Chapter 8

Responsibility Concepts and Sound Decision-Making Analytics

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Learning Objectives

Understand concepts in responsibility accounting.

Be able to provide a framework for rational business decision making, and understand how to apply these concepts for specific types of situations.

Apply capital budgeting methods and discounted cash flow concepts.

Know how to make proper long-term investment decisions.


Responsibility Accounting Concepts

In general, managers should be held accountable for the results of their decisions and business execution. Without accountability based on performance-related feedback, the business will not perform at its best, and areas in need of improvement may not be identified on a timely basis. Business feedback is often based on financial results. You have already seen how budgets and variances are used to help identify areas for improvement. Because managers are accountable for their decisions, actions, and outcomes, their performance measures should align around the department, product, division, or other business for which they are responsible. In other words, the attribution of responsibility tends to follow the organizational structure of the business.

Sometimes, a business has a highly dispersed design, with decisions nested with lower level managers. Other businesses generate decisions only at the upper levels, and lower level personnel are basically charged with execution of defined actions. Proper implementation of responsibility accounting concepts stipulates that performance measures be aligned with the business organization structure. In other words, accountability should map to responsibility. Proper design of performance measurement systems therefore requires that the management accountant carefully consider the organizational structure. Sometimes performance measures are only appropriate on an aggregated basis, such as where the organization is structured as a top–down, command-and-control, centralized decision-making entity. As lower level managers are given increased authority, so too should the accountability system be modified to provide more disaggregated performance measures. Although quite logical, this presents measurement challenges.

Different types of units must be evaluated using alternative models. For example, some units do not generate any revenue. They exist to provide support services to other departments within the entity. Other business segments may have clear cost and revenue functions, and they might be evaluated on their profits. Given this observation, it is common for businesses to characterize areas of specific responsibility as cost centers, profit centers, or investment centers.

A cost center usually lacks clear revenue functions. Typical departments that are regarded as cost centers include accounting, human resources, maintenance, and most administrative groupings. Cost control is the key evaluative element in assessing performance for a cost center. Standard costs and variances are useful tools for judging performance. Of course, it is also important to not reduce costs to the point of ineffectiveness; cost control should not be confused with cost minimization. Therefore, non-financial measures of output should also be considered for a cost center. Examples include transactions processed, error rates, and results of satisfaction surveys. Perhaps you have heard of a balanced scorecard?

A balanced scorecard is a measurement system designed to track all elements of performance, whether related to financial outcomes, customer satisfaction, innovation, or internal execution. A balanced scorecard provides a holistic approach because an array of performance measurements is developed. Each element evaluated is intended to align with the overall entity objectives. The emphasis is on meeting thresholds while concentrating on areas for continuous improvement. To find a balanced scorecard in operation, you need look no further than your next visit to a fast-food restaurant. The time from order entry to food deliver is constantly clocked, and the goal is usually to deliver in less than 2 minutes. Other important goals might relate to cleanliness, staff turnover, frequency of errors on order fulfillment, daily sales volume, and so forth.

Balanced scorecard metrics provide a tool for assessing fulfillment of key objectives. Accountants often gather essential data and may become skilled in developing graphical presentations that show how well goals are being met. These graphs are frequently posted throughout the workplace to remind employees of their importance.

A profit center manager is responsible for the control of both costs and revenues. However, costs and revenues are not evaluated independently. Instead, costs are considered in relation to revenues. A cost overrun can be perfectly fine if it is also met with increased revenues and profit enhancements. Flexible budget tools introduced in Chapter 6 are particularly well suited to the evaluation of a profit center.

At higher levels within an organization, managers may be evaluated based on the notion of investment centers. The manager of an investment center is accountable not only for its costs and revenues but also for the sufficiency of the return on the amount of capital invested within the business unit. One tool used to assess the success or failure is the return on investment (ROI). In its most elementary form, this model is simply a ratio of operating income to average assets deployed in the business unit:

ROI = Operating Income / Average Assets

However, it is sometimes useful to also assess operating income in relation to sales and sales in relation to average assets:

Margin on Sales = Operating Income / Sales

Turnover Rate = Sales / Average Assets

Algebraically, these ratios combine, as shown in Exhibit 8.1, to produce the ROI calculation.

Exhibit 8.1

Figure illustrating the Return on Investment equation. Operating income divided by sales yields the margin. Sales divided by average assets yields the turnover. The margin multiplied by the turnover yields the ROI.

Accumulation of Information to Match Centers

When responsibility measurements are to be divided according to cost, revenue, or investment centers, it also becomes necessary to develop the accounting information system to provide data in support of the assessment process. Useful reports must be generated for each unit of responsibility. Generalizing, these reports should be sufficient to provide for comparison of budget and actual data; align with the organizational units of the firm; support variance calculations when applicable; and, it is hoped, help identify areas/opportunities for targeted improvement. Aggregated data that are used to measure results for upper divisions may be disaggregated into reports applicable to lower levels within the business. For instance, a business may have two primary segments, wholesale and retail. The aggregate entity-wide performance report (in the leftmost data column in Table 8.1) is disaggregated into information applicable to each business unit:

Table 8.1: Aggregate performance

Combined Wholesale Retail

Sales $3,500,000 $2,000,000 $1,500,000

Variable expenses 2,250,000 1,500,000 750,000

Contribution margin $1,250,000 $ 500,000 $ 750,000

Traceable fixed costs 700,000 200,000 500,000

Controllable margin $550,000 $ 300,000 $ 250,000

Common fixed costs 250,000

Net margin $ 300,000

If applicable, the data column for retail could be further disaggregated into information for each retail store. Thus, aggregated data for the entire entity can be used to judge the performance of upper division corporate managers. The segment data can be used to judge the performance of midlevel managers. Also, if applicable, individual store managers can be judged on the performance of their business unit.

In examining the preceding performance report, you likely noticed that total fixed cost was divided between traceable and common components. Traceable fixed costs are those that would no longer exist if a particular responsibility center ceased to exist. Examples include the costs associated with real estate in use by the retail unit, management salaries, and so forth. In contrast, common fixed costs support the operations of multiple units and would continue regardless of any decisions about continuing or discontinuing a responsibility center. Because effective performance evaluation depends on a proper alignment of responsibility and accountability, it is important to separate fixed costs between traceable and common components. It would be inappropriate to evaluate a manager's performance based on an accounting model that burdened the manager with common costs for which there was no effective control.

Management by Exception

Management by exception is an often-used description of the way in which responsibility reports are used. It means that reviews and corrective actions should center around areas of underperformance, as identified by data that do not conform to expectations. Thus, attention is focused on areas where corrections appear to be needed. If the accounting information system does not support this objective, it is arguably of little value for management control. However, do not assume that every exception requires change. Sometimes performance can fall short of expectations because of circumstances that are beyond the control of a unit manager. Examples include shutdowns due to storms, economic recessions, and countless other disruptive events that are externally or coincidentally induced.

Rational Decision Making

You can probably think of some things you would like to try again. Perhaps you have taken an exam and done poorly. The underperformance might have been due to a lack of preparation. Then again, maybe you just made a mathematical error; or worse, maybe you marked an answer sheet wrong by accident. Whatever the cause, you probably think you should have done better. If you reflect further, you will see that there are really two different types of explanations for the poor performance: a lack of planning and poor execution. The first type is clearly subject to your control.

It is easy to make an analogy to business. Management must be diligent to control against errors in both planning and execution. Our focus now is on avoiding planning errors. Remember, management has an ethical and fiduciary duty to safeguard company resources, and this includes application of proper planning and decision-making principles. Despite the best of plans, there is no guarantee of success. However, there is no excuse for engaging in a business action that has no chance of success from the outset.

Sunk Costs

Perhaps the most frequent business mistake is to fail to distinguish between sunk costs and relevant costs. A sunk cost relates to the amount of a prior expenditure or cost. You may have invested in the stock of a particular company. If you suspect the stock is going to decline, you should consider selling it. It does not really matter whether you paid more or less than its current market value. Nevertheless, people frequently tend to fixate on sunk costs. Perhaps this is just human nature, but it has no place in making sound business decisions. Sunk costs are to be ignored in making business decisions. This facet of business decision making cannot be overemphasized; even when people have a rational comprehension of the concept, it is still difficult to set aside emotion. The age-old expression that there is no use crying over spilt milk applies.

What matters is to base business decisions on relevant items. Relevant items are those that entail future costs and revenues that differ between alternative decisions. The objective of business decision making is to identify decisions yielding the best incremental outcomes based on a comparison of just the relevant items. This can be trickier than it seems.

To illustrate, assume that a corporation has a machine with an original cost of $100,000, a 5-year remaining life, no salvage value, and accumulated depreciation equal to 40% of cost. It produces 10,000 units per year, and operating costs are $2 per unit. The company can sell the unit for $20,000 and lease a new machine for $22,000 per year for 5 years. No additional operating costs would be incurred, and the leased machine would also produce 10,000 units per year. Should the company sell its current machine and enter into the lease agreement? Immediately, you can see that the decision is not obvious. Production is the same under either option; only costs vary. Keeping and operating the existing equipment would result in incremental operating costs of $20,000 per year (10,000 units × $2 per unit). Leasing the machine would result in incremental operating costs of $22,000 per year but would be accompanied by a $20,000 upfront benefit from selling the old machine. This added $20,000 payment would more than offset the extra $2,000 per year of added costs under the lease. Thus, it is better to sell the old machine and enter into the lease agreement. Of course, selling the old machine will produce an immediate accounting loss of $40,000 ($20,000 sales price minus $60,000 net book value ($100,000 – $40,000)), but this is irrelevant. Remember that sunk costs are to be ignored in business decision making. This is a difficult lesson to learn. Many managers would avoid taking the accounting loss, even though it is not the best option. Remember that the cost of the old equipment would continue to be charged to depreciation expense if it is not sold.


A General Framework for Making Sound Business Decisions

There are simply too many possibilities to catalog every type of business decision you will confront. Thus, you must develop critical thinking skills in support of a general frame of reference for solving business problems. Perhaps you will receive a bulk order from a customer who is requesting a significant price reduction. Perhaps you will need to consider offshoring production to a country with less expensive labor. There are many such decisions that require thoughtful consideration. The general approach to such decisions begins by identifying all of the possibilities/outcomes, noting the relevant costs and benefits associated with each, and making a preliminary determination of the option with the best incremental impacts. However, the process does not end there. You must also weigh the seemingly best choice in the context of qualitative variables. Qualitative factors must include consideration of environmental, customer, and employee impacts. Although profit maximization is important, other facets also play a significant role in defining a business's ability to achieve long-run success. Sound judgment should not be replaced by overreliance on quantitative models; they are complementary.

Applying the General Framework to an Example: Bulk Orders

It is quite common for customers to request reduced pricing on bulk orders. A bulk order involves a large quantity of units, perhaps even produced under a unique brand name. The beginning point for evaluating such orders is whether the proposed price is at least sufficient to cover all variable costs that it will generate. In other words, will the order have a positive contribution margin. As a general rule, such orders will result in increased profits. However, there are some notable exceptions.

One exception occurs when there are capacity constraints. Acceptance of a bulk order will consume productive capacity. If that either results in an increase in fixed costs or displaces other more profitable work, then simple reliance on the order's positive contribution margin can produce erroneous decisions. Thus, contribution margin analysis should always be weighted against the ability to generate margin, with the objective of optimizing the total firmwide contribution margin. This is decidedly different than just looking at per-unit contribution margin. These impacts are generally calculable based on careful analysis. However, it is trickier to evaluate market impacts. A negative market consequence can arise in at least two specific ways. First, other customers may learn of the special pricing and expect similar treatment. If that results, overall margin deterioration might ensue. Second, the overall increase in supply might dampen market price to end consumers, necessitating price reductions to clear the market.

To illustrate, assume that Chip Country produces and sells a specialty snack food for $2 per bag. This price provides a gross profit of $0.75 per bag. The manufacturing costs consist of variable production costs of $1.00 per bag and allocated fixed manufacturing overhead of $0.25 per bag. The company's factory only operates one shift per day, and the addition of an extra shift would generate no additional fixed manufacturing overhead or selling, general, and administrative (SG&A) costs. Big City Markets has approached Chip Country about producing a private-label snack that would not compete with Chip Country's existing market. Big City's offer would require Chip Country to double its output, and it would fully consume capacity that can be generated via a second shift. However, Big City is only willing to pay $1.10 per bag. Should the offer be accepted? At first glance, it appears the offer is not good. After all, the gross profit is only $0.75 per bag when the selling price is $2. How can a $0.90 reduction in selling price prove viable? The answer to this question can be found in noting that gross profit is calculated after deducting the fixed manufacturing costs. Because the bulk order will not trigger any additional nonvariable or SG&A costs, it is only necessary to recover the variable manufacturing costs of $1 for this order to prove profitable. Thus, the bulk order appears to be a viable opportunity. It is only necessary to further consider the qualitative and market-related facets before deciding to go forward.

Applying the General Framework to an Example: Offshoring

You cannot help but notice that companies have increasingly turned to offshore operations to manufacture goods and provide other services such as tech support and telemarketing. This practice is often driven by a desire to obtain cheaper labor, but tax and regulatory issues have also played a significant role. A decision to offshore should be based on careful analysis of relevant costs and benefits, coupled with appropriate weighting of qualitative factors. In addition, a manager should attempt to judge the risks associated with the added prospect of political or logistical disruptions associated with global dispersion.

Offshoring sometimes entails the abandonment of domestic production facilities, in lieu of contracting with a foreign supplier on a purely variable cost basis. There is often very little alternative use or market value for abandoned domestic assets. The existence of these resources may cloud the decision to offshore, but it should not. As you know, sunk costs must be ignored, and great care must be taken to identify only the relevant items. This becomes difficult when a facility that is no longer in use will continue to generate costs. Some of the fixed overhead is apt to continue even if a service/product is no longer produced. This unavoidable fixed overhead will not vary between the alternatives and is therefore ignored in the decision-making process. Conversely, fixed factory overhead that can be avoided via offshoring should be regarded as a relevant item in any analysis. Beyond these special considerations, offshoring via a variable cost contract with a foreign vendor should generally be driven by a comparison of differences in the variable cost components.

To illustrate, assume that Ballard Corporation has a manufacturing plant in San Diego that currently produces a component part used in its main product line that is assembled in Los Angeles. There is no alternative use for the San Diego plant, and Ballard will retain it for many years, whether closed or not. The following facts have been identified:

Annual fixed manufacturing overhead at the San Diego plant $1,000,000

Fixed manufacturing overhead that can be avoided by closing the plant 40%

Variable costs of production $3.00 per unit

Annual parts production 2,500,000 units

Zhou Corporation has offered to produce and deliver to San Diego an identical component part for $3.20 per unit. The decision to offshore production to Zhou would involve no changes to SG&A. The rather obvious issue is whether or not to offshore. Table 8.2 identifies the relevant costs:

Table 8.2: Relevant costs

Manufacture Offshore

Variable costs for 2,500,000 units ($3.00 vs. $3.20) $7,500,000 $8,000,000

Reduction in fixed costs (40% of $1,000,000) (400,000)

Net of relevant items $7,500,000 $7,600,000

This fact set is relatively simple, but it is challenging to identify just the relevant items and draw the appropriate conclusion. The relevant items relate to the differential in variable and fixed costs. By comparing only relevant costs, it appears that Ballard should continue to manufacture the component. The cost difference is $100,000 less by continuing to manufacture ($7,500,000 vs. $7,600,000). What is most important for you to see within this example is how easily an error could have been made in this decision. The full cost of manufacturing is $8,500,000 ($7,500,000 variable cost and $1,000,000 fixed cost), which is more than the $8,000,000 direct cost of offshoring. Yet offshoring is not the right decision. There is another $600,000 of fixed costs (the other 60% of the $1,000,000 fixed overhead) that will be incurred even if offshoring is selected.

Offshoring involves a number of qualitative issues. When production is placed in the hands of an outside supplier, added cost may arise from the need to monitor the financial health and integrity of the vendor, the quality of production, delivery schedules, and similar issues. There are added costs associated with freight, customs, taxes, and even language barriers.


Capital Expenditures

Some business decisions relate to capital expenditures such as the construction of a factory or purchase of equipment. These activities can entail substantial initial cash outlays, and it may be many years before the investment can be recovered. Capital expenditure decisions often require the comparison of competing alternatives. Furthermore, options that appear best in the short run may not be best in the long run, and vice versa. You can probably relate to this issue in thinking about your own education. You are currently investing time and money in an accounting class; you could probably make more money in the near term by working in your job and skipping out on study time. However, you understand that your long-term interests are better served by investing in your education. This is not much different than the challenge faced by business managers. For instance, should an expensive robotic welder be purchased to replace a manual laborer? The near-term cash flow is better without the robot but worse in the long run. How are such decisions to be made intelligently?

This is the role of capital budgeting analysis. Mathematical tools are brought to bear on the evaluation process in a way that produces systematically logical outcomes. At the heart of many of these tools are concepts related to the time value of money. You likely have a sense that a dollar in the hand is worth more than a dollar to be received in the future. After all, a dollar in the hand can be reinvested to generate additional returns and grow to a greater sum than the dollar to be received in the future. This notion is sometimes referred to as the time value of money.

This fundamental principle is the starting point for understanding key capital budgeting tools. Although spreadsheet models and business analyst calculators are readily available to assist with all of the related calculations, they are all based on basic mathematical equations that you should attempt to understand.

Future Value

The first of these is known as future value (or compound interest). To illustrate, if you invest $1,000 for 1 year, at 5% interest per year, your initial investment will have grown to $1,050 by the end of the year ($1,000 × 1.05). If you then reinvest the $1,050 for another year at 5%, your investment will grow to $1,102.50 ($1,050 × 1.05). The second year produces a greater amount of interest (than the first year) because the accumulated interest from the first year is also in the investment pool and generating returns. An alternative view of this calculation is to note that initial investment is to be multiplied by 1.05 to the second power (i.e., 1.052). The compounding of a greater amount of interest each year would continue through time. Indeed, if you wanted to know the value to which the investment would accumulate after 10 years at 5% per year, you would multiply the initial investment by 1.05 to the 10th power. This observation gives rise to a general formulation for the future value factor that can be multiplied times an initial lump sum investment:

(1 + i)n

where i is the interest rate per period, and n is the number of periods.

Although it is a fairly simple matter to calculate the future value factors via the previous equation, they are also readily available by reference to a Future Value of $1 table (see Appendix A).

These tables provide predetermined values for a variety of such computations. Examine the table and satisfy yourself that a $10,000 investment will grow to $25,937 by the end of 10 years at 10% per period. You should note the future value factor of 2.5937 in the "10% column/10-period row." This factor is multiplied by the $10,000 initial investment.

Try It Yourself: Future Value of $1

Challenge: Find the future value of $1,000 if it is invested today at 5% annual interest for 15 years.

Calculation: The table in Appendix A indicates a factor of 2.07893 for 15 periods, 5% rate per period. This factor is multiplied by the $1,000 initial investment.

Answer: The amount will grow to $2,078.93.

One important point is worth noting at the outset. The interest rate from within the table is in reference to the interest rate per period. In the preceding example, we assumed annual compounding. However, interest might be compounded monthly or on some other basis. For example, if a 12% annual interest rate were to be compounded monthly, then the interest rate would be 1% per month. A 3-year investment would include 36 months. Thus, to determine the future value of the investment would entail reference to the "1% column/36-period row."


Rather than investing a single lump-sum amount, investors will sometimes make a regular stream of level payments into an account. For example, a saver might deposit $10,000 per year at the beginning of each year into a savings account. Streams of level payments occurring on regular intervals are called annuities. You may be wondering how you would determine the amount that would accumulate after 5 years under such a process. If you consider that such an annuity is really just a series of lump-sum amounts, each invested for a different number of years, you can discern that the future value of annuity can be determined by summing a series of individual lump-sum investments. Consider Exhibit 8.2.

Exhibit 8.2

Illustration showing the stream of investments for 5 years. Each year has an investment of $10,000. The investments for Years 1 through 5 are multiplied by the following annuity amounts, respectively: (1.10)⁵, (1.10)⁴, (1.10)³, (1.10)², and (1.10)¹. The resulting totals are added together for an accumulated total of $67,156.

The preceding illustration shows that the stream of investments would grow to $67,156. Because it is rather cumbersome to calculate the future value of each investment and then sum, tables are also available revealing individual factors for the future value of such annuities. The table in Appendix B reveals factors for the future value of annuity, with the first payment occurring at the beginning of the first period (sometimes called an annuity due or annuity in advance).

Examine that table and locate the value corresponding to 10% and 5 periods. You should locate a value of 6.71561. Multiplying the $10,000 annual payment by this factor also yields $67,156, but in a much quicker way.

Try It Yourself: Future Value of an Annuity

Challenge: Find the future value of beginning-of-month deposits of $25 each for 24 months, if they are invested at 6% annual interest.

Calculation: The table in Appendix B indicates a factor of 25.55912 for 24 periods, 0.5% rate per period (6% per year equals 0.5% per month). This factor is multiplied by the $25 periodic investment.

Answer: The deposits, with interest, will accumulate to $638.98.

Present Value

Although future value calculations are quite useful for financial planning, accounting and capital budgeting decisions often depend on an opposite concept called present value. Present value reveals the current worth of cash to be received in the future. As such, it is sometimes called discounting of future cash flows. For example, you may desire to know today's value associated with $1,000 to be received in 3 years. Mathematically, this is simply the reciprocal logic to that applied in calculating future value amounts. Thus, the following formula can be seen to apply:

1/(1 + i)n

here i is the interest rate per period, and n is the number of periods.

Thus, $1,000 to be received in 3 years, assuming a 5% interest rate, is worth approximately $863.84 today. In other words, it has a present value of $863.84. Stated differently, that amount invested today at 5% annual interest would grow to approximately $1,000 after 3 years. You might calculate the present value factor of 0.86384 via the formula (1/1.053) and then multiply that times the $1,000 future payment. However, as you probably suspect, there is a Present Value of $1 table (see Appendix C) that includes appropriate factors for a variety of scenarios.

You should take time to confirm that you can find the preceding factor in the 5% column/3-period row.

Try It Yourself: Present Value of $1

Challenge: Find the present value of $5,000, if it is to be received in 5 years, and the annual interest rate of 8% is compounded every 3 months.

Calculation: The table in Appendix C indicates a factor of 0.67297 for 20 periods, 2% rate per period (8% per year equals 2% per quarter; there are 20 quarters in 5 years). This factor is multiplied by the $5,000 amount to be received.

Answer: The present value of the $5,000 amount is $3,364.85.

Present value can also be calculated for annuities. As you will soon see, this proves quite useful in the evaluation of long-term capital investments. If the uniform payments occur at the end of each period, the annuity is termed an ordinary annuity. One way to determine the present value of an ordinary annuity would be to sum the present value of each payment, as shown in Exhibit 8.3 for a 5-period, 10% annuity stream of $10,000 cash flows: However, tables such as the one in Appendix D already provide summarized values associated with the present value of an annuity.

Exhibit 8.3

Illustration showing the stream of investments for 5 years. Each year has an investment of $10,000. The investments for Years 1 through 5 are multiplied by the following annuity amounts, respectively: (1/(1.10)¹), (1/(1.10)²), (1/(1.10)³), (1/(1.10)⁴), and (1/(1.10)⁵). The resulting totals are added together for an accumulated total of $37,908.

Notice that the previous annuity has a present value of $37,908. Examine the table, taking note that the factor corresponding to five periods and a 10% rate is 3.7908. Thus, one can simply multiply the $10,000 payment by that factor to calculate the present value of the annuity.

Try It Yourself: Present Value of an Annuity

Challenge: Assume that you have won a prize of $1,000 to be received at the end of each year for 20 years. The annual interest rate is 5%. How much is the present worth of this prize?

Calculation: The table in Appendix D indicates a factor of 12.46221 for 20 periods, 5% rate per period. This factor is multiplied by the $1,000 annual prize amount.

Answer: The present value of the prize is $12,462.21.


Making Decisions About Long-Term Investments

With the mathematical tools you have just learned, you should be able to understand important concepts in making intelligent decisions about long-term investments. The application of these principles is termed capital budgeting. To begin simply, assume you are faced with two alternative investment choices, and the going rate of interest is 7%. Investment A returns $1,000 at the end of each year for 10 years (a total of $10,000), and Investment B returns $1,200 per year for 8 years (a total of $9,600). Which is preferred? The answer to this question likely hinges on which investment has the higher present value. Investment A has a present value of $7,023.58 ($1,000 × 7.02358), and Investment B has a present value of $7,165.56 ($1,200 × 5.97130). Thus, Investment B is preferred to A. It is important to note that this is true even though Investment A returns more in total than Investment B.

Now, this simple example left out one important variable. Can you imagine what that is? It is the cost of the investment initially. If Investment B cost more than $7,165 up front, it would be a bad investment indeed. Thus, accountants need to consider not only the present value of cash inflows but also the present value of cash outflows associated with an investment.

Net Present Value

The net present value of an investment is the difference between the present value of cash inflows and the present value of cash outflows. To make this calculation requires the selection of an interest rate, and that rate should reflect the theoretical cost of capital incurred by a firm. The cost of capital approximates the cost of funds in use by an entity. If a company borrows heavily, it can relate to the cost of interest on debt. If a company relies on shareholder investment, it can be meant to indicate the expected rate of return that shareholders expect to generate. Or, the cost of capital can reflect a blending of both the cost of debt and equity. In any event, if the net present value of an investment is positive, then an assumption is made that the investment is worthy of further consideration. This means that the present value of cash inflows exceeds the present value of cash outflows, and the investment at least generates returns in excess of the firm's cost of capital. The opposite conclusion can be reached for investments with negative net present values.

To illustrate net present value, assume that Impact Plastic Corporation is considering the purchase of a new mold that will have an initial cost of $100,000. In addition, $25,000 will need to be spent at the end of Year 2 and again at the end of Year 4. These expenditures are necessary to refurbish and polish the mold. The mold will be leased to ski boot manufacturers that contract for plastic parts used in their products. The mold will produce annual lease payments to Impact amounting to $40,000 per year, occurring at the end of each year, for 5 consecutive years. Impact's cost of capital is 8%. Table 8.3 shows that the discounted cash flows produce a positive net present value of $19,899, suggesting that the mold will return well in excess of the cost of capital.

Table 8.3: Discounted cash flows

Cash outflow Cash inflow Net cash flow Present value factor @ 8% Present value of net annual cash flow

Initial cash outlay $100,000 ($100,000) 1.00000 ($100,000)

End of Year 1 $40,000 40,000 0.92593 37,037

End of Year 2 25,000 40,000 15,000 0.85734 12,860

End of Year 3 40,000 40,000 0.79383 31,753

End of Year 4 25,000 40,000 15,000 0.73503 11,025

End of Year 5 40,000 40,000 0.68058 27,223

Net present value $19,899

Try It Yourself: Net Present Value of an Investment That Should Be Accepted

Challenge: Find the net present value of an investment requiring a $200,000 initial outlay and returning $30,000 at the end of each year for 10 years. The company's cost of capital is 5%. The investment has no residual value.

Calculation: Using the present value factor from Appendix D, note that present value factor for the $30,000 annuity is 7.72173 (10 periods, 5%). Thus, the present value of the inflows is $231,651.90 ($30,000 × 7.72173). This is greater than the investment outflows of $200,000, all of which occurred immediately.

Answer: The net present value is positive $31,651.90, indicating that the investment returns more than the 5% cost of capital.

Try It Yourself: Net Present Value of an Investment That Should Be Rejected

Challenge: Find the net present value of an investment requiring a $200,000 initial outlay and returning $30,000 at the end of each year for 10 years. The company's cost of capital is 9%. The investment has no residual value.

Calculation: Using the present value factor from Appendix D, note that present value factor for the $30,000 annuity is 6.41766 (10 periods, 9%). Thus, the present value of the inflows is $192,529.80 ($30,000 × 6.41766). This is less than the investment outflows of $200,000, all of which occurred immediately.

Answer: The net present value is negative $7,470.20 ($192,529.80 – $200,000), indicating that the investment returns less than the 9% cost of capital.

Internal Rate of Return

Although net present value calculations are highly beneficial in showing whether a particular rate of return is cleared, they fail to exactly identify the full rate of return. This is where the internal rate of return (IRR) comes into play. The IRR essentially repeats the previous calculations based on the actual rate of return that causes the present value of the inflows to equal the present value of the outflows. It is the interest rate that causes a zero net present value. Consider the revised Table 8.4, this time using present value factors at 15.38%:

Table 8.4: Internal rate of return

Cash outflow Cash inflow Net cash flow Present value factor @ 15.38% Present value of net annual cash flow

Initial cash outlay $100,000 ($100,000) 1.00000 ($100,000)

End of Year 1 $40,000 40,000 0.86670 34,668

End of Year 2 25,000 40,000 15,000 0.75117 11,267

End of Year 3 40,000 40,000 0.65104 26,041

End of Year 4 25,000 40,000 15,000 0.56426 8,463

End of Year 5 40,000 40,000 0.48904 19,561

Net present value $0

The IRR for this project is more than 15%, as shown. The process of evaluating investments using the IRR approach is to calculate the IRR for each investment opportunity. Projects offering the highest internal rates of return are deemed best.

You may be wondering how the interest rate was found. It is quite cumbersome to do the calculations manually. Essentially, one is required to repeatedly try rates, constantly trying to close in on the rate that returns a zero net present value. Fortunately, computer programs simplify the process. The details of these calculations are deferred to more advanced-level accounting and finance classes.

You will also learn in advanced classes that the IRR has certain limitations. First, IRR mathematics can produce anomalous results. Where cash inflows and outflow are highly irregular over the span of the investment period, it is sometimes possible to find two different rates, both of which will cause the present values of inflows and outflows to be equal. Also, bear in mind that IRR is useful for ranking all investment options, but it does not tell you which ones should be accepted. Should the business only accept investments with a greater than 10% rate, 15% rate, or 20% rate? There is no answer to the question. Presumably, the business should pick the best investments with the available capital, but the method does not signal at what point it is worthwhile to obtain additional capital to pursue added opportunities (or hold back capital for future opportunities that have not yet emerged).

Simpler Capital Budgeting Methods

Evaluation of long-term projects is not always based on discounted cash flow concepts. Alternative evaluation methods include consideration of the accounting rate of return and the payback method. The accounting rate of return examines accounting income rather than cash flows. It is calculated by dividing an investment's expected increase in accounting income by the amount of the investment. If a project costs $1,000,000 and is expected to produce an ongoing average increase in accounting income of $50,000, then the accounting rate of return is 5%. Accounting income can diverge significantly from cash flows due to depreciation and other timing issues related to cash flows that differ from accrual-based income measurement. The payback method is another simplistic tool for evaluating capital expenditures. It results from dividing an initial investment by the expected annual cash inflow produced by the investment. If a project costs $1,000,000 and is expected to produce an ongoing average increase in cash flows of $100,000, then the payback is 10 years. The method can be misleading in that it fails to consider the time value of money and what happens to cash flows beyond the payback period.

Simple tools such as these can produce quick measures for considering and ranking investment alternatives, but they probably should not be solely relied on to produce consistently high-quality investment decisions. They are but single indicators, and management has an ethical duty to consider more careful analysis in deciding how to deploy firm resources before making long-term capital allocation decisions.

Recap of Using Capital Budgeting Tools for Decision Making

Table 8.5 recaps the four fundamental capital budgeting tools introduced in this chapter. The middle column includes information about the general decision-making rule. The last column includes caveats about potential weaknesses for each method.

Table 8.5: Four fundamental capital budgeting tools

Method Decision rule Caveat

Net present value (NPV) Select the investments with positive NPV. Outcomes are dynamic based on cost of capital assumptions.

Internal rate of return (IRR) Rank order investments and select those yielding the highest IRR. Fails to consider duration of an investment's life and what options will be available after an investment matures.

Accounting rate of return (ARR) Rank order investments and select those yielding the highest ARR. Fails to consider timing of cash flows.

Payback Rank order investments and select those with the shortest payback period. Fails to consider returns after the payback period, leaving the evaluator blind as to the actual return on the investment.

In no case should a manager resort to blind reliance on a single method. Remember that future inflows and all outflows, as well as assumptions about interest rates, all require some degree of prognostication about the future. Sound human judgment must always guide the final conclusion about the worthiness of a capital expenditure.

Chapter 8 Overview

Click the image below to open the Chapter 8 Overview.

Key Terms

Click on each key term to see the definition.

accounting rate of return


capital expenditures

common fixed cost

cost center

future value

internal rate of return (IRR)

investment center

management by exception

net present value

payback method

present value

profit center manager

relevant items

return on investment (ROI)

sunk cost

time value of money

traceable fixed cost

Concept Check

ACC 206 Concept Check Chapter 8

Test Section:


Test your knowledge of chapter 8 by answering the following questions:

1. Which of the following is rarely a consideration when analyzing a long-term project?

a. The cost of the investment

b. The lowest rate of return acceptable to management

c. The company's current ratio

d. The investment's cash inflows and cash outflows

2. The time value of money

a. is integrated in present value computations.

b. weights cash flows that occur in 5 years more heavily than cash flows that occur in 2 years.

c. is reflected by the accounting rate of return.

d. should not be considered when analyzing an investment.

3. Hughes Corporation is considering a $200,000 machine that promises savings in cash operating costs of $40,000 over each of the next 6 years. The company requires a 10% return on its investments. Appropriate present value factors follow: Present value of $1: 0.56447; Present value of a $1 annuity: 4.35526. Ignoring income taxes, the machine's net present value is

a. $(5,790).

b. $(25,790).

c. $(177,421).

d. some amount other than those listed above.

4. The internal rate of return

a. ignores the time value of money.

b. is another name for the accounting rate of return.

c. results in a net present value of zero.

d. cannot be used when the payback period is less than 3 years.


Critical Thinking Questions

Why must businesses exercise extreme care in the selection of long-term investments?

Describe the screening and ranking processes related to capital budgeting.

What three factors should be considered in the evaluation of an investment opportunity?

What is meant by an investment in working capital? Are such investments ever recovered? Briefly explain.

What is the lowest rate of return acceptable to a company?

Explain what is meant by the time value of money.

Explain the relationship, if any, between compound interest and present value.

What is meant by the term "present value"?

Four methods are frequently used to evaluate capital budgeting proposals. Are these methods normally used by themselves or in conjunction with each other? Why?

When examining a project's cash inflows and outflows, what present value relationship holds true at the internal rate of return?


Basic present value calculations

Calculate the present value of the following cash flows, rounding to the nearest dollar:

A single cash inflow of $12,000 in 5 years, discounted at a 12% rate of return.

An annual receipt of $16,000 over the next 12 years, discounted at a 14% rate of return.

A single receipt of $15,000 at the end of Year 1 followed by a single receipt of $10,000 at the end of Year 3. The company has a 10% rate of return.

An annual receipt of $8,000 for 3 years followed by a single receipt of $10,000 at the end of Year 4. The company has a 16% rate of return.

Present value analysis: Working backward

The following information pertains to four independent investments:


Present value $ ? $19,646 $34,625 $50,852

Interest rate 10% % ? 14% 12%

Investment period 4 years 5 years ? years 10 years

Annual cash inflows $8,000 $ 6,000 $ 7,000 $ ?

Determine the unknown for each of the investments. (Note: Amounts have been rounded to the nearest dollar; please consider this procedure in your calculations. Do not interpolate.)

Straightforward net present value calculations

Contempo Inc. is considering the acquisition of some new labor-saving equipment. Management estimates that the equipment will cost $42,000 and will produce the following savings in cash operating costs during the next 5 years: Year 1, $15,000; Year 2, $13,000; Year 3, $10,000; Year 4, $10,000; and Year 5, $6,000. The company uses the net present value method to analyze investments and desires a minimum rate of return of 12%.

Compute the net present value of the proposed investment. Ignore income taxes and round to the nearest dollar.

Considering the time value of money , should Contempo acquire the new equipment? Why?

Cash flow calculations and net present value

On January 2, 20X1, Bruce Greene invested $10,000 in the stock market and purchased 500 shares of Heartland Development Inc. Heartland paid cash dividends of $2.60 per share in 20X1 and 20X2; the dividend was raised to $3.10 per share in 20X3. On December 31, 20X3, Greene sold his holdings and generated proceeds of $13,000. Greene uses the net present value method and desires a 16% return on investments.

Prepare a chronological list of the investment's cash flows. Note: Greene is entitled to the 20X3 dividend.

Compute the investment's net present value, rounding calculations to the nearest dollar.

Given the results of part (b), should Greene have acquired the Heartland stock? Briefly explain.

Straightforward net present value and internal rate of return

The City of Bedford is studying a 600-acre site on Route 356 for a new landfill. The startup cost has been calculated as follows:

Purchase cost: $450 per acre

Site preparation: $175,000

The site can be used for 20 years before it reaches capacity. Bedford, which shares a facility in Bath Township with other municipalities, estimates that the new location will save $40,000 in annual operating costs.

Should the landfill be acquired if Bedford desires an 8% return on its investment?

Use the net present value method to determine your answer.

Compute the internal rate of return on this project.


Straightforward net present value and payback computations

STL Entertainment is considering the acquisition of a sightseeing boat for summer tours along the Mississippi River. The following information is available:

Cost of boat $500,000

Service life 10 summer seasons

Disposal value at the end of 10 seasons $100,000

Capacity per trip 300 passengers

Fixed operating costs per season (including straight-line depreciation) $160,000

Variable operating costs per trip $1,000

Ticket price $5 per passenger

All operating costs, except depreciation, require cash outlays. On the basis of similar operations in other areas of the country, management anticipates that each trip will be sold out and that 120,000 passengers will be carried each season. Ignore income taxes.


By using the net present value method, determine whether STL Entertainment should acquire the boat. Assume a 14% desired return on all investments; round calculations to the nearest dollar.

Basketball player decision

The Phoenix Kings of the United Basketball League have a moody center by the name of Orlando Dawkins. Dawkins is under contract with the team and is scheduled to earn $650,000 in both 20X3 and 20X4. A $75,000 salary increase will take effect in 20X5.

Dawkins has not gotten along with several of his teammates and, as a result, management is exploring the possibility of a trade with the Philadelphia Rockets to acquire George Harper, a star player. The Kings would pay the Rockets $350,000 immediately for the trade to take place. Harper would be paid a $270,000 signing bonus at the beginning of 20X3 that management plans to expense over the next 3 years by using straight-line amortization. Harper's annual salary would be $950,000 from 20X3 through 20X5, highest on the team because of his ability to attract fans. The Kings expect that increased attendance will produce added annual net cash inflows of $525,000.

Phoenix officials believe that both players would play 3 more years for the Kings, at which time they would become free agents and move along to other clubs. The Kings would receive $380,000 compensation from the other club for Dawkins; for Harper, the figure would increase to $500,000. Regardless of whether the trade takes place, the Kings are obligated to pay Dawkins $200,000 at the end of 20X4 under the terms of his original contract.

The Kings desire a rate of return of 14% and use the net present value method to analyze investments. Round all calculations to the nearest dollar, and ignore income taxes.


Determine whether the Kings should keep Dawkins or trade for Harper . Assume the trade would occur on January 1, 20X3.

Future cash flows are, in many cases, subject to change. List several events that could occur that might influence the cash flows in this situation.

Straightforward net present value and payback computations

The Calgary Eskimos play in the Canadian Hockey League. Although the Eskimos will soon be moving to a modern arena, management is studying the possibility of expanding the team's present facility to accommodate increased crowds. A $2.4 million expansion is planned that has a $200,000 residual value and will be depreciated by the straight-line method over four seasons. Information about the expansion follows:

Number of seats Occupancy rate Ticket price

Class 1 seats 2,500 80% $6

Class 2 seats 2,000 60 4

The team will play 50 home games each season. Total added operating costs per game (ushers, cleanup, and depreciation) are expected to average $11,800. All such costs, except depreciation, require cash outlays.


By using the net present value method and a 16% desired rate of return, determine whether the expansion should be undertaken.

In addition to the cash flows presented here, what other cash flows might change if the Eskimos add on to the arena?

Equipment replacement decision

Columbia Enterprises is studying the replacement of some equipment that originally cost $74,000. The equipment is expected to provide 6 more years of service if $8,700 of major repairs are performed in 2 years. Annual cash operating costs total $27,200. Columbia can sell the equipment now for $36,000; the estimated residual value in 6 years is $5,000.

New equipment is available that will reduce annual cash operating costs to $21,000. The equipment costs $103,000, has a service life of 6 years, and has an estimated residual value of $13,000. Company sales will total $430,000 per year with either the existing or the new equipment.

Columbia has a minimum desired return of 12% and depreciates all equipment by the straight-line method.


By using the net present value method, determine whether Columbia should keep its present equipment or acquire the new equipment. Round all calculations to the nearest dollar, and ignore income taxes.

Columbia's management believes that the time value of money should be considered in all long-term decisions. Briefly discuss the rationale that underlies management's belief.