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Unformatted text preview: 2,319.49 + 29,066.93 APV = $51,386.42 377 2. The adjusted present value (APV) of a project equals the net present value of the project if it were funded completely by equity plus the net present value of any financing side effects. In this case, the NPV of financing side effects equals the aftertax present value of the cash flows resulting from the firm’s debt, so: APV = NPV(AllEquity) + NPV(Financing Side Effects) So, the NPV of each part of the APV equation is: NPV(AllEquity) NPV = –Purchase Price + PV[(1 – tC )(EBTD)] + PV(Depreciation Tax Shield) Since the initial investment of $1.9 million will be fully depreciated over four years using the straightline method, annual depreciation expense is: Depreciation = $1,900,000/4 Depreciation = $475,000 NPV = –$1,900,000 + (1 – 0.30)($685,000)PVIFA9.5%,4 + (0.30)($475,000)PVIFA13%,4 NPV (Allequity) = – $49,878.84 NPV(Financing Side Effects) The net present value of financing side effects equals the aftertax present value of cash flows resulting from the firm’s debt. So, the NPV of the financing side effects are: NPV = Proceeds(Net of flotation) – Aftertax PV(Interest Payments) – PV(Principal Payments) + PV(Flotation Cost Tax Shield) Given a known level of debt, debt cash flows should be discounted at the pretax cost of debt, RB. Since the flotation costs will be amortized over the life of the loan, the annual flotation costs that will be expensed each year are: Annual flotation expense = $28,000/4 Annual flotation expense = $7,000 NPV = ($1,900,000 – 28,000) – (1 – 0.30)(0.095)($1,900,000)PVIFA9.5%,4 – $1,900,000/(1.095)4 + 0.30($7,000) PVIFA9.5%,4 NPV = $152,252.06 So, the APV of the project is: APV = NPV(AllEquity) + NPV(Financing Side Effects) APV = –$49,878.84 + 152,252.06 APV = $102,373.23 378 3. a. In order to value a firm’s equity using the flowtoequity approach, discount the cash flows available to equity holders at the cost of the firm’s levered equity. The cash flows to equity holders will be the firm’s net income. Remembering that the company has three stores, we find: Sales COGS G & A costs Interest EBT Taxes NI $3,600,000 1,530,000 1,020,000 102,000 $948,000 379,200 $568,800 Since this cash flow will remain the same forever, the present value of cash flows available to the firm’s equity holders is a perpetuity. We can discount at the levered cost of equity, so, the value of the company’s equity is: PV(Flowtoequity) = $568,800 / 0.19 PV(Flowtoequity) = $2,993,684.21 b. The value of a firm is equal to the sum of the market values of its debt and equity, or: VL = B + S We calculated the value of the company’s equity in part a, so now we need to calculate the value of debt. The company has a debttoequity ratio of 0.40, which can be written algebraically as: B / S = 0.40 We can substitute the value of equity and solve for the value of debt, doing so, we find: B / $2,993,684.21 = 0.40 B = $1,197,473.68 So, the value of the company is: V = $2,993,684.21 + 1,197,473.68 V = $4,191,157.89 4. a. In order to determine the cost of the firm’s debt, we need to find the yield to maturity on its current bonds. With semiannual coupon payments, the yield to maturity in the company’s bonds is: $975 = $40(PVIFAR%,40) + $1,000(PVIFR%,40) R = .0413 or 4.13% 379 Since the coupon payments are semiannual, the YTM on the bonds is: YTM = 4.13%× 2 YTM = 8.26% b. We can use the Capital Asset Pricing Model to find the return on unlevered equity. According to the Capital Asset Pricing Model: R0 = RF + βUnlevered(RM – RF) R0 = 5% + 1.1(12% – 5%) R0 = 12.70% Now we can find the cost of levered equity. According to ModiglianiMiller Proposition II with corporate taxes RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .1270 + (.40)(.1270 – .0826)(1 – .34) RS = .1387 or 13.87% c. In a world with corporate taxes, a firm’s weighted average cost of capital is equal to: RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS The problem does not provide either the debtvalue ratio or equityvalue ratio. However, the firm’s debtequity ratio of is: B/S = 0.40 Solving for B: B = 0.4S Substituting this in the debtvalue ratio, we get: B/V = .4S / (.4S + S) B/V = .4 / 1.4 B/V = .29 And the equityvalue ratio is one minus the debtvalue ratio, or: S/V = 1 – .29 S/V = .71 So, the WACC for the company is: RWACC = .29(1 – .34)(.0826) + .71(.1387) RWACC = .1147 or 11.47% 380 5. a. The equity beta of a firm financed entirely by equity is equal to its unlevered beta. Since each firm has an unlevered beta of 1.25, we can find the equity beta for each. Doing so, we find: North Pole βEquity = [1 + (1 – tC)(B/S)]βUnlevered βEquity = [1 + (1 – .35)($2,900,000/$3,800,000](1.25) βEquity = 1.87 South Pole βEquity = [1 + (1 – tC)(B/S)]βUnlevered βEquity = [1 + (1 – .35)($3,800,000/$2,900,000](1.25) βEquity = 2.31 b. We can use the Capital Asset Pricing Model to find the required return on each firm’s equity. Doing so, we find: North Pole: RS = RF + βEquity(RM – RF) RS = 5.30% + 1.87(12.4...
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 Spring '10
 eshmalwi
 Finance, Corporate Finance

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