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Unformatted text preview: side effects equals the aftertax present value of cash flows resulting from the firms’ debt. So, the APV is: APV = NPV(AllEquity) + NPV(Financing Side Effects) The NPV for an allequity firm is: NPV(AllEquity) NPV = –Initial Investment + PV[(1 – tC)(EBITD)] + PV(Depreciation Tax Shield) Since the initial investment will be fully depreciated over five years using the straightline method, annual depreciation expense is: Annual depreciation = $30,000,000/5 Annual depreciation = $6,000,000 NPV = –$30,000,000 + (1 – 0.35)($3,800,000)PVIFA5.13%,20 + (0.35)($6,000,000)PVIFA5,13%,20 NPV = –$5,262,677.95 NPV(Financing Side Effects) The NPV of financing side effects equals the aftertax present value of cash flows resulting from the firm’s debt. The coupon rate on the debt is relevant to determine the interest payments, but the resulting cash flows should still be discounted at the pretax cost of debt. So, the NPV of the financing effects is: NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Repayments) NPV = $18,000,000 – (1 – 0.35)(0.05)($18,000,000)PVIFA8.5%,15 – $18,000,000/1.08515 NPV = $7,847,503.56 384 So, the APV of the project is: APV = NPV(AllEquity) + NPV(Financing Side Effects) APV = –$5,262,677.95 + $7,847,503.56 APV = $2,584,825.61 11. If the company had to issue debt under the terms it would normally receive, the interest rate on the debt would increase to the company’s normal cost of debt. The NPV of an allequity project would remain unchanged, but the NPV of the financing side effects would change. The NPV of the financing side effects would be: NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Repayments) NPV = $18,000,000 – (1 – 0.35)(0.085)($18,000,000)PVIFA8.5%,15 – $18,000,000/((1.085)15 NPV = $4,446,918.69 Using the NPV of an allequity project from the previous problem, the new APV of the project would be: APV = NPV(AllEquity) + NPV(Financing Side Effects) APV = –$5,262,677.95 + $4,446,918.69 APV = –$815,759.27 The gain to the company from issuing subsidized debt is the difference between the two APVs, so: Gain from subsidized debt = $2,584,825.61 – (–815,759.27) Gain from subsidized debt = $3,400,584.88 Most of the value of the project is in the form of the subsidized interest rate on the debt issue. 12. The adjusted present value of a project equals the net present value of the project under allequity financing plus the net present value of any financing side effects. First, we need to calculate the unlevered cost of equity. According to ModiglianiMiller Proposition II with corporate taxes: RS = R0 + (B/S)(R0 – RB)(1 – tC) .16 = R0 + (0.50)(R0 – 0.09)(1 – 0.40) R0 = 0.1438 or 14.38% Now we can find the NPV of an allequity project, which is: NPV = PV(Unlevered Cash Flows) NPV = –$21,000,000 + $6,900,000/1.1438 + $11,000,000/(1.1438)2 + $9,500,000/(1.1438)3 NPV = –$212,638.89 Next, we need to find the net present value of financing side effects. This is equal the aftertax present value of cash flows resulting from the firm’s debt. So: NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Payments) 385 Each year, an equal principal payment will be made, which will reduce the interest accrued during the year. Given a known level of debt, debt cash flows should be discounted at the pretax cost of debt, so the NPV of the financing effects are: NPV = $7,000,000 – (1 – .40)(.09)($7,000,000) / (1.09) – $2,333,333.33/(1.09) – (1 – .40)(.09)($4,666,666.67)/(1.09)2 – $2,333,333.33/(1.09)2 – (1 – .40)(.09)($2,333,333.33)/(1.09)3 – $2,333,333.33/(1.09)3 NPV = $437,458.31 So, the APV of project is: APV = NPV(Allequity) + NPV(Financing side effects) APV = –$212,638.89 + 437,458.31 APV = $224,819.42 13. a. To calculate the NPV of the project, we first need to find the company’s 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 The market value of the company’s equity is: Market value of equity = 6,000,000($20) Market value of equity = $120,000,000 So, the debtvalue ratio and equityvalue ratio are: Debtvalue = $35,000,000 / ($35,000,000 + 120,000,000) Debtvalue = .2258 Equityvalue = $120,000,000 / ($35,000,000 + 120,000,000) Equityvalue = .7742 Since the CEO believes its current capital structure is optimal, these values can be used as the target weights in the firm’s weighted average cost of capital calculation. The yield to maturity of the company’s debt is its pretax cost of debt. To find the company’s cost of equity, we need to calculate the stock beta. The stock beta can be calculated as: β = σ S,M / σ 2 M β = .036 / .202 β = 0.90 Now we can use the Capital Asset Pricing Model to determine the cost of equity. The Capital Asset Pricing Model is: RS = RF + β(RM – RF) RS = 6% + 0.90(7.50%) RS = 12.75% 386 Now, we can calculate the company’s WACC, which is: RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS RWACC = .2258(1 – .35)(.08) + .7742(.12...
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

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