1. 1 How does leverage affect shareholders’ risk? In a CAPM context: Example: A firm’s operating assets has a beta of 1. If the firm has a debt ratio (B/V) of 25%, what is its equity beta? (Assume its debt is riskfree.) Answer: 1 = 0.75 beta(equity)  beta equity is 1.33. Assume bond beta = 0 (i.e., assume debt is riskfree), then In words, leverage increases the equity beta by the degree of leverage.

2. 2 Review question: Homemade leverage Refer to Example #2 in the lecture notes for Chapter 16. On slide 17 we showed that if the firm stayed with the original all-equity capital structure, investors who preferred the alternative with 50% debt financing could effectively do this themselves by purchasing shares and borrowing. (“homemade leverage”). Suppose instead that the firm does switch to the capital structure with 50% debt. Show that investors who prefer the original all-equity capital structure can effectively do this themselves. (i.e. to replicate the cashflows of the unlevered firm with levered firm and borrowing/lending. “homemade” unlever a firm)

3. 3 Solution Step 1: Find out the payoffs of the target Unlevered: ROE = 15%, B/S = 0 Step 2: Find out the payoffs of things on your menu levered: ROE = 20%, B/S=1, bond, r=10% Step 3: Decide your homemade leverage (or unleverage) The trick is that your personal portfolio’s leverage = leverage of target, in this case = 0. If you buy levered equity, you are buying sth. with a leverage of 1. To reduce this leverage to 0 (the target), you need to lend out an amount equal to (your implicit) borrowing (your firm is borrowing but you are lending so cancel out leverage). Solution: Buy $1 levered equity, lend $1 to bank, total investment: $2. Return: $1 (20%) + $1 (10%) = $0.3, Return = 0.3/2 = 15% = unlevered firm.