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Homework answers / question archive / Need 2 sets of 3 questions in excel Problem 27-3 Problem 27-5  Case 27-2 27 Longer-Run Decisions: Capital Budgeting Chapter Chapter 26 discussed types of alternative choice problems with a relatively short time horizon

Need 2 sets of 3 questions in excel Problem 27-3 Problem 27-5  Case 27-2 27 Longer-Run Decisions: Capital Budgeting Chapter Chapter 26 discussed types of alternative choice problems with a relatively short time horizon


Need 2 sets of 3 questions in excel

Problem 27-3

Problem 27-5

 Case 27-2

27 Longer-Run Decisions: Capital Budgeting


Chapter 26 discussed types of alternative choice problems with a relatively short time horizon. Such short-run decisions do not commit, or lock in, the organization to a cer- tain course of action over a considerable period in the future. Similarly, they usually do not significantly affect the amount of funds that must be invested in the organization. In this chapter, we extend the discussion of alternative choice decisions to those that in- volve relatively long-term differential investments of capital. Such problems are called capital investment problems; they are also commonly called capital budgeting problems because a capital budget is a list of the capital investment projects that an or- ganization has decided to carry out.

In these problems, differential costs and revenues are treated the same as in Chap- ter 26; the only difference is that the longer time horizon of capital budgeting problems magnifies the problems of estimating these cost and revenue items. However, the long- term investment aspect of capital budgeting problems leads to a more complicated analytical approach. It is important that these complications be mastered because cap- ital budgeting decisions do lock in the organization to a course of action for several, perhaps many, future years.

Nature of the Problem

When an organization purchases a long-lived asset, it makes an investment similar to that made by a bank when it lends money. The essential characteristic of both types of transactions is that cash is committed today in the expectation of recovering that cash plus some additional cash in the future: The investor commits cash today with the ex- pectation of receiving both a return of the investment and a satisfactory return on the investment.

In the case of the bank loan, the return of investment is the repayment of the prin- cipal and the return on investment is the inflow of interest payments received over the life of the loan. In the case of the long-lived asset, both the return of investment and the return on investment are in the form of cash earnings generated by use of the asset. If, over the life of the investment, the inflows of cash earnings exceed the initial investment outlays, then we know that the original investment was recovered (return

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Chapter 27 Longer-Run Decisions: Capital Budgeting 841

of investment) and that some profit was earned (positive return on investment). Thus, an investment is the purchase of an expected future stream of cash inflows.

When an organization considers whether or not to purchase a new long-lived asset, the essential question is whether the future cash inflows are likely to be large enough to warrant making the investment. The problems discussed in this chapter all have this general form: A certain amount is proposed for investment now in the expectation that the investment will generate a stream of cash inflows in future years; are the anticipated future cash inflows large enough to justify investing funds in the proposal? Some il- lustrative problems are described here:

Replacement. Shall we replace existing equipment with more efficient equip- ment? The future expected cash inflows on this investment are the cost savings re- sulting from lower operating costs, or the profits from additional volume produced by the new equipment, or both. Expansion. Shall we build or otherwise acquire a new facility? The future expected cash inflows on this investment are the cash profits from the goods and services produced in the new facility. Cost reduction. Shall we buy equipment to perform an operation now done manually? That is, shall we spend money in order to save money? The expected future cash inflows on this investment are savings resulting from lower operating costs. Choice of equipment. Which of several proposed items of equipment shall we purchase for a given purpose? The choice often turns on which item is expected to give the largest return on the investment made in it. New product. Should a new product be added to the line? The choice turns on whether the expected cash inflows from the sale of the new product are large enough to warrant the investment in equipment, working capital, and the costs required to make and introduce the product.

General Approach

All these problems involve two quite dissimilar types of amounts. First, there is the in- vestment, which is usually made in a lump sum at the beginning of the project. Al- though not literally made today, it is made at a specific point in time that for analytical purposes is called today, or Time Zero. Second, there is a stream of cash inflows ex- pected to result from this investment over a period of future years.

These two types of amounts cannot be compared directly with one another because they occur at different times. To make a valid comparison, we must bring the amounts involved to equivalent values at the same point in time. The most convenient point is at Time Zero. We need not adjust the amount of the investment since it is already stated at its Time Zero (present) value. We need only to convert the stream of future cash in- flows to their present value equivalents so that we can then compare them directly with the amount of the investment.1

1 If the reader is not familiar with the concept of present value, the appendix to Chapter 8 (up to the section titled “Calculating Bond Yields”) should be read before continuing with this chapter. (As an aid to understanding, the calculations shown here are done manually. In practice, they are greatly simplified by the use of computers.)

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To do this, we multiply the cash inflow for each year by the present value of $1 for that year at the appropriate rate of return (Appendix Table A, page 893). This process is called discounting the cash inflows. The rate at which the cash inflows are discounted is called the required rate of return, the discount rate, or the hurdle rate. The difference between the present value of the cash inflows and the amount of investment is called the net present value (NPV). If the NPV is a nonnegative amount, the pro- posal is acceptable.

A proposed investment of $1,000 is expected to produce cash inflows of $625 per year for each of the next two years. The required rate of return is 14 percent. The present value of the cash inflows can be compared with the present value of the investment as follows:

Discount Total Factor Present

Year Amount (Table A) Value

Cash inflow 1 $ 625 0.877 $ 548 Cash inflow 2 625 0.769 481______ Present values of cash inflows 1,029

Less: Investment 0 1,000 1,000______ Net present value 1.000 $ 29____________

The proposed investment is acceptable.

The decision rule given above is a general rule, and some qualifications to it will be discussed later.

So far, we have shown how the net present value can be calculated if the investment, cash inflows, and the required rate of return are given. It is useful to look at the situa- tion from another viewpoint: How can the rate of return be calculated when the invest- ment and the cash inflows are given?

Consider a bank loan. Assume that a bank lends $25,000 and receives interest pay- ments of $2,500 at the end of each year for five years, with the $25,000 loan principal being repaid at the end of the fifth year. It is correct to say that the bank earned a return of 10 percent on its investment of $25,000. The return percentage is found by dividing the annual cash inflow by the amount of investment that was outstanding (i.e., unrecovered) during the year. In this case, the amount of loan outstanding each year was $25,000 and the cash inflow was $2,500 in each year, so the rate of return was $2,500 ? $25,000 ? 10 percent.

If, however, a bank lends $25,000 and is repaid $6,595 at the end of each year for five years, the problem of finding the return is more complicated. In this case, only part of each year’s $6,595 cash inflow represents the return on investment, and the remain- der is a repayment of the principal (return of investment). This is the same loan that was used in the Kinnear Company example in the appendix to Chapter 8. As was demon- strated there, this loan also has a return of 10 percent, in the same sense as did the loan described in the preceding paragraph: The $6,595 annual payments will recover the $25,000 loan investment and in addition will provide a return of 10 percent of the amount of unrecovered investment (principal still outstanding) each year. The fact that the return is 10 percent is demonstrated in Illustration 8–1. Of the $6,595 repaid in the first year, $2,500, or 10 percent of the $25,000 then outstanding, is the return; the

Net Present Value


Return on Investment

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Chapter 27 Longer-Run Decisions: Capital Budgeting 843

$4,095 remainder of the payment reduces the principal down to $20,905. In the second year, $2,091 is a return of 10 percent on the $20,905 of principal then outstanding, and the $4,504 remainder reduces the principal to $16,401. And so on.

As seen in the above example, when an investment involves annual interest payments with the full amount of the investment being recovered in a lump sum at the end of the investment’s life, the computation of the return is simple. But when the annual payments combine both principal and interest, the computation is more complicated. Some invest- ment problems are of the simple type. For example, if a business buys land for $25,000, rents it for $2,500 a year for five years, and then sells it for $25,000 at the end of five years, the return is 10 percent. Many capital investment decisions, on the other hand, re- late to depreciable assets, which characteristically have little or no resale value at the end of their useful life. The cash inflows therefore must be large enough for the investor both to recover the investment itself during its life and also to earn a satisfactory return on the amount not yet recovered, just as in the situation shown in Illustration 8–1.

Stream of Cash Inflows The cash inflows on most capital investments are a series of amounts received over sev- eral future years. Calculating the present value of a series, or stream, of cash inflows was explained in the appendix to Chapter 8. Recall that for a level stream (i.e., equal annual inflows), the factors in Appendix Table B on page 894 can be used.

Tables A and B are often used in combination, as shown in the next example. This example also demonstrates that the return on investment for the business renting its land, mentioned above, is indeed 10 percent.

A proposed investment of $25,000 is expected to generate annual cash inflows of $2,500 a year for the next five years, with the $25,000 to be recovered in a lump sum at the end of the fifth year. Is this proposal acceptable if the required rate of return is 10 percent?

As shown by the following calculation, the cash inflows discounted at 10 percent have a present value of $25,000, which is equal to the original investment. Thus, the investment’s return is 10 percent, and it is therefore acceptable.

10 Percent Year Inflow Discount Factor Present Value

1–5 $2,500/yr. 3.791 (Table B) $ 9,478 End of 5 $ 25,000 0.621 (Table A) 15,525________

Total present value $25,003*________________

* Would be $25,000 if discount factors included more decimal places.

Other Compounding Assumptions Tables A and B are constructed on the assumption that cash inflows are received once a year, on the last day of the year. For many problems, this is not a realistic assumption because cash in the form of increased revenues or lower costs is likely to flow in throughout the year. Nevertheless, annual tables are customarily used in capital invest- ment problems on the grounds that (1) they are easier to understand than tables con- structed on other assumptions, such as monthly or continuous compounding, and (2) they are good enough, considering the inevitable margin of error in the basic estimates.

Annual tables understate the present value of cash inflows if these inflows are, in fact, received throughout the year rather than entirely on the last day of the year. Tables


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are available showing the present values of earnings flows that occur quarterly, monthly, or even continuously.

The table below illustrates the degree to which annual tables understate the present value of inflows received during the year. The numbers in the table show the ratio of the present value of periodic, within-the-year receipts to the present value of an equal annual total re- ceived at the end of one year. For example, the table shows that if the discount rate is 10 percent and cash inflows are received continuously, then the use of a PV table that as- sumes year-end inflows will understate the present value of the inflows by 4.7 percent.

Frequency Discount Rates

of Inflow 6 Percent 10 Percent 15 Percent 25 Percent

Semiannually 1.014 1.023 1.032 1.049 Monthly 1.026 1.043 1.062 1.096 Continuously 1.029 1.047 1.068 1.106

Estimating the Variables

We now discuss how to estimate each of the five elements involved in capital invest- ment calculations. These are

1. Required rate of return. 2. Economic life (number of years for which cash inflows are anticipated). 3. Amount of cash inflow in each year. 4. Amount of investment. 5. Terminal value.

Two alternative ways of arriving at the required rate of return—trial and error, and cost of capital—will be described here.

Trial and Error Recall that the higher the required rate of return, the lower the present value of the cash inflows. It follows that the higher the required rate of return, the fewer the in- vestment proposals that will have cash inflows whose present value exceeds the amount of the investment. Thus, if a given rate results in the rejection of many pro- posed investments that management intuitively feels are acceptable, or if not enough proposals are being sent to senior management for final approval, the indication is that this rate is too high. Conversely, if a given rate results in senior management’s re- ceiving a flood of project proposals, the indication is that the rate is too low. As a starting point in this trial-and-error process, a company may select a rate that other companies in the same industry use.

Cost of Capital In economic theory, the required rate of return should be equal to the company’s cost of capital. This is the cost of debt capital plus the cost of equity capital, weighted by the relative amount of each in the company’s capital structure.


Required Rate of Return

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Chapter 27 Longer-Run Decisions: Capital Budgeting 845

Assume a company in which the cost of debt capital (e.g., bonds) is 5 percent, the cost of equity capital (e.g., common stock) is 15 percent, 30 percent of the total capital is debt, and 70 percent of capital is equity. The cost of capital is calculated as follows:

Type Capital Cost Weight Weighted Cost

Debt (bonds) 5% 0.3 1.5% Equity (stock) 15 0.7 10.5___ ____

Total 1.0 12.0%________

In the example, the 5 percent used as the cost of debt capital may appear to be low. It is low because it has been adjusted for the income tax effect of debt financing. Since in- terest on debt is a tax-deductible expense, each additional dollar of interest expense ul- timately costs the company only $0.60 (assuming a tax rate of 40 percent) because income taxes are reduced by $0.40 for each additional interest dollar. For reasons to be explained, capital investment calculations should be made on an after-tax basis, so the rate of return should be an after-tax rate.

The problem with the cost-of-capital approach is that, although the cost of debt is usually known within narrow limits, the cost of equity is difficult to estimate. Concep- tually, the cost of equity capital is the rate of return that equity investors expect to earn on their investment in the company’s stock. These expectations are reflected in the stock’s market price. Unfortunately, getting from the concept of the cost of equity to a specific number can be a difficult trip. Some companies use the capital asset pricing model (CAPM) to make the estimate. This method, the use of which requires that the company’s shares be publicly traded, is described in finance texts. Suffice it to say here that the cost of equity capital is an estimate, and, unless the company’s stock is actively traded, the estimate is quite imprecise.2

Selection of a Rate Most companies use a judgmental approach in establishing the required rate of return. Either they experiment with various rates by the trial-and-error method described above or they judgmentally settle on a rate because they feel elaborate calculations are likely to be fruitless.

The required rate of return selected by the methods described above applies to in- vestment proposals of average risk. (Average here refers to the risk of all of the firm’s existing investments considered as a whole.) In general, the return demanded for an in- vestment varies directly with the investment’s risk. Thus, the required return for an individual investment project of greater-than-average risk should be higher than the average rate of return on all projects. Conversely, a project with below-average risk should have a lower required rate.

Effect of Nondiscretionary Projects Some investments are made to meet environmental, health, and safety requirements or to enhance employee wellness and satisfaction rather than based on an analysis of their profitability. These are often classified as necessity projects. Examples include pollution-control equipment, installation of devices to protect employees from injury,


2 For regulated public utilities, the cost of equity capital is treated as a cost that a utility is allowed to recover, along with operating costs and interest, through the rates the utility charges its customers. In rate hearings conducted by public utility commissions, the cost of equity is always an issue, with each side’s expert witnesses supporting different numbers as being correct.

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and in-company day care and recreational facilities. These investments use capital but provide no readily identifiable cash inflows. Thus, if the other, profit-enhancing discre- tionary investments had a net present value of zero when discounted at the cost of cap- ital, the company would not recover all of its capital costs. The discretionary projects not only must stand on their own feet but also must carry the capital-cost burden of the nondiscretionary (i.e., necessity) projects. For this reason, many companies use a required rate of return that is higher than the cost of capital.

Zelph Company typically has $10 million invested in capital projects, 20 percent of which represents necessity projects. If Zelph’s cost of capital is 12 percent, its capital projects must earn $1.2 million per year in addition to recovering the amount invested. The $8 million of discretionary projects must therefore earn 15 percent, not 12 percent (because $8 million * 0.15 ? $1.2 million). Even the 15 percent is an understatement, because the $2 million capital invested in the necessity projects also must be recovered.

The economic life of an investment is the number of years over which cash inflows are expected as a consequence of making the investment. Even though cash inflows may be expected for an indefinitely long period, the economic life is usually set at a speci- fied maximum number of years, such as 10, 15, or 20. This maximum is often shorter than the life actually anticipated both because of the uncertainty of cash inflow esti- mates for distant years and because the present value of cash inflows for distant years is so low that the amount of these cash inflows has no significant effect on the calcula- tion. For example, at a discount rate of 12 percent, a $1 cash inflow in year 21 has a pre- sent value of only 9.3 cents.

The end of the period selected for the economic life is called the investment hori- zon, which suggests that beyond this time cash inflows are not visible. Economic life can rarely be estimated exactly. Nevertheless, it is important that the best possible es- timate be made, for the economic life has a significant effect on the calculations.

When a proposed project involves the purchase of equipment, the economic life of the investment corresponds to the estimated service life of the equipment to the user. When thinking about the life of equipment, there is a tendency to consider primarily its physical life—the number of years until the equipment wears out. Although the physical life is an upper limit, in most cases the economic life of the equipment is considerably shorter than its physical life. The primary reason is that technological progress makes equipment obsolete and the investment in the equipment will cease to earn a return when it is replaced by even better equipment. (Computers provide an extreme example.)

The economic life also ends when the entity ceases to make profitable use of the equipment. This can happen because the operation performed by the equipment is made unnecessary by a change in style or process, because the market for the product made with the equipment has vanished, or because the entity decides (for whatever reason) to discontinue the product.

The key question is: Over what period of time is the investment likely to generate cash inflows for this entity? When the investment no longer produces cash inflows, its economic life has ended. In view of the uncertainties associated with the operation of an organization, most managers are conservative in estimating what the economic life of a proposed investment will be.

The earnings from an investment are the additional amounts of cash expected to flow in as a consequence of making the investment as compared with what the cash inflows would be if the investment were not made. The differential concept emphasized in the preceding chapter is therefore equally applicable here, and the discussion in that


Economic Life

Cash Inflows

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Chapter 27 Longer-Run Decisions: Capital Budgeting 847

chapter should carefully be kept in mind in estimating cash inflows for the type of problem now being considered. In particular, recall that the focus is on cash inflows. Accounting numbers based on the accrual concept are not necessarily relevant.

Consider, for example, a proposal to replace existing equipment with better equip- ment. What are the cash inflows associated with this proposal? First, the existing equipment must still be usable. If it no longer works, there is no alternative and hence no analytical problem; it must be replaced. The comparison, therefore, is between (1) continuing to use the existing equipment (the base case) and (2) investing in the proposed equipment. The existing equipment has certain labor, material, power, repair, and other costs associated with its future operation. If the new equipment is proposed as a means of reducing costs, there will be different, lower costs associated with its use. The difference between these two amounts of cost is the cash inflow anticipated if the new equipment is acquired. (Note that in this example, the differential cash inflow is really a reduction in cash outflows.)

If the proposed equipment is not a replacement but instead increases productive ca- pacity, the differential income from the higher sales volume is a cash inflow anticipated from the use of the proposed equipment. This differential income is the difference be- tween the added sales revenue and the additional costs required to produce that sales revenue. These differential costs include any material, labor, selling costs, or other costs that would not be incurred if the increased volume were not produced and sold.

Often a project’s cash flows can be analyzed with an implicit base case of the status quo, but this is not always a valid approach. For example, if a company chooses not to invest in more modern equipment, it may lose market position to competitors who are investing in such equipment. In this instance, the base case will involve a worsening of present results rather than a level continuation of them. Thus, the cash flow analysis of the investment must be done carefully to ensure that the differential flows in fact reflect the difference between a “better future” (if the investment is made) and a “deteriorat- ing past” (if it is not made).

Inflation If inflation is expected to continue in future years, the purchasing power of a $1 cash inflow decreases as the length of time until the inflow will be received increases. The question arises as to whether future inflows should therefore be restated in terms of current (Time Zero) purchasing power before discounting them. In general, the answer is no. This is because the discount rate already includes an inflation component: The discount rate is higher if inflation is expected than the rate would be if there were no expectations of future inflation. The rate is higher either because (1) management in- tentionally increases the rate to account for future inflation or (2) the company’s cost of capital reflects the financial markets’ inflation expectations (e.g., bond interest rates are higher in inflationary periods than in periods of stable prices).3

Depreciation Depreciation on the proposed equipment is not an item of differential cost. In capital in- vestment problems, we are analyzing cash flows. The cash flow associated with acqui- sition of equipment is an outflow at Time Zero. This cash outflow is the amount of the investment against which the present value of the expected future cash inflows is

3 If the cash flows being discounted are expressed in constant-dollar terms, it is important that the discount rate not include an element for inflation (or an inflation premium as it is called in some finance texts). Otherwise the cash flows would be doubly discounted for inflation, and the net present value would be understated.

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compared. Because of the matching concept, accrual accounting capitalizes this initial cost as an asset and then uses a depreciation method to charge this cost systematically to the periods in which the asset is used. Recall that the accounting entry to record de- preciation (dr. Depreciation Expense, cr. Accumulated Depreciation) has no impact on cash. Not only do these depreciation entries not affect cash; to treat them as outflows would result in double-counting the cost of the equipment in the present value analysis.

Depreciation on the existing equipment is likewise not relevant because the book value of existing equipment represents a sunk cost. For the reason explained in Chapter 26, sunk costs should be disregarded.

Income Tax Impact For alternative choice problems in which no investment is involved, after-tax income is 60 percent of pretax income, assuming a tax rate of 40 percent.4 Thus, if a proposed cost-reduction method is estimated to save $10,000 a year pretax, it will save $6,000 a year after tax. Although $6,000 is obviously not as welcome as $10,000 would be, the proposed cost-reduction method would increase income; in the absence of arguments to the contrary, the decision should be made to adopt it.This is the case with all the alternative choice problems discussed in Chapter 26: If the proposal is acceptable on a pretax basis, it is also acceptable on an after-tax basis.

When depreciable assets are involved in a proposal, however, the situation is quite different. In proposals of this type, there is no simple relationship between pretax cash inflows and after-tax cash inflows. This is the case because, although depreciation is not a factor in estimates of operating cash flows, it does affect the calculation of tax- able income; thus, it affects cash outflows because it affects the amount of tax pay- ments. Because depreciation offsets part of what would otherwise be additional taxable income, it is called a tax shield. Depreciation “shields” the pretax cash inflows from the full impact of income taxes.

To calculate the after-tax cash inflows, we must take account of this depreciation tax shield. At the same time, for the reasons given above, we must be careful not to permit the amount of depreciation itself to enter into the calculation of cash flows. Illustration 27–1 shows a net present value calculation including the tax shield.

At times, under specified conditions, income tax regulations permit a company to take an investment tax credit (ITC) when it purchases new machinery or equipment or makes certain other types of investments. Currently, companies can reduce their tax- able income by making expenditures for certain socially desirable purposes, such as construction of low-income housing, access for disabled persons, and empowerment zones. These credits also should be taken into account in calculating after-tax income.

Accelerated Depreciation For simplicity the example in Illustration 27–1 assumed straight-line depreciation. In fact, most companies use accelerated depreciation5 in calculating taxable income because it increases the present value of the deprecia- tion tax shield. Because accelerated depreciation results in nonlevel amounts of tax- able income from year to year, Table B (which assumes a level flow each year) cannot be used in calculating present values. Instead, one must compute the after-tax income each year and find the present value of each annual amount by using Table A.

4 As of 1997, the effective federal tax rate on corporations with $18.3 million or more taxable income was 35 percent. (The other extreme of the graduated rate structure was a 15 percent rate for compa- nies earning up to $50,000 pretax.) In examples in this book, we use a 40 percent tax rate because (a) it makes illustrative calculations simpler to understand than would using 35 percent and (b) many corporations pay state and/or local taxes on income that raise their overall rate to around 40 percent. 5 U.S. tax laws use the term accelerated cost recovery rather than accelerated depreciation.

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Chapter 27 Longer-Run Decisions: Capital Budgeting 849

Differential Depreciation If the proposed asset is to replace an asset that has not been fully depreciated for tax purposes, then the tax shield is based on only the differential depreciation—the difference between depreciation on the present asset and that on the new one. If the new asset is purchased, the old one will presumably be disposed of, so its depreciation will no longer provide a tax shield to the operating cash flows. In this case, the present value of the tax shield of the remaining depreciation on the old asset must be calculated (usually year by year), and this amount must be subtracted from the present value of the depreciation tax shield on the proposed asset.

Tax Effect of Interest Interest actually paid (as distinguished from imputed interest) is an allowable expense for income tax purposes. Therefore, if interest costs will be increased as a result of the investment, it can be argued that interest provides a tax shield similar to depreciation and that its impact should be estimated by the same method as for depreciation. Cus- tomarily, however, interest is not included anywhere in the calculations of either cash inflows or taxes. This is because the calculation of the required rate of return includes an allowance for the tax effect of interest: The estimate of the cost of debt is the after- tax cost of debt.

In problems where the method of financing is an integral part of the proposal, the tax shield provided by interest may appropriately be considered. In these problems, the rate of return in the calculation is a return on the part of the investment that was financed by the shareholders’ equity, not a return on the total funds committed to the investment.

A company is considering an investment in a parcel of real estate and intends to finance 70 per- cent of the investment by a mortgage loan on the property. It may wish to focus attention on the return on its own funds, the remaining 30 percent. In this case, it is appropriate to include in the calculation both the interest on the mortgage loan and the effect of this interest on tax- able income. The rationale is that these debt funds—the mortgage—would not have been avail- able to the company were it not investing in the real estate.6

Assumed situation: A proposed machine costs $10,000 and will provide estimated pretax cash inflows of $3,500 per year for five years. The required rate of return is 12 percent, the tax rate is 40 percent, and straight-line depreciation is used.

Taxable Income Present Value Calculation Calculation

Annual pretax cash inflow $3,500 $ 3,500 Less: Additional depreciation ?2,000______

Differential taxable income 1,500 Differential income tax ($1,500 * 40%) ?600_______ After-tax annual cash inflow 2,900_______ Present value of $2,900 over 5 years (factor ? 3.605) 10,455

Less: Investment 10,000_______ Net present value $ 455______________

The proposal is acceptable.

ILLUSTRATION 27–1 Calculation of Net Present Value with Tax Shield

6 Technically, this recognition of the tax effect of interest also assumes that the project-related debt (the mortgage loan, in the example) will not increase the perceived overall riskiness of the company and hence will not cause an increase in its overall cost of capital.


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The investment is the amount of funds an entity risks if it accepts an investment pro- posal. The relevant investment costs are the differential costs—the cash outlays that will be made if the project is undertaken but that will not be made if it is not under- taken. The cost of the asset itself, any shipping and installation costs, and costs of train- ing employees in the use of the new asset are examples of differential investment costs. These outlays are part of the investment, even though some of them may not be capi- talized (treated as assets) in the accounting records.

Existing Assets If the purchase of a new asset results in the sale of an asset, the net proceeds from the sale reduce the amount of the differential investment. In other words, the differential investment represents the total amount of additional funds that must be committed to the investment project. The net proceeds from the existing asset are its selling price less any costs incurred in selling it and in dismantling and removing it, and adjusted for any income tax effects (described below).

Investments in Working Capital Although our examples of investments thus far have been fixed assets, an investment ac- tually is the commitment, or long-term locking up, of funds in any type of asset. Thus, investments include long-term commitments of funds to finance additional inventories, receivables, and other current assets. In particular, if new equipment is acquired to pro- duce a new product, additional funds will probably be required for inventories, accounts receivable, and increased cash needs. Part of this increase in current assets may be fi- nanced by increased accounts payable; the remainder of the financing must come from permanent capital. This additional working capital is as much a part of the Time Zero differential investment as is the capital required to finance the equipment itself.7

Deferred Investments Many projects involve a single commitment of funds at one moment of time, which we have called Time Zero. For some projects, on the other hand, the commitments are spread over a considerable period of time. The construction of a new facility may re- quire disbursements over several years, or a proposal may involve the construction of one unit of a facility now and a second unit several years later. To make the present value calculations, these investments must be brought to a common point in time. This is done by the application of discount rates to the amounts of cash outflow involved. In general, the appropriate rate depends on the uncertainty that the investment will be made; the lower the uncertainty, the lower the rate. Thus, if the commitment is a definite one, the discount rate may be equivalent to the interest rate on high-grade bonds (which also rep- resent a definite commitment). If, however, the future investments will be made only if earnings materialize, then the rate can be the required rate of return.

Capital Gains and Losses When existing equipment is replaced by new equipment, the transaction may give rise to either a gain or loss, depending on whether the amount realized from the sale of the existing equipment is greater or less than its net book value. (If the new equipment is “of a like kind” to the equipment to be replaced, no gain or loss is recognized for tax purposes.) These gains or losses are taxed at the company’s ordinary income tax rate.


7 In Chapter 26, the differential investment in current assets was assumed to be for a short term; thus, it was assumed that short-term debt rather than permanent capital would be used to finance differ- ential current assets. The cost of this short-term debt is one element of the differential holding costs that were described in that chapter.

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When existing assets are disposed of, the relevant amount by which the new investment is reduced is the net proceeds of the sale—the sale proceeds adjusted for the tax impact associated with the disposal. The adjustment will be downward if there is a gain, since the gain will create an additional tax outflow. Conversely, a loss will result in an up- ward adjustment of the sale proceeds.

A project may have a value at the end of its time horizon. This terminal value is a cash inflow at that time.8 In the analysis of the project, the discounted amount of the termi- nal value is added to the present value of the other cash inflows. Several types of ter- minal value are described in the following paragraphs.

Residual Value A proposed asset may have a residual value (i.e., salvage or resale value) at the end of its economic life. In many cases, the estimated residual value is so small and occurs so far in the future that it has no significant effect on the decision. Moreover, any salvage or resale value realized may be approximately offset by removal and dismantling costs. In situations where the estimated residual value is significant, the net residual value (after removal costs and any tax effect from a capital gain or loss) is viewed as a cash inflow at the time of disposal and is discounted along with the other cash inflows.

Acquisitions and New Products If one company acquires another, it usually expects its investment in the acquired com- pany to produce a stream of cash inflows for an indefinitely long period. This also may be true with an investment in development of a new product. However, the estimates of cash inflows in later years are so speculative that many companies arbitrarily set the economic life of such a project at 10 years (5 in some companies).

After economic life is set, there is the problem of estimating terminal value. One ap- proach to this problem is to assume that the acquired company or the new product is sold to another party on the assumed terminal date. Since the new buyer would be buy- ing a stream of future cash inflows, the price could be arrived at by estimating the value of these cash flows, perhaps by applying a multiple to the cash flows of the terminal year. This selling price is then discounted, using the appropriate factor from Table A.

Working Capital Often, the terminal value of investments in current assets is reasonably assumed to be approximately the same as the amount of the initial investment in them. That is, it is as- sumed that at the end of the project, these items can be liquidated at their original cost. (This cost can be adjusted upward if inflation is expected to increase the investment in working capital over the life of the project.) The amount of terminal current assets, net of any related accounts payable settlements, is treated as a cash inflow in the last year of the project, and its present value is found by discounting that amount at the required rate of return.

The quantitative analysis involved in a capital investment proposal does not provide the complete solution to the problem because it encompasses only those elements that can be reduced to numbers. As was true for the short-term alternative choice problems in the preceding chapter, a full consideration of the problem involves evaluating the non- monetary factors.

Terminal Value

8 In some instances, there is an additional outlay at the end of the project horizon. A notable example is the cost of decommissioning a nuclear power plant, which is hundreds of millions of dollars.

Nonmonetary Considerations

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Many investments are undertaken without a calculation of net present value. The ne- cessity projects described earlier are a major example. For some of these, no economic analysis is necessary; if an unsafe condition is found, it must be corrected regardless of the cost. For many capital expenditure proposals in the research/development and general/administrative areas, no reliable estimate of increased revenues or decreased costs can be made, so the approach described here is not feasible.9

Even if the proposal is amenable to a quantitative analysis, the result is, at most, a guide to the decision maker. Other factors must be considered in arriving at the final decision, and, in some cases, their importance overwhelms the quantitative analysis. Among these factors are the following:

• The person proposing the project wants it to be approved and therefore may give op- timistic estimates of the numbers. Unless the person has a prior track record of such bias, it is difficult to detect.

• The status quo alternative may be incorrectly stated. For example, it may implicitly be assumed that if a proposal for a new process is rejected, the sales of the products made with the existing process will continue as is. However, failure to make the investment may cause the company’s market position to deteriorate: Competitors are making such investments, and the resulting better quality or customer responsiveness will cause the company’s sales to decline if it does not make similar investments.

• Training costs and start-up costs associated with some new technology may be in- cluded in their entirety in the first proposal that will benefit from them, when in fact these costs will benefit similar follow-on projects in the future. This causes a nega- tive bias in the analysis of the initial project and may suggest postponing invest- ments that are in fact needed to remain competitive.

• On the other hand, a project proposal may have its scope—and hence its costs— understated in order to stay below the investment threshold where board of directors approval is required. This foot-in-the-door tactic often involves one or more follow- on proposals needed to complete the original proposal’s partial solution.

• The proposal may overlook increases in “hidden” costs (usually step-function costs) that will result from the increased workload the project will create in various sup- port departments. (The “just one” paradox described in Chapter 26 applies to capi- tal investment proposals as well.)

• An investment project may provide difficult-to-foresee values that would not be avail- able if the project was not taken. For example, a research exploration into a new, unproven area of technology might provide learning that makes new applications pos- sible. These new possibilities can arise even when the original project is deemed a failure in a narrow sense, in that the projected cash flows were not forthcoming as planned.This realization changes the concept of “failure.” Some companies are trying to quantify the values of the real options that might be created using option-pricing models developed in finance theory.10 In a standard discounted cash flow analysis, high uncertainty reduces the present value of the expected future cash flows. But with option-pricing models, high uncertainty increases the value of the investment.

9 Based on a survey of 100 large industrial companies, Thomas Klammer et al. reported that only 45 percent of respondents used discounting techniques for general and administrative costs, and only 8 percent used these techniques for “social expenditures.” See “Capital Budgeting Practices—A Survey of Corporate Use,” Journal of Management Accounting Research, Fall 1991, pp. 120–21. 10 T. Copeland and P. Tufano, “A Real World Way to Manage Real Options.” Harvard Business Review, March 2004, pp. 90–99.

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In sum, the techniques described in this chapter are by no means the whole story of capital budgeting decisions. They are, however, the only part of the story that can be described as a definite procedure; the remainder generally is learned only through experience.

Following is a summary of the previous presentation of the steps involved in using the net present value method in analyzing a proposed investment:

1. Select a required rate of return. This rate applies to projects deemed to be of aver- age risk and may be adjusted for a specific proposal whose risk is felt to be above or below average.

2. Estimate the economic life of the proposed project. 3. Estimate the differential cash inflows for each year during the economic life, being

careful that the base case is properly defined and quantified. 4. Find the net investment, which includes the additional outlays made at Time Zero,

less the proceeds (adjusted for tax effects) from disposal of existing equipment and the investment tax credit, if any.

5. Estimate the terminal values at the end of the economic life, including the residual value of equipment and current assets that will be liquidated.

6. Find the present value of all the inflows identified in steps 3 and 5 by discounting them at the required rate of return, using Table A (for single annual amounts) or Table B (for a series of equal annual flows).

7. Find the net present value by subtracting the net investment from the present value of the inflows. If the net present value is zero or positive, decide that the proposal is acceptable insofar as the monetary factors are concerned.

8. Taking into account the nonmonetary factors, reach a final decision. (This part of the process is at least as important as all the other parts put together, but there is no way of generalizing about it.)

As an aid to visualizing the relationships in a proposed investment, a diagram of the flows similar to that shown in Illustration 27–2 can be useful.

Other Methods of Analysis

So far, we have limited the discussion of techniques for analyzing capital investment proposals to the net present value (NPV) method. We shall now describe three alter- native ways of analyzing a proposed capital investment: (1) the internal rate of return method, (2) the payback method, and (3) the unadjusted return on investment method.

When the NPV method is used, the required rate of return must be selected in advance of making the calculations because this rate is used to discount the cash inflows in each year. As already pointed out, the choice of an appropriate rate of return is a difficult matter. The internal rate of return (IRR) method avoids this difficulty. It computes the rate of return that equates the present value of the cash inflows with the present value of the investment—the rate that makes the NPV equal zero. This rate is called the

Summary of the Analytical Process

Internal Rate of Return Method

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internal rate of return, or the discounted cash flow (DCF) rate of return. (The IRR method is sometimes called the DCF method.)11

Level Inflows If the cash inflows are level (the same amount each year), the computation is simple. It will be illustrated by a proposed $1,200 investment with estimated cash inflow of $400 a year for four years. The procedure is as follows:

1. Divide the investment, $1,200, by the annual inflow, $400. The result, 3.0, is called the investment/inflow ratio.

0 1 2 3


4 5








Outflows (investment)

ILLUSTRATION 27–2 Cash Flow Diagram

0 1 2 3 4 5

Economic life HorizonTime zero

$8,000 1,500 (500)


Cost Installation Sale of old

Total investment




$ 362

Residual value, year 5

Present value of:

Cash outflows:

Cash inflows: Earnings Year

Total inflows

Difference = Net present value

1 2 3 4 5

2,500 2,500

2,500 2,500 1,500

Discounted at 14%

(2,500 * 3.433) (1,500 * 0.519)


11 A survey of practice found that 75 percent of Fortune 500 firms use NPV or IRR techniques in their capital budgeting analyses. Smaller firms are more likely to use the payback technique (described below). See J. R. Graham and C. R. Harvey, “The Theory and Practice of Corporate Finance: Evidence from the Field,” Journal of Financial Economics 60 (2001), pp. 187–243.

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2. Look across the four-year row of Table B. The column in which the figure closest to 3.0 appears shows the approximate rate of return. Since the closest figure is 3.037 in the 12 percent column, the return is approximately 12 percent.

3. If management is satisfied with a return of approximately 12 percent, then it should accept this project (aside from qualitative considerations). If it requires a higher re- turn, it should reject the project.

The number 3.0 in the above example is simply the ratio of the investment to the an- nual cash inflows. Each number in Table B shows the ratio of the present value of a stream of cash inflows to an investment of $1 made today, for various combinations of rates of return and numbers of years. The number 3.0 opposite any combination of year and rate of return means that the present value of a stream of inflows of $1 a year for that number of years discounted at that rate is $3. The present value of a stream of in- flows of $400 a year is in the same ratio; therefore, it is $400 times 3, or $1,200. If the number is more than 3.0, as is the case with 3.037 in the example above, then the re- turn is correspondingly more than 12 percent.

In using Table B in this method, it is usually necessary to interpolate—to estimate the location of a number that lies between two numbers in the table. There is no need to be precise about these interpolations because the final result can be no better than the basic data, which are ordinarily only rough estimates. A quick interpolation made visually is usually as good as the accuracy of the data warrants. However, widely used computer programs calculate the IRR exactly.

Uneven Inflows If cash inflows are not the same in each year, the IRR must be found by trial and error. The cash inflows for each year are listed, and various discount rates are applied to these amounts until a rate is found that makes their total present value equal to the present value of the investment. This rate is the internal rate of return. This trial-and-error process can be quite tedious if the computations are made manually; in practice, com- puter programs and calculators perform the calculations quickly.

The number referred to above as the investment/inflow ratio is also called the payback period because it is the number of years over which the investment outlay will be re- covered (paid back) from the cash inflows if the estimates turn out to be correct. That is, the project will pay for itself in this number of years. If a machine costs $1,200 and generates cash inflows of $400 a year, it has a payback of three years.

The payback method is often used as a quick but crude method for appraising pro- posed investments. If the payback period is equal to, or only slightly less than, the eco- nomic life of the project, then the proposal is clearly unacceptable. If the payback period is considerably less than the economic life, then the project begins to look attractive.

If several investment proposals have the same general characteristics, then the pay- back period can be used as a valid way of screening out the unacceptable proposals. For example, if a company finds that equipment ordinarily has a life of 10 years and if it re- quires a return of at least 15 percent, then the company may specify that new equip- ment will be considered for purchase only if it has a payback period of 5 years or less. This is because Table B shows that a payback period of 5 years is equivalent to a return of approximately 15 percent if the life is 10 years.

The danger of using payback as a criterion is that it gives no consideration to dif- ferences in the length of the estimated economic lives of various projects. There may be a tendency to conclude that the shorter the payback period, the better the project.

Payback Method

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However, a project with a long payback may actually be better than a project with a short payback if it will produce cash inflows for a much longer period of time. Also, the payback method makes no distinction between projects whose entire investment is made at Time Zero and those for which the investment is incurred over a period of several years.

Discounted Payback Method A more useful and more valid form of the payback method is the discounted payback method. In this method, the present value of each year’s cash inflows is found, and these are cumulated year by year until they equal or exceed the amount of investment. The year in which this happens is the discounted payback period. A discounted pay- back of five years means that the total cash inflows over a five-year period will be large enough to recover the investment and to provide the required return on investment. If the decision maker believes that the economic life will be at least this long, then the proposal is acceptable.

The unadjusted return on investment method computes the net income expected to be earned from the project each year, in accordance with the principles of accrual ac- counting, including a provision for depreciation expense. The unadjusted return on investment is found by dividing the annual net income either by the amount of the in- vestment or by one-half the amount of investment. (One-half of the investment is used on the premise that over the entire life of the project, an average of one-half the initial investment is outstanding because the investment is at its full amount at Time Zero and shrinks gradually to nothing by its terminal year.) This method is also referred to as the accounting rate of return method.

Since depreciation expense in accrual accounting provides, in a sense, for the re- covery of the cost of a depreciable asset, one might suppose that the return on an in- vestment could be found by relating the investment to its accrual accounting income after depreciation; but such is not the case. Earlier, we showed that an investment of $1,200 with cash inflows of $400 a year for four years has a return of 12 percent. In the unadjusted return method, the calculation would be as follows (ignoring taxes):

Gross earnings $400 Less depreciation (1⁄4 of $1,200) 300_____ Net income $100__________

Dividing net income ($100) by the investment ($1,200) gives an indicated return of 81⁄3 percent. But we know this result is incorrect: The true return is 12 percent. If we di- vide the $100 net income by one-half the investment ($600), the result is 162⁄3 percent, which is also incorrect.

This error arises because the unadjusted return method makes no adjustment for the differences in present values of the inflows of the various years. It treats each year’s in- flows as if they were as valuable as those of every other year, whereas the prospect of an inflow of $400 next year is actually more attractive than the prospect of an inflow of $400 two years from now, and the latter $400 is more attractive than the prospect of an inflow of $400 three years from now.

The unadjusted return method, based on the gross amount of the investment, will al- ways understate the true return. The shorter the time period involved, the more serious

Unadjusted Return on Investment Method

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is the understatement. If the return is computed by using one-half the investment, the result is always an overstatement of the true return. A method that does not consider the time value of money cannot produce an accurate result.

Despite the conceptual superiority of the methods that involve discounting, surveys show that the payback and unadjusted return methods are widely used in practice. Sur- veys also show that most companies use two or more methods in their investment proposal analyses—and the larger the company’s annual capital budget, the greater the variety of techniques used.12

Several factors explain the use of decision criteria that do not involve discounting. First, some corporate managers tend to be concerned about the short-run impact a proposed project would have on corporate profitability as reported in the published financial statements. Thus, a project acceptable according to the NPV criterion may be rejected because it will reduce the company’s reported net income and accounting return on investment (ROI) in the first year or two of the project. If management believes that the accounting ROI is used by securities analysts in evaluating a company’s securities, management may use the unadjusted return method as one of its decision criteria.

The manager of a profit center may have similar concerns. If the manager feels that his or her career advancement is related to near-term profitability of the profit center, then a proposal that would have an adverse short-run impact on those profits may never be submitted to corporate headquarters. This is particularly likely to happen if the man- ager has incentive compensation tied to the profit center’s short-term profitability. In this regard, one must remember that people generate capital budgeting proposals; these proposals do not magically materialize on their own.

Another factor explaining why projects that have an acceptable NPV or IRR are sometimes rejected (or not even proposed) is managers’ risk aversion. Although a given proposal may constitute an acceptable gamble from an overall company point of view, a manager may fear being penalized if the project does not work out as anticipated.13

Risk aversion probably explains the widespread use, despite its conceptual flaws, of the payback criterion. If Project A has an estimated IRR of 20 percent and a pay- back of eight years whereas Project B’s estimated IRR is 15 percent and its payback is three years, the profit center manager may well prefer Project B. Project A’s time horizon is long, increasing the uncertainty of the estimates made in calculating its IRR. Moreover, it will be a number of years until it is known for sure whether A was a good investment. By eight years from now, the manager hopes to have been pro- moted at least once, and some unknown successor will reap most of Project A’s bene- fits. But Project B can make the manager look good in the near term and help him or her to be promoted.

In sum, factors other than the true economic return (i.e., IRR) of a project greatly— and understandably—influence whether a project is approved and even whether the project is formally proposed to top management.

12 Klammer et al. (see footnote 9) report that, for expansion projects, 87 percent of the firms used the results of a discounting technique as their primary quantitative criterion. Of these, about two- thirds used IRR and one-third used NPV as the primary technique. Most firms used more than one technique. 13 Many studies have demonstrated that most people (with the notable exception of compulsive gamblers) are risk averse. One elegant study has even concluded that bumblebees are risk averse! (See Leslie A. Real, “Animal Choice Behavior and the Evolution of Cognitive Architecture,” Science, August 30, 1991, pp. 980–86.)

Multiple Decision Criteria

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Preference Problems

There are two classes of investment problems: screening problems and preference problems. In a screening problem, the question is whether or not to accept a proposed investment. The discussion so far has been limited to this class of problem. Many indi- vidual proposals come to management’s attention; by the techniques described above, those that are worthwhile can be screened out from the others.

In preference problems (also called ranking, or capital rationing, problems), a more difficult question is asked: Of a number of proposals, each of which has an adequate re- turn, how do they rank in terms of preference? If not all the proposals can be accepted, which ones are preferable? The decision may merely involve a choice between two competing proposals, or it may require that a series of proposals be ranked in order of their attractiveness. Such a ranking of projects is necessary when there are more worth- while proposals than funds available to finance them, which is often the case.

Both the IRR and NPV methods are used for preference problems. If the internal rate of return method is used, the preference rule is as follows: The higher the IRR, the bet- ter the project. A project with a return of 20 percent is said to be preferable to a project with a return of 18 percent, provided that the projects are of equal risk. If the projects entail different degrees of risk, then judgment must be used to decide how much higher the IRR of the more risky project should be.

If the net present value method is used, the present value of the cash inflows of one project cannot be compared directly with the present value of the cash inflows of an- other unless the investments are of the same size. Most people would agree that a $1,000 investment that produced cash inflows with a present value of $2,000 is better than a $1,000,000 investment that produces cash inflows with a present value of $1,001,000, even though they each have an NPV of $1,000. In order to compare two proposals under the NPV method, therefore, we must relate the size of the discounted cash inflows to the amount of money risked. This is done simply by dividing the pre- sent value of the cash inflows by the amount of investment, to give a ratio that is called the profitability index. Thus, a project with an NPV of zero has a profitability index of 1.0. The preference rule is: The higher the profitability index, the better the project.

Conceptually, the profitability index is superior to the internal rate of return as a device for ranking projects. One reason is that higher discount rates will have been used in discounting the cash flows of more risky projects; thus, no judgmental adjustment of the profitability index ranking must be made. (Of course, deciding how much higher a discount rate to use was judgmental.) Also, the IRR method will not always give the correct preference between two projects with different lives or with different patterns of earnings.

Proposal A involves an investment of $1,000 and a cash inflow of $1,200 received at the end of one year; its IRR is 20 percent. Proposal B involves an investment of $1,000 and cash inflows of $305 a year for five years; its IRR is only 16 percent. But Proposal A is not neces- sarily preferable to Proposal B. Proposal A is preferable only if the company can expect to earn a high return during the following four years on some other project in which the funds released from A at the end of the first year are reinvested. Otherwise, Proposal B, which earns 16 percent over the whole five-year period, is preferable.

Criteria for Preference Problems

Comparison of Preference Rules


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The incorrect signal illustrated in this example is not present in the profitability index method. Assuming a discount rate of 12 percent, the two proposals described above would be analyzed as follows:

(c) (a) (b) Present

Cash Discount Value (d) Index Proposal Inflow Factor (a) * (b) Investment (c) ? (d)

A $1,200–1 yr. 0.893 $1,072 $1,000 1.07 B 305–5 yrs. 3.605 1,100 1,000 1.10

The profitability index signals that Proposal B is better than Proposal A. This is, in fact, the case if the company can expect to reinvest the money released from Proposal A in order to earn no more than 12 percent on it. In most comparisons, however, IRR and the profitability index give the same relative ranking.

Although the profitability index method is conceptually superior to the IRR method and also easier to calculate (since there is no trial-and-error computation), the IRR method is widely used in practice for two reasons. First, the profitability index method requires that the required rate of return be established before the calculations are made. But many analysts prefer to work from the other direction—to find the IRR and then see how it compares with their idea of the rate of return that is appropriate in view of the risks involved. Second, the profitability index is an abstract number that is difficult to explain, whereas the IRR is similar to interest rates and earnings rates with which every manager is familiar.

Nonprofit Organizations

Nonprofit organizations make decisions involving the acquisition of capital assets, and their analytical techniques are essentially the same as those described above for profit- oriented companies.

The capital required for an investment in plant or equipment is obtained from either debt or equity capital or some combination of both. The cost of borrowed funds usually is easily measured. Equity capital is obtained either from past operations that have generated revenues in excess of expenses or from donors. If not invested in the project being ana- lyzed, equity capital can be invested in other assets providing a return. The return on those alternative investments, adjusted for differences in risk, is the required rate of return.

In most respects, estimates of cash inflows and outflows are the same in nonprofit organizations as for those described above. These organizations do not pay income taxes, so that part of the calculation is unnecessary. If the organization is reimbursed for services it performs (as is the case with hospitals and with university research con- tracts), then the proposal’s effect on the calculation of the reimbursement amount must be taken into account. The net present value method is usually preferable to the inter- nal rate of return method. The payback and unadjusted return methods have the same weaknesses in nonprofit organizations as described above.

Summary A capital investment problem is essentially one of determining whether the anticipated cash inflows from a proposed project are sufficiently attractive to warrant risking the in- vestment of funds in the project.

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In the net present value method, the basic decision rule is that a proposal is acceptable if the present value of the cash inflows expected to be derived from it equals or exceeds the present value of the investment. To use this rule, one must estimate (1) the required rate of return, (2) the economic life, (3) the amount of cash inflow in each year, (4) the amount of investment, and (5) the terminal value.

The internal rate of return method finds the rate of return that equates the present value of cash inflows to the present value of the investment—the rate that gives the project an NPV of zero. The simple payback method finds the number of years of cash inflows that are required to equal the amount of investment. The discounted payback method finds the number of years required for the discounted cash inflows to equal the initial investment. The unadjusted return on investment method computes a project’s net income according to the principles of accrual accounting and expresses this profit as a percentage of either the initial investment or the av- erage investment. The simple payback and unadjusted return methods are conceptually weak because they ignore the time value of money.

In preference problems, the task is to rank two or more investment proposals in order of their desirability. The profitability index, the ratio of the present value of cash inflows to the investment, is the most valid way of making such a ranking.

The foregoing are monetary considerations. Nonmonetary considerations are often as important as monetary considerations and in some cases are so important that no economic analysis is worthwhile. In some instances, a manager’s aversion to risk may cause a project with an acceptable return to be rejected or not even proposed.

Problems Problem 27–1.

A company owned a plot of land that appeared in its fixed assets at its acquisition cost in 1910, which was $10,000. The land was not used. In 2009, the local boys club asked the company to donate the land as the site for a new recreation building. The donation would be a tax deduction of $110,000, which was the current appraised value. The company’s tax rate was 40 percent. Some argued that the company would be better off to donate the land than to keep it or to sell it for $110,000. Assume that, other than the land, the company’s taxable income as well as its accounting income before taxes was $10,000,000.

Required: How would the company’s after-tax cash inflow be affected if (a) it donated the land or (b) it sold the land for $110,000? How would its net income be affected?

Problem 27–2. Plastic Recycling Company is just starting operations with new equipment costing $30,000 and a useful life of five years. At the end of five years, the equipment probably can be sold for $5,000. The company is concerned with its cash flow and wants a comparison of straight- line and MACRS1 depreciation to help management decide which depreciation method to use for financial statements and for its income tax return. Assume a 40 percent tax rate.

Required: a. Calculate the difference in taxable income and cash inflow under each method. As-

sume MACRS allowances are 20, 32, 18, 15, and 15 percent for years 1–5, respec- tively.

b. Which deprecation method is preferable for tax purposes? Why?

1 Modified Accelerated Cost Recovery System (effective for assets placed in use after December 31, 1986).

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Chapter 27 Longer-Run Decisions: Capital Budgeting 861

Problem 27–3. Corrine Company owns a warehouse that it no longer needs in its own operations. The warehouse was built, at a cost of $270,000, 10 years ago, at which time its estimated use- ful life was 15 years. There are two proposals for the use of the warehouse:

1. Rent it at $72,000 per year, which includes estimated costs of $27,000 per year for main- tenance, heat, and utilities to be paid by the lessor.

2. Sell it outright to a prospective buyer who has offered $225,000. Any capital gain would be taxed at the 30 percent rate.

Required: a. Calculate the after-tax income if (1) Corrine Company keeps the warehouse and

(2) if Corrine Company sells the warehouse. b. Which proposal should the company accept? Why?

Problem 27–4. (Disregard income taxes in this problem.) Compute the following:

a. An investment of $10,000 has an investment/inflow ratio of 6.2 and a useful life of 12 years. What are the annual cash inflow and internal rate of return?

b. The internal rate of return for an investment expected to yield an annual cash inflow of $2,000 is 14 percent. How much is the investment if the investment/inflow ratio is 6.14?

c. What is the maximum investment a company would make in an asset expected to produce annual cash inflow of $5,000 a year for seven years if its required rate of return is 16 percent?

d. How much investment per dollar of expected annual operating savings can a com- pany afford if the investment has an expected life of eight years and its required rate of return is 14 percent?

Problem 27–5. Wellington Corporation estimates that it will have $500,000 available for capital invest- ments next year. Half of this will be reserved for emergency projects and half will be in- vested in the most desirable projects from the following list. None of the investments has a residual value.

Project Added Expected After-Tax Estimated Number Investment Cash Inflow Life of Project

1 $100,000 $25,000 6 years 2 100,000 30,000 4 3 40,000 5,000 15 4 20,000 10,000 2 5 50,000 12,500 3

Required: Rank the projects in order of their desirability.

Problem 27–6. Baxton Company manufactures short-lived, fad-type items. The research and development department came up with an item that would make a good promotional gift for office equip- ment dealers. Aggressive effort by Baxton’s sales personnel has resulted in almost firm commitments for this product for the next three years. It is expected that the product’s nov- elty will be exhausted after three years.

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862 Part 2 Management Accounting

In order to produce the quantity demanded, Baxton will need to buy additional machin- ery and rent some additional space. About 25,000 square feet will be needed; 12,500 square feet of presently unused, but leased, space are available now. (Baxton’s present lease with 10 years to run costs $3.00 a square foot.) There are another 12,500 square feet adjoining the Baxton facility that Baxton will rent for three years at $4.00 per square foot per year if it decides to make this product.

The equipment will be purchased for $900,000. It will require $30,000 in modifications, $60,000 for installation, and $90,000 for testing. All of the expenditures will be paid for on January 1, 1990. The equipment should have a salvage value of about $180,000 at the end of the third year. No additional general overhead costs are expected to be incurred.

The following estimates of revenues and expenses for this product for the three years have been developed:

1990 1991 1992

Sales $1,000,000 $1,600,000 $800,000__________ __________ ________ Material, labor, and direct overhead 400,000 750,000 350,000 Allocated general overhead 40,000 75,000 35,000 Rent 87,500 87,500 87,500 Depreciation 450,000 300,000 150,000__________ __________ ________

977,500 1,212,500 622,500__________ __________ ________ Income before taxes 22,500 387,500 177,500 Income taxes (40%) 9,000 155,000 71,000__________ __________ ________ Net income $ 13,500 $ 232,500 $106,500__________ __________ __________________ __________ ________

Required: a. Prepare a schedule that shows the differential after-tax cash flows for this project.

b. If the company requires a two-year payback period for its investment, would it un- dertake this project?

c. Calculate the after-tax accounting rate of return for the project.

d. A newly hired business school graduate recommends that the company use net pre- sent value analysis to study this project. If the company sets a required rate of re- turn of 20 percent after taxes, will this project be accepted? (Assume all operating revenues and expenses occur at the end of the year.)

e. What is the internal rate of return of the proposed project?

(CMA adapted)


Case 27–1

Sinclair Company*

A. EQUIPMENT REPLACEMENT Sinclair Company is considering the purchase of new equipment to perform operations currently being per-

formed on different, less efficient equipment. The pur- chase price is $250,000, delivered and installed.

A Sinclair production engineer estimates that the new equipment will produce savings of $72,000 in labor and other direct costs annually, as compared with the present equipment. She estimates the proposed* Copyright © by Professor Robert N. Anthony.

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Chapter 27 Longer-Run Decisions: Capital Budgeting 863

equipment’s economic life at five years, with zero sal- vage value. The present equipment is in good working order and will last, physically, for at least five more years.

The company can borrow money at 9 percent, al- though it would not plan to negotiate a loan specifically for the purchase of this equipment. The company re- quires a return of at least 15 percent before taxes on an investment of this type. Taxes are to be disregarded.


1. Assuming the present equipment has zero book value and zero salvage value, should the company buy the proposed equipment?

2. Assuming the present equipment is being depreci- ated at a straight-line rate of 10 percent, that it has a book value of $135,000 (cost, $225,000; accu- mulated depreciation, $90,000), and has zero net salvage value today, should the company buy the proposed equipment?

3. Assuming the present equipment has a book value of $135,000 and a salvage value today of $75,000 and that if retained for 5 more years its salvage value will be zero, should the company buy the pro- posed equipment?

4. Assume the new equipment will save only $37,500 a year, but that its economic life is expected to be 10 years. If other conditions are as described in (1) above, should the company buy the proposed equipment?

B. REPLACEMENT FOLLOWING EARLIER REPLACEMENT Sinclair Company decided to purchase the equipment described in Part A (hereafter called “model A” equip- ment). Two years later, even better equipment (called “model B”) comes on the market and makes the other equipment completely obsolete, with no resale value. The model B equipment costs $500,000 delivered and installed, but it is expected to result in annual savings of $160,000 over the cost of operating the model A equipment. The economic life of model B is estimated to be 5 years. Taxes are to be disregarded.


1. What action should the company take?

2. If the company decides to purchase the model B equipment, a mistake has been made somewhere,

because good equipment, bought only two years previously, is being scrapped. How did this mistake come about?

C. EFFECT OF INCOME TAXES Assume that Sinclair Company expects to pay income taxes of 40 percent and that a loss on the sale or dis- posal of equipment is treated as a capital loss resulting in a tax saving of 28 percent of the loss. Sinclair uses an 8 percent discount rate for analyses performed on an aftertax basis. Depreciation of the new equipment for tax purposes is computed using the accelerated cost re- covery system (ACRS) allowances; assume that these allowances were 35, 26, 15, 12, and 12 percent for years 1 to 5, respectively. The new equipment qualifies for a 5 percent investment tax credit, which will not re- duce the cost basis of the asset for calculating ACRS depreciation for tax purposes.


1. Should the company buy the equipment if the facts are otherwise the same as those described in Part A (1)?

2. If the facts are otherwise the same as those de- scribed in Part A (2)?

3. If the facts are otherwise the same as those de- scribed in Part B?

D. CHANGE IN EARNINGS PATTERN Assume that the savings are expected to be $79,500 in each of the first three years and $60,750 in each of the next two years, other conditions remaining as de- scribed in Part A (1).


1. What action should the company take?

2. Why is the result here different from that in Part A (1)?

3. What effect would the inclusion of income taxes, as in Part C, have on your recommendation? (You are not expected to perform any more calculations in answering this question.)

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probably have to borrow the funds at 8 percent interest cost. Of course, our effective interest cost is less than this, since for every dollar of interest expense we report to the IRS we save 34 cents in taxes. But the lease pay- ments would also be tax deductible, so it’s still not clear to me which is the better alternative. There’s a sharp new person in my company’s accounting department; let’s not make a decision until I can ask her to do some fur- ther analysis for us.”


1. Assume that in order to purchase the carts, RCGC would have to borrow $89,600 at 8 percent interest for five years, repayable in five equal year-end in- stallments. Prepare an amortization schedule for this loan, showing how much of each year’s pay- ment is for interest and how much is applied to repay principal. (Round the amounts for each year to the nearest dollar.)

2. Assume that salesperson B’s company also would be willing to sell the carts outright at $2,240 per cart. Given the proposed lease terms, and assuming the lease is outstanding for five years, what interest rate is implicit in the lease? (Ignore tax impacts to the leasing company when calculating this implicit rate.) Why is this implicit rate different from the 8 percent that RCGC may have to pay to borrow the funds needed to purchase the carts?

3. Should RCGC buy the carts from A, or lease them from B? (Assume that if the carts are purchased, RCGC will use accelerated depreciation for income tax purposes, based on an estimated life of five years and an estimated residual value of $240 per cart. The accelerated depreciation percentages for years 1–5, respectively, are 35 percent, 26 percent, 15.6 per- cent, 11.7 percent, and 11.7 percent.)

4. Assume arbitrarily that purchasing the carts has an NPV that is $4,000 higher than the NPV of leasing them. (This is an arbitrary difference for purposes of this question and is not to be used as a “check fig- ure” for your earlier calculations.) How much would B have to reduce the proposed annual lease payment to make leasing as attractive as purchasing the cart?

864 Part 2 Management Accounting

Rock Creek Golf Club (RCGC) was a public golf course, owned by a private corporation. In January the club’s manager, Lee Jeffries, was faced with a decision involving replacement of the club’s fleet of 40 battery- powered golf carts. The old carts had been purchased five years ago, and had to be replaced. They were fully depreciated; RCGC had been offered $200 cash for each of them.

Jeffries had been approached by two salespersons, each of whom could supply RCGC with 40 new gaso- line-powered carts. The first salesperson, called here simply A, would sell RCGC the carts for $2,240 each. Their expected salvage value at the end of five years was $240 each.

Salesperson B proposed to lease the same model carts to RCGC for $500 per cart per year, payable at the end of the year for five years. At the end of five years, the carts would have to be returned to B’s com- pany. The lease could be canceled at the end of any year, provided 90 days’ notice was given.

In either case, out-of-pocket operating costs were expected to be $420 per cart per year, and annual rev- enue from renting the carts to golfers was expected to be $84,000 for the fleet.

Although untrained in accounting, Jeffries calcu- lated the number of years until the carts would “pay for themselves” if purchased outright, and found this to be less than two years, even ignoring the salvage value. Jeffries also noted that if the carts were leased, the five-year lease payments would total $2,500 per cart, which was more than the $2,240 purchase price; and if the carts were leased, RCGC would not receive the salvage proceeds at the end of five years. There- fore, it seemed clear to Jeffries that the carts should be purchased rather than leased.

When Jeffries proposed this purchase at the next board of directors meeting, one of the directors objected to the simplicity of Jeffries’ analysis. The director had said, “Even ignoring inflation, spending $2,240 now may not be a better deal than spending five chunks of $500 over the next five years. If we buy the carts, we’ll

Case 27–2

Rock Creek Golf Club*

* Adapted by James S. Reece from an example used by Gordon B. Harwood and Roger H. Hermanson in “Lease-or-Buy Decisions,” Journal of Accountancy, September 1976, pp. 83–87; © American Institute of Certified Public Accountants.

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Chapter 27 Longer-Run Decisions: Capital Budgeting 865

Mike Campbell, General Manager of Phuket Beach Hotel, paced his office and considered an offer made by Planet Karaoke Pub. Planet Karaoke Pub was ex- panding fast in Thailand. It was looking for a venue in the Patong beach area for setting up another outlet, and was eyeing an unused space owned by the Hotel. At this point, the space was located on the second floor of the main building and was very much under- utilised. It was reserved for the construction of an alley linking to a new wing for the hotel, which would not be completed until two years later.

Planet Karaoke Pub offered to sign a four-year lease agreement with the hotel for renting part of the unused space. It proposed to pay:

• a monthly rental fee of 170,000 baht for the first two years; and

• thereafter, a 5 percent increment for the next two years.

In order to accommodate the hotel’s expansion plan. Planet Karaoke Pub required only 70 percent of the unused space, which had a size of 3,000 sq. feet. This would allow the hotel to keep the remaining space for the creation of an alley two years later.

It was envisaged that the proposed pub would not affect the hotel’s future expansion plan. Neverthe- less, Mike was still a bit perplexed about the decision facing him. Similar development proposals had previ- ously been rejected by the board of directors. One of the old proposals, which involved converting the space into a cigar and champagne bar, had been rejected by the board because it required a long payback period. Another proposal for the creation of a spa was dis- carded due to its low return on investment. Given that the present capital budgeting system ranked projects according to payback period and average return on in- vestment, Mike decided to seek a careful analysis of the offer from the Pub.1

Case 27–3

Phuket Beach Hotel: Valuing Mutually Exclusive Capital Projects*

* Copyright © by The University of Hong Kong Centre for Asian Business Cases. Case HKU145. This material is used by permission of the Centre for Asian Business Cases at The Uni- versity of Hong Kong ( 1 Average return on investment ? Average annual cashflow after taxes/Net investment

That evening, Mike asked to meet with Kornkrit Manming, the hotel’s Financial Controller, to discuss the offer from Planet Karaoke Pub.

THE MUTUALLY EXCLUSIVE PROJECTS Mike’s discussion with Kornkrit went as follows:

Mike: I see you have been busy. But I still need you to evaluate the offer from Planet Karaoke Pub for me, and to give me any positive or negative insights that you think are significant.

Kornkrit: No problem. I can present to you a de- tailed analysis within this week. But don’t you think we should provide more alternatives for the hotel owners to decide?

Mike:That’s what I’ve been thinking. Perhaps we can create a pub by ourselves. Karaoke pubs are spread- ing fast inThailand.A number of surveys have shown that they attract a lot of customers and tourists.

Kornkrit: That sounds like a good idea.

Mike: Please assess the projects carefully. You may ask your new assistant Wanida to help you. This is simple, isn’t it?

Kornkrit: I think the most difficult part is to esti- mate future profits and allocate overhead costs to each project. I’ll work on this first. Then I’ll ask Wanida to rank the projects according to their pay- back period and return on investment.

Mike: Good. I would like to have the results of your analysis next Monday.

KORNKRIT’S ANALYSES Kornkrit began his evaluation by reviewing the offer from Planet Karaoke Pub and estimating the revenues and costs associated with an alternative project, Beach Karaoke Pub.

Planet Karaoke Pub To make the space ready for lease, the hotel had to set up partitions and a small kitchen. Various estimates of the up-front renovation costs ranged between 770,000 baht and 1,000,000 baht. The costs would be depreci- ated over the life of the project using the straight-line method, with zero salvage value. Since the existing toilets, elevators, and carpets would be utilised to

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Kornkrit expected revenue to be generated 50 per- cent from walk-ins and 50 percent from hotel guests. Estimated total sales would be 4,672,000 baht for the first year of operation. Kornkrit arrived at this figure by assuming an average of 64 covers per day with an average check of 200 baht.

With a seating capacity of 32, the pub had to turn tables at least twice a day. Operating hours of the pub would be from 5:00 p.m. to midnight.

The projected length of the project was six years. Sales were expected to grow at 5 percent per annum in terms of the average check. Growth in covers would be limited due to limited capacity.

Kornkrit’s estimates for operating costs were as follows:

866 Part 2 Management Accounting

support this project, Kornkrit believed that a fair share of these overhead expenses should be allocated to the project. The pro rata allocation of the costs of these fa- cilities, based on the floor area of the space used for the project, amounted to 55,000 baht. Due to the foresee- able increase in activity, Kornkrit would like to charge this project for an increase in repair and maintenance costs of 10,000 baht per annum. The pub would pay all utility and other expenses.

Beach Karaoke Pub The project would require an up-front investment rang- ing between 800,000 and 1,200,000 baht. This repre- sented the cost of a modern-style décor. Other capital investment, including chairs, bar tables, kitchen set-up, and karaoke equipment, would amount to 900,000 baht.

Food and beverage costs 25% of sales Salaries 16% of sales Other operating expenses 22% of sales Depreciation: equipment & furniture Depreciated equally over the life of the project using the straight-line

method; with zero salvage value at the end Annual capital expenditure Equalled depreciation

Kornkrit estimated that salary expenses would ac- count for 16 percent of sales. Staff could be recruited internally because the hotel had excess manpower at this point. The excess staff had long-term contracts with the hotel and were kept in order to meet the de- mands of the growing business. Repairs and mainte- nance costs were estimated to be the same as for Planet Karaoke Pub.

CAPITAL STRUCTURE Phuket Beach Hotel has a capital structure consisting of 75 percent equity and 25 percent debt. The debt consisted entirely of loans from Siam Commercial Bank bearing an interest rate of 10 percent. The hotel owners’ cost of equity was 12 percent. The corporate tax rate in Phuket was 30 percent.

THE TEST Kornkrit was quite happy with his estimates, though it had taken him more time than he had originally thought. Now, he had all the figures he needed. The next step was to rank the projects according to the cri- teria set by the hotel’s capital budgeting system. He saved his file and sent it to his new assistant Wanida, a recent graduate from Thammasat University. “Here

you go, Wanida. This will test what you learnt at busi- ness school!” he thought.

The following is an excerpt from an email from Kornkrit:

To: Wanida Daoruang ?wanida@beach-hotel. phuket> From: Kornkrit Manming ?kornkrit@beach-hotel. phuket> Subject: Ranking Capital Projects

Dear Wanida,

. . . I have provided you with all the figures you need for the projection of future profits for the two projects. Please evaluate the projects on the basis of their payback period and their average return on investment. Note that future profits should be discounted at 5%. This is the interest rate we earned from our time deposits at Siam Commer- cial Bank. I believe some of our old proposals were rejected because we used a discount rate that was too high. Since we have enough cash on hand to finance the projects, I don’t think we should take into account the cost of debt when estimating the discount rate.

Let me know if you have any questions.

Regards, Kornkrit Manming

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Chapter 27 Longer-Run Decisions: Capital Budgeting 867

Wanida pondered the details of the projects. She thought there was something wrong with the hotel’s capital budgeting system, which had not been re- viewed for many years. The existing system ranked projects according to their average return on invest- ment and payback period. It seemed to her that some- thing was omitted in the analysis.

Wanida was also aware that certain aspects of the investment decision were difficult to quantify. The Chief Security Officer had expressed his concerns and displeasure over the security problems that a karaoke pub might bring. He was worried that the pub might at- tract unwelcome guests from outside. This might be a negative factor for the pub in terms of attracting tourists travelling with children. Wanida thought they accounted for 25 percent of the total patronage [see Table A for the projection on net room revenue for the next six years].

The following are the questions that Wanida con- sidered:

1. What are the relevant cashflows associated with each project?

2. What criteria should be used to evaluate the projects?

3. How can I compare projects with different lives?

4. What discount rate should be used? Wanida thought the discount rate of 5 percent was too low. Investing in the two projects was certainly more risky than putting the money in the bank.

5. What are the key value drivers and how do they affect the attractiveness of the projects?

Year 1 2 3 4 5 6

Net room revenue 13,200,000 13,464,000 14,137,000 14,844,000 15,140,000 15,443,000

TABLE A Projection of Net Room Revenue (in Baht) (? Room Sales ? Room Operating Expenses)

6. Which investment project should be recommended to the board of directors?

When Wanida got home, she had a talk with her hus- band about the proposed projects. Her husband, a so- cial worker, reminded her of the increasing number of drug arrests in karaoke pubs. He suggested that as a good member of the community, the hotel should not be involved in this type of project.


1. Assess the economic benefits associated with each of the capital projects. What is the initial outlay? What are the incremental cashflows over the life of the project? What is an appropriate discount rate to use for discounting the cashflows of the projects?

2. Rank the projects using various measures of invest- ment attractiveness. Do all the measures rank the projects identically? Why or why not? Which crite- rion is the best?

3. Are the projects comparable based on the standard NPV measure, given that they have unequal lives? What adjustment or alternative method is required in comparing such projects?

4. How sensitive is your ranking to changes in the dis- count rate? What other “key value drivers” would affect the attractiveness of the projects? Estimate the sensitivity of your result to a change in any of the key value drivers.

5. Which project should the hotel undertake?

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