Corporate_Finance_9th_edition_Solutions_Manual_FINAL0

# 23 years there is a shortcut to calculate the payback

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Unformatted text preview: ted cash flows as of year 1 by the undiscounted cash flow of year 2. Payback period = 1 + (\$10,000 – \$6,500) / \$4,000 Payback period = 1.875 years Project B: Cumulative cash flows Year 1 = \$7,000 Cumulative cash flows Year 2 = \$7,000 + 4,000 Cumulative cash flows Year 3 = \$7,000 + 4,000 + 5,000 = \$7,000 = \$11,000 = \$16,000 To calculate the fractional payback period, find the fraction of year 3’s cash flows that is needed for the company to have cumulative undiscounted cash flows of \$12,000. Divide the difference between the initial investment and the cumulative undiscounted cash flows as of year 2 by the undiscounted cash flow of year 3. Payback period = 2 + (\$12,000 – 7,000 – 4,000) / \$5,000 Payback period = 2.20 years Since project A has a shorter payback period than project B has, the company should choose project A. b. Discount each project’s cash flows at 15 percent. Choose the project with the highest NPV. Project A: NPV = –\$10,000 + \$6,500 / 1.15 + \$4,000 / 1.152 + \$1,800 / 1.153 NPV = –\$139.72 Project B: NPV = –\$12,000 + \$7,000 / 1.15 + \$4,000 / 1.152 + \$5,000 / 1.153 NPV = \$399.11 The firm should choose Project B since it has a higher NPV than Project A has. 2. To calculate the payback period, we need to find the time that the project has taken to recover its initial investment. The cash flows in this problem are an annuity, so the calculation is simpler. If the initial cost is \$4,100, the payback period is: Payback = 4 + (\$220 / \$970) = 4.23 years There is a shortcut to calculate the payback period if the future cash flows are an annuity. Just divide the initial cost by the annual cash flow. For the \$4,100 cost, the payback period is: Payback = \$4,100 / \$970 = 4.23 years 114 For an initial cost of \$6,200, the payback period is: Payback = \$6,200 / \$970 = 6.39 years The payback period for an initial cost of \$8,000 is a little trickier. Notice that the total cash inflows after eight years will be: Total cash inflows = 8(\$970) = \$7,760 If the initial cost is \$8,000, the project never pays back. Notice that if you use the shortcut for annuity cash flows, you get: Payback = \$8,000 / \$970 = 8.25 years This answer does not make sense since the cash flows stop after eight years, so there is no payback period. 3. 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 = \$6,000/1.14 = \$5,263.16 Value today of Year 2 cash flow = \$6,500/1.142 = \$5,001.54 Value today of Year 3 cash flow = \$7,000/1.143 = \$4,724.80 Value today of Year 4 cash flow = \$8,000/1.144 = \$4,736.64 To find the discounted payback, we use these values to find the payback period. The discounted first year cash flow is \$5,263.16, so the discounted payback for an \$8,000 initial cost is: Discounted payback = 1 + (\$8,000 – 5,263.16)/\$5,001.54 = 1.55 years For an initial cost of \$13,000, the discounted payback is: Discounted payback = 2 + (\$13,000 – 5,263.16 – 5,001.54)/\$4,724.80 = 2.58 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 – 5,263.16 – 5,001.54 – 4,724.80) / \$4,736.64 = 3.64 years 4. To calculate the discounted payback, discount all future cash flows back to the present, and use these discounted cash flows to calculate the payback period. To find the fractional year, we divide the amount we need to make in the last year to payback the project by the amount we will make. Doing so, we find: R = 0%: 3 + (\$2,200 / \$2,600) = 3.85 years Discounted payback = Regular payback = 3.85 years 115 R = 10%: \$2,600/1.10 + \$2,600/1.102 + \$2,600/1.103 + \$2,600/1.104 + \$2,600/1.105 = \$9,856.05 \$2,600/1.106 = \$1,467.63 Discounted payback = 5 + (\$10,000 – 9,856.05) / \$1,467.63 = 5.10 years R = 15%: \$2,600/1.15 + \$2,600/1.152 + \$2,600/1.153 + \$2,600/1.154 + \$2,600/1.155 + \$2,600/1.156 = \$9,839.66; The project never pays back. 5. 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 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3 0 = –\$11,000 + \$5,500/(1 + IRR) + \$4,000/(1 + IRR)2 + \$3,000/(1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 7.46% Since the IRR is less than the required return we would reject the project. 6. 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 A is: 0 = C0 + C1 / (1 + IRR) +...
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## This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of Texas-Tyler.

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