■ Definition: Capital budgeting is defined as the decision-making process concerned with the firm’s decision (1) whether or not to invest financial resources and (2) how to choose between and among the available investment projects. These projects may be to replace or expand existing plant and equipment, to diversify the firm’s activities, to take over another firm, to mount an advertising campaign, to put funds into bonds, or simply to hold the funds in liquid form for future investment projects. In general, the available investment projects will involve cost reduction, revenue generation, or some combination of the two. Pure cost-reduction investments include replacement of existing assets that are now relatively inefficient because of physical depreciation and technological obsolescence. Pure revenue-generating projects may be the investment in new-product development or advertising campaigns where these are treated as an investment that leads to a future revenue stream. Expansion projects typically involve both cost reduction and revenue generation, since newer plant and equipment are typically technologically superior to that being replaced.
Where there are no limits on the availability of capital, the capital-budgeting decision is simply to accept or reject each particular project. The following section establishes a number of criteria that allow the accept/reject decision to be made. But when the investments are mutually exclusive, meaning that they are alternative ways of achieving the same end or are alternative uses of available space or other resources, the available investment projects must be ranked in order of preference. The third section of this chapter establishes the criterion for ranking mutually exclusive projects. When there are limits to the availability of capital, a criterion must be established which ensures that the available capital is efficiently allocated between and among the possible projects so that the firm’s objectives are achieved. Capital budgeting as an allocation problem is examined in the final section of this chapter.
You are already familiar with the basic structure of capital budgeting since it is essentially the same as the decision-making structure introduced in Chapters 1 and 2. In this chapter, we reconsider the expected-present-value decision criterion in the con-
text of the investment decision and discuss new and related investment decision criteria. For ease of presentation, the analysis will be presented, for the most part, in terms of the firm’s having full information about future costs and revenues associated with each investment decision. Thus we speak of the net-present-value (NPV) criterion, for example, rather than the expectecf-net-present-value criterion. The analysis is easily modified for uncertainty—the single-point estimates of future costs and revenues can be designated to represent the expected values of the probability distributions surrounding each expected future cost and revenue. Rather than repeat all the analysis of Chapter 1 dealing with decision making under uncertainty, this chapter introduces new material and presumes that you will have little difficulty implementing it in the context of uncertainty.
As stated in the introductory section, when funds are unlimited the capital budgeting decision is whether to accept or reject each available investment project. This decision must be based upon whether or not each project contributes to the attainment of the firm’s objectives. In the following paragraphs we shall take the standard view that the firm’s objective is to maximize its long-term profitability, or its net worth in present- value terms. In some cases, of course, the firm’s time horizon may be somewhat shorter because of cash-flow or accounting profit considerations. In such cases a less profitable project may be undertaken if it promises a very short payback period or relatively large immediate gains, in preference to a more profitable project that generates its income over a longer period of time.
We shall consider five separate criteria for the accept/reject decision. We shall examine the relationships between these criteria and show why some of these criteria are superior to others.
You will recall from Chapter 1 that net present value refers to the sum of the discounted value of the future stream of costs and revenues associated with a particular project. If the net present value of a project is positive, this fact indicates that the project adds more to revenues in present-value terms than it adds to cost in present- value terms and should therefore be accepted. Symbolically, we can express the net present value as follows:
NPV
n
L
t =i (1 + r)'
Cn
(15-1)
where R, signifies the contribution to overheads and profits in each future period; C 0 represents the initial cost of the project, including installation charges and any other
expenses such as increases in working capital required by the investment; r is the opportunity rate of interest; and t = 1, 2, 3, . . ., n is the number of periods over which the revenue stream is expected. Thus the revenue stream is discounted at the rate of interest that the firm could obtain in its next-best-alternative use of these investment funds at a similar level of risk. The revenue stream referred to in equation (15-1) by R, should be regarded as the net cash flow after taxes.
■ Definition: Net cash flow after taxes can be defined as incremental revenues minus incremental costs, plus tax savings that result from depreciation charges that are deductible from taxable income, plus tax credits (if any) allowed against tax liability in connection with the particular investment project. If a tax credit (for example, 15 percent of the initial cost) is available for new investment, this credit will be deducted directly from the tax liability, and it thus avoids an outflow of a certain amount. Although this is not an actual inflow of cash, it is an opportunity revenue; the avoidance of what would otherwise be an outflow of cash in effect amounts to a cash inflow. Depreciation charges against revenues enter the cash-flow picture only indirectly and as a result of the tax saving that can be obtained by subtracting the depreciation charges from the income of the firm.
Example: To demonstrate this definition, suppose an investment project involves an initial cash outlay of $10,000 and will generate revenues for three years, after which time it has a salvage value of $1,000. The value of the investment project to be depreciated over the three-year life of the project is thus $9,000, and for simplicity we use the straight-line method of depreciation to allocate $3,000 to each of the three years of the project’s life. In Table 15-1 we show the calculation of the cash flow after taxes, given the contribution stream indicated.
We assume that the firm is subject to the tax rate of 48 percent: The tax saving shown as $1,440 in each of the three years represents 48 percent of the depreciation figure. The cash-flow-after-taxes column shows the sum of the contribution and tax saving for each year. The next column shows the discount factors at an assumed opportunity rate of 10 percent, and the final column shows the net present value of the cash flow after taxes in each year and in total.
Note that the sum of the net present value of the cash flow after taxes is positive, and hence this investment project adds to the net present value, or net worth, of the
|
TABLE 15- |
-1. Calculation of NPV of Cash Flow after Taxes |
|||||
|
Year |
Contri¬ bution |
Depre¬ ciation |
Tax Saving |
Cash Flow after Taxes |
Discount Factors |
Net Present Value |
|
0 |
$-10,000 |
— |
— |
$-10,000 |
1.000 |
$-10,000.00 |
|
1 |
5,000 |
$3,000 |
$1,440 |
6,440 |
0.909 |
5,853.96 |
|
2 |
3,000 |
3,000 |
1,440 |
4,440 |
0.826 |
3,667.44 |
|
3 |
2,000 |
3,000 |
1,440 |
3,440 |
0.751 |
2,583.44 $ 2,104.84 |
572 Topics in Managerial Economics
firm. It should therefore be accepted, and the firm should continue accepting projects for implementation until it is left with only those projects that have zero or negative net present value at the appropriate opportunity rate of discount.
Different Depreciation Methods. The method of depreciation employed has important implications for the NPV of the investment project. In the example we used the straight-line method of depreciation, in which the difference between the initial cost of the asset and its salvage value is allocated equally to each year of the asset’s life. Alternatively, we might have used a method of depreciation that accelerates the recovery of the difference between the initial cost and the salvage value, so that the depreciation expense is largest in the first year and declines each year until the asset is fully depreciated. Two such methods are the sum-of-years-digits method and the double-declining- balance method.
The sum-of-years-digits method, as implied by its name, adds up the digits of the years that the asset will last and each year depreciates a proportion of the amount to be recovered equal to the ratio of the number of years remaining to the sum of the digits. In the preceding example the asset is expected to last for three years, so the sum of the years’ digits is 1 +2 + 3 = 6. Thus three-sixths, or one-half, of the total depreciation expense will be deducted in the first year; two-sixths, or one-third, will be deducted in the second year; and one-sixth will be deducted in the final year.
The double-declining-balance method takes twice the depreciation rate implied by the straight-line method but applies it to the undepreciated balance remaining in each year. Thus, using this method, we would recover two-thirds of $9,000 (that is, $6,000) in the first year; two-thirds of the remaining $3,000 (that is, $2,000) in the second year; and the remainder ($1,000) in the third year. Notice that both of these “accelerated” depreciation methods shift forward in time part of the net cash flow after taxes and thus increase the NPV of these dollars, since they will be multiplied by a larger discount factor when received earlier.
Example: To demonstrate this effect, let us rework the above example using the sum-of-years-digits depreciation method. In Table 15-2 we show half of the depreciation (that is, $4,500) being deducted in the first year; one-third being deducted in the second year; and one-sixth being deducted in the third year. The tax saving is now weighted toward the earlier years, which in turn have larger discount factors. Hence,
Table captionTABLE 15-2. Impact of Depreciation Method upon Net Present Value
|
Year |
Contri¬ bution |
Depre¬ ciation |
Tax Saving |
Cash Flow after Taxes |
Discount Factors |
Net Present Value |
|
0 |
$-10,000 |
— |
— |
$-10,000 |
1.000 |
$-10,000.00 |
|
1 |
5,000 |
$4,500 |
$2,160 |
7,160 |
0.909 |
6,508.44 |
|
2 |
3,000 |
3,000 |
1,440 |
4,440 |
0.826 |
3,667.44 |
|
3 |
2,000 |
1,500 |
720 |
2,720 |
0.751 |
2,042.72 |
Table caption$ 2,218.60
the net present value of the same project with an accelerated depreciation method can be shown to be significantly higher than it was as calculated using straight-line depreciation. In fact, the accelerated depreciation provisions of the tax laws exist primarily to encourage firms to invest in new plant and facilities for the employment multiplier impact of such investment upon the economy. 1