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Consider two firms, With and Without, that have identical assets that generate identical cash flows. Without is an all-equity firm, with one million shares outstanding that trade for a price of $24 per share. With has two million shares outstanding and $12 million in debt at an interest rate of 5%.
-Assume that MM's perfect capital markets conditions are met and that you can borrow and lend at the same 5% rate as With. You have $5 000 of your own money to invest and you plan on buying Without shares. Using homemade leverage, how much do you need to borrow in your margin account so that the payoff of your margined purchase of Without shares will be the same as a $5 000 investment in With shares?
A)$2 500
B)$0
C)$5 000
D)$10 000

Question

Quizplus · Accepted Answer

To replicate the payoff of investing $5,000 in With shares using homemade leverage, you need to borrow an amount that reflects the same debt-to-equity ratio as With. With has $12 million in debt and a market value of $24 million in equity (2 million shares at $12 per share), making the debt-to-equity ratio 0.5. To invest $5,000 with the same ratio, you need to borrow $2,500, making your total investment $7,500. However, the question asks for the amount needed to borrow to have the same payoff as a $5,000 investment in With, not to replicate the debt-to-equity ratio. Since With has a 50% leverage ratio ($12 million debt on a total value of $24 million equity + $12 million debt = $36 million total value), to achieve the same effect with a $5,000 investment, you need to borrow an additional $5,000, doubling your investment to match the leverage effect in With.

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