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Unformatted text preview: equity is: RE = R0 + (R0 – RD)(D/E)(1 – tC) RE = .1519 + (.1519 – .09)(2)(1 – .35) RE = .2324 or 23.24% With a debtequity ratio of 1.0, the cost of equity is: RE = .1519 + (.1519 – .09)(1)(1 – .35) RE = .1921 or 19.21% And with a debtequity ratio of 0, the cost of equity is: RE = .1519 + (.1519 – .09)(0)(1 – .35) RE = R0 = .1519 or 15.19% 13. a. For an allequity financed company: WACC = R0 = RE = .11 or 11% b. To find the cost of equity for the company with leverage, we need to use M&M Proposition II with taxes, so: RE = R0 + (R0 – RD)(D/E)(1 – tC) RE = .11 + (.11 – .07)(.25/.75)(1 – .35) RE = .1187 or 11.87% c. Using M&M Proposition II with taxes again, we get: RE = R0 + (R0 – RD)(D/E)(1 – tC) RE = .11 + (.11 – .07)(.50/.50)(1 – .35) RE = .1360 or 13.60% 353 d. The WACC with 25 percent debt is: WACC = (E/V)RE + (D/V)RD(1 – tC) WACC = .75(.1187) + .25(.07)(1 – .35) WACC = .1004 or 10.04% And the WACC with 50 percent debt is: WACC = (E/V)RE + (D/V)RD(1 – tC) WACC = .50(.1360) + .50(.07)(1 – .35) WACC = .0908 or 9.08% 14. a. The value of the unlevered firm is: V = EBIT(1 – tC)/R0 V = $140,000(1 – .35)/.17 V = $535,294.12 b. The value of the levered firm is: V = VU + tCB V = $535,294.12 + .35($135,000) V = $582,544.12 15. We can find the cost of equity using M&M Proposition II with taxes. First, we need to find the market value of equity, which is: V=D+E $582,544.12 = $135,000 + E E = $447,544.12 Now we can find the cost of equity, which is: RE = R0 + (R0 – RD)(D/E)(1 – t) RE = .17 + (.17 – .09)($135,000/$447,544.12)(1 – .35) RE = .1857 or 18.57% Using this cost of equity, the WACC for the firm after recapitalization is: WACC = (E/V)RE + (D/V)RD(1 – tC) WACC = ($447,544.12/$582,544.12)(.1857) + ($135,000/$582,544.12)(.09)(1 – .35) WACC = .1562 or 15.62% When there are corporate taxes, the overall cost of capital for the firm declines the more highly leveraged is the firm’s capital structure. This is M&M Proposition I with taxes. 354 16. Since Unlevered is an allequity firm, its value is equal to the market value of its outstanding shares. Unlevered has 7 million shares of common stock outstanding, worth $80 per share. Therefore, the value of Unlevered: VU = 7,000,000($80) = $560,000,000 ModiglianiMiller Proposition I states that, in the absence of taxes, the value of a levered firm equals the value of an otherwise identical unlevered firm. Since Levered is identical to Unlevered in every way except its capital structure and neither firm pays taxes, the value of the two firms should be equal. Therefore, the market value of Levered, Inc., should be $560 million also. Since Levered has 3.4 million outstanding shares, worth $100 per share, the market value of Levered’s equity is: EL = 3,400,000($100) = $340,000,000 The market value of Levered’s debt is $185 million. The value of a levered firm equals the market value of its debt plus the market value of its equity. Therefore, the current market value of Levered is: VL = B + S VL = $185,000,000 + 340,000,000 VL = $525,000,000 The market value of Levered’s equity needs to be $375 million, $35 million higher than its current market value of $340 million, for MM Proposition I to hold. Since Levered’s market value is less than Unlevered’s market value, Levered is relatively underpriced and an investor should buy shares of the firm’s stock. Intermediate 17. To find the value of the levered firm, we first need to find the value of an unlevered firm. So, the value of the unlevered firm is: VU = EBIT(1 – tC)/R0 VU = ($42,000)(1 – .35)/.15 VU = $182,000 Now we can find the value of the levered firm as: VL = VU + tCB VL = $182,000 + .35($70,000) VL = $206,500 Applying M&M Proposition I with taxes, the firm has increased its value by issuing debt. As long as M&M Proposition I holds, that is, there are no bankruptcy costs and so forth, then the company should continue to increase its debt/equity ratio to maximize the value of the firm. 355 18. With no debt, we are finding the value of an unlevered firm, so: V = EBIT(1 – tC)/R0 V = $15,000(1 – .35)/.17 V = $57,352.94 With debt, we simply need to use the equation for the value of a levered firm. With 50 percent debt, onehalf of the firm value is debt, so the value of the levered firm is: V = VU + tCB V = $57,352.94 + .35($57,352.94/2) V = $67,389.71 And with 100 percent debt, the value of the firm is: V = VU + tCB V = $57,352.94 + .35($57,352.94) V = $77,426.47 19. According to M&M Proposition I with taxes, the increase in the value of the company will be the present value of the interest tax shield. Since the loan will be repaid in equal installments, we need to find the loan interest and the interest tax shield each year. The loan schedule will be: Year 0 1 2 Loan Balance $1,400,000.0 0 700,000.00 0 Interest $112,000 56,000 Tax Shield $39,200 19,600 So, the increase in the value of the company is: Value increase = $39,200/1.08 + $19,600/(1.08)2 Value increas...
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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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