The Capital Budgeting Decision
12
12
The Capital Budgeting Decision
LEARNING OBJECTIVES
LO 12-1 | A capital budgeting decision represents a long-term investment decision. |
LO 12-2 | Cash flow rather than earnings is used in the capital budgeting decision. |
LO 12-3 | The payback method considers the importance of liquidity, but fails to consider the time value of money. |
LO 12-4 | The net present value and internal rate of return are generally the preferred methods of capital budgeting analysis. |
LO 12-5 | The discount or cutoff rate is normally the cost of capital. |
The decision on capital outlays is among the most significant a firm has to make. A decision to build a new plant or expand into a foreign market may influence the performance of the firm over the next decade. The airline industry has shown a tendency to expand in excess of its needs, while other industries have insufficient capacity. The auto industry has often miscalculated its product mix and has had to shift down from one car size to another at an enormous expense.
The capital budgeting decision involves the planning of expenditures for a project with a life of at least one year, and usually considerably longer. In the public utilities sector, a time horizon of 25 years is not unusual. The capital expenditure decision requires extensive planning to ensure that engineering and marketing information is available, product design is completed, necessary patents are acquired, and the capital markets are tapped for the necessary funds. Throughout this chapter we will use techniques developed under the discussion of the time value of money to equate future cash flows to the present, while using the cost of capital as the basic discount rate.
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As the time horizon moves farther into the future, uncertainty becomes a greater hazard. The manager is uncertain about annual costs and inflows, product life, interest rates, economic conditions, and technological change. A good example of the vagueness of the marketplace can be observed in the pocket calculator industry going back to the 1970s. A number of firms tooled up in the early 1970s in the hope of being first to break through the $100 price range for pocket calculators, assuming that penetration of the $100 barrier would bring a larger market share and high profitability. However, technological advancement, price cutting, and the appearance of Texas Instruments in the consumer market drove prices down by 60 to 90 percent and made the $100 pocket calculator a museum piece. Rapid Data Systems, the first entry into the under-$100 market, went into bankruptcy. The same type of change, though less dramatic, can be viewed in the personal computer industry over the last 20 years. IBM and Apple took the early lead in product development and had no difficulty selling their products in the $2,000 to $5,000 range. As Compaq, Dell, and foreign competitors moved into the market, prices dropped by 50 percent and consumer demand for quality went up. Not all new developments are so perilous, and a number of techniques, which will be treated in the next chapter, have been devised to cope with the impact of uncertainty on decision making.
Not only is capital budgeting important to people in finance or accounting, it is essential to people throughout the business organization. For example, a marketing or production manager who is proposing a new product must be familiar with the capital budgeting procedures of the firm. If he or she is not familiar with the concepts presented in this chapter, the best idea in the world may not be approved because it has not been properly evaluated and presented. You must be familiar not only with your product but also with its financial viability.
In this chapter, capital budgeting is studied under the following major topical headings: administrative considerations, accounting flows versus cash flows, methods of ranking investment proposals, selection strategy, capital rationing, combining cash flow analysis and selection strategy, and the replacement decision. Later in the chapter, taxes and their impact on depreciation and capital budgeting decisions are emphasized.
Administrative Considerations
A good capital budgeting program requires that a number of steps be taken in the decision-making process:
1. Search for and discovery of investment opportunities.
2. Collection of data.
3. Evaluation and decision making.
4. Reevaluation and adjustment.
The search for new opportunities is often the least emphasized, though perhaps the most important, of the four steps. The collection of data should go beyond engineering data and market surveys and should attempt to capture the relative likelihood of the occurrence of various events. The probabilities of increases or slumps in product demand may be evaluated from statistical analysis, while other outcomes may be estimated subjectively.
After all data have been collected and evaluated, the final decision must be made. Generally, determinations involving relatively small amounts of money will be made at the department or division level, while major expenditures can be approved only by top management. A constant monitoring of the results of a given decision may indicate that a new set of probabilities must be developed, based on first-year experience, and the initial decision to choose Product A over Product B must be reevaluated and perhaps reversed. The preceding factors are illustrated in Figure 12-1.
Accounting Flows versus Cash Flows
In most capital budgeting decisions the emphasis is on cash flow, rather than reported income. Let us consider the logic of using cash flow in the capital budgeting process. Because depreciation does not represent an actual expenditure of funds in arriving at profit, it is added back to profit to determine the amount of cash flow generated.1 Assume the Alston Corporation has $50,000 of new equipment to be depreciated at $5,000 per year. The firm has $20,000 in earnings before depreciation and taxes and pays 35 percent in taxes. The information is presented in Table 12-1 to illustrate the key points involved.
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Figure 12-1 Capital budgeting procedures
The firm shows $9,750 in earnings after taxes, but it adds back the noncash deduction of $5,000 in depreciation to arrive at a cash flow figure of $14,750. The logic of adding back depreciation becomes even greater if we consider the impact of $20,000 in depreciation for the Alston Corp. (Table 12-2). Net earnings before and after taxes are zero, but the company has $20,000 cash in the bank.
Table 12-1 Cash flow for Alston Corporation
Earnings before depreciation and taxes (cash inflow) | $20,000 |
Depreciation (noncash expense) | 5,000 |
Earnings before taxes | $15,000 |
Taxes (cash outflow) | 5,250 |
Earnings after taxes | $ 9,750 |
Depreciation | +5,000 |
Cash flow | $14,750 |
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Table 12-2 Revised cash flow for Alston Corporation
Earnings before depreciation and taxes | $20,000 |
Depreciation | 20,000 |
Earnings before taxes | $ 0 |
Taxes | 0 |
Earnings after taxes | $ 0 |
Depreciation | 20,000 |
Cash flow | $20,000 |
To the capital budgeting specialist, the use of cash flow figures is well accepted. However, top management does not always take a similar viewpoint. Assume you are the president of a firm listed on the New York Stock Exchange and must select between two alternatives. Proposal A will provide zero in aftertax earnings and $100,000 in cash flow, while Proposal B, calling for no depreciation, will provide $50,000 in aftertax earnings and cash flow. As president of a publicly traded firm, you have security analysts constantly penciling in their projections of your earnings for the next quarter, and you fear your stock may drop dramatically if earnings are too low by even a small amount. Although Proposal A is superior, you may be more sensitive to aftertax earnings than to cash flow and you may therefore select Proposal B. Perhaps you are overly concerned about the short-term impact of a decision rather than the long-term economic benefits that might accrue.
You must be sensitive to executives’ concessions to short-term pressures. Nevertheless in the material that follows, the emphasis is on the use of proper evaluation techniques to make the best economic choices and assure long-term wealth maximization.
Methods of Ranking Investment Proposalsn
I order to choose among competing capital projects, we must understand the methods commonly used to rank investment proposals. Let us consider two projects whose cash flows are presented as follows:
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Three widely used methods for evaluating capital expenditures will be considered, along with the shortcomings and advantages of each:
1. Payback method.
2. Internal rate of return.
3. Net present value.
The first method, while not conceptually sound, is often used. Approaches 2 and 3 are more acceptable, and one or the other should be applied to most situations.
Payback Method
Under the payback method, we compute the time required to recoup the initial investment. Assume we are called on to select between Investments A and B in Table 12-3. Notice that the values in this table match the preceding timeline.
Table 12-3 Investment alternatives
Cash Inflows (of $10,000 investment) | ||
Year | Investment A | Investment B |
1 | $5,000 | $1,500 |
2 | 5,000 | 2,000 |
3 | 2,000 | 2,500 |
4 | 5,000 | |
5 | 5,000 |
The payback period for Investment A is 2 years, while Investment B requires 3.8 years. In the latter case, we recover $6,000 in the first three years, leaving us with the need for another $4,000 to recoup the full $10,000 investment. Since the fourth year has a total inflow of $5,000, $4,000 represents 0.8 of that value. Thus the payback period for Investment B is 3.8 years.
In using the payback method to select Investment A, we ignore two important considerations. First there is no consideration of inflows after the cutoff period. The $2,000 in year 3 for Investment A in Table 12-3 is ignored, as is the $5,000 in year 5 for Investment B. Even if the $5,000 were $50,000, it would have no impact on the decision under the payback method.
Second, the method fails to consider the concept of the time value of money. If we had two $10,000 investments with the following inflow patterns, the payback method would rank them equally.
Year | Early Returns | Late Returns |
1 | $9,000 | $1,000 |
2 | 1,000 | 9,000 |
3 | 1,000 | 1,000 |
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Capital Budgeting Practices Utilized by Smaller, Privately Held Businesses Finance in ACTION Managerial
While the techniques described in this chapter are intended to be used by the modern, sophisticated business manager, not everyone uses them. It is, however, true that survey studies of large business firms over the past decade have shown an increasing acceptance of such concepts as discounted cash flow (as represented by the internal rate of return or net present value methods) and weighted average cost of capital.
But what about people who do capital budgeting analyses for smaller, privately held business firms? Extensive studies show that only a relatively small percentage of these firms (generally less than 20 percent) use discounted cash flow methods. For example, Runyon* found only 14.4 percent of his questionnaire respondents in small business firms used the internal rate of return or net present value approach. The rest used the payback method or some other unsophisticated approach.
Why do large business firms use theoretically correct approaches, while small business firms do not? There are two primary reasons. The first is that the small business manager is likely to be less sophisticated and educated in financial matters than the CFO of a larger corporation. The small businessperson’s skills are more likely to be in designing products, meeting customer demands, and hiring and satisfying employees.
But rather than be too critical, we should also realize the second reason why small business owners might be using the payback method or similar less sophisticated techniques. Small business owners must deal primarily with bankers or finance companies rather than stockholders or bondholders. When small business owners approach a banker for a loan to finance a capital investment, they should be prepared to demonstrate their capacity to repay the loan within a set period of time rather than quote their internal rate of return or net present value. That is the reason the payback method is often used, and the payback period required often is “the maturity the bank will allow on the loan.”
*L. R. Runyon, “Capital Budgeting Decision Making in Small Firms,” Journal of Business Research 11, pp. 389–97.
Although both investments have a payback period of two years, the first alternative is clearly superior because the $9,000 comes in the first year rather than the second.
The payback method does have some features that help to explain its use by U.S. corporations. It is easy to understand, and it emphasizes liquidity. An investment must recoup the initial investment quickly or it will not qualify (most corporations use a maximum time horizon of three to five years). A rapid payback may be particularly important to firms in industries characterized by rapid technological developments.
Nevertheless the payback method, concentrating as it does on only the initial years of investment, fails to discern the optimum or most economic solution to a capital budgeting problem. The analyst is therefore required to consider more theoretically correct methods.
Net Present Value
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Net present value (NPV) is often the preferred investment selection method for two important reasons. First, it is a theoretically valid method. Second, it is well understood and used by real-world finance professionals. In other words, not only is NPV a theoretically correct method, it is also often the preferred method in practice. The net present value is the sum of the present values of all outflows and inflows related to a project. The present value of each inflow and outflow is usually discounted using the weighted average cost of capital, Ka, for the firm. Thus inflows that arrive in later years must provide a return that at least equals the cost of the invested capital. In Table 12-4, we calculate the NPVs for Investments A and B using an assumed cost of capital, or discount rate, of 10 percent.
Table 12-4 Calculating NPV for Investments A and B
For Investment A, the timing of each cash flow is shown in column A with the amount of each cash flow shown in column B. Together these columns produce a vertical timeline of cash flows. The discount rate of 10 percent is shown in cell C2, and each of the values in cells C4 to C7 is the present value factor needed to convert the values in column B into the present values in column D. The net present value is simply the sum of all the individual present values in column D. The NPV of $180.32 is highlighted in cell D8.
Excel also provides an NPV function, which is shown in cell C13. Unfortunately, when the initial cash flow occurs at time zero (as the $10,000 investment outflow does in our example), the NPV function does not provide an accurate calculation unless the user conducts a slight manipulation. Excel’s NPV function behaves badly because it assumes that the first cash flow comes at the end of the first year. To treat the initial outlay properly, we must leave the initial outlay out of the NPV function. Then we must subtract the initial outlay separately. Also note that because the initial outlay is entered as a negative number in cell B4, we must actually add the outlay to the NPV calculation. For Investment A, the cash flows in cells B5 through B7 are entered inside the NPV function, and the initial outlay in cell B4 must be added to the NPV function value. Unless you look carefully at cell C13, you may overlook this subtle but important point.
The NPV for Investment B is calculated in an identical manner. The cash flow timeline is inserted in columns F and G. Present value factors are computed in column H using the 10 percent discount rate from cell H2, and the present value of each cash flow is shown in column I. The sum of the present values is the NPV of $1,414.49 value highlighted in cell I10. Using the Excel NPV function yields the same result in cell H13.
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The standard decision rule for NPV analysis is as follows:
NPV > 0; Accept the project because the project increases firm value.
NPV < 0; Reject the project because the project reduces firm value.
While both proposals here are acceptable, Investment B has a considerably higher net present value than Investment A.2
Internal Rate of Return
The internal rate of return (IRR) is another important metric used to make capital budgeting decisions. While NPV measures the attractiveness of a project in dollar (i.e., currency) terms, the IRR measures the profitability of investments as a return percentage—much like finding the interest rate (i) in a time value of money problem. The key to fully understanding the meaning of the internal rate of return is to understand how IRR relates to NPV: The internal rate of return on an investment or project is the “rate of return” that makes the net present value of the project equal to zero.
The IRR is the interest rate (i) that makes NPV = 0.
Let us return to our analysis of Investment A and Investment B. At the top of Table 12-5, the cash flows for Investment A are set up exactly as before when we calculated the NPV of the investment. However, you will notice that instead of using a discount rate of 10 percent, the discount rate is 11.16 percent. This is the discount rate that forces the NPV value shown in cell D8 to be exactly zero! Because the NPV is zero when the discount rate is 11.16 percent, we have found the IRR. The internal rate of return is 11.16 percent.
An inquisitive student like you may not be satisfied with simply understanding this definition of the IRR (the rate that makes NPV = 0). Instead, you would probably like to know how the IRR was found. Unfortunately, there is usually no simple equation to find the IRR. However, once again we can make use of the Goal Seek function that was introduced in Chapter 10. Recall that Goal Seek was used in Chapter 10 to find the yield to maturity of a bond (YTM). In fact, the concept behind IRR is almost identical to the YTM concept.
FINANCIAL CALCULATOR
IRR (Uneven Inflows)
Function
CF
2nd
CLR WORK
YTM equates the present value of inflows (bond payments) to an outflow (the bond’s cost).
IRR equates the present value of inflows (project returns) to an outflow (the project’s cost).
Excel’s Goal Seek feature doesn’t use an equation. It operates by using an iterative method to find a solution. Specifically, it tries an initial input value to see whether that value produces the result you want. If it doesn’t, Goal Seek tries other input values until it converges on a solution.
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Table 12-5 Calculating IRR for Investments A and B
FINANCIAL CALCULATOR
IRR (Uneven Inflows)
Function
CF
2nd
CLR WORK
Returning to Table 12-5, you will notice that the inputs in the Goal Seek dialog box tell Excel to set the NPV value in cell D8 to the value 0 by changing the cell C2. When Excel finds the solution that satisfies the requirement, it has found the IRR. This value is 11.16 percent.
The IRR can also be calculated using Excel’s IRR function. See cell C10 for the proper syntax. Fortunately, the IRR function is more straightforward than the NPV function. Unlike the NPV function, the IRR function treats the first value entered as occurring at the beginning of the first period. Therefore, the IRR function only requires us to enter the range of values from B4 to B7. You will see that the IRR calculated using the IRR function is 11.16 percent, the same as that found using Goal Seek. The calculator keystrokes are shown in the margin.
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The IRR can be found for Investment B in an identical manner. The IRR for Investment B is 14.33 percent because this is the value that produces NPV = 0. The IRR is shown in cell C14 using Goal Seek, and the identical value is shown in cell D24 using the IRR function.
Now that we have determined the IRR of each investment, we will need to assess whether these returns are high enough to justify investing in the firm. The final selection of any project under the internal rate of return method will depend on whether the yield exceeds some minimum threshold, such as the firm’s cost of capital. You will recall that we assumed that the firm has a 10 percent weighted average cost of capital (WACC) in the preceding NPV analysis. Given this threshold, both projects are expected to produce returns in excess of the WACC.
Under most circumstances, both the net present value and the internal rate of return methods give theoretically correct answers. Payback is simple, and it may produce useful insights, but it is not theoretically sound. Payback’s usefulness depends on rules of thumb that differ from firm to firm, and it has serious shortcomings when applied to complicated cash flow patterns. Therefore, subsequent discussion will be restricted to further examination of the NPV and the IRR methods. A summary of the various conclusions reached under the three methods is presented in Table 12-6.
Table 12-6 Capital budgeting results
Selection Strategy
In both the internal rate of return and net present value methods, the profitability must equal or exceed the cost of capital for the project to be potentially acceptable. However, other distinctions are necessary—namely, whether the projects are mutually exclusive or not. If investments are mutually exclusive, the selection of one alternative will preclude the selection of any other alternative. Assume we are going to build a specialized assembly plant, and four major international cities are under consideration, only one of which will be picked. In this situation, we select the alternative with the highest acceptable yield or the highest net present value and disregard all others. Even if certain other locations provide a marginal return in excess of the cost of capital, assumed to be 10 percent, they will be rejected. In the table below, the possible alternatives are presented.
Mutually Exclusive Alternatives | IRR | Net Present Value |
Bangkok | 15% | $300 |
Beijing | 12 | 200 |
Mexico City | 11 | 100 |
Cost of capital | 10 | − |
Singapore | 9 | (100) |
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Among the mutually exclusive alternatives, only Bangkok would be selected. If the alternatives were not mutually exclusive (for example, much-needed multiple retail outlets), we would accept all of the alternatives that provide a return in excess of our cost of capital, and only Singapore would be rejected.
Applying this logic to Investments A and B in the prior discussion and assuming a cost of capital of 10 percent, only Investment B would be accepted if the alternatives were mutually exclusive, while both would clearly qualify if they were not mutually exclusive.
The discussion to this point has assumed the internal rate of return and net present value methods will call for the same decision. Although this is generally true, there are exceptions. Two rules may be stated:
1. Both methods will accept or reject the same investments based on minimum return or cost of capital criteria. If an investment has a positive net present value, it will also have an internal rate of return in excess of the cost of capital.
2. In certain limited cases, however, the two methods may give different answers in selecting the best investment from a range of acceptable alternatives.
Reinvestment Assumption
It is only under this second state of events that a preference for one method over the other must be established. A prime characteristic of the internal rate of return is the reinvestment assumption that all inflows can be reinvested at the yield from a given investment. For example, in the case of the aforementioned Investment A yielding 11.17 percent, the assumption is made that the dollar amounts coming in each year can be reinvested at that rate. For Investment B, with a 14.33 percent internal rate of return, the new funds are assumed to be reinvested at this high rate. The relationships are presented in Table 12-7.
Table 12-7 The reinvestment assumption—internal rate of return ($10,000 investment)
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For investments with a very high IRR, it may be unrealistic to assume that reinvestment can occur at an equally high rate. The net present value method, depicted in Table 12-8, makes the more conservative assumption that each inflow can be reinvested at the cost of capital or discount rate.
Table 12-8 The reinvestment assumption—net present value ($10,000 investment)
The reinvestment assumption under the net present value method allows for a certain consistency. Inflows from each project are assumed to have the same (though conservative) investment opportunity. Although this may not be an accurate picture for all firms, net present value is generally the preferred method.
Modified Internal Rate of Return You should also be aware of an alternative methodology that combines the reinvestment assumption of the net present value method (cost of capital) with the internal rate of return. This process is termed the modified internal rate of return (MIRR). The analyst searches for the discount rate that will equate the future value of the inflows, each growing at the cost of capital, with the investment. Here is the formula:
As can be seen in this equation, the MIRR is the discount rate that equates the future value of inflows with the value of the original investment. As an example, we will return to the cash flow stream from our NPV valuation of Investment B. Notice in the MIRR spreadsheet shown in Table 12-9 that for each of the cash inflows, we have calculated a future value in Column E. As an example, in line 6 we calculate the future value of the $1,500 inflow by assuming it is reinvested for four years at the 10 percent cost of capital. Specifically, $1,500 × 1.464 = $2,196.15, the value in cell E6. The sum of these future values ($18,383.15) in cell E11 represents the numerator in Formula 12-1.
Since we now know both the future value of the cash inflows and the present value of the outflows (the investment), we can use Excel’s RATE function to find the MIRR. Being careful to enter a zero for the pmt argument in the RATE function, we find that the MIRR is 12.95 percent.
Excel also offers an MIRR function that produces the same result, shown at the bottom of Table 12-9. The list of value arguments in the MIRR function are the same as those used in Excel’s IRR function, but a finance rate and reinvestment rate must be entered also. In most instances, including our example, these rates are the same.
Recall that the conventional internal rate of return for Investment B was 14.33 percent. The modified internal rate of return, using the more realistic assumption of reinvestment at the cost of capital, gives a more conservative, and more theoretically correct, answer. For that reason you should be familiar with it. However, both NPV and IRR are used more often by financial analysts than is the MIRR. Therefore, we will end our discussion of MIRR here and continue the analyses in this chapter using IRR where an internal return measure is needed. The MIRR indicates that when you have an IRR higher than the cost of capital, the MIRR will be smaller than the IRR. In the case of Investment A, the difference between the 11.17 percent IRR and the 10 percent cost of capital is small, and while the MIRR would fall below the cost of capital, it would not decline as much as Investment B.
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Table 12-9 Calculating MIRR for Investment B
Capital Rationing
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At times management may place an artificial constraint on the amount of funds that can be invested in a given period. This is known as capital rationing. The executive planning committee may emerge from a lengthy capital budgeting session to announce that only $5 million may be spent on new capital projects this year. Although $5 million may represent a large sum, it is still an artificially determined constraint and not the product of marginal analysis, in which the return for each proposal is related to the cost of capital for the firm, and projects with positive net present values are accepted.
A firm may adopt a posture of capital rationing because it is fearful of too much growth or hesitant to use external sources of financing (perhaps there is a fear of debt). In a strictly economic sense, capital rationing hinders a firm from achieving maximum profitability. With capital rationing, as indicated in Table 12-10, acceptable projects must be ranked, and only those with the highest positive net present value are accepted.
Table 12-10 Capital rationing
Under capital rationing, only Projects A through C, calling for $5 million in investment, will be accepted. Although Projects D and E have returns exceeding the cost of funds, as evidenced by a positive net present value, they will not be accepted with the capital rationing assumption.
Net Present Value Profile
An interesting way to summarize the characteristics of an investment is through the use of the net present value profile. The profile allows us to graphically portray the net present value of a project at different discount rates. Let’s apply the profile to the investments we discussed earlier in the chapter. The projects are summarized again here:
Cash Inflows (of $10,000 investment) | ||
Year | Investment A | Investment B |
1 | $5,000 | $1,500 |
2 | 5,000 | 2,000 |
3 | 2,000 | 2,500 |
4 | 5,000 | |
5 | 5,000 | |
To apply the net present value profile, you need to know three characteristics about an investment:
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1. The net present value at a zero discount rate. That is easy to determine. A zero discount rate means no discount rate. The values simply retain their original value. For Investment A, the net present value would be $2,000 ($5,000 + $5,000 + $2,000 − $10,000). For Investment B, the answer is $6,000 ($1,500 + $2,000 + $2,500 + $5,000 + $5,000 − $10,000).
2. The net present value as determined by a normal discount rate (such as the cost of capital). For these two investments, we use a discount rate of 10 percent. As previously summarized in Table 12-6, the net present values for the two investments at that discount rate are $180 for Investment A and $1,414 for Investment B.
3. The internal rate of return for the investments. Once again referring to Table 12-6, we see the internal rate of return is 11.17 percent for Investment A and 14.33 percent for Investment B. The reader should also realize the internal rate of return is the discount rate that allows the project to have a net present value of zero. This characteristic will become more apparent when we discuss our graphic display.
We summarize the information about discount rates and net present values for each investment here:
Note that in Figure 12-2, we have graphed the three points for each investment. For Investment A we showed a $2,000 net present value at a zero discount rate, a $180 net present value at a 10 percent discount rate, and a zero net present value at an 11.17 percent discount rate. We then connected the points. The same procedure was applied to Investment B. The reader can also visually approximate what the net present value for the investment projects would be at other discount rates (such as 5 percent).
In the current example, the net present value of Investment B was superior to Investment A at every point. This is not always the case in comparing various projects. To illustrate, let’s introduce a new project, Investment C, and then compare it with Investment B.
Investment C ($10,000 Investment) | |
Year | Cash Inflows |
1 | $9,000 |
2 | 3,000 |
3 | 1,200 |
Characteristics of Investment C
1. The net present value at a zero discount rate for this project is $3,200 ($9,000 + $3,000 + $1,200 − $10,000).
2. The net present value at a 10 percent discount rate is $1,560.
3. The internal rate of return is 22.51 percent.
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Figure 12-2 Net present value profile
Comparing Investment B to Investment C in Figure 12-3, we observe that at low discount rates, Investment B has a higher net present value than Investment C. However, at high discount rates, Investment C has a higher net present value than Investment B. The actual crossover point can be viewed as approximately 8.7 percent. At lower rates (below 8.7 percent), you would choose Investment B. At higher rates (above 8.7 percent), you would select Investment C. Since the cost of capital is presumed to be 10 percent, you would probably prefer Investment C.
Why does Investment B do well compared to Investment C at low discount rates and relatively poorly compared to Investment C at high discount rates? This difference is related to the timing of inflows. Let’s examine the inflows as reproduced in the following table.
Cash Inflows (of $10,000 investment) | ||
Year | Investment B | Investment C |
1 | $1,500 | $9,000 |
2 | 2,000 | 3,000 |
3 | 2,500 | 1,200 |
4 | 5,000 | |
5 | 5,000 | |
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Figure 12-3 Net present value profile with crossover
Investment B has heavy late inflows ($5,000 in both the fourth and fifth years), and these are more strongly penalized by high discount rates. Investment C has extremely high early inflows, and these hold up well with high discount rates.
As previously mentioned in the chapter, if the investments are nonmutually exclusive or there is no capital rationing, we would probably accept both Investments B and C at discount rates below 14.33 percent because they both would have positive net present values. If we can select only one, the decision may well turn on the discount rate. Observe in Figure 12-3 at a discount rate of 5 percent we would select Investment B, at 10 percent we would select Investment C, and so on. The net present value profile helps us make such decisions. Now back to basic capital budgeting issues.
Combining Cash Flow Analysis and Selection Strategy
Many of the points we have covered thus far will be reviewed in the context of a capital budgeting decision, in which we determine the annual cash flows from an investment and compare them to the initial outlay. To be able to analyze a wide variety of cash flow patterns, we shall first consider the types of allowable depreciation.
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The Rules of Depreciation
Through tax legislation, assets are classified according to nine categories that determine the allowable rate of depreciation write-off. Each class is referred to as a “MACRS” category; MACRS stands for modified accelerated cost recovery system. Some references are also made to ADR, which stands for asset depreciation range, or the expected physical life of the asset or class of assets. Most assets can be written off more rapidly than the midpoint of their ADR. For example, an asset may have a midpoint of its ADR of four years, which means the middle of its expected useful life is four years; this asset might be written off over three years. Table 12-11 shows the various categories for depreciation, linking the depreciation write-off period to the midpoint of the ADR.
It is not necessary that you become an expert in determining the category of an asset. In problems at the end of this material you will be given enough information to easily make a determination.
Each of the nine categories in Table 12-11 has its own rate of depreciation that can be applied to the purchase price of the asset. We will direct our attention to the first six categories in the table, which apply to assets normally used in business transactions. The last three categories relate to real estate investments and, for purposes of simplicity, will not be covered.
Table 12-11 Categories for depreciation write-off
Class | |
3-year MACRS | All property with ADR midpoints of four years or less. Autos and light trucks are excluded from this category. |
5-year MACRS | Property with ADR midpoints of more than 4, but less than 10 years. Key assets in this category include automobiles, light trucks, and technological equipment such as computers and research-related properties. |
7-year MACRS | Property with ADR midpoints of 10 years or more, but less than 16 years. Most types of manufacturing equipment would fall into this category, as would office furniture and fixtures. |
10-year MACRS | Property with ADR midpoints of 16 years or more, but less than 20 years. Petroleum refining products, railroad tank cars, and manufactured homes fall into this group. |
15-year MACRS | Property with ADR midpoints of 20 years or more, but less than 25 years. Land improvement, pipeline distribution, telephone distribution, and sewage treatment plants all belong in this category. |
20-year MACRS | Property with ADR midpoints of 25 years or more (with the exception of real estate, which is treated separately). Key investments in this category include electric and gas utility property and sewer pipes. |
27.5-year MACRS | Residential rental property if 80% or more of the gross rental income is from nontransient dwelling units (e.g., an apartment building); low-income housing. |
31.5-year MACRS | Nonresidential real property that has no ADR class life or whose class life is 27.5 years or more. |
39-year MACRS | Nonresidential real property placed in service after May 12, 1993. |
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The rates of depreciation that apply to the first six classes in Table 12-11 are shown in Table 12-12.3 The rates shown in Table 12-12 are developed with the use of the half-year convention, which treats all property as if it were put in service in midyear. The half-year convention is also extended to the sale or retirement of an asset. Thus for three-year MACRS depreciation, there are four years of depreciation to be taken, as demonstrated below:
Year 1 | ½ year | |
Year 2 | 1 year | |
Year 3 | 1 year | |
Year 4 | ½ year | |
3-year MACRS depreciation | ||
For five-year depreciation, there are six years to be taken, and so on.
Table 12-12 Depreciation percentages (expressed in decimals)
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Let’s return to Table 12-12 and assume you purchase a $50,000 asset that falls in the five-year MACRS category. How much would your depreciation be for the next six years? (Don’t forget that we get an extra year because of the half-year convention.) The depreciation schedule is shown in Table 12-13.
Table 12-13 Depreciation schedule
The Tax Rate
In analyzing investment decisions, a corporate tax rate must be considered. As mentioned in Chapter 2, the rate has been changed four times since 1980, and it is almost certain to be changed again in the future. Although the maximum quoted federal corporate tax rate is now in the mid–30 percent range, very few pay this rate. Smaller corporations and those with big tax breaks for research and development, new asset purchases, or natural resource development may only pay taxes at a 15 to 20 percent rate. Larger corporations with foreign tax obligations and special state levies may pay effective total taxes of 40 percent or more. In the following examples, we shall use a rate of 35 percent, but remember, the rate varies from situation to situation and from time period to time period. In the problems at the back of the chapter, you will be given a variety of tax rates with which to work.
Actual Investment Decision
Assume in the $50,000 depreciation analysis shown in Table 12-13 that we are given additional facts and asked to make an investment decision about whether an asset should be purchased or not. We shall assume we are purchasing a piece of machinery that will have a six-year productive life. It will produce income of $18,500 for the first three years before deductions for depreciation and taxes. In the last three years, the income before depreciation and taxes will be $12,000. Furthermore, we will assume a corporate tax rate of 35 percent and a cost of capital of 10 percent for the analysis. The annual cash flow related to the machinery is presented in Table 12-14. For each year we subtract depreciation from “earnings before depreciation and taxes” to arrive at earnings before taxes. We then subtract the taxes to determine earnings after taxes. Finally, depreciation is added to earnings after taxes to arrive at cash flow. The cash flow starts at $15,525 in the first year and ends at $8,815 in the last year.
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Table 12-14 Cash flow related to the purchase of machinery
Having determined the annual cash flows, we now are in a position to discount the values back to the present at the previously specified cost of capital, 10 percent. The analysis is presented in Table 12-15. At the bottom of the same table, the present value of the inflows is compared to the present value of the outflows (simply the cost of the asset) to arrive at a net present value of $7,991. On the basis of the analysis, it appears that the asset should be purchased.
Table 12-15 Net present value
The Replacement Decision
So far our analysis has centered on an investment that is being considered as a net addition to the present plant and equipment. However, many investment decisions occur because of new technology, and these are considered replacement decisions. The financial manager often needs to determine whether a new machine with advanced technology can do the job better than the machine being used at present.
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These replacement decisions include several additions to the basic investment situation. For example, we need to include the sale of the old machine in our analysis. This sale will produce a cash inflow that partially offsets the purchase price of the new machine. In addition, the sale of the old machine will usually have tax consequences. Some of the cash inflow from the sale will be taxable if the old machine is sold for more than book value. If it is sold for less than book value, this will be considered a loss and will provide a tax benefit.
The replacement decision can be analyzed by using a total analysis of both the old and new machines or by using an incremental analysis that emphasizes the changes in cash flows between the old and the new machines. We will emphasize the incremental approach.
Assume the Bradley Corporation purchased a computer two years ago for $120,000. The asset is being depreciated under the five-year MACRS schedule previously shown in Table 12-12, which implies a six-year write-off because of the half-year convention. We will assume the old computer can be sold for $37,600. A new computer will cost $180,000 and will also be written off using the five-year MACRS schedule in Table 12-12.
The new computer will provide cost savings and operating benefits, compared to the old computer, of $42,000 per year for the next six years. These cost savings and operating benefits are the equivalent of increased earnings before depreciation and taxes. The firm has a 35 percent tax rate and a 10 percent cost of capital. First we need to determine the net cost of the new computer. We will take the purchase price of the new computer ($180,000) and subtract the cash inflow from the sale of the old computer.
Sale of Old Asset
The cash inflow from the sale of the old computer is based on the sales price as well as the related tax factors. To determine these tax factors, we first compute the book value of the old computer and compare this figure to the sales price to determine if there is a taxable gain or loss. The book value of the old computer is shown in Table 12-16.
Table 12-16 Book value of old computer
Since the book value of the old computer is $57,600 and the sales price (previously given) is $37,600, there will be a $20,000 loss.
Book value | $57,600 |
Sales price | 37,600 |
Tax loss on sale | $20,000 |
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This loss can be written off against other income for the corporation.4 The Bradley Corporation has a 35 percent tax rate, so the tax write-off is worth $7,000.
Tax loss on sale | $20,000 |
Tax rate | 35% |
Tax benefit | $ 7,000 |
We now add the tax benefit to the sale price to arrive at the cash inflow from the sale of the old computer.
Sale price of old computer | $37,600 |
Tax benefit from sale | 7,000 |
Cash inflow from sale of old computer | $44,600 |
The computation of the cash inflow figure from the old computer allows us to compute the net cost of the new computer. The purchase price of $180,000, minus the cash inflow from the sale of the old computer, provides a value of $135,400 as indicated in Table 12-17.
Table 12-17 Net cost of new computer
Price of new computer | $180,000 |
− Cash flow from sale of old computer | 44,600 |
Net cost of new computer | $135,400 |
The question then becomes this: Are the incremental gains from the new computer compared to those of the old computer large enough to justify the net cost of $135,400? We will assume that both will be operative over the next six years, although the old computer will run out of depreciation in four more years. We will base our cash flow analysis on (a) the incremental gain in depreciation and the related tax shield benefits and (b) cost savings.
Incremental Depreciation
The annual depreciation on the new computer will be:
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The annual depreciation on the old computer for the remaining four years would be:
In Table 12-18, we bring together the depreciation on the old and new computers to determine incremental depreciation and the related tax shield benefits. Since depreciation shields other income from being taxed, the benefits of the tax shield are worth the amount being depreciated times the tax rate. For example, in year 1, $12,960 (third column below) in incremental depreciation will keep $12,960 from being taxed, and with the firm in a 35 percent tax bracket, this represents a tax savings of $4,536. The same type of analysis applies to each subsequent year.
Table 12-18 Analysis of incremental depreciation benefits
Cost Savings
The second type of benefit relates to the incremental cost savings from the new computer. As previously stated, these savings are assumed to be $42,000 for the next six years. The aftertax benefits are shown in Table 12-19.
Table 12-19 Analysis of incremental cost savings benefits
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As indicated in Table 12-19, we take the cost savings in column 2 and multiply by one minus the tax rate. This indicates the value of the savings on an aftertax basis.
We now combine the incremental tax shield benefits from depreciation (Table 12-18) and the aftertax cost savings (Table 12-19) to arrive at total annual benefits in Table 12-20 (column 4). These benefits are discounted to the present at a 10 percent cost of capital. The present value of the inflows is $150,950 as indicated at the bottom of column 6 in Table 12-20.
Table 12-20 Present value of the total incremental benefits
We now are in a position to compare the present value of incremental benefits of $150,950 from Table 12-20 to the net cost of the new computer of $135,400 from Table 12-17. The answer of $15,550 is shown here:
Present value of incremental benefits | $150,950 |
Net cost of new computer | 135,400 |
Net present value | $ 15,550 |
Clearly there is a positive net present value, and the purchase of the computer should be recommended on the basis of the financial analysis.
Elective Expensing
We have stressed throughout the chapter the importance of taking deductions as early in the life of the asset as possible. Since a tax deduction produces cash flow, the earlier you can get the cash flow the better. Businesses can actually write off tangible property, such as equipment, furniture, tools, and computers, in the year they are purchased for up to $250,000 under the 2008 Economic Stimulus Act. This is clearly superior to depreciating the asset when the write-off must take place over a number of years. This feature of elective expensing is primarily beneficial to small businesses because the allowance is phased out dollar for dollar when total property purchases exceed $800,000 in a year. Thus a business that purchases $1,050,000 in assets for the year no longer has this option.
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SUMMARY
The capital budgeting decision involves the planning of expenditures for a project with a life of at least one year and usually considerably longer. Although top management is often anxious about the impact of their decisions on short-term reported income, the planning of capital expenditures dictates a longer time horizon.
Because capital budgeting deals with actual dollars rather than reported earnings, cash flow instead of operating income is used in the decision.
Three primary methods are used to analyze capital investment proposals: the payback method, the internal rate of return, and the net present value. The first method is normally unsound, while the last two are acceptable, with net present value deserving our greatest attention. The net present value method uses the cost of capital as the discount rate. In using the cost of capital as the discount, or hurdle, rate, we affirm that a project must at least earn the cost of funding to be acceptable as an investment.
As demonstrated in the chapter, the two forms of benefits attributed to an investment are (a) aftertax operating benefits and (b) the tax shield benefits of depreciation. The present value of these inflows must exceed the investment for a project to be acceptable.
LIST OF TERMS
cash flow 381
payback 384
net present value 385
internal rate of return (IRR) 387
mutually exclusive 389
reinvestment assumption 390
modified internal rate of return (MIRR) 391
capital rationing 392
net present value profile 393
modified accelerated cost recovery system (MACRS) 397
asset depreciation range (ADR) 397
replacement decisions 400
incremental depreciation 403
elective expensing 404
DISCUSSION QUESTIONS
1. What are the important administrative considerations in the capital budgeting process? (LO12-1)
2. Why does capital budgeting rely on analysis of cash flows rather than on net income? (LO12-2)
3. What are the weaknesses of the payback method? (LO12-3)
4. What is normally used as the discount rate in the net present value method? (LO12-5)
5. What does the term mutually exclusive investments mean? (LO12-4)
6. How does the modified internal rate of return include concepts from both the traditional internal rate of return and the net present value methods? (LO12-4)
7. If a corporation has projects that will earn more than the cost of capital, should it ration capital? (LO12-5)
8. What is the net present value profile? What three points should be determined to graph the profile? (LO12-4)
9. How does an asset’s ADR (asset depreciation range) relate to its MACRS category? (LO12-2)
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PRACTICE PROBLEMS AND SOLUTIONS
Cash flow
(LO12-2)
1. Systems Software has earnings before depreciation and taxes of $180,000, depreciation of $60,000, and a tax rate of 35 percent. Compute its cash flow.
Depreciation and net present value
(LO12-4)
2. Archer Chemical Corp. is considering purchasing new equipment that falls under the three-year MACRS category. The cost is $200,000. Earnings before depreciation and taxes for the next four years will be:
Year 1 | $ 90,000 |
Year 2 | 105,000 |
Year 3 | 85,000 |
Year 4 | 35,000 |
The firm is in a 30 percent tax bracket and has a 12 percent cost of capital. Should it purchase the new equipment?
Solutions
1.
Earnings before depreciation and taxes | $180,000 |
Depreciation | 60,000 |
Earnings before taxes | $120,000 |
Taxes @ 35 percent | 42,000 |
Earnings after taxes | $ 78,000 |
Depreciation | 60,000 |
Cash flow | $138,000 |
2. First determine annual depreciation based on the $200,000 purchase price. Use Table 12-12 for the annual depreciation rate for three-year MACRS depreciation.
Then determine the annual cash flow for each year.
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Finally, determine the present value of the cash flows and compare that to the $200,000 cost to determine the net present value.
The net present value is positive, and the new equipment should be purchased.
PROBLEMS
Selected problems are available with Connect. Please see the preface for more information.
Basic Problems
Cash flow
(LO12-2)
1. Assume a corporation has earnings before depreciation and taxes of $90,000, depreciation of $40,000, and a 30 percent tax bracket. Compute its cash flow using the following format:
Earnings before depreciation and taxes | _________ |
Depreciation | _________ |
Earnings before taxes | _________ |
Taxes @ 30% | _________ |
Earnings after taxes | _________ |
Depreciation | _________ |
Cash flow | _________ |
Cash flow
(LO12-2)
2. Assume a corporation has earnings before depreciation and taxes of $100,000, depreciation of $40,000, and a 40 percent tax bracket.
a. Compute its cash flow using the following format:
Earnings before depreciation and taxes | _________ |
Depreciation | _________ |
Earnings before taxes | _________ |
Taxes @ 40% | _________ |
Earnings after taxes | _________ |
Depreciation | _________ |
b. Compute the cash flow for the company if depreciation is only $20,000.
c. How much cash flow is lost due to the reduced depreciation from $40,000 to $20,000?
Cash flow
(LO12-2)
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3. Assume a firm has earnings before depreciation and taxes of $200,000 and no depreciation. It is in a 40 percent tax bracket.
a. Compute its cash flow.
b. Assume it has $200,000 in depreciation. Recompute its cash flow.
c. How large a cash flow benefit did the depreciation provide?
Cash flow
(LO12-2)
4. Assume a firm has earnings before depreciation and taxes of $440,000 and depreciation of $140,000.
a. If it is in a 35 percent tax bracket, compute its cash flow.
b. If it is in a 20 percent tax bracket, compute its cash flow.
Cash flow versus earnings
(LO12-2)
5. Al Quick, the president of a New York Stock Exchange–listed firm, is very short-term oriented and interested in the immediate consequences of his decisions. Assume a project that will provide an increase of $2 million in cash flow because of favorable tax consequences, but carries a two-cent decline in earnings per share because of a write-off against first-quarter earnings. What decision might Mr. Quick make?
Payback method
(LO12-3)
6. Assume a $250,000 investment and the following cash flows for two products:
Year | Product X | Product Y |
1 | $90,000 | $50,000 |
2 | 90,000 | 80,000 |
3 | 60,000 | 60,000 |
4 | 20,000 | 70,000 |
Which alternatives would you select under the payback method?
Payback method
(LO12-3)
7. Assume a $40,000 investment and the following cash flows for two alternatives:
Year | Investment X | Investment Y |
1 | $ 6,000 | $15,000 |
2 | 8,000 | 20,000 |
3 | 9,000 | 10,000 |
4 | 17,000 | __ |
5 | 20,000 | __ |
Which of the alternatives would you select under the payback method?
Payback method
(LO12-3)
8. Assume a $90,000 investment and the following cash flows for two alternatives:
Year | Investment A | Investment B |
1 | $25,000 | $40,000 |
2 | 30,000 | 40,000 |
3 | 25,000 | 28,000 |
4 | 19,000 | __ |
5 | 25,000 | __ |
a. Calculate the payback for investments A and B.
b. If the inflow in the fifth year for Investment A was $25,000,000 instead of $25,000, would your answer change under the payback method?
Payback method
(LO12-3)
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9. The Short-Line Railroad is considering a $140,000 investment in either of two companies. The cash flows are as follows:
Year | Electric Co. | Water Works |
1 | $85,000 | $30,000 |
2 | 25,000 | 25,000 |
3 | 30,000 | 85,000 |
4–10 | 10,000 | 10,000 |
a. Using the payback method, what will the decision be?
b. Explain why the answer in part a can be misleading.
Payback and net present value
(LO12-3 & 12-4)
10. X-treme Vitamin Company is considering two investments, both of which cost $10,000. The cash flows are as follows:
Year | Project A | Project B |
1 | $12,000 | $10,000 |
2 | 8,000 | 6,000 |
3 | 6,000 | 16,000 |
a. Which of the two projects should be chosen based on the payback method?
b. Which of the two projects should be chosen based on the net present value method? Assume a cost of capital of 10 percent.
c. Should a firm normally have more confidence in answer a or answer b?
Internal rate of return
(LO12-4)
11. You buy a new piece of equipment for $16,230, and you receive a cash inflow of $2,500 per year for 12 years. What is the internal rate of return?
Internal rate of return
(LO12-4)
12. King’s Department Store is contemplating the purchase of a new machine at a cost of $22,802. The machine will provide $3,500 per year in cash flow for nine years. King’s has a cost of capital of 10 percent. Using the internal rate of return method, evaluate this project and indicate whether it should be undertaken.
Internal rate of return
(LO12-4)
13. Home Security Systems is analyzing the purchase of manufacturing equipment that will cost $50,000. The annual cash inflows for the next three years will be:
Year | Cash Flow |
1 | $25,000 |
2 | 23,000 |
3 | 18,000 |
a. Determine the internal rate of return.
b. With a cost of capital of 18 percent, should the machine be purchased?
Net present value method
(LO12-4)
14. Aerospace Dynamics will invest $110,000 in a project that will produce the following cash flows. The cost of capital is 11 percent. Should the project be undertaken? (Note that the fourth year’s cash flow is negative.)
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Year | Cash Flow |
1 | $36,000 |
2 | 44,000 |
3 | 38,000 |
4 | (44,000) |
5 | 81,000 |
Net present value method
(LO12-4)
15. The Horizon Company will invest $60,000 in a temporary project that will generate the following cash inflows for the next three years.
Year | Cash Flow |
1 | $15,000 |
2 | 25,000 |
3 | 40,000 |
The firm will also be required to spend $10,000 to close down the project at the end of the three years. If the cost of capital is 10 percent, should the investment be undertaken?
Net present value method
(LO12-4)
16. Skyline Corp. will invest $130,000 in a project that will not begin to produce returns until after the third year. From the end of the third year until the end of the 12th year (10 periods), the annual cash flow will be $34,000. If the cost of capital is 12 percent, should this project be undertaken?
Intermediate Problems
Net present value and internal rate of return methods
(LO12-4)
17. The Hudson Corporation makes an investment of $24,000 that provides the following cash flow:
Year | Cash Flow |
1 | $13,000 |
2 | 13,000 |
3 | 4,000 |
a. What is the net present value at an 8 percent discount rate?
b. What is the internal rate of return?
c. In this problem, would you make the same decision under both parts a and b?
Net present value and internal rate of return methods
(LO12-4)
18. The Pan American Bottling Co. is considering the purchase of a new machine that would increase the speed of bottling and save money. The net cost of this machine is $60,000. The annual cash flows have the following projections:
Year | Cash Flow |
1 | $23,000 |
2 | 26,000 |
3 | 29,000 |
4 | 15,000 |
5 | 8,000 |
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a. If the cost of capital is 13 percent, what is the net present value of selecting a new machine?
b. What is the internal rate of return?
c. Should the project be accepted? Why?
Use of a profitability index
(LO12-4)
19. You are asked to evaluate the following two projects for the Norton Corporation. Using the net present value method combined with the profitability index approach described in footnote 2 of this chapter, which project would you select? Use a discount rate of 14 percent.
Reinvestment rate assumption in capital budgeting
(LO12-4)
20. Turner Video will invest $76,344 in a project. The firm’s cost of capital is 10 percent. The investment will provide the following inflows:
Year | Inflow |
1 | $15,000 |
2 | 17,000 |
3 | 21,000 |
4 | 25,000 |
5 | 29,000 |
The internal rate of return is 11 percent.
a. If the reinvestment assumption of the net present value method is used, what will be the total value of the inflows after five years? (Assume the inflows come at the end of each year.)
b. If the reinvestment assumption of the internal rate of return method is used, what will be the total value of the inflows after five years?
c. Generally is one investment assumption likely to be better than another?
Modified internal rate of return
(LO12-4)
21. The Caffeine Coffee Company uses the modified internal rate of return. The firm has a cost of capital of 11 percent. The project being analyzed is as follows ($26,000 investment):
Year | Cash Flow |
1 | $12,000 |
2 | 11,000 |
3 | 9,000 |
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a. What is the modified internal rate of return? An approximation from Appendix B is adequate. (You do not need to interpolate.)
b. Assume the traditional internal rate of return on the investment is 17.5 percent. Explain why your answer in part a would be lower.
Capital rationing and mutually exclusive investments
(LO12-4)
22. The Suboptimal Glass Company uses a process of capital rationing in its decision making. The firm’s cost of capital is 10 percent. It will only invest $77,000 this year. It has determined the internal rate of return for each of the following projects:
Project | Project Size | Internal Rate of Return |
A | $10,500 | 21% |
B | 30,500 | 22 |
C | 25,500 | 18 |
D | 10,500 | 13 |
E | 10,500 | 20 |
F | 20,500 | 11 |
G | 10,500 | 16 |
a. Select the projects that the firm should accept.
b. If Projects A and B are mutually exclusive, how would that affect your overall answer? That is, which projects would you accept in spending the $77,000?
Advanced Problems
Net present value profile
(LO12-4)
23. Keller Construction is considering two new investments. Project E calls for the purchase of earthmoving equipment. Project H represents an investment in a hydraulic lift. Keller wishes to use a net present value profile in comparing the projects. The investment and cash flow patterns are as follows:
a. Determine the net present value of the projects based on a zero percent discount rate.
b. Determine the net present value of the projects based on a 9 percent discount rate.
c. The internal rate of return on Project E is 13.25 percent, and the internal rate of return on Project H is 16.30 percent. Graph a net present value profile for the two investments similar to Figure 12-3. (Use a scale up to $8,000 on the vertical axis, with $2,000 increments. Use a scale up to 20 percent on the horizontal axis, with 5 percent increments.)
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d. If the two projects are not mutually exclusive, what would your acceptance or rejection decision be if the cost of capital (discount rate) is 8 percent? (Use the net present value profile for your decision; no actual numbers are necessary.)
e. If the two projects are mutually exclusive (the selection of one precludes the selection of the other), what would be your decision if the cost of capital is (1) 6 percent, (2) 13 percent, (3) 18 percent? Once again, use the net present value profile for your answer.
Net present value profile
(LO12-4)
24. Davis Chili Company is considering an investment of $35,000, which produces the following inflows:
Year | Cash Flow |
1 | $16,000 |
2 | 15,000 |
3 | 12,000 |
You are going to use the net present value profile to approximate the value for the internal rate of return. Please follow these steps:
a. Determine the net present value of the project based on a zero discount rate.
b. Determine the net present value of the project based on a 10 percent discount rate.
c. Determine the net present value of the project based on a 15 percent discount rate (it will be negative).
d. Draw a net present value profile for the investment and observe the discount rate at which the net present value is zero. This is an approximation of the internal rate of return based on the procedure presented in this chapter.
MACRS depreciation and cash flow
(LO12-2)
25. Telstar Communications is going to purchase an asset for $380,000 that will produce $180,000 per year for the next four years in earnings before depreciation and taxes. The asset will be depreciated using the three-year MACRS depreciation schedule in Table 12-12. (This represents four years of depreciation based on the half-year convention.) The firm is in a 35 percent tax bracket. Fill in the following schedule for the next four years:
Earnings before depreciation and taxes | _________ |
Depreciation | _________ |
Earnings before taxes | _________ |
Taxes | _________ |
Earnings after taxes + Depreciation | _________ |
Cash flow | _________ |
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MACRS depreciation categories
(LO12-4)
26. Assume $65,000 is going to be invested in each of the following assets. Using Tables 12-11 and 12-12, indicate the dollar amount of the first year’s depreciation.
a. Office furniture.
b. Automobile.
c. Electric and gas utility property.
d. Sewage treatment plant.
MACRS depreciation and net present value
(LO12-4)
27. The Summit Petroleum Corporation will purchase an asset that qualifies for three-year MACRS depreciation. The cost is $160,000 and the asset will provide the following stream of earnings before depreciation and taxes for the next four years:
Year 1 | $70,000 |
Year 2 | 85,000 |
Year 3 | 42,000 |
Year 4 | 40,000 |
The firm is in a 35 percent tax bracket and has an 8 percent cost of capital. Should it purchase the asset? Use the net present value method.
MACRS depreciation and net present value
(LO12-4)
28. Oregon Forest Products will acquire new equipment that falls under the five-year MACRS category. The cost is $300,000. If the equipment is purchased, the following earnings before depreciation and taxes will be generated for the next six years:
Year 1 | $112,000 |
Year 2 | 105,000 |
Year 3 | 82,000 |
Year 4 | 53,000 |
Year 5 | 37,000 |
Year 6 | 32,000 |
The firm is in a 30 percent tax bracket and has a 14 percent cost of capital. Should Oregon Forest Products purchase the equipment? Use the net present value method.
MACRS depreciation and net present value
(LO12-4)
29. Universal Electronics is considering the purchase of manufacturing equipment with a 10-year midpoint in its asset depreciation range (ADR). Carefully refer to Table 12-11 to determine in what depreciation category the asset falls. (Hint: It is not 10 years.) The asset will cost $120,000, and it will produce earnings before depreciation and taxes of $37,000 per year for three years, and then $19,000 a year for seven more years. The firm has a tax rate of 40 percent. With a cost of capital of 12 percent, should it purchase the asset? Use the net present value method. In doing your analysis, if you have years in which there is no depreciation, merely enter a zero for depreciation.
Working capital requirements in capital budgeting
(LO12-4)
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30. The Spartan Technology Company has a proposed contract with the Digital Systems Company of Michigan. The initial investment in land and equipment will be $120,000. Of this amount, $70,000 is subject to five-year MACRS depreciation. The balance is in nondepreciable property. The contract covers six years; at the end of six years, the nondepreciable assets will be sold for $50,000. The depreciated assets will have zero resale value.
The contract will require an additional investment of $55,000 in working capital at the beginning of the first year and, of this amount, $25,000 will be returned to the Spartan Technology Company after six years.
The investment will produce $50,000 in income before depreciation and taxes for each of the six years. The corporation is in a 40 percent tax bracket and has a 10 percent cost of capital. Should the investment be undertaken? Use the net present value method.
Tax losses and gains in capital budgeting
(LO12-2)
31. An asset was purchased three years ago for $120,000. It falls into the five-year category for MACRS depreciation. The firm is in a 35 percent tax bracket. Compute the following:
a. Tax loss on the sale and the related tax benefit if the asset is sold now for $15,060.
b. Gain and related tax on the sale if the asset is sold now for $56,060. (Refer to footnote 4 in the chapter.)
Capital budgeting with cost of capital computation
(LO12-5)
32. DataPoint Engineering is considering the purchase of a new piece of equipment for $240,000. It has an eight-year midpoint of its asset depreciation range (ADR). It will require an additional initial investment of $140,000 in nondepreciable working capital. Thirty-five thousand dollars of this investment will be recovered after the sixth year and will provide additional cash flow for that year. Here is the projected income before depreciation and taxes for the next six years:
Year | Amount |
1 | $185,000 |
2 | 160,000 |
3 | 130,000 |
4 | 115,000 |
5 | 95,000 |
6 | 85,000 |
The tax rate is 40 percent. The cost of capital must be computed based on the following (round the final value to the nearest whole number):
a. Determine the annual depreciation schedule.
b. Determine annual cash flow. Include recovered working capital in the sixth year.
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c. Determine the weighted average cost of capital.
d. Determine the net present value. Should DataPoint purchase the new equipment?
Replacement decision analysis
(LO12-4)
33. Hercules Exercise Equipment Co. purchased a computerized measuring device two years ago for $58,000. The equipment falls into the five-year category for MACRS depreciation and can currently be sold for $24,800.
A new piece of equipment will cost $148,000. It also falls into the five-year category for MACRS depreciation. Assume the new equipment would provide the following stream of added cost savings for the next six years:
Year | Cost Savings |
1 | $62,000 |
2 | 54,000 |
3 | 52,000 |
4 | 50,000 |
5 | 47,000 |
6 | 36,000 |
The firm’s tax rate is 35 percent and the cost of capital is 12 percent.
a. What is the book value of the old equipment?
b. What is the tax loss on the sale of the old equipment?
c. What is the tax benefit from the sale?
d. What is the cash inflow from the sale of the old equipment?
e. What is the net cost of the new equipment? (Include the inflow from the sale of the old equipment.)
f. Determine the depreciation schedule for the new equipment.
g. Determine the depreciation schedule for the remaining years of the old equipment.
h. Determine the incremental depreciation between the old and new equipment and the related tax shield benefits.
i. Compute the aftertax benefits of the cost savings.
j. Add the depreciation tax shield benefits and the aftertax cost savings, and determine the present value. (See Table 12-20 as an example.)
k. Compare the present value of the incremental benefits (j) to the net cost of the new equipment (e). Should the replacement be undertaken?
COMPREHENSIVE PROBLEM
Woodruff Corporations
(Replacement decision analysis)
(LO12-4)
The Woodruff Corporation purchased a piece of equipment three years ago for $230,000. It has an asset depreciation range (ADR) midpoint of eight years. The old equipment can be sold for $90,000.
A new piece of equipment can be purchased for $320,000. It also has an ADR of eight years.
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Assume the old and new equipment would provide the following operating gains (or losses) over the next six years:
Year | New Equipment | Old Equipment |
1 | $80,000 | $25,000 |
2 | 76,000 | 16,000 |
3 | 70,000 | 9,000 |
4 | 60,000 | 8,000 |
5 | 50,000 | 6,000 |
6 | 45,000 | (7,000) |
The firm has a 36 percent tax rate and a 9 percent cost of capital. Should the new equipment be purchased to replace the old equipment?
WEB EXERCISE
1. Texas Instruments was referred to in the chapter as being an innovator in the calculator industry. But that is only one of its products. Let’s see how this large company is doing today. Go to finance.yahoo.com and in the “Get Quotes” box type TXN.
2. Click on “Profile” in the left margin. Write a one-paragraph description of its major operations.
3. Returning to TXN’s summary page, record the following:
a. Last trade price.
b. 52-week low.
c. 52-week high.
4. Now click on “Basic Chart” in the left margin and scroll down to see the pattern for the last year. Scroll up and click on “5Y” and scroll down to the summary data for five years. Finally, click on the S&P (Standard & Poor’s 500 Stock Index) box above and also click on “Compare.” Scroll down and review the summary data for that period. Write a paragraph describing TXN’s stock performance.
Note: Occasionally a topic we have listed may have been deleted, updated, or moved into a different location on a website. If you click on the site map or site index, you will be introduced to a table of contents that should aid you in finding the topic you are looking for.
1As explained in Chapter 2, depreciation is not a new source of funds (except in tax savings) but represents a noncash outlay to be added back.
2A further possible refinement under the net present value method is to compute a profitability index.
For Investment A the profitability index is 1.0180 ($10,180/$10,000), and for Investment B it is 1.1414 ($11,414/$10,000). The profitability index can be helpful in comparing returns from different-size investments by placing them on a common measuring standard. This was not necessary in this example.
3The depreciation rates were temporarily increased under the Job Creation and Worker Assistance Act of 2002. Since this provision is only applicable for assets purchased after September 10, 2001, and before September 11, 2004, it is not considered here.
4Note that had there been a capital gain instead of a loss, it would have been automatically taxed at the corporation’s normal tax rate.