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BUSI 2504 (24)

suggestedProblems_ch09_sol.doc

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School
Department
Course
BUSI 2504
Professor
Robert Riordan
Semester
Fall

Description
CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA Learning Objectives LO1 How to compute the net present value and why it is the best decision criterion. LO2 The payback rule and some of its shortcomings. LO3 The discounted payback rule and some of its shortcomings. LO4 Accounting rates of return and some of the problems with them. LO5 The internal rate of return criterion and its strengths and weaknesses. LO6 The modified internal rate of return. LO7 The profitability index and its relation to net present value. Answers to Concepts Review and Critical Thinking Questions 2. (LO2, 3, 6, 7) If a project has a positive NPV for a certain discount rate, then it will also have a positive NPV for a zero discount rate; thus, the payback period must be less than the project life. Since discounted payback is calculated at the same discount rate as is NPV, if NPV is positive, the discounted payback period must be less than the project’s life. If NPV is positive, then the present value of future cash inflows is greater than the initial investment cost; thus PI must be greater than 1. If NPV is positive for a certain discount rate R, then it will be zero for some larger discount rate R*; thus the IRR must be greater than the required return. 4. (LO3) a. The discounted payback is calculated the same as is regular payback, with the exception that each cash flow in the series is first converted to its present value. Thus discounted payback provides a measure of financial/economic break-even because of this discounting; just as regular payback provides a measure of accounting break-even because it does not discount the cash flows. Given some predetermined cutoff for the discounted payback period, the decision rule is to accept projects that whose discounted cash flows payback before this cutoff period, and to reject all other projects. b. The primary disadvantage to using the discounted payback method is that it ignores all cash flows that occur after the cutoff date, thus biasing this criterion towards short-term projects. As a result, the method may reject projects that in fact have positive NPVs, or it may accept projects with large future cash outlays resulting in negative NPVs. In addition, the selection of a cutoff point is again an arbitrary exercise. c. Discounted payback is an improvement on regular payback because it takes into account the time value of money. For conventional cash flows and strictly positive discount rates, the discounted payback will always be greater than the regular payback period. 6. (LO1) a. NPV is simply the present value of a project’s cash flows. NPV specifically measures, after considering the time value of money, the net increase or decrease in firm wealth due to the project. The decision rule is to accept projects that have a positive NPV, and reject projects with a negative NPV. b. NPV is superior to the other methods of analysis presented in the text because it has no serious flaws. The method unambiguously ranks mutually exclusive projects, and can differentiate between projects of different scale and time horizon. The only drawback to NPV is that it relies on cash flow and discount rate values that are often estimates and not certain, but this is a problem shared by the other performance criteria as well. A project with NPV = \$2,500 implies that the total shareholder wealth of the firm will increase by \$2,500 if the project is accepted. 87 8. (LO7) a. The profitability index is the present value of cash inflows relative to the project cost. As such, it is a benefit/cost ratio, providing a measure of the relative profitability of a project. The profitability index decision rule is to accept projects with a PI greater than one, and to reject projects with a PI less than one. b. PI = (NPV + cost)/cost = 1 + (NPV/cost). If a firm has a basket of positive NPV projects and is subject to capital rationing, PI may provide a good ranking measure of the projects, indicating the “bang for the buck” of each particular project. 10. (LO1) There are a number of reasons. Two of the most important have to do with transportation costs and exchange rates. Manufacturing in the U.S. places the finished product much closer to the point of sale, resulting in significant savings in transportation costs. It also reduces inventories because goods spend less time in transit. Higher labor costs tend to offset these savings to some degree, at least compared to other possible manufacturing locations. Of great importance is the fact that manufacturing in the U.S. means that a much higher proportion of the costs are paid in dollars. Since sales are in dollars, the net effect is to immunize profits to a large extent against fluctuations in exchange rates. This issue is discussed in greater detail in the chapter on international finance. 12. (LO1, 7) Yes, they are. Such entities generally need to allocate available capital efficiently, just as for-profits do. However, it is frequently the case that the “revenues” from not-for-profit ventures are not tangible. For example, charitable giving has real opportunity costs, but the benefits are generally hard to measure. To the extent that benefits are measurable, the question of an appropriate required return remains. Payback rules are commonly used in such cases. Finally, realistic cost/benefit analysis along the lines indicated should definitely be used by governments and would go a long way toward balancing the budget! 14. (LO1, 6) The statement is incorrect. It is true that if you calculate the future value of all intermediate cash flows to the end of the project at the required return, then calculate the NPV of this future value and the initial investment, you will get the same NPV. However, NPV says nothing about reinvestment of intermediate cash flows. The NPV is the present value of the project cash flows. What is actually done with those cash flows once they are generated is not relevant. Put differently, the value of a project depends on the cash flows generated by the project, not on the future value of those cash flows. The fact that the reinvestment “works” only if you use the required return as the reinvestment rate is also irrelevant simply because reinvestment is not relevant in the first place to the value of the project. One caveat: Our discussion here assumes that the cash flows are truly available once they are generated, meaning that it is up to firm management to decide what to do with the cash flows. In certain cases, there may be a requirement that the cash flows be reinvested. For example, in international investing, a company may be required to reinvest the cash flows in the country in which they are generated and not “repatriate” the money. Such funds are said to be “blocked” and reinvestment becomes relevant because the cash flows are not truly available. Solutions to Questions and Problems NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic 88 2. (LO2) To calculate the payback period, we need to find the time that the project has recovered its initial investment. The cash flows in this problem are an annuity, so the calculation is simpler. If the initial cost is \$3,000, the payback period is: Payback = 3 + (\$420 / \$860) = 3.49 years There is a shortcut to calculate the future cash flows are an annuity. Just divide the initial cost by the annual cash flow. For the \$3,000 cost, the payback period is: Payback = \$3,000 / \$860 = 3.49 years For an initial cost of \$5,000, the payback period is: Payback = \$5,000 / \$860 = 5.81 years The payback period for an initial cost of \$7,000 is a little trickier. Notice that the total cash inflows after eight years will be: Total cash inflows = 8(\$860) = \$6,880 If the initial cost is \$7,000, the project never pays back. Notice that if you use the shortcut for annuity cash flows, you get: Payback = \$7,000 / \$860 = 8.14 years. This answer does not make sense since the cash flows stop after eight years, so again, we must conclude the payback period is never. 3. (LO2) Project A has cash flows of \$35,000 in Year 1, so the cash flows are short by \$15,000 of recapturing the initial investment, so the payback for Project A is: Payback = 1 + (\$15,000 / \$21,000) = 1.71 years Project B has cash flows of: Cash flows = \$15,000 + 22,000 + 31,000 = \$68,000 during this first three years. The cash flows are still short by \$2,000 of recapturing the initial investment, so the payback for Project B is: B: Payback = 3 + (\$2,000 / \$240,000) = 3.008 years Using the payback criterion and a cutoff of 3 years, accept project A and reject project B. 4. (LO3) When we use discounted payback, we need to find the value of all cash flows today. The value today of the project cash flows for the first four years is: Value today of Year 1 cash flow = \$6,500/1.14 2 = \$5,701.75 Value today of Year 2 cash flow = \$7,000/1.14 = \$5,386.27 Value today of Year 3 cash flow = \$7,500/1.14 = \$5,062.29 Value today of Year 4 cash flow = \$8,000/1.14 = \$4,736.64 To find the discounted payback, we use these values to find the payback period. The discounted first year cash flow is \$5,701.75, so the discounted payback for an \$8,000 initial cost is: Discounted payback = 1 + (\$8,000 – 5,701.75)/\$5,386.27 = 1.43 years 89 For an initial cost of \$13,000, the discounted payback is: Discounted payback = 2 + (\$13,000 – 5,701.75 – 5,386.27)/\$5,062.29 = 2.38 years Notice the calculation of discounted payback. We know the payback period is between two and three years, so we subtract the discounted values of the Year 1 and Year 2 cash flows from the initial cost. This is the numerator, which is the discounted amount we still need to make to recover our initial investment. We divide this amount by the discounted amount we will earn in Year 3 to get the fractional portion of the discounted payback. If the initial cost is \$18,000, the discounted payback is: Discounted payback = 3 + (\$18,000 – 5,701.75 – 5,386.27 – 5,062.29) / \$4,736.64 = 3.39 years 6. (LO4) Our definition of AAR is the average net income divided by the average book value. The average net income for this project is: Average net income = (\$1,632,000 + 2,106,500 + 1,941,700 + 1,298,000) / 4 = \$1,744,550 And the average book value is: Average book value = (\$18,000,000 + 0) / 2 = \$9,000,000 So, the AAR for this project is: AAR = Average net income / Average book value = \$1,744,500 / \$9,000,000 = .1938 or 19.38% 8. (LO1) The NPV of a project is the PV of the outflows minus the PV of the inflows. The equation for the NPV of this project at an 11 percent required return is: NPV = – \$30,000 + \$13,000/1.11 + \$19,000/1.11 + \$12,000/1.11 = \$5,906.83 At an 11 percent required return, the NPV is positive, so we would accept the project. The equation for the NPV of the project at a 30 percent required return is: 2 3 NPV = – \$30,000 + \$13,000/1.30 + \$19,000/1.30 + \$12,000/1.30 = –\$3,295.40 At a 30 percent required return, the NPV is negative, so we would reject the project. 10. (LO5) The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is: 0 = –\$18,000 + \$9,800/(1+IRR) + \$7,500/(1+IRR) + \$7,300/(1+IRR) 3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 18.49% 12. (LO1, 5) a. The IRR is the interest rate that makes the NPV of the project equal to zero. The equation for the IRR of Project A is: 0 = –\$37,000 + \$19,000/(1+IRR) + \$14,500/(1+IRR) + \$12,000/(1+IRR) + \$9,000/(1+IRR) 4
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