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 th