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Course: ECON 224, Spring 2012
School: Macquarie
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Financial ACCG253 Management Tutorial 5 Chapter 8 Net Present and Other Investment Criteria Solutions to Questions and Problems Basic 2. 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 \$3,400, the payback period is: Payback = 4 + \$360 / \$760 Payback...

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Financial ACCG253 Management Tutorial 5 Chapter 8 Net Present and Other Investment Criteria Solutions to Questions and Problems Basic 2. 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 \$3,400, the payback period is: Payback = 4 + \$360 / \$760 Payback = 4.47 years There is a shortcut to calculate payback period when the future cash flows are an annuity. Just divide the initial cost by the annual cash flow. For the \$3,400 cost, the payback period is: Payback = \$3,400 / \$760 Payback = 4.47 years For an initial cost of \$4,450, the payback period is: Payback = \$4,450 / \$760 Payback = 5.86 years The payback period for an initial cost of \$6,800 is a little trickier. Notice that the total cash inflows after eight years will be: Total cash inflows = 8(\$760) Total cash inflows = \$6,080 If the initial cost is \$6,800, the project never pays back. Notice that if you use the shortcut for annuity cash flows, you get: Payback = \$6,800 / \$760 Payback = 8.95 years This answer does not make sense since the cash flows stop after ei ght years, so again, we must conclude the payback period is never 9. The NPV of a project is the PV of the outflows minus by the PV of the inflows. At a zero discount rate (and only at a zero discount rate), the cash flows can be added together across ti me. So, the NPV of the project at a zero percent required return is: NPV = \$36,000 + 14,700 + 19,600 + 13,100 NPV = \$11,400 The NPV at a 10 percent required return is: NPV = \$36,000 + \$14,700/1.10 + \$19,600/1.102 + \$13,100/1.103 NPV = \$3,404.21 The NPV at a 20 percent required return is: NPV = \$36,000 + \$14,700/1.20 + \$19,600/1.202 + \$13,100/1.203 NPV = \$2,557.87 And the NPV at a 30 percent required return is: NPV = \$36,000 + \$14,700/1.30 + \$19,600/1.302 + \$13,100/1.303 NPV = \$7,132.00 Notice that as the required return increases, the NPV of the project decreases. This will always be true for projects with conventional cash flows. Conventional cash flows are negative at the beginning of the project and positive throughout the rest of the project. 11. The IRR is the interest rate that makes the NPV of the project equal to zero. The equation to calculate the IRR of Project X is: 0 = \$8,000 + \$4,300/(1+IRR) + \$2,700/(1+IRR)2 + \$3,800/(1+IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 17.16% For Project Y, the equation to find the IRR is: 0 = \$8,000 + \$4,100/(1+IRR) + \$2,775/(1+IRR)2 + \$3,950/(1+IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 16.98% To find the crossover rate, we subtract the cash flows from one project from the cash flows of the other project, and find the IRR of the differential cash flows. We will subtract the cash flows from Project Y from the cash flows from Project X. It is irrelevant which cash flows we subtract from the other. Subtracting the cash flows, the equation to calculate the IRR for these differential cash flows is: Crossover rate: 0 = \$200/(1+R) \$75/(1+R)2 \$150/(1+R)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: R = 7.36% The table below shows the NPV of each project for r different equired returns. Notice that Project Y always has a higher NPV for discount rates below 7.36 percent, and always has a lower NPV for discount rates above 7.36 percent. R 0% 5% 10% 15% 20% 25% \$NPVX 2,800.00 1,826.80 995.49 279.28 342.59 886.40 \$NPVY 2,825.00 1,833.93 988.35 260.71 370.37 921.60 21. At a zero discount rate (and only at a zero discount rate), the cash flows can be added together across time. So, the NPV of the project at a zero percent required return is: NPV = \$487,160 + 170,605 + 189,895 + 150,387 + 135,867 NPV = \$159,594 If the required return is infinite, future cash flows have no value. Even if the cash flow in one year is \$1 trillion, at an infinite rate of interest, the value of this cash flow today is zero. So, if the future cash flows have no value today, the NPV of the project is simply the cash flow today. So at an infinite interest rate: NPV = \$487,160 The interest rate that makes the NPV of a project equal to zero is the IRR. The equation for the IRR of this project is: 0 = \$487,160 + 170,605/(1 + IRR) + 189,895/(1 + IRR)2 + 150,387/(1 + IRR)3 + 135,867/(1 + IRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 13.01% 22. a. The payback period for each project is: F: 2 + (\$25,000/\$80,000) = 2.31 years G: 3 + (\$40,000/\$190,000) = 3.21 years H: 3 + (\$10,000/\$160,000) = 3.06 years The payback criterion implies accepting project F because it pays back sooner than Projects G and H. Projects G and H does not meet the minimum payback of three years. b. The NPV for each project is: F: NPV = \$175,000 + \$85,000/1.10 + \$65,000/1.102 + \$80,000/1.103 + \$70,000/1.104 + \$55,000/1.105 NPV = \$98,058.53 G: NPV = \$275,000 + \$55,000/1.10 + \$70,000/1.102 + \$110,000/1.103 + \$190,000/1.104 + \$135,000/1.105 NPV = \$129,092.80 H: NPV = \$200,000 + \$60,000/1.10 + \$70,000/1.102 + \$60,000/1.103 + \$160,000/1.104 + \$40,000/1.105 NPV = \$91,594.59 NPV criterion implies we should accept project G because project G has a higher NPV than Projects F and H. c. Even though project G does not meet the payback period of three years, it does provide the largest increase in shareholder wealth, therefore, choose project G. Payback period should generally be ignored in this situation. Challenge 32. a. Here the cash inflows of the project go on forever, which is a perpetuity. Unlike ordinary perpetuity cash flows, the cash flows here grow at a constant rate forever, which is a growing perpetuity. If you remember back to the chapter on share valuation, we presented a formula for valuing a share with constant growth in dividends. This formula is actually the formula for a growing perpetu ity, so we can use it here. The PV of the future cash flows from the project is: PV of cash inflows = C1/(R g) PV of cash inflows = \$60,000/(.13 .06) = \$857,142.86 NPV is the PV of the outflows minus by the PV of the inflows, so the NPV is: NPV of the project = \$925,000 + 857,142.86 = \$67,857.14 The NPV is negative, so we would reject the project. b. Here we want to know the minimum growth rate in cash flows necessary to accept the project. The minimum growth rate is the growth rate at which we would have a zero NPV. The equation for a zero NPV, using the equation for the PV of a growing perpetuity is: 0 = \$925,000 + \$60,000/(.13 g) Solving for g, we get: g = .0651 or 6.51%
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