Veronica Tanner, the president of Tanner Enterprises, is considering two investm
ID: 2366488 • Letter: V
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Veronica Tanner, the president of Tanner Enterprises, is considering two investment opportunities. Because of limited resources, she will be able to invest in only one of them. Project A is to purchase a machine that will enable factory automation; the machine is expected to have a useful life of four years and no salvage value. Project B supports a training program that will improve the skills of employees operating the current equipment. Initial cash expenditures for Project A are $100,000 and for Project B are $40,000 The annual expected cash inflows are $31, 487 for Project A are $100,000 and $13,169 for Project B. Both investments are expected to provide cash flow benefits for the next four years. Tanner enterprise's cost of capital is 8 percent. a. Compute the net present value of each project. Which project should be adopted based on the net present value approach? b. Compute the approximate internal rate of return of each project. Which one should be adopted based on the intermal rate of return approach? c. Compare the net present value approach with the internal rate of return approach. Which method is better in the given circumstances? Why?Explanation / Answer
Internal Rate of Return The second discounted cash flow measure, IRR, has traditionally been defined as the [sic, any] discount rate at which NPV is equal zero. NPV has been applauded and IRR criticized for decades. While the focus of the criticism has been on using IRR in capital budgeting decisions, the unfavorable coverage has spilled over into other areas. Analysis of the reasons given for supposed IRR inferiority is the focus of this paper. Correcting the misperception is the result. IRR is used extensively despite the textbook criticism. Business people often favor it. For one thing, IRR is very good for screening projects. NPV is highly sensitive to the discount rate, while IRR bypasses the problem of deciding the "correct" one. Because IRR is a rate or ratio, not an absolute amount, it is more useful for comparing unlike investments, say stocks and bonds. It also is more useful for making comparisons between different periods and different sized firms and for making international comparisons. The intention here is not to argue for either point of view, but instead to put the issue into balance. The aim is to show: NPV and IRR have essentially equivalent utility; they are complementary ways of looking at a problem or opportunity; IRR and NPV together give a better analysis than either alone; if properly viewed, NPV and IRR give identical signals, including capital budgeting decisions; IRR is particularly useful for comparing different sized projects, where it receives some of its greatest criticism; and IRR is useful alone. We will critically examine the professed reasons for the superiority of NPV over IRR in capital budgeting.(2) Criticism Number One: Inflows versus Outflows IRR is the same even if the cash flows are reversed or inverted. For example, the IRR is 25 percent for both of the following: Table 1. Positive versus Negative Cash Flows Project Year 0 Year 1 NPV @ 10% IRR A -$1,000 +$1,250 +$136.36 25% B +$1,000 -$1,250 -$136.36 25% See S05A.TXT & S05B.TXT for these calculations. This criticism, simply stated, is that IRR does not keep track of the sign. This is misdirected. If you borrow money, you will pay the interest, not receive it. Interest rate tables use positive amounts and rates. Interest rate calculation routines use positive principal. We are accustomed to keeping track of borrower and lender outside the actual calculations.(3) Why should IRR be treated differently from its interest rate counterpart? Why would we even analyze a project that will lose money or a government project with higher costs and lower benefits?(4) Project B should be eliminated in preliminary screening, but the reason is not always as obvious as it is in Table 1. The criticism is typically presented as it is in Table 2, but without the total. Table 2. "Conflicting" IRR/NPV Signals Project Year 0 Year 1 Year 2 Year 3 Total NPV @ 10% IRR C +$1,000 -$3,600 +$4,300 -$1,760 -$60 -$41.32 60% See S05C.TXT for these calculations. Although the IRR is 60 percent, NPV is negative at all discount rates including zero. (Note that undiscounted net cash flow is a negative $60). This is simply a variation of negative versus positive cash flows discussed above. Look at the project from the perspective of making money, not losing it. Then IRR and NPV give identical decisions.(5) It is tempting to correct this supposed problem by simply redefining IRR. Internal rate of return in this case is at best misleading. The Project C "IRR" is a rate of payment or outflow, not a rate of return. If IRR were simply redefined, much of its criticism would go away. Interest as something we either pay or receive. We should treat IRR the same.(6) This is a good place to deviate briefly and examine the relationships between IRR and positive and negative NPVs. See Table 3. Table 3. NPV/IRR Relationships Discount Rate 0% 20% 40% 60% 80% 100% Net Present Value Normal IRR Noninterest +$60.00 +$32.41 +$18.75 $0.00 -$25.38 -$55.00 Inverted IRR Nonsensical -$60.00 -$32.41 -$18.75 $0.00 +$25.38 +$55.00 Note that tripling the discount rate from 20 to 60 percent only changed NPV by $32.31--hardly worth analyzing. Yet, if NPV were in millions of dollars, we would pay closer attention, though IRR would be unchanged. Large changes in the discount rate may change NPV significantly or very little, depending on the size of the cash flows. IRR, on the other hand, is dependent more so on the structure of the cash flows. NPV is a better absolute measure; IRR is a better relative measure. The two measures complement each other. With net-positive cash flows, NPV decreases from maximum at a zero percent discount rate and converges on zero as it increases. This is normal. But once past zero NPV, where IRR is determined, NPV is negative at all discount rates. This latter area is of no interest. Finally, with net-negative cash flows, NPV also converges on zero NPV with an increasing discount rate. After zero, NPV increases with an increasing discount rate. This implies that although we were losing money at all discount rates below 60 percent, the project became profitable at 80 percent. Worse still, the higher the discount rate, the more attractive it becomes. This suggests we can turn around an unfavorable project by increasing our opportunity cost of capital. This is nonsensical, but incorporated then ignored in the negative-positive criticism. Criticism Number Two: Mutually Exclusive Projects IRR can supposedly give a different decision from NPV on mutually exclusive projects. See Table 4. Table 4. Mutually Exclusive Projects Project Year 0 Year 1 NPV @ 0% NPV @ 10% IRR E -$1,000 +$2,000 +$1,000 +$818.18 100.0% F -$10,000 +$15,000 +$5,000 +$3,636.36 50.0% See S05E.TXT or S05F.TXT for these calculations. The criticism is that although the IRR of Project E is greater, investing in Project F will make you $3,636.36 better off and is therefore preferred. Of course this is correct! We would clearly expect that an investment that is 10 times larger would create the larger NPV. But it is only 4.4 times larger. We also get a larger NPV by investing in two bonds at 5 percent yield than by investing in one at 6 percent. But this does not mean we should always look for the lowest yield and buy more of them. We should expect the same in capital budgeting. Being able to invest in only one of the two projects is called a "constrained financing" assumption in capital budgeting parlance
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