Present value methods of analyzing capital investments

27 Longer-Run Decisions: Capital Budgeting

Chapter

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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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

Example

Return on Investment

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$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

Example

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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.

Example

Required Rate of Return

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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,

Example

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

Example

Economic Life

Cash Inflows

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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.