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10 Capital Investment Decisions

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Learning Objectives

After studying Chapter 10, you will be able to:

• Explain the nature and importance of capital investment decisions.

• Identify the relevant cash inflows and outflows in an investment proposal.

• Use four different evaluation methods to evaluate investments.

• Appreciate ethical issues relating to capital investment decisions.

• Comprehend how income taxes and depreciation impact the cash flows of capital investments.

• Understand how the cost of capital is determined.

• Evaluate investment decisions that include inflation, working capital, uneven project lives, differing initial investments, and asset disposal gains and losses.

• Understand the basic principles of time value of money.

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Chapter Outline

10.1 The Importance of Capital Investment Decisions

10.2 The Capital Investment Decision Cash Flows Decision Criteria Time Perspectives An Example—Equipment Replacement and Capacity Expansion Formatting the Relevant Data

10.3 The Evaluation Methods Net Present Value Method Internal Rate of Return (IRR) Method Payback Period Method Accounting Rate of Return Method

10.4 Ethical Issues and Pressures on Management

10.5 Taxes and Depreciation Income Taxes and Capital Investments Depreciation Expense The Tax Shield

10.6 Cost of Capital

10.7 Calculation Issues Inflation and Future Cash Flows Working Capital Uneven Project Lives Evaluation of Projects With Different Initial Investments Gains and Losses on Asset Disposals

10.8 The Time Value of Money Present Value of Money Present Value of a Series of Future Cash Flows Present Value Analysis Applied

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Capital Investment Alternatives

Rose Stanley, President of Eddington Instruments, grabs her briefcase and heads for the airport. After clearing security, running to her gate, and just making her flight, Rose settles into her coach seat, in front of two screaming kids and behind two salespeople who apparently have just made the deal of the century. She opens her briefcase and finds the Capital Spending Proposals file. The deadline for submitting proposals to her was yesterday. She plans to review these on her cross-country flight. The variety surprises her.

• Engineering is pushing to integrate a newly announced semiconductor into an aging product. The new technology will push Eddington into new markets with great sales potential but against stiff competition.

• Adding space to the corporate headquarters will bring three administrative departments together, increase efficiency, and reduce operating expenses.

• Her Production Planning Manager proposes rearranging several work centers to improve production efficiency for a family of current products.

• Another project adds capacity to a specialized assembly operation. • The Plant Manager requests funding for an air purification system, which must be

installed by year-end to meet new state air quality requirements. • An information systems proposal would automate several manual operations, save

personnel, and reduce inventory by an estimated 10%. • Her Finance Manager is negotiating for controlling interest in a firm with technical

expertise that Eddington needs for new product development. • Marketing has proposed a major jump in advertising spending for a product line that

has not been meeting sales targets.

Rose clearly wants to get the “biggest bang for the bucks” from Eddington’s limited capital investment budget. A quick calculation shows her that this year’s investment dollars will fund about half of these proposals. Some proposals are risky, while others have predictable outcomes. Some are straightforward, but many include a host of extraneous issues. Also, financial data are overstated for some proposals and understated for others. Some generate immediate returns; others promise big cash flows years from now.

This chapter extends the study of incremental analysis begun in Chapter 9 into multiperiod decisions, which are called capital investment decisions. This chapter discusses:

1. Identification of relevant cash flows in capital investments 2. Techniques and methods for analyzing project data

Capital investment analysis is a planning task and is directly linked to budgeting, as discussed in Chapter 7. Capital budgeting is the process of evaluating specific projects, estimating ben- efits and costs of the projects, and selecting which projects to fund.

Capital budgeting depends on an understanding of the time value of money. For those who are unfamiliar with the time value of money or have not applied present values in financial accounting or other courses, section 10.8 explains the concept. Present value tables neces- sary for discounting future cash flows are located in section 10.8.

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Section 10.2 The Capital Investment Decision

Relevant revenues and operating costs for multiperiod decisions are assumed to be cash inflows and cash outflows, respectively. Since these decisions extend over a period of years, timing of these cash flows is a major factor.

10.1 The Importance of Capital Investment Decisions Capital investment is the acquisition of assets with an expected life greater than a year. These decisions attract managers’ interest for good reasons:

1. Long-term commitments. Capital decisions often lock the firm into assets for many years.

2. Large amounts of dollars. Capital projects often involve large dollar amounts. From Ford Motor Company with an annual investment budget of $7 billion to a small firm buying a $50,000 truck, large relative dollar amounts get attention.

3. Key areas of the firm. New products, new production technology, and research efforts are crucial to a firm’s ongoing competitiveness.

4. Source of future earnings. Investing with foresight is the key to the firm’s future profits and financial performance.

5. Scarce capital dollars. In most firms, more demands exist for capital funds than the firm can meet. Only the best opportunities should be funded.

Excellent analyses and decisions increase the firm’s capacity, technology, efficiency, and cash generating power. Poor decisions waste resources, lose opportunities, and impact profits for many years.

10.2 The Capital Investment Decision A capital investment generally includes a cash outflow, which is the investment, and cash inflows, which are the returns on the investment. The decision maker expects cash inflows to exceed cash outflows. The typical investment project has cash outflows at the beginning and cash inflows over the life of the project.

Cash Flows Cash flows are the key data inputs in capital investment analyses. Cash has an opportunity cost, since it could be used to buy a productive or financial asset with earning power. Cash is a basic asset. Prices, costs, and values can all be expressed in cash amounts. If the decision impacts several time periods, cash-flow timing becomes a relevant factor.

Cash outflows commonly include:

1. The cash cost of the initial investment plus any startup costs 2. Incremental cash operating costs incurred over the project’s life

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Section 10.2 The Capital Investment Decision

3. Incremental working capital such as inventories and accounts receivable 4. Additional outlays needed to overhaul, expand, or update the asset during the proj-

ect’s life 5. Additional taxes owed on incremental taxable income

Cash inflows include:

1. Incremental cash revenues received over the project’s life 2. Reduced operating expenses received over the project’s life (A reduction of a cash

outflow is treated as a cash inflow.) 3. Cash received from selling old assets being replaced in the new project, net of any

tax impacts 4. Released working capital, perhaps at the project’s end 5. Salvage value (net of taxes) realized from asset disposition at the project’s end

These relevant cash flows occur after the “go” decision is made to proceed with the project. Therefore, we are estimating future cash flows. Certain cash flows are estimated based on current prices and known technology, whereas others are estimates based on vague facts and unproven methods. Often, cost savings and project benefits are not easily quantified. Much time and expense are spent to develop supporting forecast data. It is important to understand that the same cash-flow estimates are used regardless of the project evaluation method used.

Decision Criteria Capital investment decisions are either:

Accept or reject or Select A or B or C, etc. (or some combination of these)

In the first type, we decide whether the return is acceptable or unacceptable. This is a screen- ing decision. Is the return “good enough?” The second type is a preference or ranking deci- sion—select the best choice from a set of mutually exclusive projects. By picking A, we reject B, C, and any other choices. One possible choice is to do nothing—the status quo.

Generally, projects are ranked on a scale of high to low returns. The highest-ranking proj- ects are selected, until the capital investment budget is spent. Often, funds are limited; many acceptable projects will go unfunded. The firm’s goal is to select projects with the highest returns. As in Chapter 9, pertinent nonquantitative factors may sway a decision and cause lower-ranked projects to be selected.

Time Perspectives In the real world, every conceivable combination of cash-flow timing can exist. However, we assume a simplified timeline. The present point in time is today, Year 0. This is when we assume investments are made—new assets acquired, old assets sold, and any tax conse- quences of these changes assessed. In real life, several years of cash outflows may precede the start of a project’s operation.

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Section 10.2 The Capital Investment Decision

Generally, annual time periods are used. Using shorter time periods is possible, such as one- month periods for monthly lease payments. Annual flows of cash are assumed to occur at year-end due to the mathematics underlying the construction of the present value tables.

An Example—Equipment Replacement and Capacity Expansion As an illustration, Clairmont Timepieces is considering a device costing $100,000 to replace an obsolete production device:

1. The new device’s expected life is five years and can probably be sold at the end of Year 5 for $10,000.

2. The vendor recommends an overhaul in Year 3 at a cost of $20,000. 3. Capacity will immediately increase by 1,000 units per year. Each unit sells for $55

and has $30 of variable costs. 4. Additional inventory of $3,000 is needed and will be released at the project’s end

(i.e., inventory will be returned to the level it was at immediately prior to the pur- chase of the new production device).

5. Operating costs will be reduced by $15,000 per year. 6. The old device can be sold for $8,000 now, which is its book value. Alternatively, as

another option, it could be used for five more years with no salvage or book value at that time.

Remember that any cash revenue or cost that does not change is irrelevant and can be ignored. Any cash flow that differs among decision choices is relevant. Additional taxes or tax savings on incremental income or expenses are also relevant cash flows. But, until income tax issues are discussed, taxation implications are ignored.

Formatting the Relevant Data As in Chapter 9, adopting a uniform format for analysis of capital investments helps to orga- nize data and to present it in a logical pattern. Using data from the previous example, the time- frame format shown in Figure 10.1 is used throughout our capital investment discussions.

Cash outflows are displayed as negative amounts, and inflows are displayed as positive amounts. Project years begin now (Year 0 or today), and are shown as columns. Specific cash-flow items are shown as rows. The investments of $100,000 in equipment and $3,000 in inventory costs are reduced by the sale of old equipment for $8,000. The net initial invest- ment is $95,000 and appears as a negative amount as it is a cash outflow. The additional 1,000 units of sales generate incremental contribution margin of $25,000, using a $55 sales price less a $30 variable cost per unit.

Remember that volumes of analytical support may be developed to back up each number in Figure 10.1. The $100,000 device cost would result from evaluations of many devices and negotiations with vendors. Estimates of additional revenues and variable costs come from marketing studies and capacity use. Estimates of cost savings come from production, indus- trial engineering, and cost accounting analyses.

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Section 10.3 The Evaluation Methods

10.3 The Evaluation Methods The evaluation methods discussed here are:

1. Present value methods (also called discounted cash-flow methods) a) Net present value method (NPV) b) Internal rate of return method (IRR)

2. Payback period method 3. Accounting rate of return method

Nearly all managerial accountants agree that methods using present value (Methods 1a and 1b) give the best assessment of long-term investments. Methods that do not involve the time value of money (Methods 2 and 3) have serious flaws; however, since they are commonly used for investment evaluation, their strengths and weaknesses are discussed.

Net Present Value Method The net present value (NPV) method includes the time value of money by using an interest rate that represents the desired rate of return or, at least, sets a minimum acceptable rate of return. The decision rule is:

If the present value of incremental net cash inflows is greater than the incre- mental investment net cash outflow, approve the project.

Using the time value of money Tables 1 and 2 found at the end of this chapter, the net cash flows for each year are brought back (i.e., discounted) to Year 0 and summed for all years. An interest rate must be specified. This rate is often viewed as the cost of funds needed to finance the project and is the minimum acceptable rate of return. To discount the cash flows, we use the interest rate and the years that the cash flows occur to obtain the appropriate present value factors from the present value tables. A portion of Table 1 appears below showing the present value factors (the shaded numbers), corresponding to an interest rate of 12%, for each year during the Clairmont Timepieces project’s life.

Figure 10.1: Format for relevant capital investment data—Clairmont Timepieces

Cash Flows:

Life of the Project

New device Salvage value Sale of old device Added inventory Added contribution margin Operating cost savings Updating costs Net cash investment Net cash inflows

Today Year 1 Year 2 Year 3 Year 4 Year 5

$ (100,000) 8,000

(3,000)

$ (95,000)

$ 25,000 15,000

$ 40,000

$ 25,000 15,000

$ 40,000

$ 25,000 15,000

(20,000)

$ 20,000

$ 25,000 15,000

$ 40,000

$ 25,000 15,000

$ 53,000

$ 10,000

3,000

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Section 10.3 The Evaluation Methods

These present value factors are used in Figure 10.2 to discount the yearly cash flows to their present values. In Figure 10.2, the net cash investment ($95,000) is subtracted from the sum of cash-inflow present values ($137,331). When the difference is positive, the project’s rate of return (ROR) is greater than the minimum acceptable ROR. If:

Present value of incremental net cash inflows ≥ Incremental investment cash outflows

then:

Project’s ROR ≥ Minimum acceptable ROR

Net present value is the difference between the present value of the incremental net cash inflows and the incremental investment cash outflows. If net present value is zero or positive, the project is acceptable because the project is earning the acceptable rate of return. When the sum is negative, the project’s ROR is less than the discount rate. If:

Present value of incremental net cash inflows < Incremental investment cash outflows

then:

Project’s ROR < Minimum acceptable ROR

If net present value is negative, the project should be rejected because its rate of return is below the minimum acceptable level.

The Interest Rate. What interest rate should be used for discounting the cash flows? This rate has many names that help explain its source and use. Among them are:

Periods (n) 1% 2% 4% 5% 6% 8% 10% 12% 14% 15% 16%

0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

1 0.990 0.980 0.962 0.952 0.943 0.926 0.909 0.893 0.877 0.870 0.862

2 0.980 0.961 0.925 0.907 0.890 0.857 0.826 0.797 0.769 0.756 0.743

3 0.971 0.942 0.889 0.864 0.840 0.794 0.751 0.712 0.675 0.658 0.641

4 0.961 0.924 0.855 0.823 0.792 0.735 0.683 0.636 0.592 0.572 0.552

5 0.951 0.906 0.822 0.784 0.747 0.681 0.621 0.567 0.519 0.497 0.476

6 0.942 0.888 0.790 0.746 0.705 0.630 0.564 0.507 0.456 0.432 0.410

7 0.933 0.871 0.760 0.711 0.665 0.583 0.513 0.452 0.400 0.376 0.354

8 0.923 0.853 0.731 0.677 0.627 0.540 0.467 0.404 0.351 0.327 0.305

9 0.914 0.837 0.703 0.645 0.592 0.500 0.424 0.361 0.308 0.284 0.263

10 0.905 0.820 0.676 0.614 0.558 0.463 0.386 0.322 0.270 0.247 0.227

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Section 10.3 The Evaluation Methods

1. Cost of capital—a weighted-average cost of long-term debt and equity funding. Only projects that can earn at least what the firm pays for funds should be accepted. Later, we illustrate a calculation of cost of capital.

2. Minimum acceptable rate of return—a particular rate that is considered to be the lowest ROR that management will accept.

3. Desired rate of return, target rate of return, or required rate of return—a rate that reflects management ROR expectations.

4. Hurdle rate—a threshold that a project’s ROR must “jump over” or exceed. 5. Cutoff rate—the rate at which projects with a higher ROR are accepted and those

with a lower ROR are rejected; often the rate where all available capital investment funds are committed.

A firm will use one or more of these terms as its discount rate. While these terms sometimes produce different rates in the business world, we will use these terms interchangeably here. Generally, if a project’s ROR is below the chosen discount rate, it is rejected; above this rate, the project is acceptable. Still, whether it is funded depends on the availability of capital funds.

In the Clairmont Timepieces example, we assume that management has decided that 12% is the minimum acceptable rate of return. Calculations needed to obtain a net present value are shown in Figure 10.2. The net present value is a positive $42,331; therefore, the project earns more than a 12% ROR. The net present value method does not provide information about the project’s exact ROR; it merely informs whether the project is earning more than, less than, or equal to the minimum acceptable ROR.

Figure 10.2: Net present value of capital investment cash flows

Life of the Project

Net annual cash flow (Figure 10.1) Cash Flows: Present value factors at 12% Present values at 12% Sum of PVs for Years 1 to 5 Net present value

Today Year 1 Year 2 Year 3 Year 4 Year 5

$ (95,000) × 1.000

$ (95,000) 137,331 $42,331

$ 40,000 × .893

$ 35,720

$ 40,000 × .797

$ 31,880

$ 20,000 × .712

$ 14,240

$ 40,000 × .636

$ 25,440

$ 53,000 × .567

$ 30,051

Cash Flows:

Percentage Present Value of Net

Cash Inflows* − Investment = Net Present Value

16% $124,328 $95,000 $29,328

20 113,246 95,000 18,246

24 103,713 95,000 8,713

28 95,523 95,000 523

30 91,797 95,000 (3,203)

If other discount rates had been selected, we would find the following net present values:

* If Excel is used, the present values will be slightly different due to the rounding of the present value factors used here.

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Section 10.3 The Evaluation Methods

Notice that, as the interest rate increases, the present values of the future cash flows decrease. At 30% per year, the project’s net present value is negative, and the project is unacceptable. The project’s rate of return must be between 28 and 30%.

Project Ranking. Even though a project has a positive net present value, too many attractive projects may exist, given the investment dollars available. A ranking system is needed. We can rank projects by the amount of net present value each generates, but this ignores the relative size of the initial investments. An extension of the net present value method is the profit- ability index. It is found by dividing the present value of a project’s net cash inflows by its net initial investment. The resulting ratio is cash in to cash out. The higher the ratio is, the more attractive the investment becomes. Notice that an acceptable project should have a profitabil- ity index of at least 1. The following projects are ranked by the profitability index.

Project

Present Value of Net Cash Inflows

Initial Investment

Net Present Value

Profitability Index Ranking

A $235,000 $200,000 $35,000 1.18 5

B 170,000 140,000 30,000 1.21 4

C 80,000 60,000 20,000 1.33 1

D 98,000 80,000 18,000 1.23 3

E 52,000 40,000 12,000 1.30 2

We would typically accept projects with the highest profitability index until we exhaust the capital budget or the list of acceptable projects.

Internal Rate of Return (IRR) Method The internal rate of return (IRR) is the project’s ROR and is the rate where the:

Net initial investment cash outflow = Present value of the incremental net cash inflows

Without calculator or computer assistance, the specific ROR is found by trial and error. We search for the rate that yields a zero net present value.

In the Clairmont Timepieces example, the internal rate of return was found to be between 28% and 30%. The net present value at 28% is positive and at 30% is negative. By interpola- tion, we can approximate a “more accurate” rate as follows:

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Section 10.3 The Evaluation Methods

In most cases, however, knowing that the rate is between 28% and 30% is adequate.

Estimating the Internal Rate of Return. By using Table 2 and knowing certain project vari- ables, we can estimate other unknown variables, including a project’s internal rate of return. This estimate requires that the annual net cash inflows be an annuity (i.e., annual net cash flows that are uniform). The variables and a sample set of data are:

Rate of Return Net Present Value Calculations

28% $523 Base rate = 28.00%

30 (3,203) ($523 ÷ $3,726) × 2% = 0.28%

2% difference $3,726 absolute difference Internal rate of return 28.28%

Variable Example Data

A = Initial investment cash outflow $37,910

B = Life of project 5 years

C = Annual net cash inflow $10,000 per year

D = Internal rate of return 10%

E = Present value factor at 10% (Table 2) 3.791

If we know any three of A, B, C, or D, we can find E and the missing variable. A variety of ques- tions can be answered:

1. What is the internal rate of return of the project? If A, B, and C are known, we can calculate E and find D as follows:

E = A ÷ C

$37,910 ÷ $10,000 = 3.791

On Table 2, we go to the 5-period (year) row and move across until we find 3.791 (E) in the 10% column (D). At 10%, the cash outflow ($37,910) equals the present value of the net cash inflows (3.791 × $10,000). The internal rate of return is 10%.

2. What annual cash inflow will yield a 10% IRR from the project? If A, B, and D are known, we can find E and calculate C. E is found in Table 2 by using five years and 10% ROR. The annual cash inflow is found as follows:

C = A ÷ E

$37,910 ÷ 3.791 = $10,000 per year

We need $10,000 per year in cash inflow to earn a 10% IRR.

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Section 10.3 The Evaluation Methods

3. What can we afford to invest if the project earns $10,000 each year for five years and we want a 10% IRR? If we know B, C, and D, we can find E and then calculate A. The investment is found by using the annual net cash inflow and 3.791 as follows:

A = C × E

$10,000 × 3.791 = $37,910

We can pay no more than $37,910 and still earn at least a 10% return.

4. How long must the project last to earn at least a 10% IRR? If we know A, C, and D, we calculate E and find B as follows:

E = A ÷ C

$37,910 ÷ $10,000 = 3.791

For a 10% IRR, 3.791 is on the 5-period row. The project’s life must be at least five years.

Most spreadsheet software and business calculators have built-in functions to find the inter- nal rate of return. This simplifies the calculation burden that has limited its use in the past.

Project Ranking. Since each project has a specific rate of return, ranking projects under the IRR method is relatively simple. All projects are listed according to their rates of return from high to low. The cost of capital or a cutoff rate can establish a minimum acceptable rate of return. Then, projects are selected by moving down the list until the budget is exhausted or the cutoff rate is reached.

Reinvestment Assumption. The internal rate of return method assumes that cash flows are reinvested at the project’s internal rate of return. While this assumption may be realistic for cost of capital rates, it may be wishful thinking for projects with high internal rates of return. This issue, however, is best left to finance texts and courses.

High Discount Rates. A concern exists about the use of high discount rates in present value methods. A project with significant long-term payoffs may not appear favorable because the long-term payoffs will be discounted so severely. Even huge cash inflows due 10 years or more into the future appear to be less valuable than minor cost savings earned in the first year of another project. High discount rates may encourage managers to think only short term; to ignore research, market innovations, and creative product development projects; and to ignore long-term environmental effects. Thus, positive or negative impacts can result from the wise or unwise use of accounting tools and policies.

Payback Period Method The payback period method is a “quick and dirty” evaluation of capital investment projects. It is likely that no major firm makes investment decisions based solely on the payback period,

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Section 10.3 The Evaluation Methods

but many ask for the payback period as part of their analyses. The payback period method asks:

How fast do we get our initial cash investment back?

No ROR is given, only a time period. If annual cash flows are equal, the payback period is found as follows:

Net initial investment ÷ Annual net cash inflow = Payback period

If the investment is $120,000 and annual net cash inflow is $48,000, the payback period is 2.5 years. We do not know how long the project will last nor what cash flows exist after the 2.5 years. It might last 20 years or 20 days beyond the payback point.

If annual cash flows are uneven, the payback period is found by recovering the investment cost year by year. In the Clairmont Timepieces example:

Year Cash Flows Unrecovered Investment

0 $(95,000) $95,000

1 40,000 55,000

2 40,000 15,000

3 20,000 0

In Year 3, the cost is totally recovered, using only $15,000 of Year 3’s $20,000 (75%). The payback period is 2.75 years.

The payback method is viewed as a “bail-out” risk measure. How long do we need to stick with the project just to get our initial investment money back? It is used frequently in short-term projects where the impact of present values is not great. Such projects as efficiency improve- ments, cost reductions, and personnel savings are examples. Several major companies set an arbitrary payback period, such as six months, for certain types of cost-saving projects.

Using the Payback Reciprocal to Estimate the IRR. The payback period can be used to esti- mate a project’s IRR, assuming a fairly high ROR (over 20%) and project life that is more than twice the payback period. For example, if a $40,000 investment earns $10,000 per year for an expected 12 years, the payback period is four years. The reciprocal of the payback period is 1 divided by 4 and gives an IRR estimate of 25%. From Table 2 for 12 years, the present value factor (payback period) of 4 indicates a rate of return of between 22 and 24%. The payback reciprocal will always overstate the IRR somewhat. If the project’s life is very long, say 50 years, the payback reciprocal is an almost perfect estimator. (See the present value factor of 4.000 for 25% and 50 periods on Table 2.)

Ranking Projects. When the payback period is used to rank projects, the shortest payback period is best. Thus, all projects are listed from low to high. A firm’s policy may say that no project with a payback period of over four years will be considered. This acts like a cutoff

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point. After that, projects would be selected until capital funds are exhausted. The major com- plaints about the payback period method are that it ignores:

1. The time value of money 2. The cash flows beyond the payback point 3. The timing of cash flows within the payback period

These are serious deficiencies, but the method is easily applied and can be a rough gauge of potential success.

Accounting Rate of Return Method This method:

1. Ignores the time value of money 2. Presumes uniform flows of income over the project’s life 3. Includes depreciation expense and other accounting accruals in the calculation of

project income, losing the purity of cash flows

In fact, we only discuss this approach because many internal corporate performance report- ing systems use accrual accounting data. Many companies use discounted cash flows for investment decisions but report actual results using accrual income and expense measures.

The accounting rate of return (ARR) method attempts to measure the return from accrual net income from the project. When using the ARR method, depreciation expense on the incremental investment is subtracted from the annual operating net cash inflow. Accrual net income is arrived at by deducting all expenses, but only cash expenses have been deducted in obtaining annual net cash inflow. Therefore, noncash expenses such as depreciation expense must be deducted from annual net cash inflow to obtain accrual net income. Other accrual adjustments may also be made. The general formula is:

Annual net operating cash inflow – Annual depreciation expense on incremental investment

Average investment = Accounting rate of return

The average investment, the denominator, is the average of the net initial investment and the ending investment base ($0 if no salvage value exists). This is the average book value (i.e., net initial investment less its accumulated depreciation) of the investment over its life. Some ana- lysts prefer to use the original cost of the investment or replacement cost as the denominator. The numerator is the annual incremental accrual net income from the project. To illustrate, assume the following:

Initial investment $110,000

Salvage value $10,000

Annual cash inflow $35,000

Project life 5 years

Depreciation expense $20,000

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ARR calculations are:

$35,000 – $20,000 ($110,000 + $10,000) ÷ 2

= $15,000 $60,000

= 25%

The 25% must be viewed relative to other projects’ ARR and cannot be compared to present value rates of return. For ranking purposes, projects are ranked from high to low. An arbitrary percentage may be set as a minimum rate.

Another problem with the ARR is the impression it gives of an increasing ROR on an annual basis as an asset grows older. A manager would see this project’s performance on the annual investment center responsibility report as follows:

Average Investment

(Book Value) Project Net

Income Annual ARR

Year 1 $100,000 $15,000 15.0%

Year 2 80,000 15,000 18.8

Year 3 60,000 15,000 25.0

Year 4 40,000 15,000 37.5

Year 5 20,000 15,000 75.0

The average annual book value declines each year, and net income is assumed to remain con- stant. As the asset gets older, the ARR increases. It is tempting for managers to reject any pro- posal that will make their performance reports look less favorable. This is particularly true when their bonuses are tied to accrual accounting performance numbers. Managers will be biased toward sticking with older assets with higher accounting rates of return. They forgo new investments that offer new technology, lower operating costs, and greater productivity.

Contemporary Practice 10.1: Capital Budgeting Practices in British Food Companies

A survey of 122 management accountants at British companies that manufacture food products and beverages revealed that “41 per cent of respondents used traditional accounting measures such as accountin g rate of return and payback period to evaluate major capital projects, while the equivalent figure for discounted cash flow models such as internal rate of return and net present value is only 19 per cent.”

Source: Abdel-Kader, M. & Luther, R. (2006). Management accounting practices in the British food and drinks industry. British Food Journal, 336–357.

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Section 10.5 Taxes and Depreciation

10.4 Ethical Issues and Pressures on Management In many corporate situations, managers are under pressure to earn high rates of return in the short run. All capital investment analyses depend on the credibility of future cash-flow estimates. Unlike past facts, which are measured very objectively, future values are based on predictions, opinions, judgments, and perhaps wishful thinking. The quality of decision mak- ing rests on a premise that future estimates are made objectively and in good faith. A man- ager trying to get a needed project approved may develop estimates that are too optimistic because of the manager’s enthusiastic support of the idea.

Company policies compound the problem by setting very high hurdle or cutoff rates that encourage proposal developers to overestimate future revenues and underestimate invest- ment costs. Managers have been heard to say, “Show me the hurdle, and I’ll make the project jump over it.” In fact, a vicious cycle may develop: higher hurdles, more bias in estimates; higher hurdles, and so on.

To control these problems, many firms have special analysts who evaluate proposals indepen- dent of the sponsoring managers. Others perform post-audits to compare actual results to the estimates. Tying responsibility for the project’s promises to the manager’s future evaluations may help solve some of these problems.

The second issue is the severe pressure on managers to show growth in immediate earnings. Key investment analysts and shareholders watch quarterly earnings announcements and other short-term information about the company to make almost daily buy and sell decisions. Capital investment proposals include a mix of short-term and long-term projects. Short-term projects often emphasize cost savings, which may be worthwhile but not strategically impor- tant. Long-term projects include research and development and new technology. Unfortu- nately, these projects often have long payback periods, but they offer significant future poten- tial. If hurdle rates are high, long-term projects will rarely rank as high as short-term projects. The long-run competitiveness and success of a firm may be damaged severely if its managers are biased toward short-term rewards.

Japanese firms, for a number of reasons, are said to have a much longer-term investment hori- zon. They are less concerned about the immediate profitability of new products and markets. Market penetration and market share are more important. This allows managers to develop a strategic plan that emphasizes the long-run success of the firm.

10.5 Taxes and Depreciation The illustrations have thus far ignored income taxes. Also, depreciation expense, being non- cash, was considered only in the accounting rate of return method. These factors impact capi- tal budgeting significantly.

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Section 10.5 Taxes and Depreciation

Income Taxes and Capital Investments Except for nonprofit organizations, the real world is a tax-paying world, and capital invest- ment analysis must consider taxes. Taxation rules are complex and impact many cash flows. Taxable income and gains include:

1. Incremental revenues minus incremental expenses 2. Incremental operating expense savings 3. Gains on sales of old assets now and of new assets at the project’s end

Incremental expenses and losses reduce taxes and include:

1. Incremental operating expenses 2. Losses on sales of old assets now and of new assets at the end of a project’s life

The tax rate should be the expected marginal tax rate for the future year being analyzed. The marginal tax rate is the tax rate applied to any incremental taxable income. For simplicity, we assume that the marginal income tax rate is 40% for all income tax-related issues. Clearly, income taxes reduce the ROR on capital projects by reducing net cash inflows.

Depreciation Expense The only role that depreciation expense plays in cash-flow-based capital investment analysis is as a deduction in calculating income taxes. If taxes are ignored or are not applicable, as in nonprofit organizations, depreciation expense is also ignored. To simplify our deprecia- tion expense and taxation discussions, we assume that: (1) straight-line depreciation is used, (2) depreciation expense calculations ignore salvage values, and (3) salvage values are net of tax consequences.

To understand the tax and depreciation expense impacts, let us look again at the Clairmont Timepieces example in Figure 10.2 and now apply a tax rate of 40% to the incremental oper- ating cash flows. For now, we ignore the effects of depreciation. This is shown in Figure 10.3.

Figure 10.3: Net present value analysis with taxes but without depreciation

Cash Flows:

Life of the Project

Net investment cash flows Annual cash inflows (taxable) Taxes on taxable income (40%) Aftertax cash inflows Net annual cash flows Present value factors at 12% Present values at 12% Sum of PVs for Years 1 to 5 Net present value

Today Year 1 Year 2 Year 3 Year 4 Year 5

$ (95,000)

$ (95,000) × 1.000

$ (95,000) 85,347

$ (9,653)

$ 40,000 (16,000) $ 24,000 $ 24,000

× .893 $ 21,432

$ 40,000 (16,000) $ 24,000 $ 24,000

× .797 $ 19,128

$ 20,000 (8,000)

$ 12,000 $ 12,000

× .712 $ 8,544

$ 40,000 (16,000) $ 24,000 $ 24,000

× .636 $ 15,264

$ 13,000 $ 40,000 (16,000) $ 24,000

37,000 × .567

$ 20,979

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Section 10.5 Taxes and Depreciation

As Figure 10.3 shows, suddenly a very profitable project (just under 30% on a no-tax basis) now has a negative net present value using a 12% discount rate. We assume that the overhaul in Year 3 is a deductible expense, salvage value is net of taxes, and inventory recovery has no tax effects.

The Tax Shield Depreciation expense is a noncash expense, provides a legitimate deduction for tax purposes, and creates a tax shield. By reducing taxable income, cash paid for taxes is reduced. Depre- ciation saves cash by reducing tax payments. Thus, if depreciation expense increases, tax payments decrease. Cash outflow is reduced. A reduced outflow has the same effect as an increased inflow.

The depreciation impact is seen in the Clairmont Timepieces example. The increase in depre- ciable assets is $92,000 ($100,000 minus $8,000) and is spread over five years. Currently, salvage value is ignored in most IRS depreciation calculations. Assuming straight-line depre- ciation, the incremental depreciation expense is $18,400 per year. Aftertax cash flows, from Figure 10.1, are:

Year 1

Added contribution margin $25,000*

+ Operating cost savings 15,000*

Incremental cash inflow $40,000

− Depreciation expense −18,400

Taxable income $21,600

− Incremental taxes (40%) −8,640*

Aftertax project net income $12,960

+ Add back depreciation expense 18,400

Aftertax cash inflow $31,360

The project’s Year 1 aftertax profit, $12,960, and the incremental depreciation expense, $18,400, are summed to find the Year 1 aftertax cash inflow. Tax cash outflows for the entire project are included in the Figure 10.4 analysis. The increased tax deduction for depreciation moves the net present value of the project from a negative $9,653 to a positive $16,879, a $26,532 change. This is the present value of the depreciation expense tax savings, as follows (the one dollar difference is due to rounding of present value factors):

* Cash flows

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Section 10.6 Cost of Capital

Accelerated Depreciation Benefits. The cash-saving power of depreciation can be increased by using accelerated depreciation to deduct, for income tax purposes, more depreciation earlier in a project’s life. Deferring taxes has a time value of money effect. By merely changing depreciation methods, the net present value can increase or decrease. This is strictly from speeding up or slowing the depreciation expense deductions and the time value of the tax deferrals. That is, having more depreciation expense earlier reduces taxable income, which in turn, reduces the cash outflow for taxes. This earlier reduction of cash outflow, which is tantamount to an increased cash inflow, increases the present value of cash flows.

10.6 Cost of Capital Throughout our discussions, cost of capital is mentioned frequently. Long-term money has a cost, either real as in interest paid on bonds payable or an opportunity cost as in the use of earnings retained in the business. A basic approach is explained here to show the source of this rate.

A weighted-average cost of capital pools a firm’s long-term funds and is used because the relative amount of each fund’s source affects the average cost. Debt generally is less costly than equity since the creditor assumes less risk and interest is deductible for tax purposes. If a firm has a pretax debt cost of 10% and a 40% tax rate, the after-tax cost is 6%. Dividends, on the other hand, are not deductible for tax purposes and are profit distributions to owners, not a business expense.

Figure 10.4: Net present value analysis with depreciation and taxes

Cash Flows:

Life of the Project

Today Year 1 Year 2 Year 3 Year 4 Year 5

$ (95,000)

$ (95,000) × 1.000

$ (95,000) 111,879 16,879

$ 40,000 (8,640)

$ 31,360 $ 31,360

× .893 $ 28,004

$ 40,000 (8,640)

$ 31,360 $ 31,360

× .797 $ 24,994

$ 20,000 (640)

$ 19,360 $ 19,360

× .712 $ 13,784

$ 40,000 (8,640)

$ 31,360 $ 31,360

× .636 $ 19,945

$ 13,000 $ 40,000

(8,640) $ 31,360

44,360 × .567

$ 25,152

(Depreciation Expense × Tax Rate × Present Value Factor (for 5 years at 12%) = Present Value of Tax Shield)

($18,400 × .040 × 3.605 = $26,533)

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Section 10.7 Calculation Issues

Assume that a firm has the following long-term funds structure and cost of funds:

Book Value Mix

Percentage Pretax Cost Aftertax

Cost Weighted Average

Bonds payable $10,000,000 25% 10% 6% 1.5%

Preferred stock 4,000,000 10 12 12 1.2

Common Stock 14,000,000 35 18 18 6.3

Retained earnings 12,000,000 30 18 18 5.4

Total long-term funds $40,000,000 100% 14.4%

The pretax cost percentages come from financial markets calculations. The weighted-average cost of capital is 14.4% [(25% × 6%) + (10% × 12%) + (35% × 18%) + (30% × 18%)]. Often financially strong companies have low cost of funds. High risk, financially unstable, or new firms often have high funds costs.

10.7 Calculation Issues The variety of issues surrounding capital investment decisions is sufficient that entire textbooks have been written about them. Here, we introduce a few of the more significant complexities.

Inflation and Future Cash Flows Inflation is a common economic problem. Over the past 40 years in the United States, annual inflation rates have ranged from a high of over 12% to a low of under 2%. These levels are moderate compared to rates in many other countries. Yet, capital investment decisions should consider inflationary impacts on future cash flows.

While several approaches could be used to incorporate inflation into the analysis, the approach we suggest is to build the impacts of inflation into the expected future cash flows. This allows the use of specific inflation rates for each cash-flow component. Also, rates can be changed for each future period.

To illustrate inflation impacts on estimates of future cash flows, assume that Kazen Motors plans to expand its engine diagnostic business. Equipment will cost about $120,000 and should last about three years. After three years, it is thought that greater on-board com- puter use will require more powerful testing technology. Annual revenues are expected to be $150,000, personnel costs are $60,000, and other support costs would be about $30,000. Kazen uses a 10% desired rate of return.

Economic forecasts indicate that inflation will be 6% per year for the next few years. But Kazen feels that, at best, prices could be raised no more than 4% per year. Personnel costs will

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Section 10.7 Calculation Issues

probably increase at a 10% rate, primarily because of benefits costs. Other costs will increase at an average of 6% annually. The equipment, which has no salvage value, will be depreciated on a straight-line basis. Assume a 40% tax rate. Cash flows related to the equipment are as follows:

Cash Flows:

Investment Life of the Project

Year 0 Year 1 Year 2 Year 3

Initial investment $(120,000)

Revenues $150,000 $156,000 162,240

Personnel costs (60,000) (66,000) (72,600)

Other costs (30,000) (31,800) (33,708)

Incremental taxes* ______ (8,000) (7,280) (6,373)

Net cash flows $(120,000) $ 52,000 $ 50,920 $ 49,559

*Taxes in Year 1: ($150,000 − 60,000 − 30,000 − 40,000) × 0.4 = $8,000 Taxes in Year 2: ($156,000 − 66,000 − 31,800 − 40,000) × 0.4 = $7,280 Taxes in Year 3: ($162,240 − 72,600 − 33,708 − 40,000) × 0.4 = $6,373

Notice that depreciation, being based on the historical cost of the investment, is still $40,000 in each year. While all other revenues and costs have inflation built into them, the tax law requires that the depreciation expense is always expressed in historical-cost dollars from the year of acquisition. Using historical cost-based depreciation in tax calculations often leads to higher tax payments since profits grow from inflated revenues.

It is dangerous to ignore inflation. To do so assumes that all inflation effects sum to zero, which is rarely the case. Certain cost areas, such as health care, have had unusually high increases in recent years. Forecasting these costs should include estimated inflationary impacts to make cash-flow estimates credible.

Working Capital When expansion occurs, inventories and receivables often grow. Financing working capital growth is an integral part of a project’s total investment. Unlike depreciable equipment and fixed assets, working capital is committed and can probably be recovered at the end of the project. Often, working capital requirements grow slowly over time as sales increase. Incre- mental inventories and accounts receivable net of incremental accounts payable can easily be overlooked and omitted from a project’s analysis. In contrast, JIT projects often release work- ing capital by reducing inventories, which can help finance the project itself.

Assume that Belmar Athletics operates a chain of sporting goods stores in shopping malls. Opening a new store requires layout, equipment, and fixtures costing about $450,000. In addition, about $200,000 of inventory is needed to stock a new store. Experience shows that inventory and other working capital needs will grow at about $20,000 per year for the first five years. If Belmar Athletics uses an eight-year timeframe for evaluating a store location,

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Section 10.7 Calculation Issues

assumptions will be needed about the equipment salvage value and the recovery of the work- ing capital investment. The fixed assets’ salvage values are estimated to be $50,000 net of taxes, and the entire working capital investment (now $300,000) is thought to be recovered. The cash flows would look like:

Life of the Project

Cash Flows: Today Year 1 Year 2 · · · Year 5 · · · Year 8

Initial construction $(450,000) $ 50,000

Working capital needs (200,000) $(20,000) $(20,000) · · · $(20,000) · · · 300,000

Working capital recovery is not automatic. Inventory may be obsolete, and receivables might not be collectible. A going-concern assumption can generally be made if the business is expected to continue past the timeframe cutoff.

Uneven Project Lives When comparing projects, lives of each project may not match. How can a three-year solu- tion to a problem be compared to a five-year or an eight-year solution? The decision must be viewed from the timeframe of the job to be done. Do we want a solution for three, five, or eight years? How long can the physical asset last? Often, technology changes make an asset’s eco- nomic life shorter than its physical life. A three-year solution may be sought, while an asset’s physical life might well be twice that long.

If the time period is based on the needs of the problem, the task is to find salvage or market values for assets at the end of the defined time period. If the time period is based on the physical lives of the proposed assets, different useful lives of the proposed solutions must be somehow matched. One approach is to use a shorter-lived project as the comparison time period. This requires finding salvage or market values for assets at midpoints in their lives. While no specific rule exists, the investment’s timeframe as defined by management seems to be the better choice. Management’s intent and common sense, rather than the physical lives of assets, should govern the time period choice.

Evaluation of Projects With Different Initial Investments Up to this point, most of the illustrations have assumed that a single investment alternative existed. The firm had to decide whether or not to invest in that project. Actually, a firm may have several alternatives but still have to select only one. In such a case, care must be exer- cised in using the internal rate of return method, because the project with the highest internal rate of return may not be the most desirable. This can happen in those cases where the dol- lar investment is not the same. The dollar amount of the return from a larger investment, in many cases, will exceed the dollar return from a smaller investment having a better internal rate of return.

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Section 10.7 Calculation Issues

Assume that Behar Transit Company must choose between two delivery vans. Each has an estimated life of five years with annual returns as follows:

Van I Van II

Net investment $75,000 $100,000

Net cash inflow for each of 5 years 26,000 33,000

Investments are expected to earn a desired rate of return of at least 12%. Van II requires an investment of an additional $25,000 versus Van I. The approximate internal rate of return is computed for each alternative and for the incremental investment as follows:

Van I Van II Incremental

(II – I)

Net investment $(75,000) $(100,000) $(25,000)

Annual return 26,000 33,000 7,000

Payback period 2.885 3.030 3.571

Nearest PV factor on Table 2 for 5 periods 2.864 2.991 3.605

Nearest IRR given on Table 2 22% 20% 12%

It appears that Van I should be selected because the internal rate of return is higher. The additional $25,000 investment needed by Van II yields a much lower rate of return: 12%. But, if the rate of return on the incremental investment is greater than the hurdle rate of return, the larger investment could still be made. In this example, an additional $7,000 per year is returned on an additional investment of $25,000. The rate of return on the incremen- tal investment barely meets the 12% desired rate of return.

In another situation, Van I could be a Phase I of a pair of sequential jobs and Van II could be Phases I and II combined. Phase I may be executed without Phase II but not vice versa. Advo- cates of Phase II would clearly argue that both phases be approved at one time. However, as we have seen, Phase II has an IRR of about 12%. If the cutoff rate is 15%, Phase I and the com- bined phases are acceptable. But Phase II by itself is unacceptable. Breaking down projects into their subcomponents can give useful insight into the yields on incremental investments.

Gains and Losses on Asset Disposals If assets are sold at more or less than their book values, gains or losses appear with tax impli- cations. The book value is an asset’s original cost minus its accumulated depreciation. In the business world, accounting book values and tax cost bases often differ. In our discussions here, unless specifically mentioned, these two amounts are assumed to be the same. If the sale is for more than the book value, a gain occurs; if for less, a loss occurs.

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Section 10.8 The Time Value of Money

Gains and losses on disposals and their impacts on cash flows arise at two points in the capital investment decision:

1. Old assets may be sold at the same time as a new asset is acquired 2. New assets may be sold at the end of the project’s expected life

10.8 The Time Value of Money Dollars promised in the future are not equal to dollars received now. When given a choice, we all prefer getting $100 today versus $100 two years from now. Dollars due in different time periods should be valued on a uniform scale that recognizes the time value of money. Pres- ent value converts future dollars into current dollar equivalents. Future value converts all dollars into equivalent dollars as of some future date. To find these values, we need an inter- est rate and the number of time periods between today and the future cash flows.

Money has earning power. Dollars today grow to larger sums through earning interest on the principal plus earning interest on interest. The investment principal plus compound inter- est is the future value (FV). The future value of $100 in two years, with interest compounded at the rate of 10% annually, is $121. The formula for the future value of $1 is:

FV = (1 + i)n where i = interest rate

n = number of years

In the example, the future value is computed as follows:

FV of $1 = (1.10)2 = $1.21

FV of $100 = $100 × $1.21, or $121

An investor who is happy with a 10% ROR looks at the receipt of $121 in two years as equiva- lent to $100 today, assuming certainty. This investor is indifferent between the $100 today or $121 in two years.

The interest rate influences the values. If a decision maker has a choice of investments, the preferred choice is the investment with the highest ROR. The reason, of course, is that the investment with the highest ROR will yield the largest future amount or require the smallest current investment. For example, an alternative investment will earn a 15% ROR. Assuming certainty, the future value in two years of the $100 at 15% is:

$100 × (1.15)2 = $100 × 1.3225 = $132.25

Since $132.25 is larger than $121, the project earning 15% is preferred to the 10% project.

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Section 10.8 The Time Value of Money

Present Value of Money Because decisions are made today and because future cash flows come in many different pat- terns and time periods, present values of future dollars are more useful and easier to analyze. It is conventional to use present value analysis.

How much money must we invest today to earn a given dollar amount in the future? Or, given an investment, how much will be earned in the future? Or, given an investment and a set of future cash inflows, what is the ROR? Answers to these questions can be found by computing the present value of the future cash flows and comparing it with the amount invested.

The present value (PV) of a future value can be computed by multiplying the future value by the present value of $1. The present value of $1 is:

PV of $1 = 1 ÷ (1 + i)n

Assume, for example, that $121 is needed in two years, and the rate of interest is 10%. How much must be invested today to have $121 after two years? We first determine the present value of $1 due in two years with interest compounded annually at 10%:

PV of $1 for 2 years at 10% = 1 ÷ (1.10)2 = 0.826

Next, we multiply by the future value:

PV of $121 for 2 years at 10% = $121 × 0.826 = $100 (rounded)

The computation can be viewed as:

0 21

Year 1 Year 2

$100 $121$110

Present Value Future Value

$121 ÷ 1.10 = $110 is the value at the end of Year 1.

$110 ÷ 1.10 = $100 is the investment at the start of Year 1, or today.

This is summarized as follows:

$121 ÷ (1.10)2 or [1 ÷ (1.10)2] × $121 = $100

The process of reducing a future amount to a present value is called discounting. The present value is sometimes called the discounted value. The rate of interest is the discount rate. The 0.826 is called the present value factor or discount factor.

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Section 10.8 The Time Value of Money

It is seldom necessary to calculate either future values or present values as done here. Calcu- lators and spreadsheet software easily perform these functions. Tables 1 and 2, found at the end of this chapter, give present value factors for various discount (interest) rates for various time periods expressed in years. Table 1 gives the present value of $1 to be received at the end of the various time periods at interest or discount rates shown across the top row of the table. Thus, it is a tabulation of the factor 1 ÷ (1 + i)n, where n is the number of years and i is the discount rate. The factor for two years at 10% is 0.826, and the present value (PV) of $121 to be received in two years is calculated as follows:

PV = $121 × 0.826 = $100 (rounded)

The discount factors appearing in Tables 1 and 2 are rounded to the third digit, which is suf- ficient precision for most capital investment problems.

Present Value of a Series of Future Cash Flows Often, a series of future cash inflows are earned from an investment instead of one cash inflow. As an example, a machine costing $3,500 today is forecast to generate cash inflows of $1,000 each year for five years. The time interval for most decisions is annual, but any time interval (a day, week, month, quarter, etc.) can be used as long as the interest rate (i) is adjusted to correspond to the time period.

Calculating present values depends on whether the cash flows series are equal or unequal amounts. An annuity refers to a series of equal cash flows. In either case, however, the under- lying concepts are the same. The present value of a series is the sum of the present values of the individual amounts. The present value of these five annual receipts of $1,000 using a 10% discount rate is computed as follows:

Year Computation Explanation

1 $1,000 × (1 ÷ 1.10) = $909 PV of $1,000 received at the end of Year 1

2 1,000 × [1 ÷ (1.10)2] = 826 PV of $1,000 received at the end of Year 2

3 1,000 × [1 ÷ (1.10)3] = 751 PV of $1,000 received at the end of Year 3

4 1,000 × [1 ÷ (1.10)4] = 683 PV of $1,000 received at the end of Year 4

5 1,000 × [1 ÷ (1.10)5] = 621 PV of $1,000 received at the end of Year 5

$3,790 PV of an annuity of $1,000 for 5 years

The present value can also be computed as follows:

$1,000 × [1/1.10 + 1/(1.10)2 + 1/(1.10)3 + 1/(1.10)4 + 1/(1.10)5] = $3,790

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Section 10.8 The Time Value of Money

The decimal equivalents of the fractions can be found in Table 1 and applied to the annual cash inflow:

0.909 + 0.826 + 0.751 + 0.683 + 0.621 = 3.790

$1,000 × 3.790 = $3,790

Note that the factor, 3.791, can be found on Table 2 using the 10% column and the 5-period row. The factors in Table 2 are the sums of the present value factors in Table 1. The difference between 3.790 and 3.791 is due to rounding. The following calculations using interest rates of 8%, 10%, and 12% for five years illustrate this point.

8% 10% 12%

Years Table 1 Table 2 Table 1 Table 2 Table 1 Table 2

1 0.926 0.909 0.893

2 0.857 0.826 0.797

3 0.794 0.751 0.712

4 0.735 0.683 0.636

5 0.681 0.621 0.567

Total 3.993 3.993 3.790* 3.791* 3.605 3.605

* Difference due to rounding.

When calculating, it is easier to add the annual factors and make one computation. Thus, Table 2 is more convenient for evaluating equal cash flows. If the annual cash-flow amounts are not equal, it is necessary to use Table 1.

Present Value Analysis Applied Assume that we sell machinery and offer financing to our customers using long-term notes payable. When a contract is signed, the customer makes two promises:

1. To pay the principal amount (the face value of the note) at maturity 2. To pay interest periodically at the rate stated in the contract

We can either hold the note (earning interest and collecting the principal at the end of the contract) or sell the contract to an investor to get the cash for the sale now. The contract’s market value depends on several factors, including the market rate of interest for similar contracts. The sum of the present values of the two promises is the contract’s market price. As the market rate of interest rises, the contract’s value declines, and vice versa.

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Section 10.8 The Time Value of Money

To illustrate, assume that Hillcrest Corp. sells a $100,000 machine. The buyer signs a ten-year $100,000 contract with an interest rate of 10%, paid annually. This contract specifies the fol- lowing cash payments:

Year Interest at 10% Payment of Principal Total Cash Outflow

1 $10,000 $10,000

2 10,000 10,000

. . . . . . . . . . . . . . . . . . . . . . .

9 10,000 10,000

10 10,000 $100,000 110,000

Suppose that the current market rate of interest is 12%. In this case, investors are not willing to buy the contract at face value, because they could earn 12% elsewhere. To sell the contract, Hillcrest must price the contract below face value. Selling at a price below face allows the investor to increase the rate of return by paying less for the two promises.

Promise 1: $100,000 × 0.322 (10 periods at 12% from Table 1) $32,200

Promise 2: $ 10,000 × 5.650 (10 payments at 12% from Table 2) 56,500

Proceeds from sale of the contract $88,700

Discount $11,300

The investor that purchases the contract from Hillcrest at $88,700 will earn 12% interest on the $88,700 invested. The 12% earned is usually called the yield or the effective rate of inter- est. An effective interest rate or yield to maturity is the rate of interest earned regardless of the compounding period or the stated interest rate.

Likewise, if the current market rate of interest is 8%, an investor will pay a premium for a contract with a 10% interest rate. The selling price and premium are determined as follows:

Promise 1: $100,000 × 0.463 (10 periods at 8% from Table 1) $46,300

Promise 2: $ 10,000 × 6.710 (10 payments at 8% from Table 2) 67,100

Proceeds from sale of the contract $113,400

Premium $13,400

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Section 10.8 The Time Value of Money

Present Value Tables

Table 1 Where:

Present Value of $1 P = 1/(1 + i)n P = Present Value Factor i = Interest Rate n = Number of Periods

Periods (n) 1% 2% 4% 5% 6% 8% 10% 12% 14% 15%

0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

1 0.990 0.980 0.962 0.952 0.943 0.926 0.909 0.893 0.877 0.870

2 0.980 0.961 0.925 0.907 0.890 0.857 0.826 0.797 0.769 0.756

3 0.971 0.942 0.889 0.861 0.840 0.794 0.751 0.712 0.675 0.658

4 0.961 0.924 0.855 0.823 0.792 0.735 0.683 0.636 0.592 0.572

5 0.951 0.906 0.822 0.784 0.747 0.681 0.621 0.567 0.519 0.497

6 0.942 0.888 0.790 0.746 0.705 0.630 0.564 0.507 0.456 0.432

7 0.933 0.871 0.760 0.711 0.665 0.583 0.513 0.452 0.400 0.376

8 0.923 0.853 0.731 0.677 0.627 0.540 0.467 0.404. 0.351 0.327

9 0.914 0.837 0.703 0.645 0.592 0.500 0.424 0.361 0.308 0.284

10 0.905 0.820 0.616 0.614 0.558 0.463 0.386 0.322 0.270 0.247

11 0.896 0.804 0.650 0.585 0.527 0.429 0.350 0.287 0.237 0.215

12 0.887 0.788 0.625 0.557 0.497 0.397 0.319 0.274 0.208 0.187

13 0.879 0.773 0.601 0.530 0.469 0.368 0.290 0.229 0.182 0.163

14 0.870 0.758 0.577 0.505 0.442 0.340 0.263 0.205 0.160 0.141

15 0.861 0.743 0.555 0.481 0.417 0.315 0.239 0.183 0.140 0.123

16 0.853 0.728 0.534 0.458 0.394 0.292 0.218 0.163 0.123 0.107

17 0.844 0.714 0.513 0.436 0.371 0.270 0.198 0.146 0.108 0.093

18 0.836 0.700 0.494 0.416 0.350 0.250 0.180 0.130 0.095 0.081

19 0.828 0.686 0.475 0.396 0.331 0.232 0.164 0.116 0.083 0.070

20 0.820 0.673 0.456 0.377 0.312 0.215 0.149 0.104 0.073 0.061

21 0.811 0.660 0.439 0.359 0.294 0.199 0.135 0.093 0.064 0.053

22 0.803 0.647 0.422 0.342 0.278 0.184 0.123 0.083 0.056 0.046

23 0.795 0.634 0.406 0.326 0.262 0.170 0.112 0.074 0.049 0.040

24 0.788 0.622 0.390 0.310 0.247 0.158 0.102 0.066 0.043 0.035

25 0.780 0.610 0.375 0.295 0.233 0.146 0.092 0.059 0.038 0.030

30 0.742 0.552 0.308 0.231 0.174 0.099 0.057 0.033 0.020 0.015

35 0.706 0.500 0.253 0.181 0.130 0.068 0.036 0.019 0.010 0.008

40 0.672 0.453 0.208 0.142 0.097 0.046 0.022 0.011 0.005 0.004

45 0.639 0.410 0.171 0.111 0.073 0.031 0.014 0.006 0.003 0.002

50 0.608 0.372 0.141 0.087 0.054 0.021 0.009 0.003 0.001 0.001

∞ 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

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440

Section 10.8 The Time Value of Money

Present Value Tables

Table 1 (continued) Where:

Present Value of $1 P = 1/(1 + i)n P = Present Value Factor i = Interest Rate n = Number of Periods

Periods (n) 16% 18% 20% 22% 24% 25% 30% 40%

0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

1 0.862 0.847 0.833 0.820 0.806 0.800 0.769 0.714

2 0.743 0.718 0.694 0.672 0.650 0.640 0.592 0.510

3 0.641 0.609 0.579 0.551 0.524 0.512 0.455 0.364

4 0.552 0.516 0.482 0.451 0.423 0.410 0.350 0.260

5 0.476 0.437 0.402 0.370 0.341 0.328 0.269 0.186

6 0.410 0.370 0.335 0.303 0.275 0.262 0.207 0.133

7 0.354 0.314 0.279 0.249 0.222 0.210 0.159 0.095

8 0.305 0.266 0.233 0.204 0.179 0.168 0.123 0.068

9 0.263 0.225 0.194 0.167 0.144 0.134 0.094 0.048

10 0.227 0.191 0.162 0.137 0.116 0.107 0.073 0.035

11 0.195 0.162 0.135 0.112 0.094 0.086 0.056 0.025

12 0.168 0.137 0.112 0.092 0.076 0.069 0.043 0.018

13 0.145 0.116 0.093 0.075 0.061 0.055 0.033 0.013

14 0.125 0.099 0.078 0.062 0.049 0.044 0.025 0.009

15 0.108 0.084 0.065 0.051 0.040 0.035 0.020 0.006

16 0.093 0.071 0.054 0.042 0.032 0.028 0.015 0.005

17 0.080 0.060 0.045 0.034 0.026 0.023 0. 012 0.003

18 0.069 0.051 0.038 0.028 0.021 0.018 0.009 0.002

19 0.060 0.043 0.031 0.023 0.017 0.014 0.007 0.002

20 0.051 0.037 0.026 0.019 0.014 0.012 0.005 0.001

21 0.044 0.031 0.022 0.015 0.011 0.009 0.004 0.001

22 0.038 0.026 0.018 0.013 0.009 0.007 0.003 0.001

23 0.033 0.022 0.015 0.010 0.007 0.006 0.002 0.000

24 0.028 0.019 0.013 0.008 0.006 0.005 0.002 0.000

25 0.024 0.016 0.010 0.007 0.005 0.004 0.001 0.000

30 0.012 0.007 0.004 0.003 0.002 0.001 0.000 0.000

35 0.006 0.003 0.002 0.001 0.001 0.000 0.000 0.000

40 0.003 0.001 0.001 0.000 0.000 0.000 0.000 0.000

45 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000

50 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000

∞ 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

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441

Section 10.8 The Time Value of Money

Present Value Tables

Table 2 Where:

Present Value of $1 Received Periodically for n Periods

P = [1 − (1/(1 + i)n]/i P = Present Value Factor i = Interest Rate n = Number of Periods

Periods (n) 1% 2% 4% 5% 6% 8% 10% 12% 14%

0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

1 0.990 0.980 0.962 0.952 0.943 0.926 0.909 0.893 0.877

2 1.970 1.942 1.886 1.859 1.833 1.783 1.736 1.690 1.647

3 2.941 2.884 2.775 2.723 2.673 2.577 2.487 2.402 2.322

4 3.902 3.808 3.630 3.546 3.465 3.312 3.170 3.037 2.914

5 4.853 4.713 4.452 4.329 4.212 3.993 3.791 3.605 3.433

6 5.795 5.601 5.242 5.076 4.917 4.623 4.355 4.111 3.889

7 6.728 6.472 6.002 5.786 5.582 5.206 4.868 4.564 4.288

8 7.652 7.325 6.733 6.463 6.210 5.747 5.335 4.968 4.639

9 8.566 8.162 7.435 7.108 6.802 6.247 5.759 5.328 4.946

10 9.471 8.983 8.111 7.722 7.360 6.710 6.145 5.650 5.216

11 10.368 9.787 8.760 8.306 7.887 7.139 6.495 5.938 5.453

12 11.255 10.575 9.385 8.863 8.384 7.536 6.814 6.194 5.660

13 12.134 11.348 9.986 9.394 8.853 7.904 7.103 6.424 5.842

14 13.004 12.106 10.563 9.899 9.295 8.244 7.367 6.628 6.002

15 13.865 12.849 11.118 10.380 9.712 8.559 7.606 6.811 6.142

16 14.718 13.578 11.652 10.838 10.106 8.851 7.824 6.974 6.265

17 15.562 14.292 12.166 11.274 10.477 9.122 8.022 7.120 6.373

18 16.398 14.992 12.659 11.690 10.828 9.372 8.201 7.250 6.467

19 17.226 15.678 13.134 12.085 11.158 9.604 8.365 7.366 6.550

20 18.046 16.351 13.590 12.462 11.470 9.818 8.514 7.469 6.623

21 18.857 17.011 14.029 12.821 11.764 10.017 8.649 7.562 6.687

22 19.660 17.658 14.451 13.163 12.042 10.201 8.772 7.645 6.743

23 20.456 18.292 14.857 13.489 12.303 10.371 8.883 7.718 6.792

24 21.243 18.914 15.247 13.799 12.550 10.529 8.985 7.784 6.835

25 22.023 19.523 15.622 14.094 12.783 10.675 9.077 7.843 6.873

30 25.808 22.396 17.292 15.372 13.765 11.258 9.427 8.055 7.003

35 29.409 24.999 18.665 16.374 14.498 11.655 9.644 8.176 7.070

40 32.835 27.355 19.793 17.159 15.046 11.925 9.779 8.244 7.105

45 36.095 29.490 20.720 17.774 15.456 12.108 9.863 8.283 7.123

50 39.196 31.424 21.482 18.256 15.762 12.233 9.915 8.304 7.133

∞ 100.000 50.000 25.000 20.000 16.667 12.500 10.000 8.333 7.143

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442

Section 10.8 The Time Value of Money

Present Value Tables

Table 2 (continued) Where:

Present Value of $1 Received Periodically for n Periods

P = [1 − (1/(1 + i)n]/i P = Present Value Factor i = Interest Rate n = Number of Periods

Periods (n) 15% 16% 18% 20% 22% 24% 25% 30% 40%

0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

1 0.870 0.862 0.847 0.833 0.820 0.806 0.800 0.769 0.714

2 1.626 1.605 1.566 1.528 1.492 1.457 1.440 1.361 1.224

3 2.283 2.246 2.174 2.106 2.042 1.981 1.952 1.816 1.589

4 2.855 2.798 2.690 2.589 2.494 2.404 2.362 2.166 1.849

5 3.352 3.274 3.127 2.991 2.864 2.745 2.689 2.436 2.035

6 3.784 3.685 3.498 3.326 3.167 3.020 2.951 2.643 2.168

7 4.160 4.039 3.812 3.605 3.416 3.242 3.161 2.802 2.263

8 4.487 4.344 4.078 3.837 3.619 3.421 3.329 2.925 2.331

9 4.772 4.607 4.303 4.031 3.786 3.566 3.463 3.019 2.379

10 5.019 4.833 4.494 4.192 3.923 3.682 3.571 3.092 2.414

11 5.234 5.029 4.656 4.327 4.035 3.776 3.656 3.147 2.438

12 5.421 5.197 4.793 4.439 4.127 3.851 3.725 3.190 2.456

13 5.583 5.342 4.910 4.533 4.203 3.912 3.780 3.223 2.469

14 5.724 5.468 5.008 4.611 4.265 3.962 3.824 3.249 2.478

15 5.847 5.575 5.092 4.675 4.315 4.001 3.859 3.268 2.484

16 5.954 5.668 5.162 4.730 4.357 4.033 3.887 3.283 2.489

17 6.047 5.749 5.222 4.775 4.391 4.059 3.910 3.295 2.492

18 6.128 5.818 5.273 4.812 4.419 4.080 3.928 3.304 2.494

19 6.198 5.877 5.316 4.843 4.442 4.097 3.942 3.311 2.496

20 6.259 5.929 5.353 4.870 4.460 4.110 3.954 3.316 2.497

21 6.312 5.973 5.384 4.891 4.476 4.121 3.963 3.320 2.498

22 6.359 6.011 5.410 4.909 4.488 4.130 3.970 3.323 2.498

23 6.399 6.044 5.432 4.925 4.499 4.137 3.976 3.325 2.499

24 6.434 6.073 5.451 4.937 4.507 4.143 3.981 3.327 2.499

25 6.464 6.097 5.467 4.948 4.514 4.147 3.985 3.329 2.499

30 6.566 6.177 5.517 4.979 4.534 4.160 3.995 3.332 2.500

35 6.617 6.215 5.539 4.992 4.541 4.164 3.998 3.333 2.500

40 6.642 6.233 5.548 4.997 4.544 4.166 3.999 3.333 2.500

45 6.654 6.242 5.552 4.999 4.545 4.166 4.000 3.333 2.500

50 6.661 6.246 5.554 4.999 4.545 4.167 4.000 3.333 2.500

∞ 6.667 6.250 5.556 5.000 4.545 4.167 4.000 3.333 2.500

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443

Summary & Resources

Chapter Summary Capital investment decisions are critical to the firm’s long-term success. The relevant data for making investment decisions are incremental cash flows, using criteria established in Chap- ter 9. Capital investments generally have multiperiod cash flows, requiring the use of the time value of money. The opportunity cost of cash to be received in the future can be a significant variable in measuring returns.

Four methods are discussed to evaluate the cash flows. Two methods use present values for all cash flows:

1. Net present value, where a rate of return is set and decisions are made based on whether the net present value is positive or negative

2. Internal rate of return, where the rate of return is found by setting the initial invest- ment equal to the present value of future net cash inflows

Two other methods discussed that do not use the time value of money are the payback period and the accounting rate of return methods.

Rarely are funds available to finance all attractive projects. Projects are selected based on rankings of their relative attractiveness. Taxes on profits from capital investments must be calculated and do affect the ROR of projects. The cost of capital is often used to develop a minimum acceptable rate of return.

Computational issues such as uneven lives, working capital needs, incremental investment analysis, and inflationary impacts on forecasts are examined.

Key Terms accelerated depreciation Depreciation methods that charge larger amounts of depreciation in the early years of an asset’s life and relatively smaller amounts to the later years.

accounting rate of return (ARR) method A method of calculating a rate of return on a capital investment project in which the average annual net income from the project is divided by the average book value of the investment.

annuity A series of equal cash flows received or paid over equal time intervals.

capital budgeting The process of evaluat- ing, selecting, controlling, and financing capital investments.

capital investment The cash outflow needed to acquire long-term assets or to obtain access to cash inflows in future periods.

capital investment decisions A decision of whether to acquire assets with an expected life in excess of one year.

compound interest Interest on the princi- pal plus the previously earned interest.

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Summary & Resources

cost of capital The weighted average cost, expressed as a percentage, of obtaining long- term financial resources for an organization.

cutoff rate The minimum acceptable rate of return set by management that a capital investment project can earn and still be approved.

desired rate of return A target rate of return on capital investments as selected by top management for determining the mini- mum rate of return acceptable.

discount factor The multiplier used to determine the present value.

discount rate The interest rate used in reducing a future amount to a present value.

discounted value The value now for an amount to be received in the future; the amount to be paid now to settle a debt that becomes due in the future.

discounting The process of reducing a future amount to a present value using a specific interest rate.

effective interest rate The actual rate of interest earned in one year, regardless of the compounding period associated with the stated interest rate.

face value The principal amount due at maturity.

future value The compound amount of any principal plus interest at the end of a specific time period, using a specific interest rate.

going-concern assumption Can generally be made if the business is expected to con- tinue past the timeframe cutoff.

hurdle rate The minimum acceptable rate of return set by management that a capital investment project can earn and still be approved.

inflation General increases in the prices of goods and services.

internal rate of return (IRR) The rate of return that equates the present value of the future cash inflows with amount of the capi- tal investment outlay.

marginal tax rate The tax rate that would be applied to the next dollar of taxable income.

market rate of interest The effective yield that is currently earned on similar types of financial instruments.

minimum acceptable rate of return The lowest rate of return that a capital invest- ment project can earn and still be approved.

net initial investment The net outflow of cash, a commitment of cash, or the sacrifice of an inflow of cash that occurs at the begin- ning of a project.

net present value The difference between the investment and the present value of future returns discounted at a specific inter- est rate.

net present value method The capital investment evaluation method that dis- counts future cash flows to arrive at present values.

payback period The amount of time required to recover the net initial investment.

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Summary & Resources

payback period method A quick way to evaluate potential capital investments by asking only how long it will take to recover the net initial investment.

payback reciprocal The percentage obtained by dividing the payback period into 1.

premium Amount in excess of the principal or face amount that an investor will pay for a fixed-rate instrument because the coupon rate is higher than the current market rate.

present value The value now for an amount to be received in the future; the amount to be paid now to settle a debt that becomes due in the future.

profitability index The ratio of the present value of net cash inflows divided by the net initial investment.

required rate of return The minimum acceptable rate of return set by management that a capital investment project can earn and still be approved.

target rate of return The minimum accept- able rate of return set by management that a capital investment project can earn and still be approved.

tax shield The amount of taxes saved because of the tax deductibility of an expenditure.

time value of money The concept that a future sum of money is of less value than the same dollar amount today.

weighted-average cost of capital The cost of debt capital and equity capital weighted by their respective proportions in the total long-term capital structure.

working capital Current assets minus cur- rent liabilities.

yield to maturity The actual rate of inter- est earned in one year regardless of the com- pounding period associated with the stated interest rate.

Problem for Review Pam Williams, owner of a self-storage business, has just received an offer that is worth $600,000 after taxes for the storage buildings. She is interested in another investment oppor- tunity that can probably yield an annual discounted return of 15% after taxes. The storage business is expected to continue to yield an annual cash inflow, before taxes, of $170,000 for a period of 15 years. The book value of the storage buildings is $660,000, and straight-line depreciation is used for tax purposes. Zero salvage value is predicted. A 40% tax rate applies.

Question:

Should the offer to sell the storage business be accepted? Explain.

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Summary & Resources

Solution:

First, solve for the net aftertax cash flow if the business is kept:

Cash flow before taxes $170,000

Minus depreciation (44,000) ($660,000 ÷ 15 years)

Taxable cash flow $126,000

Taxes (40%) (50,400)

Aftertax cash flow $ 75,600

Plus depreciation 44,000

Net aftertax cash flow $119,600

Investment Life of the Project

Year: 0 1 15

Purchase offer ($600,000)

Net cash flow $119,600 . . . $119,600

PV – Years 1 to 15 699,301

(15%, 15 years): $119,600 × 5.847

NPV $ 99,301

Since the PV of the flows is greater than the offer of $600,000, the business should not be sold.

Questions for Review and Discussion

1. Why is timing important in a capital investment decision? What is meant by the time value of money?

2. Could the net present value method and the internal rate of return use the same interest rate? Explain.

3. Are the returns from an investment the same as the accounting profit? Explain. 4. What are the advantages and disadvantages of the accounting rate of return method? 5. Explain the difference between the internal rate of return method and the net pres-

ent value method. 6. How can project rankings using the internal rate of return and the profitability index

differ? 7. Explain the tax shield. Tie this explanation to the comment: “Depreciation is a source

of cash.” 8. Why is an initial investment in additional inventory different than an investment in

machinery? Explain the difference in cash flows. 9. What is the advantage of accelerated depreciation over straight-line depreciation in

a capital investment decision?

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Summary & Resources

10. Knowing the cost of capital is a necessary part of present value analysis. What does it represent? Explain one way to measure it.

11. How can inflation can be incorporated into capital investment analysis? 12. What problem arises if alternative investments have different useful lives? Identify

at least one solution.

Exercises

10-1. Determining the Life of an Investment. Arborvista Electronics is considering expanding its business by adding one more store in Amsterdam. The building and its operating contents will cost 1 million euros and generate about €200,000 in cash inflows each year after taxes. The manager, Sarah Keren, feels the investment should not be made unless the store realizes a 10% rate of return on the cash invested.

Question:

For how many years must the store operate to earn a 10% return?

10-2. Four Methods. Avondale Company purchased a farm tractor for $100,000. The cash inflow from using the tractor is expected to be $30,000 per year for eight years. Avondale uses a 15% cutoff rate.

Question:

Use straight-line depreciation where needed, and ignore taxes. What is the payback period, the estimated IRR, the NPV, and the ARR?

10-3. Payback Method. Elbein Company purchased a machine for $125,000 and will depreciate it on a straight-line basis over a five-year period with an aftertax sal- vage value of $15,000. The related cash operating savings, before income taxes, is expected to be $50,000 a year.

Questions:

1. Find the payback period, ignoring taxes. 2. Assume that Elbein’s effective income tax rate is 40% and that salvage value is

ignored when calculating depreciation. What is the payback period?

10-4. Different Capital Investment Methods. Warrensville Center Company plans to acquire equipment costing $600,000. Depreciation on the new equipment would be $100,000 each year for six years. The annual cash inflow before income tax from this equipment has been estimated at $210,000. The tax rate is 40%.

Questions:

1. Find the payback period. 2. Find the ARR using the average investment. 3. Find the NPV if Warrensville’s minimum acceptable rate of return is 16%. 4. Estimate the IRR from Table 2 (e.g., between 10 and 12%).

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Summary & Resources

10-5. Investments With Uneven Cash Flows. Glenmont Consolidated has data on two $100,000 investment opportunities. With only $100,000 in cash available, the own- ers must decide which is the better opportunity. The controller has gathered the following data:

Investment 1: $30,000 of cash inflow for each of the first three years and $90,000 for each of the last three years.

Investment 2: $80,000 of cash inflow in the first year, $60,000 in the next four years, and $40,000 in the sixth year.

Question:

If a 14% ROR is needed, which investment will be preferred? Why?

10-6. Equipment Replacement. By replacing an old refrigeration unit, Sheila Marshall of Victoria Estates Produce in Liverpool, U.K., thinks that sales from the greater capac- ity will increase by £100,000 per year and that cash operating costs will decline by £60,000 per year. The new refrigerator will cost £350,000. Her variable contribution margin is 40%. The old equipment is fully depreciated but can be sold for £8,000. The new refrigerator will use straight-line depreciation, has a five-year life, and is expected to have a salvage value of £40,000. Ignore taxes.

Question:

Format the cash flows for the refrigeration unit proposal.

10-7. Net Returns and Discounted Rate of Return. The Eastway Company is considering new equipment that can reduce personnel costs by an estimated $60,000 a year. The new equipment is also expected to generate annual intangible customer service ben- efits of $70,000. The new equipment will cost $400,000 and will be depreciated on a straight-line basis for tax purposes. The asset will have no residual value at the end of ten years, the estimated life of the equipment. Income tax is estimated at 40%.

Questions:

1. Determine the annual net cash inflow from the proposed investment. 2. Will the investment earn an 18% aftertax rate of return? 3. Comment on the NPV.

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Summary & Resources

10-8. Uneven Cash Flows. The following projects of YABI Enterprises each require an $80,000 investment.

Cash inflows:

Project

98-A4 98-G3 98-K1 98-P6 98-S4

Year 1 $20,000 $10,000 $40,000 $60,000

Year 2 20,000 10,000 30,000

Year 3 20,000 15,000 40,000 10,000

Year 4 20,000 15,000 $160,000 (60,000)

Year 5 20,000 25,000 40,000

Year 6 20,000 25,000 40,000

Year 7 20,000 30,000 40,000

Year 8 20,000 30,000 80,000

Questions:

1. For each project, find the payback period. 2. For each project, find the ARR. 3. For each project, find the NPV (using a 15% discount rate).

10-9. New Business. Wrenford Co. purchased a new machine for $50,000 to expand capacity. Sales are expected to increase by 20%. The only additional fixed expense is the depreciation on the new machine (straight-line over five years with no salvage value). The income statement for the past year is:

Sales $300,000

Variable expenses (180,000)

Fixed expenses (100,000)

Net income before taxes $20,000

Taxes (40%) (8,000)

Net income after taxes $12,000

Questions:

1. What is the expected annual aftertax cash inflow from the new machine? 2. Find the NPV using a hurdle rate of 15% and the payback period.

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Summary & Resources

10-10. Equipment Replacement. By replacing present equipment with more efficient equipment, Belvoir Company estimates that cash operating costs can be reduced by $65,000 a year. In addition, increased sales volume can result in a larger contribu- tion margin of $25,000 a year without considering the efficiency savings. Deprecia- tion of $50,000 per year will be taken on new equipment. Depreciation on present equipment is $10,000 per year. The income tax rate is 40%.

Question:

What is the estimated incremental annual aftertax cash inflow on this investment?

10-11. Find the Missing Values. The table below compares six projects for Cedar Corpora- tion, but it is incomplete.

Internal Rate of Return

Initial Investment

Life of the Project

Annual Net Cash Inflow Percentage

Present Value Factor

(Table 2)

Project 1 $118,932 6 years $34,000 ? % ?

Project 2 ? 5 years 12,000 ? % 3.605

Project 3 68,000 15 years ? 16 % ?

Project 4 84,750 ? years 15,000 12 % ?

Project 5 ? ? years 20,000 20 % 2.991

Project 6 111,925 20 years ? 8 % ?

Question:

Provide the missing values for these projects.

10-12. Gains and Losses on Disposal. Hinsdale Enterprises is considering the purchase of a new machine for $200,000. It would have a five-year life. The company would sell for $50,000 its old machine, which cost $180,000 and has a book value of $20,000. Gains, losses, and profits have a tax rate of 40%. The new machine will require about $30,000 less in raw materials inventory to operate.

Question:

What is the net cash outflow for the investment?

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10-13. Comparing Alternatives. Superior Company is considering a new popper for one of its portable caramel popcorn stands. The analysis is narrowed to the “Bang” or the “Pow.” Information on the two devices is:

Bang Pow

Purchase price $90,000 $60,000

Annual cash inflows 34,000 24,000

Salvage value in 5 years 8,000 5,000

Useful life 5 years 5 years

Either device will do the job equally as well. Superior uses a 16% cost of capital. Ignore taxes.

Questions:

1. Which machine has the higher NPV? Is this a proper basis for making this invest- ment decision?

2. Using the profitability index, which machine is more attractive? 3. If Superior has $180,000 to invest in popping machines, what should it do? Why?

10-14. Inflation and Investment Analysis. Lavista Health Spas is evaluating an expan- sion of its existing facilities this fall. The proposal calls for a six-year building rental contract at $10,000 a year. Equipment purchases and facility improvements are expected to cost $60,000. Straight-line depreciation is used. Other cash operating expenses are estimated at $25,000 annually. Based on past experience, the com- pany thinks new revenues should be $50,000 annually. Lavista Health Spas will not expand unless the project covers its 14% cost of capital. The company’s effective tax rate is 40%.

Inflation is a concern. The controller, Evie Weinreich, thinks that revenues and cash expenses will inflate by 5% per year. Round the discount rate to the next highest rate available in Table 2.

Question:

Using NPV, suggest whether the expansion project should be adopted.

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10-15. Multiple Projects. Marvin Gross manages a temporary hiring service and is consid- ering several investments for his business. He expects a 16% ROR. Ignore taxes. The basic facts about three opportunities are:

a. More office space. The space will cost $400,000, earn a net cash inflow of $120,000 per year after taxes, last 5 years, have no salvage value, and be depreci- ated using straight-line.

b. An opportunity to run a training program. The project will earn $50,000 per year and have a life of five years.

c. New computer equipment. Marvin thinks the cost of the equipment needed is $60,000. The expected cash inflow per year is $12,000.

Questions:

1. What is the new present value of Investment A (more office space)? 2. What is the most Marvin should pay for upfront preparations for Investment B (an

opportunity to run a training program) and still meet his ROR expections? 3. How long must the new computer equipment in Investment C last (in years) to meet

Marvin’s ROR expectations?

10-16. Unequal Lives. Having given the matter some thought, you decide that you would be equally happy buying and driving any of the following cars:

a. A Supreme Deluxe and trading every sixth year. b. A Premium Fairmont and trading every third year. c. An Economy Delight and trading every second year.

You have decided to base your decision on the present value of the expected future costs. You have predicted your costs as follows:

Supreme Deluxe

Premium Fairmont

Economy Delight

Original cost $30,000 $20,000 $15,000

Market value at trade in time 8,000 8,000 8,000

Annual cash operating costs 2,400 2,000 1,500

Overhaul, fourth year 2,000 0 0

Overhaul, second year 0 1,000 0

You believe that you will stick with this approach for at least six years. Your minimum desired rate of return is 10%. Ignore taxes.

Question:

Select the alternative that promises the greatest financial advantage.

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Problems 10-17. Relevant Costs. Aussie Auto Wash Company has just installed a special machine

for washing cars in its Perth outlet. The machine cost A$20,000. Its operating costs, based on a yearly volume of 100,000 cars, total A$15,000, exclusive of depreciation. After the machine has been used one day, a salesperson offers a different machine that promises to do the same job at a yearly operating cost of A$9,000, exclusive of depreciation. The new machine will cost A$24,000, installed. The “old” machine is unique and can be sold outright for only A$8,000, less A$2,000 removal cost. The old and new machines will have a four-year useful life and no residual value. Sales, all in cash, will be A$150,000 per year, and other cash expenses will be A$110,000 annu- ally, regardless of this decision.

Questions:

1. Ignore taxes. Calculate net income for each of the four years assuming that the new machine is not purchased and then assuming that it is purchased. Sum the net incomes for the four years for each alternative. What should be done?

2. Ignore taxes, and consider the time value of money. If a 15% return on investment is desired, what should be done?

10-18. Value of a Business. Miramar, Inc., makes and sells candy in large lots for other firms that package and sell the candy under various brand names. The firm could acquire a small candy exporting firm that has sold about 800,000 boxes of candy annually to Korea and Japan. To operate the firm, Miramar would have to hire specialized sales reps for $1,200,000 annually, including travel and entertainment expenses. Additional packaging machinery costing $1,600,000 must be acquired. The machinery would last five years, have no salvage value, and be depreciated on a straight-line basis.

Other data are as follows:

a. Variable costs are $0.80 per box. b. Selling price on the export business is $4 per box. c. Annual cash costs of operating the new machinery are $320,000. d. Tax rate is 40%. e. Cost of capital is 16%.

Question:

On the basis of this information and a five-year time horizon, what is the most Miramar should pay for this investment opportunity?

10-19. Investment Returns and Sales Volume. Judy Yank, whose uncle whispered “plas- tics” into her ear soon after she graduated from college years ago, founded Maple Leaf Plastics, Inc. Judy is considering an investment of $2,000,000 in a new product line. Depreciation of $200,000 is to be deducted in each of the next ten years. Salvage value is estimated at zero. A selling price of $50 per unit is decided upon; unit vari- able cost is $30. The sales division believes that a sales estimate of 50,000 units per year is realistic. Joseph Samuels, the controller, states that a solid market exists for

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only 20,000 units a year. Projects must meet a minimum rate-of-return requirement of 15%. Income tax is estimated at 40% of income before tax.

Questions:

1. Evaluate the project using each of the sales volume estimates. Use the NPV method. 2. At what volume will the project earn exactly a 15% return?

10-20. Sell or Use Equipment. An offer of $130,000 has been received for equipment that Lancashire Products has been using to make certain parts. The equipment is fully depreciated but can be used for five more years. After five years, it is expected to have little, if any, value.

The variable cost of producing the parts is $10 per unit. A total of 10,000 units are needed each year. If the parts are not manufactured, the company must buy them from an outside supplier at a cost of $15 per unit. Also, if the parts are not produced, the space occupied by the equipment can be rented for $12,000 per year. Income tax is estimated at 40% of the income before tax. The company uses a 12% hurdle rate on this type of investment.

Question:

Prepare a recommendation for Lancashire’s president on the proposed equipment sale.

10-21. Expanding a Product Line. Sutherland Company makes office equipment, such as tables, desks, computer equipment consoles, and work tables. The sales manager, Blossom Newman, is trying to decide whether to expand the relatively new com- puter equipment console product line. The average desk will sell for $300 and has a variable cost of $140 per unit. Volume is expected to be 4,000 units per year for five years. To make the desks, the firm will have to buy additional machinery that will cost $900,000, has a five-year life, and has a $100,000 salvage value net of taxes. Straight-line depreciation is used, and salvage value is ignored in depreciation calcu- lations. Additional fixed cash operating costs will be $200,000 per year. Sutherland has a 40% tax rate, and its cost of capital is 16%.

Questions:

1. Using NPV, determine whether the computer console line should be expanded. 2. Compute the payback period. 3. Determine the approximate IRR that the firm expects to earn on the investment.

Ignore salvage value.

10-22. Equipment Replacement Concerns. The molding department of Stonehaven, Inc. has been investigating the acquisition of new equipment costing $100,000. Cash savings before income taxes from the use of this equipment are estimated to be $40,000 per year for ten years. At the end of five years, the new equipment must be overhauled at a cost of $35,000. The new equipment will have no salvage value after ten years. The new machine would replace an old machine that would need a $30,000 overhaul now, and again in five years, if it is not replaced. The old machine

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is fully depreciated but can still function. To remove the old machine, environmen- tal precautions (mainly an asbestos problem) will cost the firm $40,000. The rate used in evaluating investments is 10%. The income tax rate is 40%. Stonehaven uses straight-line depreciation.

Questions:

1. Calculate the NPV. Make a recommendation. 2. If the asbestos will need to be removed within two years anyway, how does this

impact your answer to Part 1? Comment.

10-23. Ranking Investment Alternatives. Grosvenor Industries has designated $1.2 mil- lion for capital investment expenditures during the upcoming year. Its cost of capital is 14%. Any unused funds will earn the cost of capital rate. The following investment opportunities along with their required investment and estimated net present val- ues have been identified:

Project Net

Investment NPV Project Net

Investment NPV

A $200,000 $22,000 F $250,000 $30,000

B 275,000 21,000 G 100,000 7,000

C 150,000 6,000 H 200,000 18,000

D 190,000 (19,000) I 210,000 4,000

E 500,000 40,000 J 250,000 35,000

Questions:

1. Rank the projects using the profitability index. Considering the limit on funds avail- able, which projects should be accepted?

2. Using the NPV, which projects should be accepted, considering the limit on funds available?

3. If the available investment funds are reduced to only $1,000,000: a. Does the list of accepted projects change from Part 2? b. What is the opportunity cost of the eliminated $200,000?

10-24. Comparing Unequals. Data relating to three possible investments are as follows:

X Y Z

Cost $34,000 $25,000 $75,000

Annual cash savings 8,111 7,458 14,011

Useful life - years 10 5 20

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The firm’s cost of capital is 14%, and a 40% tax rate is applicable to all taxation items.

The firm plans to replace the truck with one costing $80,000 and having an expected salvage value net of taxes of $5,000, annual cash operating costs of $3,000, and a useful life of five years. Straight-line depreciation of $16,000 per year would be taken on the new truck. Additionally, because the new truck is more dependable, the firm could reduce its repair parts inventory by $15,000.

Question:

Determine whether the new truck should be bought. Use whatever capital investment meth- ods you believe will best present the facts to Houston Mill’s management.

Questions:

1. Ignoring taxes, rank the investments according to their desirability using the pay- back period, IRR, NPV with a discount rate of 12%, and profitability index.

2. Comment on the impact that the unequal lives have on the rankings. 3. Comment on the impact that the unequal investments have on the rankings.

10-25. Equipment Replacement. Houston Mill Company owns a specialty truck with the following attributes:

Book value $55,000

Current market value 40,000

Expected salvage value (after five-year remaining useful life) 0

Annual depreciation expense, straight-line method 11,000

Annual cash operating costs 18,000

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Case: Stewart Machining

Stewart Machining purchased a new grinding machine one year ago at a cost of $68,000. The machine has been working very satisfactorily, but the shop manager, Jack Tudy, has just received information on an electronically controlled grinder that is vastly superior to the machine that he now uses. While both machines can meet all required existing quality standards and tolerances, the new machine’s quality potential can far exceed the old machine’s capabilities. Comparative data on the two machines follow:

Jack makes a few quick computations and exclaims, “Wow! We need that machine and its capabilities. But, no way can I sell it upstairs. When the boss sees the loss on the old machine, he’ll have kittens.” He’s looking at this:

Stewart Machining uses straight-line depreciation and ignores salvage value in its depreciation calculations. Sales from the grinding operation are expected to remain unchanged at $300,000 per year indefinitely. Other cash costs of the grinding operation total $80,000 annually. The corporate tax rate is 40%.

Questions:

1. Prepare summary income statements covering the next six years for the grinding operation, assuming that: a. The new machine is not purchased b. The new machine is purchased

2. What do you recommend? Show any needed additional analysis. 3. Comment on the reality of the $25,000 loss Jack has calculated. Can or should this be

ignored? 4. Comment on why introducing new technology is difficult to justify to management. 5. Develop a policy that would encourage investment in new technology and yet would

avoid wasting scarce capital investment money.

Present Machine Proposed New Machine

Purchase cost new (including installation costs)

$70,000 $90,000

Salvage value today 35,000

Salvage value at end of life 5,000 10,000

Annual costs to operate 95,000 75,000

Estimated useful life when new 7 years 6 years

Remaining book value of the old machine $60,000

Salvage value now of the old machine 35,000

Net loss from disposal (before tax deduction of the loss) $25,000

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