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chapter 9 hw solutions

# chapter 9 hw solutions - The payback period for the...

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The payback period for the following set of cash flows is years. (Round your answer to 2 decimal places. (e.g., 32.16)) Year Cash Flow 0 −\$2,800 1 1,300 2 2,000 3 1,800 4 1,400 Explanation: To calculate the payback period, we need to find the time that the project has recovered its initial investment. After one year, the project has created: 1300 in cash flows. The project still needs to create another: \$2,800 − 1,300 = \$1,500 in cash flows. During the second year, the cash flows from the project will be \$2,000. So, the payback period will be 1 year, plus what we still need to make divided by what we will make during the second year. The payback period is: Payback = 1 + (\$1,500 / \$2,000) = 1.75 years

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An investment project provides cash inflows of \$760 per year for 14 years. If the initial cost is \$2,280, the project payback period is years. If the initial cost is \$5,396, the project payback period is years. If the initial cost is \$11,400, the project payback period is years. (Enter 0 when there is no payback period. Round your answers to 2 decimal places. (e.g., 32.16)) Explanation: To calculate the payback period, we need to find the time that it takes the project to recover its initial investment. The cash flows in this problem are an annuity, so the calculation is simpler. If the initial cost is \$2,280, the payback period is: Payback = 3 + (\$0 / \$760)) = 3 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 \$2,280 cost, the payback period is: Payback = \$2,280 / \$760 = 3 years For an initial cost of \$5,396, the payback period is: Payback = \$5,396 / \$760 = 7.1 years The payback period for an initial cost of \$11,400 is a little trickier. Notice that the total cash inflows after 14 years will be: Total cash inflows = 14(\$760) = \$10,640 If the initial cost is \$11,400, the project never pays back. Notice that if you use the shortcut for annuity cash flows, you get:
Payback = \$11,400 / \$760 = 15 years. This answer does not make sense since the cash flows stop after 14 years, so again, we must conclude the payback period is never. Buy Coastal, Inc., imposes a payback cutoff of 3 years for its international investment projects. Suppose the company has the following two projects available. Project A has payback period of years, while project B has a payback period of years. Therefore, it should accept project A and reject project B. (Round your answers to 3 decimal places. (e.g., 32.162)) Year Cash Flow (A) Cash Flow (B) 0 −\$42,000 −\$54,000 1 24,000 9,000 2 35,000 15,000 3 15,000 25,000 4 2,000 261,000 Explanation: Project A has cash flows of \$24,000 in Year 1, so the cash flows are short by \$18,000 of recapturing the initial investment, so the payback for Project A is: A: Payback = 1 + (\$18,000 / \$35,000) = 1.514 years Project B has cash flows of: Cash flows = \$9,000 + \$15,000 + \$25,000 = \$49,000 during the first three years. The cash flows are still short by \$5,000 of recapturing the initial investment, so the payback for Project B is:

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B: Payback = 3 + (\$5,000 / \$261,000) = 3.019 years Using the payback criterion and a cutoff of 3 years, accept project A and reject project B.
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