# Practice problem--it's very helpful ~

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University of Toronto Mississauga

Economics

ECO359H5

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ECO3592011 UniversityofToronto PracticeProblems3 DepartmentofEconomics ECO 359 Practice Problems 3 Solutions to selected Textbook questions Question 16.1 a. Since Alpha Corporation is an all-equity firm, its value is equal to the market value of its outstanding shares. Alpha has 5,000 shares of common stock outstanding, worth $20 per share. Therefore, the value of Alpha Corporation is $100,000 (= 5,000 shares * $20 per share). b. 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 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. ModiglianiMiller Proposition I (No Taxes): V L =V U. Alpha Corporation, an unlevered firm, is worth $100,000 = V . U Therefore, the value of Beta Corporation (V L) is $100,000. c. The value of a levered firm equals the market value of its debt plus the market value of its equity. V L = B + S. The value of Beta Corporation is $100,000 (V ), Lnd the market value of the firms debt is $25,000 (B). The value of Betas equity is S= V L B = $100,000 $25,000 = $75,000. Therefore, the market value of Beta Corporations equity (S) is $75,000. d. Since the market value of Alpha Corporations equity is $100,000, it will cost $20,000 (= 0.20* $100,000) to purchase 20% of the firms equity. Since the market value of Beta Corporations equity is $75,000, it will cost $15,000 (= 0.20* $75,000) to purchase 20% of the firms equity. e. Since Alpha Corporation expects to earn $35,000 this year and owes no interest payments, the dollar return to an investor who owns 20% of the firms equity is expected to be $7,000 (= 0.20*$35,000) over the next year. While Beta Corporation also expects to earn $35,000 before interest this year, it must pay 13% interest on its debt. Since the market value of Betas debt at the beginning of the year is $25,000, Beta must pay $3,250 (= 0.13*$25,000) in interest at the end of the year. Therefore, the amount of the firms earnings available to equity holders is $31,750 (=$35,000 $3,250). The dollar return to an investor who owns 20% of the firms equity is $6,350 (= 0.20*$31,750). f. The initial cost of purchasing 20% of Alpha Corporations equity is $20,000, but the cost to an investor of purchasing 20% of Beta Corporations equity is only $15,000 (see part d). 1 www.notesolution.com

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