Corporate_Finance_9th_edition_Solutions_Manual_FINAL0

# 89 43745831 apv 22481942 13 a to calculate the npv

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Unformatted text preview: 0% – 5.30%) RS = 18.58% South Pole: RS = RF + βEquity(RM – RF) RS = 5.30% + 2.31(12.40% – 5.30%) RS = 21.73% 6. a. If flotation costs are not taken into account, the net present value of a loan equals: NPVLoan = Gross Proceeds – Aftertax present value of interest and principal payments NPVLoan = \$5,350,000 – .08(\$5,350,000)(1 – .40)PVIFA8%,10 – \$5,350,000/1.0810 NPVLoan = \$1,148,765.94 b. The flotation costs of the loan will be: Flotation costs = \$5,350,000(.0125) Flotation costs = \$66,875 So, the annual flotation expense will be: Annual flotation expense = \$66,875 / 10 Annual flotation expense = \$6,687.50 381 If flotation costs are taken into account, the net present value of a loan equals: NPVLoan = Proceeds net of flotation costs – Aftertax present value of interest and principal payments + Present value of the flotation cost tax shield NPVLoan = (\$5,350,000 – 66,875) – .08(\$5,350,000)(1 – .40)(PVIFA8%,10) – \$5,350,000/1.0810 + \$6,687.50(.40)(PVIFA8%,10) NPVLoan = \$1,099,840.40 7. First we need to find the aftertax value of the revenues minus expenses. The aftertax value is: Aftertax revenue = \$3,800,000(1 – .40) Aftertax revenue = \$2,280,000 Next, we need to find the depreciation tax shield. The depreciation tax shield each year is: Depreciation tax shield = Depreciation(tC) Depreciation tax shield = (\$11,400,000 / 6)(.40) Depreciation tax shield = \$760,000 Now we can find the NPV of the project, which is: NPV = Initial cost + PV of depreciation tax shield + PV of aftertax revenue To find the present value of the depreciation tax shield, we should discount at the risk-free rate, and we need to discount the aftertax revenues at the cost of equity, so: NPV = –\$11,400,000 + \$760,000(PVIFA6%,6) + \$2,280,000(PVIFA14%,6) NPV = \$1,203,328.43 8. Whether the company issues stock or issues equity to finance the project is irrelevant. The company’s optimal capital structure determines the WACC. In a world with corporate taxes, a firm’s weighted average cost of capital equals: RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS RWACC = .80(1 – .34)(.072) + .20(.1140) RWACC = .0608 or 6.08% Now we can use the weighted average cost of capital to discount NEC’s unlevered cash flows. Doing so, we find the NPV of the project is: NPV = –\$40,000,000 + \$2,600,000 / 0.0608 NPV = \$2,751,907.39 9. a. The company has a capital structure with three parts: long-term debt, short-term debt, and equity. Since interest payments on both long-term and short-term debt are tax-deductible, multiply the pretax costs by (1 – tC) to determine the aftertax costs to be used in the weighted average cost of capital calculation. The WACC using the book value weights is: RWACC = (wSTD)(RSTD)(1 – tC) + (wLTD)(RLTD)(1 – tC) + (wEquity)(REquity) RWACC = (\$3 / \$19)(.035)(1 – .35) + (\$10 / \$19)(.068)(1 – .35) + (\$6 / \$19)(.145) RWACC = 0.0726 or 7.26% 382 b. Using the market value weights, the company’s WACC is: RWACC = (wSTD)(RSTD)(1 – tC) + (wLTD)(RLTD)(1 – tC) + (wEquity)(REquity) RWACC = (\$3 / \$40)(.035)(1 – .35) + (\$11 / \$40)(.068)(1 – .35) + (\$26 / \$40)(.145) RWACC = 0.1081 or 10.81% c. Using the target debt-equity ratio, the target debt-value ratio for the company is: B/S = 0.60 B = 0.6S Substituting this in the debt-value ratio, we get: B/V = .6S / (.6S + S) B/V = .6 / 1.6 B/V = .375 And the equity-value ratio is one minus the debt-value ratio, or: S/V = 1 – .375 S/V = .625 We can use the ratio of short-term debt to long-term debt in a similar manner to find the shortterm debt to total debt and long-term debt to total debt. Using the short-term debt to long-term debt ratio, we get: STD/LTD = 0.20 STD = 0.2LTD Substituting this in the short-term debt to total debt ratio, we get: STD/B = .2LTD / (.2LTD + LTD) STD/B = .2 / 1.2 STD/B = .167 And the long-term debt to total debt ratio is one minus the short-term debt to total debt ratio, or: LTD/B = 1 – .167 LTD/B = .833 Now we can find the short-term debt to value ratio and long-term debt to value ratio by multiplying the respective ratio by the debt-value ratio. So: STD/V = (STD/B)(B/V) STD/V = .167(.375) STD/V = .063 383 And the long-term debt to value ratio is: LTD/V = (LTD/B)(B/V) LTD/V = .833(.375) LTD/V = .313 So, using the target capital structure weights, the company’s WACC is: RWACC = (wSTD)(RSTD)(1 – tC) + (wLTD)(RLTD)(1 – tC) + (wEquity)(REquity) RWACC = (.06)(.035)(1 – .35) + (.31)(.068)(1 – .35) + (.625)(.145) RWACC = 0.1059 or 10.59% d. The differences in the WACCs are due to the different weighting schemes. The company’s WACC will most closely resemble the WACC calculated using target weights since future projects will be financed at the target ratio. Therefore, the WACC computed with target weights should be used for project evaluation. Intermediate 10. The adjusted present value of a project equals the net present value of the project under all-equity financing plus the net present value of any financing side effects. In the joint venture’s case, the NPV of financing...
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