# The npv of the project at the firms 10 cost of

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Unformatted text preview: he NPV of the project (at the firm’s 10% cost of capital) is \$16,867 and its IRR is 15%. Clearly, the project is acceptable (NPV = \$16,867 \$0 and IRR = 15% 10% cost of capital). Table 9.5 demonstrates calculation of the project’s future value at the end of its 3-year life, assuming both a 10% (its cost of capital) and a 15% (its IRR) rate of return. A future value of \$248,720 results from reinvestment at the 10% cost of capital (total in column 5), and a future value of \$258,496 results from reinvestment at the 15% IRR (total in column 7). If the future value in each case in Table 9.5 were viewed as the return received 3 years from today from the \$170,000 initial investment, the cash flows would be those given in Table 9.6. The NPVs and IRRs in each case are shown below the cash flows in Table 9.6. You can see that at the 10% reinvestment rate, the NPV remains at \$16,867; reinvestment at the 15% IRR produces an NPV of \$24,213. From this result, it should be clear that the NPV technique assumes reinvestment at the cost of capital (10% in this example). (Note that with reinvestment at 10%, the IRR would be 13.5%.) On the other hand, the IRR technique assumes an ability to reinvest intermediate cash inflows at the IRR. If reinvestment does not occur at this rate, the IRR will differ from 15%. Reinvestment at a rate below the IRR would result in an IRR below that calculated (at 13.5%, for example, if the reinvestment rate were only 10%). Reinvestment at a rate above the IRR would result in an IRR above that calculated. In general, projects with similar-size investments and lower cash inflows in the early years tend to be preferred at lower discount rates.6 Projects that have 6. Because differences in the relative sizes of initial investments can also affect conflicts in rankings, the initial investments are assumed to be similar. This permits isolation of the effect of differences in the magnitude and timing of cash inflows on project rankings. 410 PART 3 Long-Term Investment Decisions TABLE 9.6 Project Cash Flows After Reinvestment Reinvestment Rate 10% Initial investment Year 15% \$170,000 Operating cash inflows 1 \$ 0 \$ 0 2 0 0 3 248,720 258,496 \$ 16,867 \$ 24,213 13.5% 15.0% NPV @ 10% IRR higher cash inflows in the early years tend to be preferred at higher discount rates. Why? Because at high discount rates, later-year cash inflows tend to be severely penalized in present value terms. For example, at a high discount rate, say 20 percent, the present value of \$1 received at the end of 5 years is about 40 cents, whereas for \$1 received at the end of 15 years it is less than 7 cents. Clearly, at high discount rates a project’s early-year cash inflows count most in terms of its NPV. Table 9.7 summarizes the preferences associated with extreme discount rates and dissimilar cash inflow patterns. EXAMPLE Bennett Company’s projects A and B were found to have conflicting rankings at the firm’s 10% cost of capital (as depicted in Figure 9.4). If we revi...
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