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Unformatted text preview: the outstanding equity in the company will be: Market value of equity = $17.83(431,775.70) = $7,700,000 The marketvalue balance sheet after the restructuring is: Old assets PV(tax shield) Total assets $9,500,000 Debt 1,200,000 Equity $10,700,000 Total D&E $3,000,000 7,700,000 $10,700,000 g. According to ModiglianiMiller Proposition II with corporate taxes RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .1137 + ($3,000,000 / $7,700,000)(.1137 – .06)(1 – .40) RS = .1262 or 12.62% 362 25. a. 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 We do not have the company’s debttovalue ratio or the equitytovalue ratio, but we can calculate either from the debttoequity ratio. With the given debtequity ratio, we know the company has 2.5 dollars of debt for every dollar of equity. Since we only need the ratio of debttovalue and equitytovalue, we can say: B / (B+S) = 2.5 / (2.5 + 1) = .7143 S / (B+S) = 1 / (2.5 + 1) = .2857 We can now use the weighted average cost of capital equation to find the cost of equity, which is: .15 = (.7143)(1 – 0.35)(.10) + (.2857)(RS) RS = .3625 or 36.25% b. We can use ModiglianiMiller Proposition II with corporate taxes to find the unlevered cost of equity. Doing so, we find: RS = R0 + (B/S)(R0 – RB)(1 – tC) .3625 = R0 + (2.5)(R0 – .10)(1 – .35) R0 = .2000 or 20.00% c. We first need to find the debttovalue ratio and the equitytovalue ratio. We can then use the cost of levered equity equation with taxes, and finally the weighted average cost of capital equation. So: If debtequity = .75 B / (B+S) = .75 / (.75 + 1) = .4286 S / (B+S) = 1 / (.75 + 1) = .5714 The cost of levered equity will be: RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .20 + (.75)(.20 – .10)(1 – .35) RS = .2488 or 24.88% And the weighted average cost of capital will be: RWACC = [B / (B+S)](1 – tC)RB + [S / (B+S)]RS RWACC = (.4286)(1 – .35)(.10) + (.5714)(.2488) RWACC = .17 363 If debtequity =1.50 B / (B+S) = 1.50 / (1.50 + 1) = .6000 E / (B+S) = 1 / (1.50 + 1) = .4000 The cost of levered equity will be: RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .20 + (1.50)(.20 – .10)(1 – .35) RS = .2975 or 29.75% And the weighted average cost of capital will be: RWACC = [B / (B+S)](1 – tC)RB + [S / (B+S)]RS RWACC = (.6000)(1 – .35)(.10) + (.4000)(.2975) RWACC = .1580 or 15.80% Challenge 26. M&M Proposition II states: RE = R0 + (R0 – RD)(D/E)(1 – tC) And the equation for WACC is: WACC = (E/V)RE + (D/V)RD(1 – tC) Substituting the M&M Proposition II equation into the equation for WACC, we get: WACC = (E/V)[R0 + (R0 – RD)(D/E)(1 – tC)] + (D/V)RD(1 – tC) Rearranging and reducing the equation, we get: WACC = R0[(E/V) + (E/V)(D/E)(1 – tC)] + RD(1 – tC)[(D/V) – (E/V)(D/E)] WACC = R0[(E/V) + (D/V)(1 – tC)] WACC = R0[{(E+D)/V} – tC(D/V)] WACC = R0[1 – tC(D/V)] 364 27. The return on equity is net income divided by equity. Net income can be expressed as: NI = (EBIT – RDD)(1 – tC) So, ROE is: RE = (EBIT – RDD)(1 – tC)/E Now we can rearrange and substitute as follows to arrive at M&M Proposition II with taxes: RE = [EBIT(1 – tC)/E] – [RD(D/E)(1 – tC)] RE = R0VU/E – [RD(D/E)(1 – tC)] RE = R0(VL – tCD)/E – [RD(D/E)(1 – tC)] RE = R0(E + D – tCD)/E – [RD(D/E)(1 – tC)] RE = R0 + (R0 – RD)(D/E)(1 – tC) 28. M&M Proposition II, with no taxes is: RE = RA + (RA – Rf)(B/S) Note that we use the riskfree rate as the return on debt. This is an important assumption of M&M Proposition II. The CAPM to calculate the cost of equity is expressed as: RE = β E(RM – Rf) + Rf We can rewrite the CAPM to express the return on an unlevered company as: R0 = β A(RM – Rf) + Rf We can now substitute the CAPM for an unlevered company into M&M Proposition II. Doing so and rearranging the terms we get: RE = β A(RM – Rf) + Rf + [β A(RM – Rf) + Rf – Rf](B/S) RE = β A(RM – Rf) + Rf + [β A(RM – Rf)](B/S) RE = (1 + B/S)β A(RM – Rf) + Rf Now we set this equation equal to the CAPM equation to calculate the cost of equity and reduce: β E(RM – Rf) + Rf = (1 + B/S)β A(RM – Rf) + Rf β E(RM – Rf) = (1 + B/S)β A(RM – Rf) β E = β A(1 + B/S) 365 29. Using the equation we derived in Problem 28: β E = β A(1 + D/E) The equity beta for the respective asset betas is: Debtequity ratio 0 1 5 20 Equity beta 1(1 + 0) = 1 1(1 + 1) = 2 1(1 + 5) = 6 1(1 + 20) = 21 The equity risk to the shareholder is composed of both business and financial risk. Even if the assets of the firm are not very risky, the risk to the shareholder can still be large if the financial leverage is high. These higher levels of risk will be reflected in the shareholder’s required rate of return RE, which will increase with higher debt/equity ratios. 30. We first need to set the cost of capital equation equal to the cost of capital for an allequity firm, so: B S RB + RS = R0 B+S B+S Multiplying both sides by (B + S)/S yields: B B+S RB + RS = R0...
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 Spring '10
 eshmalwi
 Finance, Corporate Finance

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