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# 2PracticeAnswers - Optional Practice Problems Project...

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[1] Optional Practice Problems Project Evaluation ANSWERS Problem #1 Consider the following projects: Cash Flows (\$) PROJECT C 0 C 1 C 2 C 3 C 4 C 5 A -1,000 +1,000 0 0 \$500 0 B -2,000 +1,000 +1,000 +1,000 +2,000 0 C -3,000 +1,200 +1,000 0 +1,000 +500 a. If the opportunity cost of capital is 10%, which projects have a positive NPV? °±² = \$1000 + \$1000 (1 + .10) + \$500 (1 + .10) ³ = +\$250.60 °±² ´ = \$2000 + \$1000 (1 + .10) + \$1000 (1 + .10) µ + \$1000 (1 + .10) + \$2000 (1 + .10) ³ + \$0 (1 + .10) · = +\$1852.88 °±² ¸ = \$3000 + \$1200 (1 + .10) + \$1000 (1 + .10) µ + \$1000 (1 + .10) ³ + \$500 (1 + .10) · = \$89.17 b. Calculate the IRR for each project. Project A = % Project B = % Project C = 8.64% c. Calculate the Payback Period for each project. Payback A = 1 year Payback B = 2 years Payback C = 4 years Problem #2 As a result of improvements in product engineering, United Automation is able to sell one of its two milling machines. Both machines perform the same function but differ in age. The newer machine could be sold today for \$50,000. Its operating costs are \$20,000 a year, but in five years the machine will require a \$20,000 overhaul. Thereafter operating costs will be \$30,000 until the machine is finally sold in year 10 for \$5,000. The older machine could be sold today for \$25,000. If it is kept, it will need an immediate \$20,000 overhaul. Thereafter operating costs will be \$30,000 a year until the machine is sold in year 5 for \$5,000. Both machines are fully depreciated for tax purposes. The company pays tax at 35%. Cash flows have been forecasted in real terms. The real cost of capital is 12%. Which machine should United Automation sell? Explain your assumptions.

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[2] Calculate each of two alternatives: Alternative 1 – Sell the new machine. Receive cash flow from sale, pay taxes on gain, and pay the costs associated with keeping the old machine. The costs associated with the old machine are -20 in the first year, 30 per year for 5 years, and sale for 5 in year 5. °± = 50 [0.35(50 0)] 20 30 1.12 30 1.12 ² 30 1.12 ³ 30 1.12 ´ 30 1.12 µ + 5 1.12 µ 0.35(5 0) 1.12 µ = \$93.80 EAC for 5-year period (calculate 5-year annuity for PV 1 ): PV 1 = EAC 1 * [5-year annuity, 12%] = -26.02 (EAC = \$26,020) Alternative 2—Sell the old machine. Receive the cash flow from the sale, pay taxes on the gain, and pay cost associated with keeping new
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2PracticeAnswers - Optional Practice Problems Project...

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