Review Questions

1
Review Questions

• 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 youll
  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 , youll get
• 6 (.1) (1m) (1-.4) 3,600 every year, plus
  60,000 after-tax special div. at T5.
• 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 Us cost of
  equity is 12 per annum. Firm L has 400,000
  debt outstanding, and its cost of debt is 5 per
  annum.
• Find the value of U. (2 pts)
• b. Find Ls 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 Ls equity
• Cost Payoff
• 60,000 ( 10 600,000) 10,000
• (10(120,000 5400,000))
• Replicate with U and borrowing. Suppose buy X
  dollar of Us equity and borrow Y dollar.
• Cost Leverage
• X-Y 60,000 Y/(X-Y) 2/3 gt 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 rs r0 B/S (r0 rB) .12 2/3
  (.12 - .05) 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 Us equity
• Cost Payoff 100,000 ( 10 1,000,000)
  12,000 (10120,000)
• Replicate with L and lending. Suppose buy X
  dollar of Ls equity and lend out Y dollar.
• Cost Leverage
• XY 100,000 B/S X - Y 0 gt Y 2/3
  X
• gt X 60,000, Y 40,000
• Verify your payoff
• 60,000/600,000 120,000-0.05(400,000) 0.05
  (40,000) 12,000