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# Ch006

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Chapter 6: Some Alternative Investment Rules 6.1 a. The payback period is the time that it takes for the cumulative undiscounted cash inflows to equal the initial investment. Project A : Cumulative Undiscounted Cash Flows Year 1 = \$4,000 = \$4,000 Cumulative Undiscounted Cash Flows Year 2 = \$4,000 +\$3,500 = \$7,500 Payback period = 2 Project A has a payback period of two years. Project B : Cumulative Undiscounted Cash Flows Year 1 = \$2,500 = \$2,500 Cumulative Undiscounted Cash Flows Year 2 = \$2,500+\$1,200 = \$3,700 Cumulative Undiscounted Cash Flows Year 3 = \$2,500+\$1,200+\$3,000 = \$6,700 Project B ’s cumulative undiscounted cash flows exceed the initial investment of \$5,000 by the end of year 3. Many companies analyze the payback period in whole years. The payback period for project B is 3 years. Project B has a payback period of three years. Companies can calculate a more precise value using fractional years. 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 \$5,000. 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 + (\$5,000 - \$3,700) / \$3,000 = 2.43 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 = -\$7,500 + \$4,000 / (1.15) + \$3,500 / (1.15) 2 + \$1,500 / (1.15) 3 = - \$388.96 Project B = -\$5,000 + \$2,500 / (1.15) + \$1,200 / (1.15) 2 + \$3,000 / (1.15) 3 = \$53.83 The firm should choose Project B since it has a higher NPV than Project A has. 6.2 a. Find the payback period for the project. Since the cash inflows are constant, divide the initial investment by the annual cash inflow to determine the payback period. Payback Period = Initial Investment / Annual Cash Inflow = \$1,000,000 / \$150,000 = 6.67 B-92

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The payback period is 6.67 years. Since the payback period is shorter than the cutoff period of ten years, the project should be accepted. b. Find the number of years needed for the discounted cash inflows to equal the initial investment of \$1 million. Apply the annuity formula, discounted at 10 percent, to find the approximate discounted payback period. The approximate discounted payback period is the year in which the PV of the initial investment is surpassed. Since the discounted payback period will always be greater than the undiscounted payback period when there are positive cash inflows, start the approximation at year 7. Cumulative Discounted Cash Flows Year 7 = \$150,000 A 7 0.1 = \$730,262.82 Cumulative Discounted Cash Flows Year 8 = \$150,000 A 8 0.1 = \$800,238.93 Cumulative Discounted Cash Flows Year 9 = \$150,000 A 9 0.1 = \$863,853.57 Cumulative Discounted Cash Flows Year 10 = \$150,000 A 10 0.1 = \$921,685.07 Cumulative Discounted Cash Flows Year 11 = \$150,000 A 11 0.1 = \$974,259.15 Cumulative Discounted Cash Flows Year 12 = \$150,000 A 12 0.1 = \$1,022,053.77 The cumulative discounted cash flows exceed the initial investment of \$1,000,000 by the end of year 12. Many companies analyze the payback period in whole years. The payback period for the project is 12 years.
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