthey might not follow this rule and overall optimality may not ensue. Where the market for the intermediate product is imperfect corporate headquarters must gather data from the divisions to set the optimal transferprice at the marginal cost of the supplying division at the optimal output forthe company as a whole. To achieve this objective divisions cannot have fullautonomy. If divisions are given full autonomy it is unlikely that optimalitywill be achieved where the market for the intermediate product is imperfect.The motivational advantages of corporate headquarters not interferingexcessively must also be taken into account and the benefits arising from thismay outweigh any loss of profits. In addition to the above points the answer could also discuss negotiated transfer pricing where divisions are allowed to establish transfer prices bynegotiation rather than using prices set by corporate headquarters. See‘Negotiated transfer prices’ in Chapter 20 for a discussion of the issuesinvolved.

(b) See ‘Domestic transfer pricing recommendations’ in Chapter 20 for the answer to this question.

(a) The major disadvantage of the transfer price is that it will not motivate the receiving division to operate at the optimal output level for the company as awhole (see ‘Cost-plus a mark-up transfer prices’ in Chapter 20). The mainadvantage is that it will enable the supplying division to earn a profit on inter-group transfers. Also using standard cost, rather than actual cost, ensures thatinefficiencies cannot be passed on to the receiving division by the supplyingdivision. Distinguishing between planning and operating variances enables onlyplanning variances, that are due to environmental changes, to be included in anychanges in the transfer price. Any increase in costs due to inefficiencies will resultin operating variances. Separately identifying operational variances ensures thatany inefficiencies will not be incorporated into the transfer price.

(b) This situation would apply when external selling expenses are significant but such costs would be either avoided or lower on inter-group transfers. See LearningNote 20.1 on the open access website for a more detailed explanation of thissituation. The question does not limit the answer to domestic transfer pricing. Solution IM 20.3 Solution IM 20.4 TRANSFER PRICING IN DIVISIONALIZED COMPANIES 202 Therefore issues relating to multinational transfer pricing could be included in the answer. For an explanation of these issues see ‘International transfer pricing’ inChapter 20.

(c) To maximize group profits a linear programming model must be formulated centrally which incorporates all relevant information relating to the divisions involved. The solution to the model will provide information on the opportunitycosts (shadow prices) of the scarce resources. The transfer price that will motivatethe optimal output for the group as a whole is incremental cost plus theopportunity cost of any scarce resources. This will result in a transfer price whereall of the profits are allocated to the supplying division that has the scarceresources.

The report should include an estimate of divisional profits and return on investment (ROI) based on current demand: Division A Division B(£000) (£000) Contribution from outside sales 1500 250 Contribution from internal transfers 375 –––– –––– Total contribution 1875 250 Fixed costs 500 225 –––– –––– Profit 1375 25 –––– –––– Investment 6625 1250 ROI 20.8% 2% Assuming there is a single market price of £30, the current system is motivating correct decisions since both managers are encouraged to expand output. However,the current transfer pricing system is causing motivational problems because it underestimates the contribution which division B makes to overall company profits. In other words, the current system results in an inadequate measure of divisionalperformance. Division A has 30 000 units capacity available to meet the demand of Division B.

Therefore Division A can meet the demand of Division B without forgoing any sales to outside customers. Consequently the relevant cost of the transfers is £15 per unitvariable cost. A transfer price of £15 per unit would be unfair to Division A, sinceinternal transfers would not provide any contribution to fixed costs. A possible solution is to set the transfer price at £15 per unit, and Division B should also pay Division A an annual lump sum contribution to cover the fixed costs ofDivision A. Total output of Division A is 125 000 units, consisting of 100 000 unitsoutside sales and 25 000 units internal transfers. Therefore 20% of Division A’scapacity is devoted to Division B, and thus the lump sum payment should be £100 000(20% of £500 000 fixed costs). If in any year it is anticipated that demand in theexternal market will be in excess of Division A’s capacity, the transfer price should beset at the prevailing market price. It is assumed that additional sales of 5000 units of product J can only be obtained if a new branch is opened. The incremental costs to the company are £175 000 (£125000 variable cost + £50 000 establishment costs) and the incremental revenues are £250 000. Therefore total company profits will increase by £75 000 if the new branchis opened. However, with the present transfer pricing system Division B will regardthe transfer price as an incremental cost. Consequently contribution will be £10 per unit and the annual establishment costs of £50 000 will equal Division B’s total contribution of £50 000. Therefore Division B profits will remain unchanged and themanager will not be motivated to open the new branch. If the new branch is opened then, with the present transfer pricing system, the £75 000 additional profit will beallocated to Division A. Solution IM 20.5 TRANSFER PRICING IN DIVISIONALIZED COMPANIES 203 A transfer price system consisting of £15 variable cost plus a lump sum payment is recommended. The revised transfer pricing system will motivate the manager of Division B to open the new branch. The divisional profit calculations (without the newbranch) based on the proposed transfer pricing system are as follows:

Division A Division B(£000) (£000) Contribution from outside sales 1500 625 Contribution from internal transfers — — –––– –––– Lump sum payment 100 (100) Fixed costs (500) (225) –––– –––– Profit 1100 300 –––– –––– Investment 6625 1250 ROI 16.6% 24% (a) Figure Q20.6 illustrates the inter-group trading:

A market price exists for the transfers between the departments. Therefore thetransfer price for the repair department work is assumed to be the market price of£8 per hour plus the cost of materials. The transfer of the second-hand machineshould be at the market price. The second-hand machine quoted in the questionhas a market price of £3700 (without any repairs being necessary). In order torepair the machine on the outside market, a cost of £850 (100 £8 + material cost) would be incurred. Therefore the current market value of the machine in itscurrent state is assumed to be £2850 (£3700 £850).

New machine department (£) Net sales value of new machine (£16 000 £5000) 11 000 Transfer price of second-hand machine 2 850 ––––– 13 850 Cost of new machine 12 000 ––––– Profit contribution 1 850 Second-hand machine department (£) (£) Sale to ST Ltd 4200 Less: Transfer price paid to new machines department 2850 Transfer price paid for repairs to repairs department 850 3700 ––– –––– Profit contribution 500 –––– Repairs department Transfer price received from second-hand machine department 850Less: Variable costs Materials 50 Variable costs (100 £4.50) 450 500 ––– –––– Contribution to fixed costs and profit 350 –––– Solution IM 20.6 204 TRANSFER PRICING IN DIVISIONALIZED COMPANIES Second-hand machines RepairsSecond-hand department Repair department New machine department Figure 20.6 Solution IM 20.7 TRANSFER PRICING IN DIVISIONALIZED COMPANIES205 (b) (i) The repairs department will charge an additional £400 for repairs to the second-hand machine department. The repairs department should earn the normal revenue on the extra work, since Walker was not responsible for therepair cost estimate error. The question is to whom should £400 be charged?Because both Newman and Handley were responsible for the repairs estimate, there is a case for apportioning the £400 between them. An alter-native view is that Handley could obtain £500 profit by buying the similarmachine from another dealer for £3700. However, he chose to supportNewman in selling the new machine. Therefore there is a case for Handleybeing allowed to maintain the £500 profit. Assuming that the £400 is charged to the new machine department, the revised profit contributions will be asfollows: (£) New machine department 1450 Second-hand machine department 500 Repairs department 525 [£350 + (50 £3.50 contribution)] (ii) In this situation Walker is responsible for the error, and should bear the cost of repairs. Consequently, the contribution of the repairs department will be reduced from £350 to £125 (£350 original contribution less £225 variablecost of repairs).

(c) (i) Because the new machines department will make additional profit margins on the sale of the new machines in the form of a reduced purchase price, the cost of the warranty repairs (including profit margins) should be chargedto the new machines department. Because the warranty decision waspresumably taken by Newman, the warranty excess repairs should be chargedto the new machines department.

(ii) If the normal charge of £8 is made, the repairs department will gain because it will obtain an additional contribution to fixed costs and profits. Also, therepairs department will maintain its budgeted contribution from outsidecustomers. If the profit centres were individual firms then the new andsecond-hand machine departments would pay £8 per hour and the repairsdepartment would receive £8 per hour. Therefore there are strong argumentsfor maintaining the normal charge and thus enabling the repairs departmentto obtain an additional contribution to fixed costs and profits. However, ifthe second-hand department can obtain cheaper repairs from outside thegroup, the £8 charge should be reviewed.

(a) (i) Normal selling price less variable selling and distribution costs (£) Normal selling price 12.00 Less variable selling cost (£20 000 /100 000) 0.20 –––– Transfer price proposed by EMD 11.80 –––– (ii) Standard variable manufacturing cost plus 20% profit margin (£) Direct manufacturing costs (£630 000 /100 000) 6.30 Variable overheads (£10 000 /100 000) 0.10 –––– Variable manufacturing cost 6.40 20% profit margin 1.28 –––– Transfer price proposed by OPD 7.68 –––– (iii)Standard full manufacturing cost plus 15% (£) Full manufacturing cost per unit (£880 000 /100 000) 8.80 15% margin 1.32 –––– Proposed transfer price 10.12 –––– It could be argued that since the company will be operating at 100% capacity if the transfers take place, the unit fixed costs ought to be determined on the basisof 120 000 units instead of 100 000 units. This will result in the followingrevised calculations: (£) Unit variable manufacturing cost 6.40 Fixed overhead unit cost [(30 + 150 + 60) /120] 2.00 –––– Full manufacturing cost per unit 8.40 15% profit margin 1.26 –––– Transfer price 9.66 Comments In 2013 EMD has 20 000 units surplus capacity. Therefore any price inexcess of its variable manufacturing cost of £6.40 per unit will be acceptable to the manager of EMD. Orders in excess of 20 000 units will result in lostsales on the external market. The minimum transfer price acceptable for internal transfers in excess of 20 000 units is £11.80 (lost sales revenue lesssavings on variable selling costs). With a transfer price of £11.80, OPDwould purchase externally at a price of £9 per unit. This is the correctdecision for the group as a whole. A transfer price of £7.68 would be acceptable to both EMD and OPD for the first 20 000 units. This transfer price will not be acceptable to EMD fordemand in excess of 20 000 units and OPD would buy externally. A transfer price of £9.66 or £11.80 would encourage OPD to purchase 30 000 units from the external market. However, only 10 000 units are available externally, and OPD will seek to purchase 20 000 units internally.At a transfer price of £9.66, EMD would be willing to allocate only itsunused capacity to meet internal demand. With the £11.80 transfer price,EMD would be prepared to transfer 120 000 units to OPD. In 2013 EMD’s external sales will utilize all its available capacity. EMD will only be prepared to transfer goods to OPD at a transfer price of £11.80.At any of the other prices suggested, the lost external sales revenue willexceed the revenue generated by inter-divisional transfers.

(b) The transfer pricing system should be based on the opportunity cost approach. This is derived from the sum of the incremental cost of the supplying divisionfrom meeting the internal demand plus any lost contribution. Where EMD has spare capacity (the first 20 000 units), the resulting transfer price will be £6.40 (£6.40 + zero lost contribution). For demand in excess of 20 000 units theresulting transfer price will be £11.80 (£6.40 incremental cost + £5.40 lostcontribution). Note that the lost contribution is £11.80 net selling price less £6.40variable cost.With the £6.40 transfer price, OPD would purchase from EMD, but EMD would be indifferent about transferring goods to OPD. Any negotiation ought tolead to a transfer price between £6.40 and £9 for the first 20 000 units capacity.

With the £11.80 transfer price, OPD would buy 10 000 units from the foreignsupplier. This is the correct decision if EMD is operating at full capacity. 206 TRANSFER PRICING IN DIVISIONALIZED COMPANIES (a) To answer this question, it is necessary to adopt an approach similar to thatillustrated in Exhibits 20A.3 and 20A.4 in Chapter 20. The following schedule provides details of the marginal cost of the supplying division Engcorp (denotedby MC), the marginal revenue from the sale of the intermediate product byEngcorp (MR) and the net marginal revenue from the transfer of the intermediateproduct and the sale as a final product by Flotilla (NMR).

MC MR NMR Total net revenue Output (£000) (£000) (£000) (£000) 100 115 204 (1) 133 (3) 133 (703 570) 200 70 158 (2) 122 (5) 255 (1375 1120) 300 76 124 (4) 111 (7) 366 (2036 1670) 400 83 112 (6) 90 456 (2676 2220) 500 91 105 (8) 79 535 (3305 2770) 600 100 100 68 603 (3923 3320) 700 110 95 57 660 (4530 3870) 800 121 90 46 706 (5126 4420) The numbers in parentheses in columns 3 and 4 refer to the order of ranking for the allocation of the intermediate product on the basis of MR and NMR. The optimal output is 700 units. At this output level, MC is £110 000 and NMR is £111 000.

At an output level of 800 units, MC is £121 000, and the most beneficial use of this output is to sell it in the intermediate market where MR is £105 000. Thereforeoutput should not be expanded from 700 to 800 units.

At the optimal output level 400 units should be sold on the intermediate market and 300 units should be transferred to Flotilla and sold as a final product.

(b) Where the market for the intermediate product is imperfect, it is unlikely that market prices will represent the optimal transfer price. With imperfect markets, it is necessary for central headquarters to intervene and examine the MC, MR andNMR schedules of the supplying and receiving divisions and set the transfer priceat the point where MCs is equal to the sum of MRs and NMR of the supplyingand receiving divisions (i.e. MCs of the supplying division at the optimum outputlevel of the group). Applying this rule will result in an optimal transfer price whichis greater than £1100) (£110 000 /100) per unit but less than £1110 per unit (£111 000 /100). At a transfer price of, say, £1105, the supplying division will choose to sell 400 units on the external market (the supplying division’s MR is above £1105per unit for the first 400 units) and transfer 300 units to the receiving division (MC per unit is less than the transfer price at output levels up to 700 units). At a transfer price of £1105 per unit, the receiving division will purchase 300 unitsinternally (at output levels above 300 units, NMR is less than the transfer price). Both divisions will therefore select the optimal output levels at a transfer price of £1105. Total group profit will be £319 000 (£598 000 total revenue from theintermediate market plus £366 000 total net revenue from the final productmarket less £645 000 total cost of the supplying division). With the transfer priceset at £1105, divisional profits will be: (£) Engcorp 284 500 (£598 000 external sales + 300 £1105 internal sales £645 000 production cost) Flotilla 34 500 (£2 036 000 sales £1 670 000 conversion costs 300 £1105 internal purchases) If central headquarters do not intervene, Engcorp would examine its cost and revenue schedules and choose to produce 600 units, which is the level at which itmaximizes profits. At this output level, profits are £268 000 (£803 000 £535 000) Solution IM 20.8 TRANSFER PRICING IN DIVISIONALIZED COMPANIES 207 and the selling price per unit of output is £1338 (£803 000/600 units). Note that the question states that the current market price is £1350. The manager of Engcorp is not prepared to transfer engines to Flotilla at a price of £1300, since this is less thanthe current market price. The manager of Engcorp could improve divisional profitsby transferring the remaining capacity of 200 units at £1300 each, since this is inexcess of the marginal cost (£231 000).

At a market price of £1350 (or £1338), the manager of Flotilla will purchase 100 units externally to be converted into the final product. The group and divisional profits, assuming that Engcorp sells 600 units on the intermediatemarket, will be:

(£) Engcorp 268 000 (£803 000 £535 000) Flotilla 3 000 (£133 000 (100 £1300)) –––––– Group 271 000 –––––– At the optimum transfer price of £1105, both divisions increase their profits, and group profit is increased by £48 000 (£319 000 £271 000).

From the above discussion the following points emerge:

(i) Transfer prices set at the prevailing or planned market price when markets are imperfect are not optimal.

(ii) Central intervention is necessary in order to ensure that optimal output levels are set but this process may undermine divisional autonomy.

(iii) To induce optimal output levels, transfer price is not equal to market price where markets are imperfect.

(iv) If both m anagers had been provided with all the information and were educated to use the information correctly, it is likely that a negotiatedsolution would have emerged which would have been acceptable to both thedivisions and the group.

The major issue is therefore whether to intervene and impose an optimal transfer price. The advantage is that short-term profits will be increased by £48000, but the disadvantage of this policy is that divisional autonomy will beundermined.

(c) The major considerations are: (i) Taxation.

(ii) Import duties.

(iii) Restrictions on dividend repatriations. (iv) Legislation: situations may arise where multinationals can transfer goods atlow prices, which would result in the transferred product being sold at pricessignificantly below the prices charged by local firms. Legislation may beintroduced in the importing country which protects local firms and affectsthe transfer prices of imported goods.

(v) Exchange rates: reported profits may be severely affected by adverse changes in the exchange rates. Transfer pricing can be used to influence the locationand level of profits so that group reported profits are maximized.

For a discussion of items (i)–(iii) above see ‘International transfer pricing’ inChapter 20.

(a) At a selling price of £2200 estimated demand is 1000 beasts. Each increase or decrease in price of £100 results in a corresponding decrease or increase of 125beasts. Therefore if the selling price were increased to £3000 demand would bezero. To increase demand by one unit the selling price must be reduced by £0.80(£100 /125). Thus the maximum selling price for an output of xunits is: Solution IM 20.9 208 TRANSFER PRICING IN DIVISIONALIZED COMPANIES SP = £3000 £0.80 x Total revenue for an output of xunits = £3000 x £0.80 x2 Marginal revenue = dTR = £3000 1.60 x d x Marginal cost = variable cost = £1050 (£700 + £350) At the optimum output level where MR = MC: £3000 1.60 x= £1050 x = 1218.75 units (say 1219 units) The highest selling price at which this output can be sold is: SP = £3000 0.80(1219) = £2025 (b) At a selling price of £700 estimated demand is 9000 engines. Each increase or decrease in selling price of £1 results in a corresponding decrease or increase of 10 engines. Therefore if the selling price were increased to £1600 demand would bezero. To increase demand by one unit the selling price must be reduced by £0.10.Thus the maximum selling price for an output of xunits is:

SP = £1600 £0.10 x Total revenue for an output of xunits = £1600 x £0.10 x2 Marginal revenue = dTR = £1600 0.20 x d x Marginal cost = variable cost = £350 At the optimum output level: £1600 0.20 x= £350 x = 6250 units The highest selling price at which this output can be sold is: SP = £1600 0.10(6250) = £975 If the transfer price is set at the profit maximizing market price for the sale of engines the marginal cost of the motorcycle division will be £1675 (£975 trans-fer price plus £700 variable conversion cost). The motorcycle division’s revisedoptimum output level will be where: £3000 1.60 x= £1675 x = 828 units At the optimum output level of 828 units:

SP = £3000 £0.80(828) = £2337.60 (c) The engineering division produces an intermediate product that is sold in an imperfect final product market with a declining marginal revenue schedule. In thissituation it is necessary for central headquarters to intervene and gather cost andrevenue schedules for each division in order to determine the selling prices thatwill maximize the profits for the group as a whole. This process will underminedivisional autonomy but if the divisions are allowed to set their own selling pricesthey may seek to maximize their own profits at the expense of the group as awhole. For a more detailed discussion of the issues arising in this part of thequestion see ‘Economic theory of transfer pricing’ in the Appendix to Chapter 20. TRANSFER PRICING IN DIVISIONALIZED COMPANIES 209 210COST MANAGEMENT Solution IM 21.1 Solution IM 21.2 The answer to this question should include a description of JIT manufacturing, the benefits of JIT and the impact of JIT on a firm’s costing system. For adiscussion of these items see Chapter 21, and ‘Criticism of standard costing’ inLearning Note 18.4 on the open access website.

In particular, the answer should stress the following effects of JIT on the costing system: (i) There will be a move towards process costing techniques, since there will be less need to track the flow of costs through the production process.

(ii) Much less emphasis w ill be placed on detailed inventory product costing techniques, and a backflushing system may be used to derive the productioncost of sales for the period.

(iii) Greater emphasis will be placed on non-financial measures and the measure- ment of quality, delivery times, set-up times etc., rather than inefficiencies.

(iv) There will be less emphasis on labour efficiency and material price variances.

(a) See Chapter 21 for a description of life-cycle costing. At the planning stage, before a decision is made to introduce a new product, it is necessary to estimate revenuesand costs incurred over the whole life of the product. Periodically it is appropriateto undertake a post-audit by comparing revenues and costs incurred pluspredictions of costs and revenues to the end of the product’s life. These costs andrevenues should be compared with the original estimates that were made to justifythe launch of the product. Therefore the answer should focus on the difficulty inestimating costs and revenues from the design stage to the abandonment of theproduct. Difficulties are encountered with determining how joint costs should beassigned to the product and learning rates. Where unit costs are computed,volume estimates significantly influence the accuracy of unit cost calculations.

(b) See ‘Product life cycle’ in Chapter 10 for an explanation of the terms. At the start- up (introductory) stage accurate costs will be difficult to determine becauseproduction volumes are extremely difficult to predict and learning effects mayalso exist. The emphasis at this stage is likely to be on actual costs rather thanstandard costs. Planned costs are extremely difficult to estimate but closemonitoring of costs is essential so that continuous improvements in terms of costreduction are encouraged.At the growth stage uncertainties will still remain relating to volume and poss- ibly learning effects. If a high-margin product is involved then accurate costestimates may not be critical but for low-margin products inaccurate estimatesmay lead to incorrect volume and pricing decisions. Target costing is likely to beparticularly appropriate at this stage. At the maturity and harvest stages learning effects are unlikely to apply and volume will be easier to predict. Thus standard costing may be appropriate andmore accurate product costs are likely to be reported. At the harvest stage thefocus will be on the short-term and maximizing short-term cash flows. Greater Cost management Solutions to Chapter 21 questions emphasis will be given to using short-term marginal costs for pricing and output decisions. For a discussion of the impact of product life cycles on pricing decisionssee ‘Product life cycle’ in Chapter 10.It is claimed that in today’s competitive markets product life cycles have shortened considerably for many products.

(a) The main requirements for effective operational control are described in Chapter 16. In particular, see ‘Results or output controls’. The answer should also stressthe importance of incorporating non-financial measures.The aim of a product costing system is to accurately trace the resources consumed by products. For a more detailed answer to this question see Chapter11, and ‘Backflush costing’ in Chapter 4.

(b) The answer should discuss the limitations of traditional product costing systems which are based on arbitrary overhead allocations (see Chapters 3 and 11).

For a di scussion of the deficiencies of traditional operational control and performance measurement systems see ‘Side-effects from using accountinginformation for performance evaluation’ in Chapter 16 and ‘Criticisms ofstandard costing’ in Learning Note 18.4 on the open access website.

(c) The answer to this question should incorporate ‘The future role of standard costing’ in Learning Note 18.5 on the open access website and aspects of thebalanced scorecard in Chapter 22. In addition, the answer should also focus onthe methods of tracing more accurately the resources consumed by cost objectsusing an ABC system.

(a) See ‘A comparison of ABC with traditional costing systems’ and ‘The emergence of ABC systems’ in Chapter 11 for the answer to this question.

(b) See ‘Activity-based budgeting’ in Chapter 15 for the answer to (b)(i), ‘Activity- based management’ in Chapter 21 for the answer to (b)(ii) and Example 10.1,relating to a pricing decision, for the answer to (b)(iii). Alternatively, the answercould draw off the content in the sections in Chapter 10 entitled ‘A price-takerfirm facing a long-run product-mix decision’ and ‘Customer profitability analysis’if you wish to focus on product or customer discontinuation decisions.

(a) The benefits of JIT are gained by rearranging the factory layout from a batch production layout towards a product layout using flow lines. In addition, workpractices are changed with the aim of achieving zero defects and batch sizes of oneand adopting JIT purchasing techniques. For a description of these items youshould refer to ‘Just-in-time systems’ in Chapter 21. The answer should also drawattention to the fact that the JIT approach involves a change in company culture,commitment to the pursuit of excellence and continuous improvement in allphases of manufacturing systems design and operations. The full benefits of JITare not obtained overnight.

(b) For a discussion of how management information systems should be developed in order to facilitate and make the best use of JIT see ‘Just-in-time systems’ inChapter 21 and ‘The future role of standard costing’ in Learning Note 18.5 on theopen access website. In particular, the answer should indicate the need to placegreater emphasis upon developing fast feedback performance measures which arecongruent with the JIT philosophy. Such performance measures are more likely tobe of a non-financial nature. Solution IM 21.3 Solution IM 21.4 Solution IM 21.5 COST MANAGEMENT 211 (a) (i)(ii) See ‘Feedback and feedforward controls’ in Chapter 16 for the answer to this question.

(b) (i) For the answer to this question see ‘Cost of quality’ in Chapter 21. In particular, the answer should indicate that quality costs should be classified as follows:1. Prevention costs.

2. Appraisal costs.

3. Internal failure costs.

4. External failure costs.

(ii) The two philosophies appear to be directly opposed. The first accepts the fact that 100% quality cannot be maintained, and seeks to monitor and measure the cost of inferior quality output. The second philosophy aims to achievezero defects. Thus standards and budgets should be based on zero defects, andany deviation from this goal should be regarded as unacceptable. Theemphasis is on doing the job correctly the first time rather than accepting andmonitoring the costs of inferior quality. The cost of reporting inferior qualityoutput is regarded as a non-value-added activity.The two approaches adopt different philosophies to achieve the same objective (i.e. reducing waste and defective work). The cost of quality reportcan be used as an attention-directing device to make top management aware ofhow much is being spent on quality-related costs. This information can providethe justification for the need to adopt a ‘zero-defects’ philosophy.Furthermore, once such a philosophy has been introduced, cost of qualityreports can be used to monitor the reduction in costs arising from implementing such a policy. It is therefore possible to reconcile the two philos-ophies. 212 COST MANAGEMENT Solution IM 21.6 The traditional approach in the management control literature has been to view results controls as a simple cybernetic system. This process is illustrated in the diagram below. The control system consists of the following elements:

1. The process (the room’s temperature) is continually monitored by an automatic regulator (the thermostat).

2. Deviations from a predetermined level (the desired temperature) are identi ed by the automatic regulator.

3. Corrective actions are started if the output is not equal to the prede-termined level. The automatic regulator causes the input to be adjusted by turning the heater on if the temperature falls below a predetermined level. The heater is turned off when the output (temperature) corre-sponds with the predetermined level.

The output of the process is monitored, and whenever it varies from the predetermined level, the input is automatically adjusted. Emmanuel et al.

(1990) state that four conditions must be satis ed before any process can be said to be controlled. First, objectives for the process being controlled must exist. Without an aim or purpose control has no meaning. Secondly, the out-put of the process must be measurable in terms of the dimensions de ned by the objectives. In other words, there must be some mechanism for ascertaining whether the process is attaining its objectives. Thirdly, a predictive model of the process being controlled is required so that causes for the non-attainment can be identi ed and proposed corrective actions evaluated. Finally, there must be a capability for taking action so that deviations from objectives can be reduced. Emmanuel et al. stress that if any of these conditions are not met the process cannot be considered to be ‘in control’. Result controls and therefore management accounting controls resemble the thermostat control model. Standards of performance are determined, measure- ment systems monitor performance, comparisons are made between the stand-ard and actual performance and feedback provides information on the variances. Note 1: Variable cost of reduction for curing/moulding process Existing cost(£) Type AX 964 706 × £15/100 = 144 706 Type BX 1 447 059 × £25/100 = 361 765 ––––––– 506 471 Amended cost Type AX 826 667 × £12/100 (99 200) Type BX 1 243 077 × £20/100 (248 615) ––––––– Net reduction in cost 158 656 ––––––– (b) See ‘Cost of quality’ in Chapter 21 for the answer to this question. COST MANAGEMENT 213 (a)Evaluation of quality management programme Synthetic slabs cost reduction (£) Elimination of synthetic slabs stores losses 68 711 units × (£40 1)/100 26 797 specification check 14 000 Savings on purchase quantity of synthetic slabs: (2 748 450 2 090 651) × £40/100 263 120 Less: increase price: 2 090 651 × £4/100 (83 626) Curing/moulding process costs: variable cost reduction(2 679 739 2 090 651) × £20/100 117 818 scrap sales forgone of sub-components (267 974 20 907) × £5/100 (12 353) Finishing process cost reduction: variable cost reduction (see note 1) 158 656 scrap sales forgone (361 765 51 744) × £10/100 (31 002) Finished goods stock: holding costs (45 000 1500) × £15/1000 653 ––––––– 454 063 Less: cost of quality management programme 250 000 ––––––– Net (cost)/benefit of proposed changes 204 063 ––––––– ––––––– Solution IM 21.7 214STRATEGIC MANAGEMENT ACCOUNTING Solution IM 22.1 Solution IM 22.2 Solution IM 22.3 Solution IM 22.4 Solution IM 22.5 See ‘Strategic management accounting’ and ‘The balanced scorecard as a strategic management system’ for the answer to this question. In addition the answer shoulddescribe the role of strategic management accounting in the selection of strategy (see‘Stages in the planning process’ in Chapter 15) and the evaluation of strategic options.There is also a need for the organization to be aware of its own cost structure and anysignificant differences between its cost structure and those of its main competitors inorder for that area of competitive advantage to be identified.

(a) See ‘Criticisms of standard costing’ in Learning Note 18.4 on the open access website, ‘Harmful side-effects of controls’ in Chapter 16 and ‘JIT and management accounting’ in Chapter 21 for the answer to this question.

(b) See ‘Future role of standard costing’ in Learning Note 18.5 on the open access website and the content relating to incorporating a wider range of performancemeasures within the balanced scorecard perspective described in Chapter 22.

(a) See a description of the customer, internal business and learning and growth perspectives within the balanced scorecard in Chapter 22 and also ‘Performancemeasurement in service organizations’ in Learning Note 22.1 on the open accesswebsite for the answer to this question.

(b) The answer should incorporate some of the content relating to ‘The future role of standard costing’ in Learning Note 18.5 on the open access website, ‘Addressingthe dysfunctional consequences of short-term financial performance measures’ inChapter 19, ‘Dealing with the distorting effects of uncontrollable factors’ inChapter 16 and issues relating to the balanced scorecard perspective andperformance measurement in service organizations in Chapter 22.

(i) See ‘The balanced scorecard’ in Chapter 22 for the answer to this question.

(ii) For service organizations in general see ‘Performance measurement in service organizations’ in Learning Note 22.1 on the open access website. For a firm ofconsultants the answer could be related to Question IM 22.6 which adopts abalanced scorecard perspective for measuring the performance of a consultingorganization.

(a) See Chapters 16 and 19 for a description of cost centres, profit centres and investment centres. Note that because investment centres are accountable forinvestment decisions, performance should be evaluated over longer periods thanfor profit and cost centres. The benefits from using different types ofresponsibility centres are to enable the accounting system to stress the authority,responsibility and specialization within the organization and to tailor the internalreporting system to the elements of an organization’s structure. Besides identifyingmanagement responsibilities, establishing responsibility centres can have animportant motivational influence. The main problems are:

Strategic management accounting Solutions to Chapter 22 questions (i) distinguishing between controllable and uncontrollable costs; (ii) dual responsibility; (iii) determining the lowest level of responsibility for reporting purposes; (iv) determining which information should be reported and the frequency of reports; (v) avoiding dysfunctional behaviour and a lack of goal congruence.

For a more detailed discussion of the above items you should refer to Chapter 16.

(b) The regional companies are investment centres, and therefore broader performance measures should be used. Examples include:(i) return on capital employed; (ii) residual income; (iii) gross profit and net profit percentages; (iv) market share percentages; (v) sales growth rates; (vi) profit per square metre; (vii) average debtors credit period; (viii) capital expenditure (actual, planned and committed expenditure).

The outlets are profit centres, and the following measures should be used: (i) total sales value; (ii) controllable net profit; (iii) controllable net profit as a percentage of sales; (iv) gross profit as a percentage of sales; (v) each category of expense expressed as a percentage of sales; (vi) controllable and non-controllable cost variances; (vii) stock turnover; (viii) gross profit per square metre (by departments and overall); (ix) sales per trade sales representative.

(c) Because the regional company can take capital investment on expenditure below £100 000, an assessment of performance should relate to the amount of capitaltied up as a result of investment decisions. ROCE provides a relative measure of performance, and this measure can be further divided into two subcomponents –net profit as a percentage of sales and the ratio of sales to capital employed.Residual income and economic value added (see Chapter 19) can also be used asan absolute profit measure after deducting the opportunity cost of funds investedby the regional company. Gross and net profit percentages should be comparedwith other regional companies and similar companies outside the group. Thiscomparison should indicate whether costs are being efficiently controlled. Salesgrowth and market share statistics provide an indication of the sales functionrelative to the external environment. Profit per square metre can be used as aninter-company performance comparison in relation to space. Debtors arecontrolled at regional offices, and therefore average credit periods should bemonitored. It is also necessary to monitor capital expenditure. The outlets should be regarded as profit centres and evaluated on controllable net profit (i.e. sales less controllable expenses such as bad debts). Outlet managerswill be evaluated in terms of sales performance and their ability to control costs.Total sales revenue, gross profit per square metre and sales per trade represen-tative provide an indication of sales performance (e.g. pricing and marketing mixdecisions). Outlet managers are responsible for the performance of the trade salesrepresentatives, and their performance should be monitored using measures suchas number of calls made, number of new customers, increase in customers’ ordersand invoice value per trade call. Costs should be controlled by comparing actualcosts against budgets, with expense items segregated into controllable anduncontrollable categories. Flexible budgets should be used to control costs.Various expense categories as a percentage of sales should be compared between STRATEGIC MANAGEMENT ACCOUNTING 215 outlets. Outlet managers are responsible for stock control, and therefore stock turnover ratios should be used to monitor stock levels.

(d) Monthly report Building Timber Kitchen supplies Sawmill Total a(B) a a(A) a (B) (A) (B) (A) (B) (A) (B) (A) (£) (£) (£) (£) (£) (£) (£) (£) (£) (£) Sales: Retail Trade –– –– –– –– –– –– –– –– –– –– Less cost of sales –– –– –– –– –– –– –– –– –– –– Gross profit Less other department costs –– –– –– –– –– –– –– –– –– –– Departmental profit Less other controllable overhead –– –– Controllable profit Less non-controllable expenses –– –– Outlet net profit –– –– Notes a B = budget, A = actual.

Comments (i) The statement should also show expenses and profits as a percentage of sales.

(ii) Some form of cumulative comparisons should be included or percentages under /over budget to date, but care should be taken to avoid information overload. One possibility is to report only those cumulative variances orpercentages under /over budget which significantly deviate from the budget.

(iii) An additional supplementary statement should be given for cost control purposes. This statement should provide a detailed analysis by individualexpenses for the ‘other controllable overheads’ in the above statement (e.g.vehicle running expenses and energy costs).

(iv) An add itional statement should be presented giving details of key performance efficiency ratios. It might take the following format:

Building Timber Kitchen supplies Sawmill Total (B) (A) (B) (A) (B) (A) (B) (A) (B) (A) Gross profit per square metreSales per square metreStock turnover ratio 216 STRATEGIC MANAGEMENT ACCOUNTING (a)Financial statement for the year ended 31 May Medical Dietary Fitness Total(£000) (£000) (£000) (£000) Budget Client fees 450.0 600.0 450.0 1500.0 Healthfood mark-up (cost × 110%) 120.0 120.0 Salaries (240.0) (336.0) (225.0) (801.0) ––––– ––––– ––––– ––––– Budget gross margin 210.0 384.0 225.0 819.0 Variances:

Fee income – favourable/(adverse) (37.5) (100.0) 275.0 137.5 Healthfood mark-up loss (30.0) (30.0) Salaries increase (15.0) (75.0) (90.0)Extra fitness equipment (80.0) (80.0) ––––– ––––– ––––– ––––– Actual gross margin 157.5 254.0 345.0 756.5 Less: company costs:Enquiry costs – budget (240.0) – variance (60.0) General fixed costs (300.0) Software systems cost (50.0) ––––– Actual net profit 106.5 ––––– Budget margin per consultation (£) 35.00 32.00 25.00 Actual margin per consultation (£) 28.64 25.40 23.79 (b) Competitiveness Compared with the budget new business enquiries have increased by 60% and theexisting business enquiries have declined by 33%.

The uptake from enquiries was : New business – Budget (30%) and Actual (25%)Repeat business – Budget (40%) and Actual(50%) Repeat business represents a measure of customer loyalty and the figures areencouraging whereas there has been a decline in the take up rate for new business.

Even though there has been a decline in the uptake from new enquiries theincreased number of enquiries has resulted in new business exceeding budget by5000 consultations in absolute terms. However, repeat business consultations are2000 below budget arising from a decline in the number of client enquiries.

Medical and dietary consultations are below budget by approximately 8% and16% respectively and fitness has exceeded budget by approximately 60%.

Ideally, competitiveness should also be measured against external benchmarksrather than the budget.

Flexibility Flexibility relates to the responsiveness to customer enquiries. For example, the ability to cope with changes in volume, delivery speed and the employment of staff who areable to meet changing customer demands. Outside medical specialists have been employed thus providing greater flexibility on the type of advice offered and additional fitness staff have been appointed to copewith the increasing volume. The measure of the uptake of new enquiries (seecompetitiveness above) can also provide an indication of the responsiveness tocustomer enquiries. It could be argued that the organization has failed to respond to achange in demand, given that dietary consultations have declined by 16%, but staffnumbers have remained unchanged. The organization may, however, be anticipatingan upsurge in future demand. Solution IM 22.6 STRATEGIC MANAGEMENT ACCOUNTING 217 Resource consultation The average consultations per consultant are budgeted at 1000 for each type of consultant. The actual figures and utilization percentages are: full-time medical (900 – a 10% decline) dietary (833 – a 16.7% decline) fitness (1208 – a 21% increase) The fact that full-time medical consultants appear to be under-utilized raises the question as to whether too many clients are being referred to outside specialists. Thismay be a consequence of pursuing the flexibility objective in the use of outsidespecialists to provide greater flexibility on the type of advice offered. It is alsoapparent from the above figures that dietary consultants are under-utilized whereasfitness consultants are over-utilized. Staffing levels should be investigated taking intoaccount the long-term needs of the business. Quality of service The number of complaints has risen from 1% to 2% of all clients and should be investigated. The purchase of new equipment may be indicative of the provision of abetter quality service. Quality may also have been improved by the better managementof client appointments and records resulting from the introduction of new softwaresystems. Innovation Innovation relates to the ability of the organization to provide new and better quality services. Here there is a need to ascertain whether the appointment of outsideconsultants has provided a wider range of medical services. Also the new computersoftware may have provided a better quality of service relating to schedulingappointments. 218STRATEGIC MANAGEMENT ACCOUNTING Solution IM 22.7 Lecturers please note that this question appeared in a recent examination of a professional body so it is possible that students may be able to access the answer to the question.

(a) $000 $000 Sales revenue (625m 0.04 25m) $1.80) a 45 000 Ingredients (25m $0.70) 17 500 Packaging (25m $0.15) 3 750 Fixed overheads 5 401 Distribution (0.08 $45m) 3 600 30 251 Pro t 14 749 Pro t/sales (%) 32.78% Target rate of return (%) 32.00% Target return ($000) 14 400 The above gures indicate that the nance director was correct in stating that a total sales margin of 32 per cent can be achieved. If the cost of the ingredients increases by $349 000 the target return will be less than 32 per cent. This represents an increase of 1.994 per cent. Therefore the nance director is correct to be concerned about an increase in the cost of the ingredients. (b)The following are ve critical success factors:

Supply quality This is of vital importance since 90 per cent of sandwiches are sold in the s uper- markets before 2pm each day. Therefore supply chain management is of critical importance.

Maintaining target and gross net margins Maintaining target pro t margins is essential to the future success of the organization.

Health and safety Strict compliance with health and safety regulations is essential if HSC is to maintain its reputation as a supplier of high quality food products. Correctly storing food that is produced for human consumption is vital to future success.

Product quality Production staff have no previous experience in food production so it is essential that they are adequately trained to ensure that they can immediately achieve a high level of quality. Product quality is of vital importance in achieving target sales volumes and margins.

Developing new products Consumer tastes may change so it is essential that HSC monitors market demand and continuously concentrates on new product development.

(c) See ‘Enterprise Resource Planning Systems’ in Chapter 1 for the answer to this question.

STRATEGIC MANAGEMENT ACCOUNTING 219 Solution IM 23.1 Solution IM 23.2Solution IM 23.3 Solution IM 23.4 COST ESTIMATION AND COST BEHAVIOUR See Chapter 23 for the answer to the question. See Chapter 23 for the answer to this question.See ‘Cost estimation when the learning effect is present’ in Chapter 23 for an explanation of the learning curve. If the learning effect is ignored and standards are setwhen cumulative output is low then the resulting standards will ignore the costreductions resulting from the learning curve. Consequently the standards will representeasily attainable standards, and favourable variances which are not due to improvedefficiency will occur. Alternatively standards might be set at the steady-state level, andthis will result in adverse variances throughout the ‘start-up’ phase. In order thatmeaningful targets can be set, it is essential that the learning-curve principles be appliedwhen setting standards.

(a) For a detailed answer to this question see Chapter 23. In particular, the answershould stress the following points:(i) The answer should describe the different techniques used to analyse fixed and variable costs, and illustrate the weaknesses of specific methods. For example, the high–low method only uses two extreme observations to derivethe cost estimate equation.

(ii) The presence of fixed cost step functions makes it difficult to derive a simple cost regression equation which will accurately predict the changes in costsarising from changes in volume.

(iii) Changes in production technology and product mix will mean that equations derived from past cost observations will be inaccurate when predictingfuture cost–volume relationships.

(iv) Costs may be influenced by other variables besides activity /volume. Therefore simple regression equations will yield inaccurate cost–volume relationships.Under these circumstances, multiple regression analysis should be used.

(v) Choice of the wrong activity base for example, different measures such as direct labour hours, machine hours or units of output can be used to meas-ure activity. Inaccurate cost estimation equations will be derived if activitybases are used which are not highly correlated with total cost.

(vi) An insufficient number of observations is used to derive the cost estimation equation.

(b) Analysis of costs into their fixed and variable elements is used by the management accountant in the following areas:(i) Planning : An analysis of costs into fixed and variable costs is necessary to predict costs for a range of output levels in order to determine the targetactivity level at which the budget should be set.

(ii) Control : Flexible budgets are needed for cost control purposes.

(iii) Decision-making : Analysis of fixed and variable costs is necessary in order to determine the incremental costs for various short-term decisions. Forexample, the incremental costs of making a component would be assessed Cost estimation and cost behaviour Solutions to Chapter 23 questions 220 where a company has spare capacity and wishes to evaluate a make or buy decision.

(a) The number of employees ( X 2) is likely to be the least good estimator of total costs. There is a large decline in total costs in month 8 and a large increase inmonth 9. The number of employees remains unchanged whereas the other twoindependent variables decrease in month 8 and increase in month 9. Consequentlychanges in the number of employees will not predict changes in total costs. Forexample, the number of employees will remain unchanged when output and totalcosts decline because of sickness, idle time or holiday periods.

(b) (i) X 1 and Y = (373.5374 10 6 ) [12 (6300 /12) 637 200 /12] (3.8582 10 6 ) [12(6300 /12) 2 ] = 70.83 = (637 200 /12) [70.83 (6300 /12)] = 15 912.99 R 2 = (15 912.99 637 200) + (70.83 373.5374 106 ) [12(637 200 /12) 2 ] (36 614.05 106 ) [12(637 200 /12) 2 ] = 0.994 (ii) X 3 and Y = (3692.2774 10 6 ) [12 (65 220 /12) 637 200 /12] (374.423 10 6 ) [12(65 220 /12) 2 ] = 11.48 = (637 200 /12) [11.48 (65 220 /12)] = 9305.51 R2 = (–9305.51 637 200) + (11.48 3692.2774 10 6 ) [12(637 200 /12) 2 ] (36 614.05 10 6 ) [12(637 200 /12) 2 ] = 0.9467 (c) X 1 should be used, because this variable has the largest coefficient of deter- mination. A coefficient of determination of 0.994 implies that 99.4% of the variation in total cost is explained by X 1and 0.6% by other variables. Another reason for favouring X 1 is that X 3 is difficult to interpret and is of little practical significance because it implies that fixed costs are negative.

(d) (i) X 1 X1 Y (£) Lowest activity 250 32 720 Highest activity 820 75 800 –––– –––––– Difference 570 43 080 –––– –––––– Unit variable cost = £75.58 (= £43 080 /£570) Fixed costs = £32 720 (250 £75.58) = £13 825 Therefore the equation is Y= 13 825 + 75.58X 1 Solution IM 23.5 COST ESTIMATION AND COST BEHAVIOUR 221 (d) (ii)X 3 X3 Y (£) Lowest activity 3200 32 720 Highest activity 7300 75 800 –––– –––––– Difference 4100 43 080 –––– –––––– Unit variable cost = £10.51 (= £43 080 /4100) Fixed costs = £32 720 (3200 £10.51) = –£912 Therefore the equation is Y = –912 + 10.51X 3 The differences arise because the regression technique used in (b) makes use ofall the data, whereas the high–low method uses only the extreme values, whichmight not be typical of normal operating conditions (e.g. economies or disec-onomies of scale).

(e) See Chapter 23 for criticisms of the high–low and least-squares regression methods. For a discussion of the advantages and problems of multiple regressionsee Appendix 23.1. In view of the large coefficient of determination of variableX1, there is a strong justification for relying on the least-squares method and not using multiple regression analysis.

Coefficient of determination r 2 = ( n xy x y)2 [ n x2 ( x)2 [n y2 ( y)2 ]] Applying to x 1: r2 = [(10 58 040) (113 4550)] 2 (10 1533 12 769)(10 2 451 300 20 702 500) = 66 250 2 2561 3 810 500 =4 389 062 500 9 758 690 500 = 0.4498 Applying to x2 : r2 = [(10 121 100) (212 4550)] 2 (10 6120 44 944)(10 2 451 300 20 702 500) = 246 400 2 16 256 3 810 500 =60 712 960 000 61 943 488 000 = 0.9801 Regional advertising has the higher coefficient of determination, and this implies that the level of sales varies more with regional advertising than local advertising. Acoefficient of 0.9801 implies that 98.01% of the variation in total sales is explainedby regional advertising. Solution IM 23.6 222 COST ESTIMATION AND COST BEHAVIOUR (a)Units (packets) Costs a (£) Lowest activity 10 000 3 600 Highest activity 50 000 11 600 ––––– ––––– Increase 40 000 8 000 ––––– ––––– Variable cost per unit = £8000 /40 000 = £0.20 per packet Note a £0.36 10 000 = £3600, £0.232 50 000 = £11 600.

Note that factory overhead costs are fixed for the factory as a whole, and are notincluded in the analysis.

(b) Price is assumed to be the dependent variable ( y) and sales volume the indepen- dent variable ( x). The price received by CBC is 50% of the retail price. Sales volume for each price level is calculated by dividing the revenue received by theprice received by CBC:

(1) (2) (3) (4) Retail Price received Total Sales volume, price by CBC revenue (3) /(2) (£) (£) (£) (£) 0.62 0.31 15 190 49 000 0.68 0.34 14 960 44 000 0.78 0.39 11 310 29 000 0.84 0.42 10 500 25 000 0.90 0.45 10 350 23 000 0.98 0.49 4 900 10 000 The regression equation can be derived from the following two equations and solving for aand b:

y = Na +b x xy =a x + b x2 xy x 2 xy (000) (price in pence) 49 31 2401 1519 44 34 1936 1496 29 39 841 1131 25 42 625 1050 23 45 529 1035 10 49 100 490 ––– ––– –––– –––– 180 240 6432 6721 ––– ––– –––– –––– Inserting the above computations into the formulae: 240 = 6a+ 180 b (1) 6721 = 180 a+ 6432 b (2) Multiplying equation (1) by 30 gives: 7200 = 180a+ 5400 b (3) Subtracting equation (3) from equation (2) gives: – 479 = 1032b b = – 0.4641 Substituting the value for bin one of the above equations gives a value of 53.9244 for a. Solution IM 23.7 COST ESTIMATION AND COST BEHAVIOUR 223 Alternatively the formula outlined in the question could have been used: b= n xy x y n x2 ( x)2 = 6(6721) 180(240) = 0.4641 6(6432) (180) 2 y = a+ bx a = y– bx– a = (240 /6) [– 0.4641 (180 /6)] = 53.923 Therefore y= 54 0.46 x(i.e. p(price) = 54 0.46 Q) Note that Q= quantity demanded, in thousands.

(c) Optimum price Optimum output is where MC = MR:

p= 54 – 0.46 Q TR = 54 Q– 0.46 Q2 MR = 54 – 0.92 Q MC = 20 Optimal output is where 20 = 54 – 0.92 Q Q = 36.96 Optimum price ( p) = 54 – 0.46(36.96) = 37 pence per packet Sensitivity of solution of changes in priceIt is assumed that this part of the question refers to how sensitive profit is tochanges in prices with other factors (e.g. variable costs and demand function heldconstant). Contribution (c) = total revenue total variable cost TR = price ( p) quantity ( Q) = Qp p =54 0.46 Q Q=54 p = 117.39 2.174 p 0.46 Qp = 117.39 p 2.174 p2 Total VC = 20 Q= 20(117.39 2.174 p) = 2348 43.48 p Contribution (TR TC) = 117.39 p 2.174 p2 (2348 43.48 p) = 160.87 p 2.174 p2 – 2348 The relationship between the variation in contribution (c) with variations in selling price is:

d c = 160.87 4.348 p d p (d) The answer should stress that direct costs can be obtained without too much difficulty using engineering methods outlined in Chapter 23. It is important that appropriate activity bases (cost drivers) be selected which adequately explainvariations in costs when establishing variable overhead rates. Unit product costscan then be calculated by multiplying cost drivers by the appropriate variableoverhead rates. For a discussion of the problems involved in determining variableoverhead rates see Chapter 3. The major problems faced in deriving appropriateunit costs relate to tracing fixedoverheads to products. Determining appropriate cost drivers for some fixed overhead costs can be difficult and time-consuming.Assumptions must also be made concerning the level of future volume in order todetermine fixed overhead rates. Consequently it is necessary to predict demandprior to selling the new product. Other problems include predicting future 224 COST ESTIMATION AND COST BEHAVIOUR inflation rates, learning effects as the workforce become more familiar with producing the product, and the effect on the economies of scale if more intensiveuse is made of existing resources. For a more detailed explanation of some of the above items see ‘Limitations of cost-plus pricing’ in Chapter 10.

(b) (2) (3) (4) (5) (1) Total Average production Cumulative Percentage Units production time per unit in average production decline in produced time successive lots time per unit (4) (hours) (hours) (hours) (%) 1 1 000 1000 1000 0 2 1 800 800 900 10 4 3 240 720 810 10 8 5 832 648 729 10 16 10 498 583 656 10 (a) 6 months 12 months (£) (£) Direct materials a 271 000 514 000 Direct labour b 191 340 315 423 Variable overhead c 76 536 126 169 Directly attributable fixed costs 90 000 180 000 ––––––– –––––––– Total costs 628 876 1 135 592 Sales revenues 720 000 1 260 000 ––––––– –––––––– Net cash inflow d 91 124 124 408 ––––––– –––––––– Required return (£75 000 + 33.33%) 100 000 ( £75 000 + 50%) 112 500 Shortfall 8 876 The target return is achieved over the 12 month life cycle but not over the 6month life cycle Notes a (200 batches at £500) + (200 batches at £450) + (200 batches at £405) = £271 000 for 6 months, £271 000 + (600 × £405) = £514 000 for 12 months b For the first 6 months: y= axb = £2500 × 600 –0.3219 = £318.90 Total cost = £318.90 × 600 batches = £191 340 For the first 7 months: y= axb = £2500 × 700 –0.3219 = £303.461 Total costs = £303.461 × 700 batches = £212 423 All batches after the first 700 have the same labour cost of the 700th batch For 699 batches: y= axb = £2500 × 699 –0.3219 = £303.601 Total cost = £303.601 × 699 batches = £212 217 Therefore the cost of the 700th batch = £212 423 – £212 217 = £206 Total costs for 12 months = £212 423 + (£206 × 500) = £315 423 c Variable overheads vary with direct labour hours at £4 per direct labour which isequivalent to 40% of the direct labour cost.

d For 6 months: 100 batches per month = 600 batches at £1200 per batchFor 12 months: 100 batches per month = 1200 batches at £1050 per batch (b) The maximum labour and variable overhead cost of £259 000 given in the question can also be derived from part (a): Direct labour cost (£191 340) + variable overheads (£76 536) – shortfall (£8876)= £259 000 Solution IM 23.8 Solution IM 23.9 COST ESTIMATION AND COST BEHAVIOUR 225 Maximum direct labour costs = £259 000/1.4 = £185 000 (Variable overhead costs are 40% of direct labour costs) Required average direct labour cost for a cumulative output of 600 batches = £308.333 (£185 000/600)y = axb so that, £308.333 = a × 600 –0.3219 £308.333 = 0.1276 a a = £2416 giving initial labour hours of 483.2 (£2416/£5) (c)(i) Product X could be viewed as an example of target costing because of thefollowing:

(i) The market has been identified in terms of a target selling price and demand.

(ii) A required profit margin over the whole life of the project has been established.

(iii) A target cost to achieve the required six month profit has been established.

(c)(ii) The following actions could be considered: (i) Investigate how the learning rate can be improved. For example, changes inproduction methods or additional training could be considered.

(ii) Investigate ways of reducing the material losses that occur in the batchesprior to the steady state being reached.

(iii) Ascertain the content of the directly attributable fixed costs and investigateways of eliminating any non-value-added elements; (iv) Investigate whether direct materials can be sourced more cheaply.

(c)(iii) All of the items included in the evaluation are subject to uncertainty. Inparticular, sales demand may be less than anticipated or the learning ratemight not be achieved.

(a) The first batch was completed in 120 hours (£1400 /£12). Applying a 90% learning curve the average time per batch is calculated as follows.

Average time per batch Total time per batch Number of batches (hours) (hours) 1 120 120 2 108 (0.9 120) 216 4 97.2 (0.9 108) 388.8 Hours required for batch 2 = 96 hours (216 120).

Hours required for batches 3 and 4 = 172.8 hours (388.8 216).

(b) The data given in the question have been derived from the learning-curve formula Y x = axb where Y x is the cumulative average time required to produce x units, ais the time required to complete the first unit of output and xis the number of units of output under consideration. The exponent bis defined as the ratio of the logarithm of the learning-curve improvement rate (0.9 for a 90%learning curve) divided by the logarithm of 2. Therefore b= log 0.9 = 0.105 = 0.152 log 2 0.6931 The average time taken to produce 15 and 120 batches can be calculated as fol- lows. Y15 = 120 15 –0.152 = 79.51 hours Y 120 = 120 120 –0.152 = 57.96 hours The above values are equal to the data given in the question. Solution IM 23.10 226 COST ESTIMATION AND COST BEHAVIOUR Calculation of labour cost Cumulative production is 30 batches at the end of the fourth quarter, 75 batchesat the end of the first quarter and 120 batches at the end of the second quarter.

Time for the first 30 batches = 2146.8 hours (30 71.56 hours) Time for the first 75 batches = 4668.75 hours (75 62.25 hours) ––––––– Time required for 45 batches 2521.95 hours ––––––– Labour cost for quarter 1 = £30 265 (2521.95 hours £12) Time for first 75 batches 4668.75 hours (75 62.25 hours) Time for first 120 batches 6955.20 hours (120 57.96 hours) ––––––– Time required for 45 batches (quarter 2) 2286.45 hours ––––––– Labour cost for quarter 2 = £27 437 (2286.45 hours £12) Calculation of material costs Quarter 4: Units required for first 20 batches (200 200) 4000 Units required for next 10 batches (0.98 200 10) 1960 –––– Total units required 5960 –––– Quarter 1: Units required for first 10 batches (0.98 200 10) 1960 Units required for next 20 batches (0.96 200 20) 3840 Units required for final 15 batches (0.94 200 15) 2820 –––– Total units required 8620 –––– Quarter 2: Units required for first 5 batches (0.94 200 5) 940 Units required for next 20 batches (0.92 200 20) 3680 Units required for next 20 batches (0.90 200 20) 3600 –––– Total units required 8220 –––– Material costs: (£) Quarter 1 (8620 £1.80) 15 516 Quarter 2 (8220 £1.80) 14 796 Stockholding costs: Quarter 1 [(8620 /2) £0.30] 1 293 Quarter 2 [(8220 /2) £0.30] 1 233 Average stocks = total usage /2 Budget for Quarters 1 and 2 Quarter 1 Quarter 2(£) (£) Sales revenue (45 £1600) 72 000 72 000 Less: Variable costs: Direct materials (15 516) (14 796) Stockholding costs (1 293) (1 233)Labour costs (30 265) (27 437) Variable overhead (50% of direct labour) (15 132) (13 718) –––––– –––––– Contribution –––––– ––––––9 794 1 4 816 COST ESTIMATION AND COST BEHAVIOUR 227 (c) (i)Quarter 1 Quarter 2(£) (£) Increase in purchase cost 862 (8620 £0.10) 1644 (8200 £0.20) Holding costs avoided 1293 1233 –––– –––– (Increase) /Decrease in costs 431 (411) –––– –––– On the basis of the above information the just-in-time delivery alternative would be acceptable for quarter 1 but not acceptable for quarter 2.

(ii) Other factors that should be considered are any further benefits arising fromeliminating raw material stocks. Examples include cash flow savings orpotential revenues from sub-letting released storage space, reducedobsolescence and insurance costs, and reduced materials handling costs.However, the company will be dependent on the reliability of the supplier interms of the delivery if buffer stocks are not held. Any delays in delivery,changes in demand or process losses may result in stockouts and lost sales.The probability of such events occurring should be carefully checked beforeadopting the just-in-time delivery alternative.

(d) The first part of the answer to part (b), which describes the learning-curve formula, can be used to answer this question. In addition, the answer shouldexplain, or illustrate, the application of the formula for producing 12 batches inquarter 3. Y132 = 120 132 –0.152 = 57.13 average hours per batch Y 120 = 120 120 –0.152 = 57.92 average hours per batch Total hours required for 132 batches = 7541 hours (132 57.13 hours) Total hours required for 120 batches = 6950 hours (120 57.92 hours) –––––––––– Incremental hours for 12 batches 591 hours –––––––––– Labour cost = £7092 (591 hours £12) 228 COST ESTIMATION AND COST BEHAVIOUR Solution IM 24.1 Solution IM 24.2 EOQ = 2DO/H Demand (D) = 90 800 units Ordering cost (O) = £5910/30 × 1.02 = £200.94 per orderHolding cost (H) = £20 per unit × 15% = £3 per unit EOQ = = 3448 units (349 boxes) Orders per year = = 26 orders Order frequency = Every 2 weeks (52 weeks/26 orders per year) (a) EOQ =2 DO H where D = total demand for period = 12 500 (3125 4) O = ordering cost per batch = £10 H = holding cost per unit in stock for one year = £l Therefore EOQ = ( 2 12 500 10 ) = 500 1 Annual ordering cost = number of orders £10 =12 500 £10 500 = £250 Annual cost of holding stock = average stock £1 =500 £1 2 = £250 Therefore minimum annual cost = £500 (£250 + £250) (b) Quarterly sales of 781 units Total demand for period = 3124 (781 4) Therefore EOQ = 2 3124 10 = 250 1 9080 boxes annual demand 349 boxes per order 2 × 200.94 × 90 800 3 Quantitative models for the planning and control of inventories Solutions to Chapter 24 questions QUANTITATIVE MODELS FOR THE PLANNING AND CONTROL OF INVENTORIES 229 Quarterly sales of 6250 units Total demand for period = 25 000 (6250 4) Therefore EOQ = 2 25 000 10 = 707 1 The EOQ formula shows that the optimum batch size varies in proportion to the square root of total demand (sales volume). Therefore when quarterly sales are 781units, sales volume changes by a factor of compared with (i). Consequently the optimal batch size changes by a factor of ( = ) When quarterly sales are 6250 units, sales volume increases by a factor of 2.

Therefore the optimal batch size increases by a factor of 2 = 1.414 approximately.

(c) For an explanation of the economic batch size (2 DO /H ) see ‘Determining the economic order quantity’ in Chapter 24.

The cost of placing an order when the component is purchased is not given. This can be obtained from the EOQ formula: Q =2 DO –––– H Q2 = 2 DO H HQ 2 =2 DO O = HQ 2 2 D = 0.25(2000) 2 2(20 000) = £25 (cost of placing an order).

Average stock level = Minimum stock level + EOQ = 400 + (2000) = 1400 units Comparison of annual costs Make Buy(£) (£) Purchase cost 20 000 £9 = £180 000 Storage 1400 £0.25 = 350 Ordering costs 10 £25 = 250 Direct labour 20 000 £6 = 120 000 Direct material 20 000 £2 = 40 000 Leasing = 2 400 = ––––––– ––––––– = 163 000 180 000 = ––––––– ––––––– It is cheaper to make the component unless the released facilities have some alternative use. If this opportunity cost is greater than £17 000 per annum then it will be cheaper tobuy the component. Note that direct labour is assumed to be a variable cost. The qualita-tive factors arising from the direct labour force being made redundant should be consid-ered if the component is not made by the company. Solution IM 24.3 230 QUANTITATIVE MODELS FOR THE PLANNING AND CONTROL OF INVENTORIES (a) For a definition of variable, semi-variable and fixed costs see Chapter 2. Examples ofeach cost are as follows. Variable : The purchase price of raw materials, the cost of placing an order at £50 per order and the cost of holding stocks at £0.40 per unit per annum are allvariable.Semi-variable : Ordering costs and stock holding costs are both semi-variable since they consist of a variable and fixed portion.Fixed : The £40 element of placing an order is a fixed cost. These costs will consist of staff involved in placing and handling orders, and their salaries will beunaffected by the number of orders placed.

(b) Annual usage is 6000 kg (12 000 0.4 10 /8). It is assumed that the apportioned order costs and the £0.50 long-term holding costs are not relevantcosts in the short term for establishing the economic order quantity. Becausepurchase costs are not constant per unit, it is not possible to use the EOQformula. Annual costs Purchase Holding costs Order cost of Order at £0.40 Total quantity 6000 kg p.a. costs at £50 per unit ( W1) costs (£) (£) (£) (£) 1000 6000 300 (6 £50) 200 6500 1500 5880 200 (4 £50) 300 6380 2000 5790 150 (3 £50) 400 6340 2500 5700 120 (2.4 £50) 500 6320 3000 5640 100 (2 £50) 600 6340 3500 5640 86 (1.71 £50) 700 6426 Working ( W1 ) Assuming constant usage, the relevant average stock is one half of the order quantity. The safety stock of 250 units will be the same for all orderquantities, and is therefore not included in the analysis. The order quantitywhich minimizes the costs in the short term is 2500 kg.

(a) EOQ = 2DO/H where D = Demand for the period (20 000 units) O = Ordering cost (£31.25 actual and £120 proposed) H = Holding cost per unit (20% of £6.25 = £1.25 actual and 20% of£6 = £1.20 proposed) The current EOQ is = 1000 units per order The EOQ after the change will be = 2000 units The EOQ will thus increase by 1000 units and the number of orders required willbe reduced from 20 to 10.

(b) The present ordering and holding costs are: £ Ordering costs (20 orders at £31.25) 625 Holding costs (1000/2 × £1.25) 625 –––– 1250 –––– 2 × 20 000 × £120 £1.20 2 × 20 000 × £31.25 £1.25 Solution IM 24.5 Solution IM 24.4 QUANTITATIVE MODELS FOR THE PLANNING AND CONTROL OF INVENTORIES 231 The ordering costs for the proposed method are: Ordering costs (10 orders at £120)1200 Holding costs (2000/2 × £1.20) 1200 –––– 2400 –––– The additional holding and ordering costs are £1150 (£2400 – £1250) but this isoffset by the quantity discounts of 20 000 units £0.25 = £5000. Hence the overallannual savings are £3850 (5000 – £1250). The annual after tax cash flows are: Year 0 1 2 3 onwards (£) (£) (£) (£) Outlay (10 000) Tax saving 3300 Annual cost savings 3850 3850 3850 Tax on cost savings (1271) (1271) –––––– –––– ––––– ––––– Net cash flow (10 000) 7150 2579 2579 –––––– –––– ––––– ––––– The net cash inflows after 2 years amount to £9729 and so the payback period is just over 2 years. If the cash flows were to accrue evenly throughout the years theprecise payback period would be: 2 years + (£10 000 – £9729)/£2579 = 2.11 years. A payback period of 2 yearswould suggest the new policy is likely to be beneficial but ideally the discountedpayback period should be calculated to ascertain how long the savings shouldcontinue for the new policy to be justifiable.

(c) See ‘Payback method’ in Chapter 13 for the answer to this question.

(a) The hourly opportunity cost of checking an order is £9 (£8 labour cost plus £1 contribution). Note that the employees are paid irrespective of output or the activities on which they are engaged, and opportunity cost is thus represented bylost cash inflows before the labour cost is deducted. The relevant ordering cost forthe EOQ model is therefore £75 [£30 + (£ )]. EOQ = 2 £75 4000 = 200 units £15 (b) The savings available if the firm purchases in batches of 400 units are: (£) Saving in purchase price (4000 £0.24) 960 Saving in ordering cost {[(4000 /200) (4000 /400)] £75} 750 –––– Total savings 1710 –––– The additional holding cost if the larger order is purchased is:

[(400 200) /2] £15 = £1500 The savings exceed the additional costs by £210. Therefore the company should accept the discount.

(c) See ‘Uncertainty and safety stocks’ and ‘The use of probability theory for determining safety stocks’ in Chapter 24 for the answer to this question.

(a) Preliminary calculations D(total demand for period) = 24 000 units O (ordering cost per order) = (£1000 fixed shipment charge per order = + £500 administration costs) H (holding cost per unit) = £18 [£10 + warehouse space = opportunity cost (2 £4)] Solution IM 24.6 Solution IM 24.7 9 5 232 QUANTITATIVE MODELS FOR THE PLANNING AND CONTROL OF INVENTORIES Note that the acquisition cost and delivery charge per unit remain unchanged irre- spective of the order quantity. Therefore they are not relevant to the EOQ model. Calculation of EOQ EOQ =2 DO H = 2 24 000 1500 18 = 2000 –––– –––– The annual cost of purchasing, ordering and holding Lakers based on an EOQ of 2000 units is: holding cost + ordering cost + purchase cost + base stock cost 20 200 (£18) + 2 24 0 0 0 0 0 0 (£1500) + 24 000(£15.50) + 1000(£18) = £18 000 + £18 000 + £372 000 + £18 000 = £426 000 (£) Annual revenue 480 000(24 000 £20) Annual costs 426 000 –––––– Profit from purchase and sale of Lakers 54 000 –––––– (b) Purchase price of £15.25 + £0. 50 delivery cost : This purchase price should not be considered, since the EOQ would still be 2000 units and for this order quantitythe purchase price will be in excess of that of May Ltd. Purchase price of £14.50 + £0.50 delivery cost : The annual cost if the firm purchases the minimum batch size of 3000 units necessary to obtain the cheaper purchase price is as follows: holding cost + ordering cost + purchase cost + base stock cost 30 200 (£18) + 2 34 0 0 0 0 0 0 (£1500) + 24 000(£15) + 1000(£18) = £27 000 + £12 000 + £360 000 + £18 000 = £417 000 Purchase price of £14.25 + £0.50 delivery cost : The annual cost if the firm purchases the minimum batch size to obtain the £14.25 purchase price is as follows:

holding cost + ordering cost + purchase cost + base stock cost 50200 (£18) + 2 54 0 0 0 0 0 0 (£1500) + 24 000(£14.75) + 1000(£18) = £45 000 + £7200 + £354 000 + £18 000 = £424 200 The annual costs are: (£) Purchase at £15 from May Ltd 426 000 Purchase at £14.50 from Richardson Ltd 417 000 Purchase at £14.25 from Richardson Ltd 424 200 QUANTITATIVE MODELS FOR THE PLANNING AND CONTROL OF INVENTORIES 233 Therefore batches of 3000 units at £14.50 per unit should be obtained from Richardson Ltd.

(c) The limitations of the above analysis are as follows. (i) The model assumes that annual demand can be predicted and constant usageapplies throughout the year.

(ii) The relevant order cost (incremental cost) per unit is extremely difficult to estimate. In practice most of the order costs are likely to be semi-fixed.

(iii) The costs of placing an order are assumed to be constant and not to vary with the size of the order.

(iv) Some of the holding costs are extremely difficult to estimate. Examplesinclude materials handling and obsolescence.

For a discussion of the above points see ‘Assumptions of the EOQ formula’ inChapter 24. It should be noted that the EOQ model is very insensitive to errors inpredictions. (a) (i) EOQ = 2 £48.46 4095 = 315 4 (ii) Order frequency = 4095 = 13 times per annum 315 (iii) Total annual procurement costs = C sd Q = £48.46 4095 = £630 315 Total annual holding costs = 1 2 EOQ C h = 315 £4 = £630 2 (b) (i) The EOQ model is based on an annual demand of 4095 units. Demand per four-week period is assumed to be constant at 315 units. If demand is less than 315 units in a four-week period, there will always be sufficient stock inhand to meet demand. However, if demand is in excess of 315 units,stockouts will occur. Possible corrective actions would be:1. To maintain a level of safety stocks in excess of the expected use during the lead time in order to provide a cushion against running out of stocks.

2. To continue to order the EOQ, but vary the re-order point based on the latest estimate of the trend in sales demand.

3. To adjust the EOQ according to the latest estimate in sales demand.

(ii) If the lead time is certain at three weeks, the order should be placed when stocks fall to 237 units [(315 /4) 3]. With an EOQ of 315 units and an annual demand of 4095 units, 13 orders will be placed at four-weeklyintervals. However, with a lead time of three weeks, an order will be placedone week after the first delivery, when stocks will have fallen to 237 units(315 units EOQ less one week’s usage). The order will then be repeated atthree-weekly intervals. Should the lead time turn out to be five weeks insteadof three then an order will be placed when stock reaches the re-order level of237 units, but demand during the lead time will be 394 units [(315 units /4) 5 weeks]. Therefore two weeks’ sales demand of 157 units will not be met.The normal way of overcoming uncertain lead times is to maintain a level ofsafety stocks to cover sales demand during the delivery delay.

(c) For the answer to this question see ‘Uncertainty and safety stocks’ and ‘The use of probability theory for determining safety stocks’ in Chapter 24. In particular, the Solution IM 24.8 234 QUANTITATIVE MODELS FOR THE PLANNING AND CONTROL OF INVENTORIES answer should stress that re-order level is determined by adding safety stocks to the expected usage during normal delivery time. If normal lead time is threeweeks then the re-order point will be 237 units (three weeks’ normal usage) plus asafety stock. If the objective is to reduce the probability of a stockout to zero thentwo weeks’ safety stock consisting of 157 units should be maintained [(315units/4) 2 weeks]. Therefore the re-order point will be 394 units (237 units + 157 units). At this point a purchase order will be placed for the EOQ of 315 unitsand, under normal conditions, this order will be delivered when the stock hasfallen to the safety level of 157 units. At this point in time, stocks will be at amaximum level of 472 units (315 + 157 units). If there was a delay in the leadtime from three to five weeks then usage during this period would be 394 units, and therefore a stockout would be avoided. For an i llustration of a graph see Figure 24.3 in Chapter 24. A re-order point of 394 units and safety stock of 157 should be entered on the horizontal axis. Demands of 237, 315 and 394 unitsfor lead times of 3, 4 and 5 weeks should then be plotted.

(a) Annual purchases are £6 m divided equally between three suppliers. Therefore £2 m is purchased from each supplier consisting of 100 000 units at £20 each. EOQ = 2 DO H = 2 100 0 200 100 = 3162 units from each supplier Note that the variable cost per unit of £0.10 is the same irrespective of the number of orders placed and is not relevant in determining the EOQ.

(b) The expected value of demand per month is 25 000 units (i.e. the sum of each potential outcome multiplied by the probability factor). Assuming no safety stocks and a lead time of 1 month the re-order level will be 25 000 units (25 000 units 1 month). Safety stocks are required to cover monthly demands of 27 000 or 30000 units as all other levels of demand can be satisfied from a re-order point of 25000 units. The expected costs for various levels of safety stock are as follows.

Stockout Stockout Expected Total Safety Re-order per per Probability stockout Holding expected stock point order year a of stockout cost b costc cost (units) (units) (units) (units) (£) (£) (£) 5000 30 000 0 0 0 0 10 000 10 000 2000 27 000 3000 94 860 0.12 4553 4 000 8 553 0 25 000 2000 63 240 0.20 (5059) 0 5000 158 100 0.12 (7589) 12 648 Notes a During the year 31.62 orders will be made from each supplier (100 000 units annual demand /EOQ of 3162 units). Stockout per year in units is calculated by multiplying the stockout per order by 31.62 orders.

b Expected stockout costs = annual stockout in units probability of stockout £0.40 c Holding cost = safety stock £2 Expected costs are minimized when 2000 units of safety stock are held. Solution IM 24.9 QUANTITATIVE MODELS FOR THE PLANNING AND CONTROL OF INVENTORIES 235 (c) Total relevant costs for three suppliers are:(£) Holding costs (£2 EOQ /2 = £2 3162 /2) 3 162 Fixed ordering costs (100 000 /3162 £100) 3 162 ––––– Relevant costs per supplier 6 324 ––––– Relevant costs for three suppliers 18 972 Total relevant costs for one supplier: EOQ = 2 100 300 000 = 5477 units 2 (£) Holding costs (£2 5477 /2) 5 477 Fixed ordering costs (300 000 /5477 £100) 5 477 ––––– 10 954 ––––– Annual relevant costs are £8018 lower when only one supplier is used. Note that the above analysis ignores variable ordering costs since they are common to bothalternatives.

(d) Advantages of JIT include: (i) large reduction in stockholding costs; (ii) quicker response to customer demand via closer liaison with suppliers; (iii) risk of obsolete stocks being passed on to suppliers; (iv) benefits arising from increased storage space that is no longer required.

Disadvantages of JIT include: (i) possible occurrence of major production stoppages or stockouts if suppliers do not meet the scheduled delivery dates; (ii) possible increase in suppliers’ prices to recoup the increased stockholding and ordering costs. The net effect is that stock management costs are merelytransferred to suppliers with no overall reduction in costs.

The company should implement JIT if the incremental benefits (reduced stock management costs plus other qualitative benefits) exceed the increased purchasecosts. However, a crucial factor in the decision will be the reliability of Mexet’ssuppliers.

(a) (i) Annual cost if plant is retainedVariable cost per 1000 litres (£840 000 /3 m 1000) = £280 (£) Holding costs per 1000 litres: Storage cost 20 Evaporation cost (5% £280) 14 Cost of capital (15% £280) 42 –– 76 –– (£) Total annual cost: Production costs (£840 000 + £330 000) 1 170 000 Storage costs (60 000 /1000 £76) 4 560 ––––––––– 1 174 560 ––––––––– Solution IM 24.10 236 QUANTITATIVE MODELS FOR THE PLANNING AND CONTROL OF INVENTORIES The opportunity cost on the lost sale proceeds should be added to the above cost. This item is considered in more detail in (iii) below.

(ii) Annual cost if plant is sold and materials purchased externallyPurchase price per litre (£370 + £30) /1000 = £0.40 (£) Holding cost per 1000 litres: Storage cost 20 Evaporation cost (5% £0.40 1000) 20 Cost of capital (15% £0.40 1000) 60 ––– 100 ––– Holding cost per litre (£100 /1000) = £0.10 In order to calculate total annual cost, it is necessary to establish the EOQ: EOQ = (2 DO /H ) = [(2 3 m £60) /0.10] = 60 000 (£) Total annual cost: Purchase price (3 m £0.40) 1 200 000 Storage cost ( 1 2 60 000 £0.10) 3 000 Ordering costs [(3 m /60 000) £60] 3 000 Cost of holding safety stocks (100 000 £0.10) 10 000 Administration costs 15 000 ––––––––– 1 231 000 ––––––––– (iii) Comments and interpretationThe above figures show that the annual cost of purchasing externally is £56 440 greater than the cost of manufacturing the materials. However, thisanalysis ignores the opportunity cost from the alternative use of the plant.

The question states that the site would have to be sold for £400 000 orretained ‘for the time being’. This implies that the alternative is to sell theplant now or at some future point in time. The analysis requires details of thepoint in time when the plant would be sold. If the alternative is to sell the plant in one year’s time, the present value of the sale proceeds will be £347 826 compared with £400 000 if the materials were purchased and theplant closed down immediately. The opportunity cost of operating the plant for one more year would be £52 174. If this opportunity cost is incorporated into the analysis, there is a saving of £4266 (£56 440 £52 174). Given the small value of the savings, the decision is likely to depend on qualitativefactors such as the reliability of the supplier, future purchasing costs and thecompetitiveness of the market for the materials. If the market is notcompetitive, Rainbow Ltd will have little bargaining power when negotiatinga new purchasing contract.

(b) (i) It is assumed that demand during the lead time can only be 10 000 or 14 000 units per day. The possible demand levels during the lead time are:

Lead time demand (litres) Probability Expected value 50 000 0.5 0.8 = 0.4 20 000 70 000 0.5 0.8 = 0.4 28 000 100 000 0.5 0.2 = 0.1 10 000 140 000 0.5 0.2 = 0.1 14 000 ––––– 72 000 ––––– QUANTITATIVE MODELS FOR THE PLANNING AND CONTROL OF INVENTORIES 237 This would suggest a re-order point of 172 000 litres (expected usage + safety stock). Maximum demand would be 140 000 units and the probability of a stockout would be zero. It is assumed that the 100 000 safety stock is intendedto represent the re-order point (consisting of 72 000 expected usage and 28 000 safety stocks). The probability of a stockout (i.e. demand being greater than 100 000 units) is 0.1. During the period, 50 orders would be placed (3 mdemand/60 000 EOQ), and this would result in the expected value of annual stockouts in litres being:

0.1 (140 000 100 000) 50 orders = 200 000 litres (ii) In order to determine whether it is worthwhile increasing the re-order level, it is necessary to compare the annual cost of holding the safety stocks plus thestockout costs for the re-order points prescribed in the question. Re-order level of 100 000 litres (28 000 litres safety stock) Let S= stockout cost per litre Cost of holding safety stocks (28 000 £0.10) £2 800 Expected cost of stockout 200 000S Re-order level of 120 000 litres (48 000 litres safety stock)Cost of holding safety stocks (48 000 £0.10) £4 800 Expected value of annual stockouts in litres: 0.1 (140 000 120 000) 50 orders 100 000 litres Expected stockout cost 100 000S It would be appropriate to increase the re-order level to 120 000 litres, where: £4800 + 100 000 S< £2800 + 200 000 S S < £0.02 per litre (c) The requirements for the successful adoption of a JIT inventory policy are: (i) Production of a small range of stable and high-volume products.

(ii) Rearrangement of factory floor away from batch production.

(iii) Close co-operation with suppliers. (iv) Reduction in the number of suppliers. (v) Negotiation of purchasing contracts with suppliers who are in close proximity.

(vi) More frequent deliveries and smaller re-order quantities.

(vii) A strong emphasis on training so that the employees fully understand the JIT philosophy and are committed to operating JIT techniques.The benefits of JIT are:

(i) Substantial savings in stockholding costs.

(ii) Elimination of waste.

(iii) Savings in factory and warehouse space. (iv) Reduction in obsolete stocks. (v) Reduction in paperwork arising from the issue of blanket purchase orders. The costs of operating a JIT policy include:

(i) Investment costs in rearranging plant layout and goods inwards facilities.

(ii) Increased risk due to greater probability of stockout costs arising from strikes or other unforeseen circumstances which restrict production or supplies.

For a more detailed answer to this question see ‘JIT purchasing andmanufacturing’ in Chapters 21 and 24. 238 QUANTITATIVE MODELS FOR THE PLANNING AND CONTROL OF INVENTORIES Solution IM 25.1 (a)Pixie Elf Queen King (£) (£) (£) (£) Selling price 111 98 122 326 Direct material (25) (35) (22) (25) Variable overhead (17) (18) (15) (16) Direct labour (40) (30) (75) (175) ––– –– ––– ––– Contribution 29 15 10 110 ––– –– ––– ––– Type 1 labour hours 8 6 Contribution per Type 1 labour hour £3.63 £2.50Ranking 1 2 In order to maximize the contribution from Type 1 labour the company should maximize the output of Pixie by producing 1000 units (8000 hours /8 units per hour). There are two production constraints applying to Queen and King and it is therefore necessary to use linear programming to determine the optimumproduction mix. The LP model is: Maximize 10 Q+ 110 Ksubject to:

10 Q+ 10 K 20 000 (Type 2 labour) 5 Q + 25 K 25 000 (Type 3 labour) Q 1 500 (Demand) 10Q+ 10 K 1 500 (Demand) The above constraints are plotted on the graph (Figure Q25.1) as follows: Type 2 labour: line from Q= 2000, K= 0 to K= 2000, Q= 0 Type 3 labour: line from Q= 5000, K= 0 to K= 1000, Q= 0 The optimum solution is where the lines intersect on the graph. The optimum output can be determined exactly by solving the simultaneous equations for theconstraints that intersect: 5Q + 25 K= 25 000 (1) 10 Q + 10 K= 20 000 (2) Multiplying equation (1) by 2 and equation (2) by 1 gives: 10Q+ 50 K= 50 000 (3) 10 Q+ 10 K= 20 000 (4) Subtracting equation (4) from equation (3) gives: 40K= 30 000 K = 750 The application of linear programming to managementaccounting Solutions to Chapter 25 questions THE APPLICATION OF LINEAR PROGRAMMING TO MANAGEMENT ACCOUNTING 239 Substituting this value for Kin equation (4) gives:

10 Q+ 10 (750) = 20 000 Q= 1250 Therefore the production mix and contribution which maximizes profits is: (£) 1000 units of Pixie at £29 unit contribution 29 000 1250 units of Queen at £10 unit contribution 12 500 750 units of King at £110 unit contribution 82 500 –––––– Total contribution 124 000 Less: Fixed costs 15 000 –––––– Profit 109 000 –––––– (b) Pixie yields the largest contribution per scarce labour hour and therefore the additional hours should be allocated to producing pixies. The revised contributionper labour hour is £1.13 (£3.63 £2.50 overtime premium). Hence profits will increase by £1130 (1000 hours £1.13).

(c) The principles used were: (i) maximization of an objective function subject to constraints; (ii) assumption of linear relationships. In practice it is questionable whetherlinearity applies throughout the entire output range.

(d) Software linear programming packages are available which enable the model to be formulated and solved using the Simplex method. The output from the model willgenerate details of the optimum output level, binding constraints and shadowprices based on the principles outlined in Chapter 25. 0 1000 2000 3000 400010Q + 10K 20 000 5Q + 25K 25 000 (Type 3) 5000 4000 3000 2000 1000 Output Q Output K Figure Q25.1 240 THE APPLICATION OF LINEAR PROGRAMMING TO MANAGEMENT ACCOUNTING (a) Maximize 124X+ 80 Ysubject to 2.5 X+ 1.5 Y 225 (department 1) 1.67 X+ 2 Y 200 (department 2) Y 75 (sales demand) X , Y 0 The above constraints are plotted on the graph shown in Figure Q25.2 as follows: Department 1: line from X= 90, Y= 0 to Y= 150, X= 0 Department 2: line from X= 120, Y= 0 to Y= 100, X= 0 The feasible region is area OABCD on the graph and the optimum output is at point C, where X= 60 and Y= 50. The revised contribution is:

(£) X (60 £124) = 7 440 Y (50 £80) = 4 000 ––––– 11 440 ––––– At the optimum output level, contribution will increase by £1720 (£11 440 £9720 current contribution).

(b) It is assumed that the capacity of both departments cannot be increased at the same time. In other words, the decision is to increase capacity in one departmentonly. If the department 1 capacity constraint is removed, line DG will no longer be a constraint and the optimal output level will be 120 units of X. This will yielda total contribution of £14 880 (120 £124).

If the department 2 capacity constraint is removed, line EF will no longer be a constraint and the optimal output level will be at point H (75 units of Y and 45 units of X). This output level will yield a total contribution of £11 580. It istherefore preferable to increase capacity in department 1. The total hours requiredin department 1 in order to achieve the optimal output level of 120 units are 300 Solution IM 25.2 AB H C DF Sales restriction 15 30 45 60 75 90 105 120 0 X 15 30 45 75 60 90 E 105 120 135 150 G Department 2 Department 1 Y Figure Q25.2 THE APPLICATION OF LINEAR PROGRAMMING TO MANAGEMENT ACCOUNTING 241 (120 2.5 hours). Therefore 75 additional hours (300 225) will be required, and the revised contribution will be £14 842.50 [£14 880 (75 £0.5)]. This represents an increase in contribution of £3402.50 (£14 842.50 £11 440).

(c) Department 1 Department 2 Total hours 225 200 Hours required for 30 units for Y 45 (30 1.5) 60 (30 2) ––– ––– Hours available for X 180 140 Hours per unit of X 2.5 1.67 Production of X 72 units 84 units Therefore maximum production of X is 72 units (£) Revised contribution [(£124 £72) + (£80 30)] 11 328 Contribution per (a) 11 440 ––––– Decrease in contribution 112 ––––– The sale of the rights to the quota should yield a minimum total revenue of £112.

The minimum price per unit depends on the number of rights purchased.Assuming that the maximum rights of 45 units (75 30) are purchased, the min- imum price per unit will be £2.49.

(a) (i) Let R= number of units of Razzle Let D= number of units of Dazzle The model is as follows: Maximize C= 12 R+ 10 Dsubject to:

5 R + 12.5 D 75 (Raz constraint) 8 R + 10 D 80 (Ma constraint) 2 R 15 (Taz constraint) D , R 0 The constraints are plotted on the graph shown in Figure Q25.3(i) as follows:

Raz constraint: line from R= 0, D= 6 to D= 0, R= 15 Ma constraint: line from R = 0, D= 8 to D= 0, R= 10 Taz constraint: line from R= 7.5 The optimal production plan is at point X, where the lines 2 R 15 and 8 R+ 10 D 80 intersect. The output X is where Razzle = 7.5 sales units.

The output of Dazzle can be read from the graph, but a more accurate calculation can be obtained by solving the equation:

8R + 10 D= 80 at point X, where R= 7.5 Therefore 8 (7.5) + 10 D= 80 D = 2 So the optimal production is Dazzle = 2 units and Razzle = 7.5 units. Contribution at this output level:

R (7.5 £12) + D(2 £10) = £110 Profit per day = £110 contribution less fixed costs (£60) = £50––– ––– At the optimal output level, total sales revenue per day is: Razzle (7.5 20) + Dazzle (2 £30) = £210 Solution IM 25.3 242 THE APPLICATION OF LINEAR PROGRAMMING TO MANAGEMENT ACCOUNTING (ii) The model is as follows:Maximize S (sales) = 20 R+ 30 Dsubject to:

5 R + 12.5 D 75 (Raz constraint) 8 R + 10 D 80 (Ma constraint) 2 R 15 (Taz constraint) 12 R+ 10 D 104 (profit constraint) D , R 0 The constraints are plotted on the graph in Figure Q25.3(ii) based on the calculations in (i). The profit constraint is: line from R= 8.67, D= 0 to D= 10.4, R= 0 Note that the objective function changes.The feasible output range is VWX.The maximum sales mix subject to the profit constraint is at X.

The optimal point can be determined by solving the simultaneous equations for the constraints that intersect at point X:

8R + 10 D= 80 (1) 12 R+ 10 D= 104 (2) 1 2345678910 Dazzle ( D ) Razzle (R ) 15 14 13 12 11 10 9 7 8 6 5 4 3 21 0 W X Y Z 2R 15 (Taz constraint) C = 12 R+ 10 D 5 R + 12.5 D 75 (Raz constraint) 8R + 10 D 80 (Ma constraint) Feasible region is OWXYZ Optimal sales mix is at point X Figure Q25.3(i) THE APPLICATION OF LINEAR PROGRAMMING TO MANAGEMENT ACCOUNTING 243 Subtracting equation (1) from equation (2):4R = 24 R = 6 Substituting in equation (1):

8(6) + 10D= 80 D = 3.2 The optimal solution is Razzle = 6 units and Dazzle = 3.2 units. Contribution at this output level: R (6 £12) + D(3.2 £10) = £104 Profit per day = £104 contribution less fixed costs (£60) = £44––– ––– At the optimal output level, total revenue per day is: Razzle (6 £20) + Dazzle (3.2 £30) = £216 1234567891 0 Dazzle ( D) Razzle ( R) 15 1413 12 11 10 9 7 8 6 54 3 21 0 W X V Z 2 R 15 (Taz constraint) 5 R + 12.5 D 75 (Raz constraint) 12 R + 10 D 104 (Profit constraint) 11 U Y 8R + 10 D 80 (Ma constraint) S = 30 D+ 20 R(Objective function) Figure Q25.3(ii) 244 THE APPLICATION OF LINEAR PROGRAMMING TO MANAGEMENT ACCOUNTING (b) The objective of maximizing sales revenue subject to a profit constraint is anexample of a ‘satisfying’ model of business behaviour. This model recognizes that single objectives such as profit maximization or revenue maximization may onlyrepresent the goal of one of the major interest groups. In practice, a number ofdifferent groups seek to achieve goals within the organization.The objective of maximizing sales revenue subject to a profit constraint can be associated with two interest groups: (i) The achievement of the minimum profit level represents the interests of existing and potential investors in the firm. It is assumed that managers willbe aware that they are relatively free from shareholder interference as long asdecisions satisfy dividend expectations and support the share’s market value.It is assumed that substantial separation of ownership and control exists.

(ii) The achievement of maximum sales subject to the profit constraint reflectsthe desire of management to achieve high sales because it is seen as consistentwith growth objectives and desire for management power and status.Individual managers might view their personal career progression as beinglinked to higher output levels and the growth in the size of the organization.Also, securing high market shares in terms of sales might be considered asimportant in determining what is successful performance.

(a) Assuming that blending hours are the only scarce factor, profits will be maximized by concentrating on the product that yields the largest contribution per blending hour: Gamma Delta Contribution per kg £4000 £8000 Blending hours per kg 100 250 Contribution per blending hour £40 £32 Since the company can sell all of its output, the scarce resources should be devoted to producing Gamma. There are 1050 blending hours available enabling 10.5 kg(1050 /100) of Gamma to be produced. The profit for the period will be:

(£) Contribution (10.5 £4000) 42 000 Fixed costs 36 000 ––––– Profit 6 000 ––––– (b) The optimal production programme is found using linear programming: Letx= kg of Gamma produced and sold Let y = kg of Delta produced and sold The linear programming formulation is: Maximize 4000 x+ 8000 ysubject to:

400 x+ 120 y 1200 (heating constraint) 100 x+90 y 450 (refining constraint) 100 x+ 250 y 1050 (blending constraint) x 0 y 0 The above constraints are plotted on the graph in Figure Q25.4 as follows:Heating constraint : line from x= 3, y= 0 to y= 10, x= 0 Refining constraint: line from x= 4.5, y= 0 to y = 5, x = 0 Machine time constraint : line from x= 10.5, y= 0 to y= 4.2, x= 0 Solution IM 25.4 THE APPLICATION OF LINEAR PROGRAMMING TO MANAGEMENT ACCOUNTING 245 The feasible region is area OABCD. The dashed line on the graph represents an arbitrarily chosen contribution figure of £16 000 giving a maximum output ofeither 4 kg of Gamma or 2 kg of Delta. By extending the contribution line outwards the optimum production mix can be derived at point B. The optimumpoint can be determined mathematically by solving the simultaneous equationsfor the constraints that intersect at point B:100x+ 250 y= 1050 100 x+ 90 y= 450 The values of xand ywhen the above equations are solved are 3.75 for yand 1.125 for x. The budgeted loss for the period is:

(£) Contribution from Gamma (1.125 £4000) 4 500 Contribution from Delta (3.75 £8000) 30 000 ––––– 34 500 Fixed costs 36 000 ––––– Loss (1 500) (c) The optimum production plan results in a loss of £1500. The company must decide whether or not to produce during the period. In the short term this willdepend on whether any of the fixed costs can be avoided. If the company ceasesproduction for the period a loss equal to the fixed costs will be incurred.Therefore the company might be worse off if it ceases production.The company should focus on the long term and ascertain whether future demand is likely to continue to exceed production capacity. If this situation islikely to occur then a financial appraisal should be undertaken to determinewhether an expansion of production capacity can be justified after taking intoaccount long-term considerations. Attention should also be given to the possibility of increasing selling prices or reducing variable costs.

(d) The shadow price can be found by increasing refining time by 1 hour. If one extra hour of refining time is available the optimum solution will still occur at theintersection of the refining and blending contraints where: 10 8 6 4 2 0 A B C C = 16 000 2D 4 6 8 10 12 400 x+ 120 y 1200 100 x+ 250 y 1050 100 x+ 90 y 450 x , of Gamma y , kg of Delta Figure Q25.4 246 THE APPLICATION OF LINEAR PROGRAMMING TO MANAGEMENT ACCOUNTING 100x+ 90 y= 451 (refining) 100 x+ 250 y= 1050 (blending) The revised values when the above simultaneous equations are solved are: x= 1.140625 y = 3.74375 The revised maximum contribution is: (1.140625 £4000) + (3.74375 £8000) = £34 512.50 Thus contribution is increased by £12.50 and this represents the shadow price for one hour of refining time. Shadow prices are also known as opportunitycosts. For an explanation of how shadow price information can be used, see ‘Usesof linear programming’ in Chapter 25. The limitations inherent in the shadowprice calculations relate to those that apply to linear programming in general. Fora discussion of these limitations see the answer to question 25.3(f) in theStudent’s Manual.

(a) Maximize 12.5A + 9.5B + 11C + 8D + 14E (Contribution) Subject to A + B + C + D + E 30 000 (Production capacity) 90A + 75B + 100C + 120D + 200E 3 000 000 (Funds) A 1000 B 2000 C 1200 D 2500 E 600 A, B, C, D, E 0 Note that the minimum capacity constraints for each division are 5% of the existing capacity. For example, the capacity constraint for Division A is 1000hours (5% × 20 000) (b) (i) The objective function indicates that the maximum contribution from the additional 30 000 hours within the £3 million budget is £359 263.60. Theadditional hours in each division are as follows: Division A 22 090.9 hours B 2 000 C 1 200 D 2 500 E 2 209.1–––––––30 000.0 ––––––– Divisions A and E have been allocated more hours than the minimumrequired.

(b) (ii) The shadow prices represent the opportunity cost of the constraints. Fordivisions B, C and D the shadow prices indicate the cost per hour ofproviding the minimum capacity to achieve the strategy. For example,allocating a scarce hour to Division B results in a loss of contribution ofapproximately £2.80 per hour. There is no loss in contribution fromallocating scarce hours to divisions A and E.

(b) (iii) The shadow prices indicate the opportunity cost of the constraints. For each extra hour of machine time a contribution of £11.27 can be obtainedwhereas an additional £1 of investment will yield an extra contribution of£0.0136. Solution IM 25.5 THE APPLICATION OF LINEAR PROGRAMMING TO MANAGEMENT ACCOUNTING 247 (b) (iv)The table for the sensitivity analysis of objective function constraints indicates that decreases in contribution will have no effect on the plannedallocations for divisions B, C and D. For division A the contribution wouldhave to be in excess of £14 per hour or below £10.70 per hour for a changein the planned allocation to occur. The contribution would have to beoutside the range of £12.50 to £27.78 per hour in division E for a change inthe planned allocation to occur.

(b) (v) The sensitivity analysis of right-hand side values indicates that, if all para- meters to the model are to remain unchanged, the capacity hours canincrease by 1966.67 hours to 31 966.67 hours. Each additional hour yields acontribution of £11.2727 resulting in an additional contribution of £22 170(1966.67 hours at £11.2727 per hour). The additional hours, however, must be obtained within the funds constraint of £3 million. The negative shadow prices for divisions B, C and Dmean that additional contribution is obtained from either divisions A or E.Because the investment cost per hour in division E is higher than that fordivision A, 2.2222 hours in division A can be obtained for each 1 hour offunds invested in division E (£200/£90). In other words, for each hourallocated from division E to division A an extra 1.2222 hours can obtained.Therefore to obtain the extra 1966.67 hours, 1609.1 hours (1966.67hours/1.2222 hours) of investment cost at £200 hours should be transferredfrom division E to division A. The investment cost released of £321 820(£200 × 1609.1 hours) will enable 3575.77 hours (£321 820/£90 per hour)to be utilized in division A consisting of 1609.1 existing hours plus thebalance of 1966.67 additionalhours. This would leave the minimum requirement of 600 hours in division E.

(b) (vi) The sensitivity analysis of right-hand side values indicates for the parameters to remain unchanged the investment funds can decline to £2 823 000, areduction of £177 000. Contribution will decline by £177 000 × £0.0136 = £2 407. That is, the decline in investment funds multiplied by the shadowprice per £1 of investment.Based on the explanation in (b)(v) this strategy should be implemented by reducing the number of hours in division E to the minimum of 600 andtransferring the balance of 1609.1 hours to division A. This will reduce theinvestment in division E by £321 820 (£200 × 1 609.1 hours) but theinvestment in division A will cost £144 820 (1 609.1 hours at £90) giving anet reduction in investment of £177 000 (£321 820 – £144 820).

(c) See answer to 25.3(f) in the Students’ Manual for the answer to this question. (a) Budgeted weekly profit and loss account Product X Y Z Total (£) (£) (£) Selling price 70 60 150 Variable costs: Aragons (£5 each) (5) (5) (15) Bovons (£8 each) (16) (8) (16) Direct labour (£5 per hour) (30) (35) (80) Other assembly costs (4) (5) (15) Contribution per unit 15 7 24 Total contribution 1500 700 2400 4600 Fixed costs (900) (1050) (2400) (4350) Profit /(loss) 600 (350) – 250 Solution IM 25.6 248 THE APPLICATION OF LINEAR PROGRAMMING TO MANAGEMENT ACCOUNTING (i)No external availability of Aragons and Bovons Let X, Y and Zrepresent the number of Xylos, Yo-yos and Zicons produced each week and Crepresent the total contribution. The LP model is:

Maximize C=15 X+ 7 Y+ 24 Zsubject to:

22 X+ 14 Y+ 34 Z 9600 (process L) 15 X+ 10 Y+ 25 Z 7000 (process M) Z X (process N) Note that product Xrequires one Aragon and two Bovons, and these components require a total of 22 minutes in process L [1 6 + (2 8)].

Process N must produce at least one Aragon for each Bovon produced. This constraint will not be met if production of Xis in excess of Z. Hence the process N constraint is added to meet this production requirement.

(ii) External availability of Aragons and Bovons Let A= number of Aragons bought each week B = number of Bovons bought each week If one Aragon is bought, process L capacity will be increased by 6 minutes and Process M capacity will be increased by 5 minutes. If one Bovon is bought,process L capacity will be increased by 8 minutes and process M capacity will beincreased by 5 minutes. Hence the constraints for processes L and M capacityare: 22X+ 14 Y+ 34 Z 9600 + 6 A+ 8 B (process L) 15 X+ 10 Y+ 25 Z 7000 + 5 A+ 5 B (process M) Purchasing Aragons and Bovons externally results in an increase in variablecosts and a reduction in contribution of £5 for Aragons (£10 £5) and £4 (£12 £8) for Bovons. The revised objective function and constraints are:

Maximize C=15 X+ 7 Y+ 24 Z 5A 4B subject to:

22 X+ 14 Y+ 34 Z 6A 8B 9600 (process L) 15 X+ 10 Y+ 25 Z 5A 5B 7000 (process M) Z A X B (process N) 0 A 200 0 B 300 Note that the number of Aragons ( A) and Bovons ( B) purchased externally is deducted from Zand Xin the equation for process N so that the constraint maintains the internalproduction requirement of producing at least one Aragon for each Bovon.

(b) The optimum production plan indicates weekly production of 50 units of X and 250 units of Z. This will result in a production of 800 Aragons and 600 Bovons,and thus satisfy the production requirement of process N. The shadow pricesarising in processes L and M indicate that these processes are fully utilized. Forevery minute of additional production time that can be obtained in processes Land M, contribution will increase by £0.375 and £0.45 respectively. If one moreAragon or Bovon became available, contribution would increase by £9.50 and£13.25 respectively. The optimal plan also indicates that product Y should not beproduced. However, if one unit of product Y were produced, it would benecessary to divert resources from X and Z, and this would result in a loss of£2.75 for each unit of product Y produced.The binding constraints are processes L and M. If process L were increased by one additional minute, the revised constraints would be: THE APPLICATION OF LINEAR PROGRAMMING TO MANAGEMENT ACCOUNTING 249 22X+ 34 Z= 9601 (revised process L constraint) 15 X+ 25 Z= 7000 (unchanged process M constraint) The revised optimum output when the above equations are solved is 249.63 units of Z and 50.62 units of X. Therefore if an additional minute of process L is obtained, X should be increased by 0.62 units and Zdecreased by 0.37 units.

If an additional minute of process M could be obtained, the revised constraints would be:

22X+ 34 Z= 9600 15 X+ 25 Z= 7001 Solving the above equation results in a revised output of 250.55 units of Z and49.15 units of X. Therefore production of Z should be increased by 0.55 units andX decreased by 0.85 units. Assuming that 300 Bovons became available and optimal output requires that only X should be made, the external purchase of Bovons would enable 150 units of X tobe made. This output would require 150 Aragons to be produced internally, thususing in processes L and M 900 minutes (150 6) and 750 minutes (150 5) respectively. The unused capacities would be 8700 minutes for process L and 6250minutes for process M. Maximum production from this remaining capacity is:

process L: 395 (8700/22) process M: 416 (6250 /15) Consequently production will be restricted to a further 395 units. Process L will bea binding constraint, but capacity will not be fully utilized in process M.Consequently process M will have a zero shadow price. If capacity of process L canbe increased, it will be used to produce product X, thus yielding a contribution of£15. One unit of product X requires 22 minutes in process L. Thus the shadowprice for one minute in process L is £0.68 (£15 /22).

(a) In Chapter 25 the approach adopted was to formulate the first tableau with positive contribution signs and negative signs for the slack variable equations.The optimal solution occurs when all the signs in the contribution row arenegative. The opposite procedure has been applied with the tableau presented inthe question. Therefore if the approach explained in Chapter 25 is adopted it isnecessary to reverse all the signs given in the question and ignore the entries of 0and 1.(i) £1 053 671.4This is the total contribution obtained from producing the optimal outputpresented in the linear programming model. This can be checked bymultiplying the optimum production by the product contributions:

X1: 43 287 units at £5.70 contribution 1 X 2: 13 333.3 units at £10.10 contribution = £1 053 671.4 X 6: 48 019.2 units at £14 contribution (ii) 43 287.0 unitsThis is the production of X 1 in the optimal solution.

(iii) 15 747.87 hoursThis represents the unused hours of the slack variable X 3 (forming time) in the optimum solution. The forming hours required in the optimal solutionare: 43 287.0 +13 333.3 +48 019.2 = 252.19 hours 450 450 380 The total forming hours are 16 000, resulting in 15 747.81 unused hours (16 000 252.19 hours). Solution IM 25.7 250 THE APPLICATION OF LINEAR PROGRAMMING TO MANAGEMENT ACCOUNTING (iv)£10 The optimal solution results in zero output of X 3. If one unit of X 3 is produced, it will be necessary to adjust the optimal programme in order tocreate the resources to produce X 3. The optimal adjustment if a unit of X 3 is to be produced is: Contribution (£) Increase output of X 1 by 1.6 units +9.12 (1.6 £5.7) Decrease output of X 2 by 0.53 units 5.35 (0.53 £10.10) Decrease output of X 6 by 1.9 units 26.60 (1.9 £14) Extra unit of X 3 +12.30 –––– 10.53 –––– The £10 figure refers to the amount by which total contribution woulddecrease if the company made one unit of X 3 instead of the optimal mix. The difference between £10 and £10.53 is assumed to be due to rounding errors.

(v) £16This is the shadow price of drilling time ( X 9). If an additional hour of drilling time can be obtained, contribution will increase by £16. An additional hour ofdrilling time should be used to increase output of X 2 by 3.33 units and reduce the output of X 1 by 3.0 units. Contribution will be increased by:

(3.33 £10.10) (3.0 £5.7) = £16.53 The difference between £16.53 and £16 is assumed to be due to roundingerrors.

(vi) 18.50If X 10 is increased by one hour then X 1 should be decreased by 18.5 units and X 6 should be increased by 12 units.

(vii) 15 806.72 hoursThis represents unused hours of the slack variable X 11 (coating time) in the optimum solutions.

(b) (i) If one unit of X 4 is made instead of the optimal mix, total contribution will fall by £4. As long as the contribution from X 4 does not increase by more than £4, the optimal mix will remain unchanged. If the contribution from X 4 increases by more than £4 to over £13.80 the optimal solution will change.

(ii) The optimal solution indicates 15 806.72 spare coating hours. The optimalproduction programme requires: 43 287 +48 019.2 = 193.28 coating hours 500 450 Hence 15 806.72 coating hours are unused. Consequently coating time could fall to 193.28 hours before the optimal solution changes.

(c) Assuming that contribution per unit remains unchanged, the revised model is: Maximize Z= 5.7 X 1 + 10.1 X 2 + 12.3 X 3 + 9.8 X 4 + 17.2 X 5 + 14.0 X 6 subject to:

700 X 1 + 770 X 2 + 410 X 3 + 500 X 4 + 330 X 5 + 470 X 6 + X 7 = 12 000 540 X 1 + 540 X 2 + 620 X 4 + 220 X 5 + 460 X 6 + X 8= 16 000 200 X 2 + 380 X 3 + 300 X 5 + X 9 = 4 000 380 X 3 + 670 X 4 + 400 X 5 + 720 X 6 + X 10 = 4 000 500 X 1 + 540 X 3 + 480 X 4 + 600 X 5 + 450 X 6 + X 11 = 16 000 X 3 + X 12 = 150 000 X 5 + X 13 = 20 000 X 6 + X 14 = 70 000 THE APPLICATION OF LINEAR PROGRAMMING TO MANAGEMENT ACCOUNTING 251 (d) The revised contribution can be obtained by multiplying the binding constraintsby the shadow prices: (£) X 7 0(cutting): 12 000 hours £59.30 711 600 X 9 0(drilling): 4 000 hours £14.20 56 800 X 10 (welding): 4 000 hours £71.50 286 000 –––––––– 1 054 400 Cost of change 200 –––––––– Revised contribution 1 054 200 Original contribution 1 053 671 –––––––– Increase in contribution 529 –––––––– The changes will lead to a small increase in profitability.

(e) See ‘Uses of linear programming’ in Chapter 25 for the answer to this question. 252 THE APPLICATION OF LINEAR PROGRAMMING TO MANAGEMENT ACCOUNTING