Corporate_Finance_9th_edition_Solutions_Manual_FINAL0

# 35 80 540 1 035 qa 1045576 or about 10456

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Unformatted text preview: + \$340,000(PVIFA12%,9)] / 1.12 NPV1 = \$126,432.97 Year 2: NPV2 = [–\$1,540,000 + \$340,000(PVIFA12%,8)] / 1.122 NPV2 = \$118,779.91 Year 3: NPV3 = [–\$1,410,000 + \$340,000(PVIFA12%,7)] / 1.123 NPV3 = \$100,843.05 Year 4: NPV4 = [–\$1,280,000 + \$340,000(PVIFA12%,6)] / 1.124 NPV4 = \$74,913.91 Year 5: NPV5 = [–\$1,150,000 + \$340,000(PVIFA12%,5)] / 1.125 NPV5 = \$42,911.04 Year 6: NPV6 = [–\$1,150,000 + \$340,000(PVIFA12%,4)] / 1.126 NPV6 = –\$59,428.45 The company should purchase the machine one year from now when the NPV is the highest. 6. We need to calculate the NPV of the two options, go directly to market now, or utilize test marketing first. The NPV of going directly to market now is: NPV = CSuccess (Prob. of Success) + CFailure (Prob. of Failure) NPV = \$22,000,000(0.50) + \$9,000,000(0.50) NPV = \$15,500,000 Now we can calculate the NPV of test marketing first. Test marketing requires a \$1.5 million cash outlay. Choosing the test marketing option will also delay the launch of the product by one year. Thus, the expected payoff is delayed by one year and must be discounted back to year 0. NPV= C0 + {[CSuccess (Prob. of Success)] + [CFailure (Prob. of Failure)]} / (1 + R)t NPV = –\$1,500,000 + {[\$22,000,000 (0.80)] + [\$9,000,000 (0.20)]} / 1.11 NPV = \$15,977,477.48 The company should test market first with the product since that option has the highest expected payoff. 7. We need to calculate the NPV of each option, and choose the option with the highest NPV. So, the NPV of going directly to market is: NPV = CSuccess (Prob. of Success) NPV = \$1,500,000 (0.50) NPV = \$750,000 192 The NPV of the focus group is: NPV = C0 + CSuccess (Prob. of Success) NPV = –\$135,000 + \$1,500,000 (0.65) NPV = \$840,000 And the NPV of using the consulting firm is: NPV = C0 + CSuccess (Prob. of Success) NPV = –\$400,000 + \$1,500,000 (0.85) NPV = \$875,000 The firm should use the consulting firm since that option has the highest NPV. 8. The company should analyze both options, and choose the option with the greatest NPV. So, if the company goes to market immediately, the NPV is: NPV = CSuccess (Prob. of Success) + CFailure (Prob. of Failure) NPV = \$28,000,000(.55) + \$4,000,000(.45) NPV = \$17,200,000.00 Customer segment research requires a \$1.8 million cash outlay. Choosing the research option will also delay the launch of the product by one year. Thus, the expected payoff is delayed by one year and must be discounted back to year 0. So, the NPV of the customer segment research is: NPV= C0 + {[CSuccess (Prob. of Success)] + [CFailure (Prob. of Failure)]} / (1 + R)t NPV = –\$1,800,000 + {[\$28,000,000 (0.70)] + [\$4,000,000 (0.30)]} / 1.15 NPV = \$16,286,956.52 Graphically, the decision tree for the project is: Success Research \$16.287 million at t = 0 Start \$28 million at t = 1 (\$24.348 million at t = 0) Failure \$4 million at t = 1 (\$3.478 million at t = 0) Success No Research \$17.20 million at t = 0 Failure \$4 million at t = 0 \$28 million at t = 0 The company should go to market now since it has the largest NPV. 193 9. a. The accounting breakeven is the aftertax sum of the fixed costs and depreciation charge divided by the aftertax contribution margin (selling price minus variable cost). So, the accounting breakeven level of sales is: QA = [(FC + Depreciation)(1 – tC)] / [(P – VC)(1 – tC)] QA = [(\$750,000 + \$360,000/7) (1 – 0.35)] / [(\$80 – 5.40) (1 – 0.35)] QA = 10,455.76 or about 10,456 units b. When calculating the financial breakeven point, we express the initial investment as an equivalent annual cost (EAC). Dividing the initial investment by the seven-year annuity factor, discounted at 15 percent, the EAC of the initial investment is: EAC = Initial Investment / PVIFA15%,7 EAC = \$360,000 / 4.1604 EAC = \$86,529.73 Note that this calculation solves for the annuity payment with the initial investment as the present value of the annuity. In other words: PVA = C({1 – [1/(1 + R)]t } / R) \$360,000 = C{[1 – (1/1.15)7 ] / .15} C = \$86,529.73 Now we can calculate the financial breakeven point. The financial breakeven point for this project is: QF = [EAC + FC(1 – tC) – Depreciation(tC)] / [(P – VC)(1 – tC)] QF = [\$86,529.73 + \$750,000(.65) – (\$360,000/7)(.35)] / [(\$80 – 5.40) (.65)] QF = 11,621.57 or about 11,622 units 10. When calculating the financial breakeven point, we express the initial investment as an equivalent annual cost (EAC). Dividing the initial investment by the five-year annuity factor, discounted at 8 percent, the EAC of the initial investment is: EAC = Initial Investment / PVIFA8%,5 EAC = \$390,000 / 3.99271 EAC = \$97,678.02 Note that this calculation solves for the annuity payment with the initial investment as the present value of the annuity. In other words: PVA = C({1 – [1/(1 + R)]t } / R) \$390,000 = C{[1 – (1/1.08)5 ] / .08} C = \$97,678.02 The annual depreciation is the cost of the equipment divided by the economic life, or: Annual depreciation = \$390,000 / 5 Annual depreciation = \$78,00...
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