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Unformatted text preview: e = $53,100.14 20. a. Since Alpha Corporation is an all-equity firm, its value is equal to the market value of its outstanding shares. Alpha has 10,000 shares of common stock outstanding, worth $20 per share, so the value of Alpha Corporation is: VAlpha = 10,000($20) = $200,000 b. Modigliani-Miller 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 Beta Corporation is identical to Alpha Corporation in every way except its capital structure and neither firm pays taxes, the value of the two firms should be equal. So, the value of Beta Corporation is $200,000 as well. 356 c. The value of a levered firm equals the market value of its debt plus the market value of its equity. So, the value of Beta’s equity is: VL = B + S $200,000 = $50,000 + S S = $150,000 d. The investor would need to invest 20 percent of the total market value of Alpha’s equity, which is: Amount to invest in Alpha = .20($200,000) = $40,000 Beta has less equity outstanding, so to purchase 20 percent of Beta’s equity, the investor would need: Amount to invest in Beta = .20($150,000) = $30,000 e. Alpha has no interest payments, so the dollar return to an investor who owns 20 percent of the company’s equity would be: Dollar return on Alpha investment = .20($55,000) = $11,000 Beta Corporation has an interest payment due on its debt in the amount of: Interest on Beta’s debt = .12($50,000) = $6,000 So, the investor who owns 20 percent of the company would receive 20 percent of EBIT minus the interest expense, or: Dollar return on Beta investment = .20($55,000 – 6,000) = $9,800 f. From part d, we know the initial cost of purchasing 20 percent of Alpha Corporation’s equity is $40,000, but the cost to an investor of purchasing 20 percent of Beta Corporation’s equity is only $30,000. In order to purchase $40,000 worth of Alpha’s equity using only $30,000 of his own money, the investor must borrow $10,000 to cover the difference. The investor will receive the same dollar return from the Alpha investment, but will pay interest on the amount borrowed, so the net dollar return to the investment is: Net dollar return = $11,000 – .12($10,000) = $9,800 Notice that this amount exactly matches the dollar return to an investor who purchases 20 percent of Beta’s equity. g. The equity of Beta Corporation is riskier. Beta must pay off its debt holders before its equity holders receive any of the firm’s earnings. If the firm does not do particularly well, all of the firm’s earnings may be needed to repay its debt holders, and equity holders will receive nothing. 357 21. a. A firm’s debt-equity ratio is the market value of the firm’s debt divided by the market value of a firm’s equity. So, the debt-equity ratio of the company is: Debt-equity ratio = MV of debt / MV of equity Debt-equity ratio = $14,000,000 / $35,000,000 Debt-equity ratio = .40 b. We first need to calculate the cost of equity. To do this, we can use the CAPM, which gives us: RS = RF + β [E(RM) – RF] RS = .06 + 1.15(.13 – .06) RS = .1405 or 14.05% We need to remember that an assumption of the Modigliani-Miller theorem is that the company debt is risk-free, so we can use the Treasury bill rate as the cost of debt for the company. In the absence of taxes, a firm’s weighted average cost of capital is equal to: RWACC = [B / (B + S)]RB + [S / (B + S)]RS RWACC = ($14,000,000/$49,000,000)(.06) + ($35,000,000/$49,000,000)(.1405) RWACC = .1175 or 11.75% c. According to Modigliani-Miller Proposition II with no taxes: RS = R0 + (B/S)(R0 – RB) .1405 = R0 + (.40)(R0 – .06) R0 = .1175 or 11.75% This is consistent with Modigliani-Miller’s proposition that, in the absence of taxes, the cost of capital for an all-equity firm is equal to the weighted average cost of capital of an otherwise identical levered firm. 22. a. To purchase 5 percent of Knight’s equity, the investor would need: Knight investment = .05($2,532,000) = $126,600 And to purchase 5 percent of Veblen without borrowing would require: Veblen investment = .05($3,600,000) = $180,000 In order to compare dollar returns, the initial net cost of both positions should be the same. Therefore, the investor will need to borrow the difference between the two amounts, or: Amount to borrow = $180,000 – 126,600 = $53,400 358 An investor who owns 5 percent of Knight’s equity will be entitled to 5 percent of the firm’s earnings available to common stock holders at the end of each year. While Knight’s expected operating income is $400,000, it must pay $72,000 to debt holders before distributing any of its earnings to stockholders. So, the amount available to this shareholder will be: Cash flow from Knight to shareholder = .05($400,000 – 72,000) = $16,400 Veblen will distribute all of its earnings to shareholders, so the shareholder will receive: Cash flow from Veblen to shareholder = .05($400,000) = $20,000 However, to have the same initial cost, the investor has borrowed $53,400 to invest in Veblen, so interest must be paid on the bor...
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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 Texas-Tyler.

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