1 Review Questions 1.Over the last 30 years, the proportion of the market value of stocks held by pension funds has increased substantially. Holding everything else constant, what implication does this trend have for dividend policy in the aggregate and why? A: More companies pay cash dividends in aggregate, b/c pension funds are tax-exempt and are likely to prefer dividend payment. (Clientile argument)

2 2. Suppose that a firm has $1,000,000 that it can either pay out as a special dividend or retain for internal investment. If the firm retains the money, it can earn an after-tax return of 6% per year over the next five years. This return will be distributed to shareholders as an additional dividend over the next five years. After the five-year period is up, the $1,000,000 will be paid out as a special dividend. 5 year Treasury bonds are currently yielding 7%, which you’ll invest in. You own 10% of the shares and face a 40% tax rate on both interest and dividend income. Would you prefer the firm to pay out the $1,000,000 today? A: (1) If firm pays 1M today, you get with 10% ownership.1(1m) (1-Ts) = 60,000 You use this income to invest in T-bill and get (1-.4) (7%) 60,000 = 2,520 Every year, plus 60,000 principal at the end of year 5. (2) If firm retains $, you’ll get: 6% (.1) (1m) (1-.4) = 3,600 every year, plus 60,000 after-tax special div. at T=5. Clearly, alternative 2 prevails. (A shortcut comparison: -pays div., after-tax return (1-.4) (7%), which is smaller than -Retained earnings, after-tax return: 6% )

3 Practice Question Assume perfect capital markets (i.e., no taxes, no bankruptcy costs, no transaction costs, etc.). U and L are identical in all aspects except that U is all-equity financed, and L is leveraged. Each firm generates perpetual operating cash flows of $120,000 per year. Firm U’s cost of equity is 12% per annum. Firm L has $400,000 debt outstanding, and its cost of debt is 5% per annum. a.Find the value of U. (2 pts) b. Find L’s debt-equity ratio. (2 pts) c. Assume that you can borrow and lend at 5% as well. Show that you can replicate the return of L with a portfolio that consists of U and borrowing only (homemade leverage). (4 pts) d. Show that you can replicate the return of U with a portfolio that consists of L and lending only.

4 (c) Solution 1 Assume that you buy 10% of L’s equity CostPayoff $60,000 (= 10% * 600,000) $10,000 (=10%*(120,000 – 5%*400,000)) Replicate with U and borrowing. Suppose buy X dollar of U’s equity and borrow Y dollar. CostLeverage X-Y = $60,000Y/(X-Y) = 2/3 => X = 2.5Y So Y = $40,000 X = $100,000 Verify your payoff:

5 (c) Solution 2 Achieve same rate of return with same leverage Buy L: Return: r s = r 0 + B/S (r 0 – r B ) = /3 ( ) = 16.67% B/S = 2/3 Replicate with U and borrowing –Spend $3 of your own –Borrow 3* (B/S) = $2 from bank (same leverage) –Use all the $5 to buy U –Return: [$5(.12) - $2(0.05)]/$3 = 16.67%

6 (d) Solution 1 Assume that you buy 10% of U’s equity CostPayoff $100,000 (= 10% * 1,000,000) $12,000 (=10%*120,000) Replicate with L and lending. Suppose buy X dollar of L’s equity and lend out Y dollar. CostLeverage X+Y = $100,000B/S * X - Y = 0 => Y = 2/3 X => X = $60,000, Y = $40,000 Verify your payoff: 60,000/600,000 [120, (400,000)] (40,000) = 12,000