Solutions to Practice Problems – Chapter 17
1 a) WACC = (D/V) Rd + (E/V) Re
=> 0.13 = 0.15*Rd + 0.85*0.145
=>
Rd = (.13 - .85*.145)/.15 = 4.5%
b) In PCM, a levered firm’s
WACC always equals the unlevered firm’s cost of capital. So, if the firm was unlevered, its cost of capital would be
13%.
2 a) D/E = .9
=> D = .9*E
=> D/V =
.9E/(E+.9E) = .9/1.9 = .4737
WACC = (D/V) Rd +
(E/V) Re = .4737*.12 + (1 -
.4737)*.156 = 13.8947%
b) A lovely little trick
question. You don’t compute out
WACC at the new debt-equity ratio using the same cost of debt and equity.
At a different debt level, both Rd and Re
would be lower than before, but the weighted average cost of capital still stays
the same, so the answer is 13.8947%.
3 a)
0.12 = 0.45*Rd
+ 0.55*0.18
=>
Rd = (.12 - .55*.18)/.45 = 4.6667%
b) The new cost of debt would
be 1.2*.046667 = 5.6%
The WACC doesn’t change;
it’s still 12%.
Re = Ra
+ (Ra – Rd)*(D/E) = .12 + (.12 - .056)*(.6/.4) = 21.6%
(remember, WACC = Ra)
4) In perfect capital
markets, VL = VU = 220,000/0.11 = 2,000,000
E = VL - D =
2,000,000 - 800,000 = 1,200,000
The required return on the
firm’s assets, Ra, is the same as the required return on its equity
if it stays unlevered. So WACC = Ra
= 11%
Re = Ra + (Ra – Rd)*(D/E) =
.11 + (.11 - .06)*(8/12) = 14.3333%
5 a) The required return on
assets is the same as the WACC, so:
Ra = (D/V)
Rd + (E/V) Re = (8/25)*.115 + (17/25)*.165 = 14.9%
b) Debt would then be $5
million, and equity would be $20 million.
Re = Ra
+ (Ra – Rd)*(D/E) = .149 + (.149 - .10)*(5/20) = 16.125%
6 a) V = 1,250,000/.09625 =
12,987,012.99
D = 300,000/.06 = 5,000,000
E = 12,987,012.99 - 5,000,000
= 7,987,012.99
b) Re = Ra
+ (Ra – Rd)*(D/E) = .09625 + (.09625 - .06)*(5/7.987) =
11.8943%
7 a) Since dividend policy
and capital structure are both irrelevant in PCM, the two pieces of news they
announce on Tuesday have no effect on the stock price.
So the value of the firm on Tuesday = 1000*60 = $60,000
On Wednesday, the value of
the firm increases by the $15,000 they raise by issuing the debt.
Firm value is now $75,000.
On Thursday, the value of the
firm falls by the $17,000 they pay out as dividend.
Firm value is now $58,000.
b) The stock price doesn’t
change on Tuesday; it’s still $60.
On Thursday it falls by the
amount of the dividend per share, which is $17.
Stock price is now $43.
c) Stockholder’s wealth
cannot change; in PCM it is unaffected by capital structure or dividend
decisions.
Initial wealth = value of
shares = 1000*60 = 60,000
Final wealth = dividend +
ex-dividend value of shares = 17,000 + 1000*43 = 60,000
Moral: In PCM, it doesn’t
matter whether a dividend payment is financed by issuing new equity or issuing
new debt. Either way, there’s no
effect on stockholder wealth.
8 a) When making capital
structure decisions, managers can maximize either the stock price or the value
of the firm; stockholder wealth is maximized either way. F The value of the firm
is D + E. Maximizing the stock
price will be the same as maximizing E, but no the same as maximizing D + E.
Stockholder wealth is maximized by maximizing the value of the firm.
b)
When a firm makes a pure capital structure change, the proceeds from
issuing new debt must be paid out to stockholders.
T Since we hold the assets of the
firm constant, the cash that is raised by issuing debt cannot be retained by the
firm, it has to be paid out to stockholders.
c)
An investor who is more risk averse prefers to invest in the equity of
the unlevered firm. T
The risk of equity increases with leverage (since financial risk gets added to
the business risk coming from the assets); equity of the levered firm is
riskier, and a more risk averse investor wants less risk.
d)
Given an unlevered firm U and an otherwise identical levered firm L,
buying 2% of U’s equity or buying 1% of L’s equity and 1% of L’s debt
yields identical investments. F We need to buy 1% of U’s equity, not 2%.
e)
Borrowing money to buy shares of the unlevered firm has the same effect
as buying shares in the levered firm. T
Personal borrowing increases the risk of the investment in exactly the same way
as corporate borrowing; borrowing money to buy shares of U creates an identical
investment to buying shares of L.
f)
In perfect capital markets, capital structure is irrelevant because
investors are indifferent between dividends and capital gains. F
Indifference between dividends and capital gains is what makes dividend policy
irrelevant. Capital structure is
irrelevant because investors have equal access, and can mimic or undo the
effects of leverage.
g)
In perfect capital markets, as a firm increases its debt ratio, the cost
of debt and the weighted average cost of capital both stay constant.
F WACC stays constant (at Ra)
but the cost of debt increases (since the debt gets more risky).
h)
If the cost of debt was always less than the cost of equity, a firm would
be able to reduce its weighted average cost of capital just by using more debt
and less equity. F
The cost of debt is always less than the cost of equity (Rd
< Ra < Re) but the WACC still stays constant as you
increase debt. You are using
more of the cheaper source of capital but this is offset by the fact that the
cost of debt and the cost of equity both increase as you increase your debt.
The weighted average doesn’t change.
i)
In PCM maximizing firm value is the same as minimizing WACC, but this is
not necessarily true in the real world because capital structure decisions can
affect the cashflows generated by assets. T Since
firm value is computed by discounting expected CFs at the WACC, maximizing firm
value is the same as minimizing WACC only if the expected CFs stay constant.
In the real world, debt financing affects expected CFs since it can make
firms deviate from the NPV rule when making investment decisions.