Lecture 5 Sol

# And unlevered inc are identical in every respect

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Levered Inc. and Unlevered Inc. are identical in every respect except for capital structure. Both companies expect to earn \$96 million in perpetuity (before taxes), and both distribute all of their earnings as dividends. Levered’s perpetual debt has a market value of \$275 million and the required return on its debt is 8%. Levered’s stock sells for \$100 per share, and there are 4.5 million shares outstanding. Unlevered has 10 million shares outstanding worth \$80 each. Unlevered has no debt. These firms operate in the Modigliani-Miller world with taxes. Both firms face a 40% tax rate. How can you take advantage of this scenario? Solution We know that in the MM world with taxes we should have V L = V U + τ C D. Does this hold? V U = \$80 × 10 million = \$800 million V L = \$275 million + \$100 × 4.5 million = \$725 million But according to MM1 we should have V L = \$800M +.4 × \$275M = \$910M Thus, V L < V U + τ C D. In other words, the current market value of Levered (\$725M) is too low; it should be \$910 according to MM 1. Since this violates MM 1, we know that an arbitrage opportunity exists. To take advantage of it, use the MM intuition as in class notes. Form two portfolios with the same future cash flows, one using Levered’s stock (portfolio L) and the other using Unlevered’s stock plus borrowing (portfolio U). You already know that you will have to buy the portfolio based on the undervalued firm (Levered), and (short) sell the portfolio based on the overvalued firm (Unlevered). To do this, we can choose any α we like, say 5%. Portfolio L: Buy 5% of the equity of Levered (225,000 shares). Cash flows: Initial cost: 225,000 × \$100 = \$22,500,000 Future: .05 × [\$96,000,000 - 0.08 × \$275,000,000] × (1-.4) = \$2,220,000 Portfolio U: buy 5% of the equity of Unlevered (500,000 shares) and also borrow 5% of (1-.4) × \$275,000,000 at 8%. Cash flows: Initial cost: 500,000 × \$80 – .05 × (1-.4) × \$275,000,000 = \$31,750,000 Future: .05 × \$96,000,000 × (1-.4) - 0.08 × .05 × (1-.4) × \$275,000,000 = \$2,220,000 Future cash flows are the same, but L costs less than U. Sell U and buy L! This is an arbitrage opportunity!!! Today you make a profit for sure of \$31,750,000 - \$22,500,000 = \$9,250,000

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COMM370 – Elena Simintzi 7 Question 7. Seashell has 100 million shares worth \$12 per share and no debt. Its cost of capital is 10%. It has a perpetual (before tax) random CF with mean \$200 million and it pays taxes at a 40% tax rate. Seashell plans a leveraged recapitalization, in which it will issue \$600 million in perpetual debt at an interest rate of 5% per year and use the proceeds to repurchase shares. The firm operates in the Modigliani-Miller world with taxes. a) What are Seashell’s firm value, cost of equity, and WACC before the recapitalization? b) What are Seashell’s firm value, equity value, debt value, cost of equity, and WACC after the recapitalization? Compare you results to those in a) and interpret the differences. c) What happens with Seashell’s equity values and share price at the time of the announcement but before the recapitalization is executed? Solution a) Before the recap: V U = 100M×\$12 = \$1200M (=\$200M×(1-.4) / .1) r E = r u = r WACC = 10% b) After the recap, and recalling that MM1 should hold: V L = \$1200M + .4×\$600M = \$1440M (by MM 1) D = \$600M V L = \$1440M = \$600M + E L , and thus E L = \$840M (V L = D + E L ) r E solves: \$840M = [\$200M - .05×\$600M]×(1-.4) / r E ; this gives r E = 12.14% or use MM 2: r E = 10% + (600/840)×(10% - 5%)×(1-.4) = 12.14% r WACC = (600/1440)×5%×(1-.4) + (840/1440)×12.14% = 8.33%
• Winter '12
• VincentGregoire
• Debt, Elena Simintzi

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