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CHAPTER 9 B-157 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 1. To calculate the payback period, we need to find the time that the project has recovered its initial investment. After three years, the project has created: \$1,600 + 1,900 + 2,300 = \$5,800 in cash flows. The project still needs to create another: \$6,400 – 5,800 = \$600 in cash flows. During the fourth year, the cash flows from the project will be \$1,400. So, the payback period will be 3 years, plus what we still need to make divided by what we will make during the fourth year. The payback period is: Payback = 3 + (\$600 / \$1,400) = 3.43 years 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 \$2,400, the payback period is: Payback = 3 + (\$105 / \$765) = 3.14 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 \$2,400 cost, the payback period is: Payback = \$2,400 / \$765 = 3.14 years For an initial cost of \$3,600, the payback period is: Payback = \$3,600 / \$765 = 4.71 years The payback period for an initial cost of \$6,500 is a little trickier. Notice that the total cash inflows after eight years will be: Total cash inflows = 8(\$765) = \$6,120 If the initial cost is \$6,500, the project never pays back. Notice that if you use the shortcut for annuity cash flows, you get: Payback = \$6,500 / \$765 = 8.50 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.

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