Question I and II: Choose the right answer(s) based on the Marriott case.
I. The cost of capital for each division is the same as the corporate cost of capital.
a) True, as long as investors are diversified.
b) True, because it is Marriott Corporation that pays back investors, not the
operating divisions.
c) True, as long as the new investment in each division has the same risk as the
division’s existing assets.
d) False, because the new investment in each division has a different risk than the
average risk of Marriott assets. (True)
e) False, because the new investment in each division has a different risk than the
assets of other divisions.
II. As a result of leverage a division carrying more debt faces lower weighted average
cost of capital.
a) False, because debt is always cheaper than equity.
b) False, because debt increases the required rate of return on the equity.
c) True, because debt offers a tax shield. (True)
d) True, because any amount of debt creates agency conflicts.
e) True, because equity is always more expensive than debt.
III. Consider two firms, C and D, that differ only in terms of their payout policy. Both
firms are all-equity financed, and hold initially some risky assets (which are identical
for both firms), plus $ 1 million in excess cash. Firm D decides to distributes the
excess cash as a dividend to its shareholders, whereas firm C decides to retain the
cash within the firm. Which of the following statement(s) is (are) true
a) After D has distributed the cash dividend investors will require a higher rate of
return for holding stock D than for holding stock C. (True)
b) After D has distributed the cash dividend investors will require a lower rate of
return for holding stock D than for holding stock C.
c) Because answer ‘a)’ is correct, the stock price of firm D is expected to drop by
more than the amount of the cash distribution.
d) Because alternative ‘b)’ is correct, the stock price of firm D is expected to react
positively (increase) upon the dividend announcement.
e) On the day of the dividend payment the stock price of firm D is expected to drop
exactly by the amount of the cash distribution. (True)
iv The management of firm A is considering to start a new project. The project requires
an initial investment equal to $ 1,000,000. The risk of the project is identical to that
of the firm’s current risky assets. The expected rate of return on the new project is
15% annually, forever.
The firm’s balance sheet (market values) prior to the announcement of the investment
project is as follows:
Risky Assets $ 5,000,000
Cash 1,000,000
__________
Total $ 6,000,000
Equity $ 4,000,000
Debt 2,000,000
__________
Total $ 6,000,000
There are 100,000 shares outstanding.
The beta of the firm’s stock is equal to 1.35, the beta of its debt is equal to 0.15.
The risk-free rate is equal to 4%, and the expected market risk premium is 7%.
a) Calculate (1) the Beta of the firm, and (2) the Beta of the firm’s risky assets.
(1) BETA OF THE FIRM:
Market value of equity: 4,000,000
Market value of debt: 2,000,000
Beta of the firm is equal to the weighted average of the beta of debt and equity:
Beta(Firm) = 4/6 * 1.35 + 2/6 * 0.15 = 0.90 + 0.05 = 0.95
(2) BETA IF THE RISKY ASSETS:
The beta of the risky assets will be different from the beta of the firm, since the
firm also holds cash, which has a beta equal to zero:
5/6 * Beta of risky assets + 1/6 * Beta of the cash = Beta of the firm
5/6 * Beta of the risky assets = 0.95
Beta of the risky assets = 6/5 * 0.95 = 1.14
b) Calculate the NPV of the new project. Ignore tax considerations.
REQUIRED RATE OF RETURN:
Project risk is identical to the risk of “Risky Assets”, hence
Beta of Project = 1.14
Required rate of return for the project:
R = Risk-free rate + Project beta * Market risk premium
= 4% + 1.14 * 7% = 11.98% (its fine if you rounded to 12%)
The investment yields an expected annual CF of:
15% * 1,000,000 = 150,000
The project payoff is a perpetuity, so that:
PV = 150,000 / 0.1198 = 1,252,086.8
To find the net present value we have to subtract the investment outlay:
NPV = PV – I = 1,252,086.7 – 1,000,000 = 252,087
(250,000 is fine, too)
c) Within the board of directors there is a discussion about the optimal financing choice.
The CFO prefers debt since this increases the firm’s profit per share, and, thus, the
value of the shares.
Do you agree with the CFO (ignore taxes!)? Motivate your answer.
Financing with debt will indeed increase expected EPS.
However, leverage will also increase the friskiness of the firm’s equity.
The two effects cancel each other out, so that the value of the shares is
unaffected.
The CFO’s argument is therefore not correct.
d) The CEO also wants to finance with (risk-free) debt. However, she claims that due to
a tax advantages of debt financing, using risk-free debt will reduce the firm’s
weighted average cost of capital (WACC), and thus also the hurdle rate for future
investments.
Do you agree with the CEO? Again, motivate your answer.
The CEO is right that the tax advantage of debt implies that debt financing
reduces the firm’s WACC.
However, it is not quite clear whether financing this project with debt would
also reduce the hurdle rate for future investments. The latter depends of the risk
of the future projects, and on the degree to which this future investment can be
financed with debt (because of the tax advantage of debt financing).6
Question V
Consider an economy with three different types of firms that we will refer to as the Good
(G), the Bad (B), and the Ugly (U). The firm type is known only to the manager, who
acts in the best interest of the firm’s original shareholders. The uninformed investors
consider all three types equally likely (type G, type B, and type U are each encountered
with probability 1/3).
Each firm has access to an investment project that requires an investment outlay of
$3million. The firm types differ in terms of the NPV of this investment project, as well as
in terms of the value of their assets in place (all numbers represent $ million):
Value of assets in place Investment NPV
Good (G) 8 3 2
Bad (B) 10 3 -1
Ugly (U) 3 3 -1
Average 7 3 0
Firms are all-equity financed. The only way to raise capital for the new investment
project is by issuing equity to the public. A firm that issues equity has to undertake its
investment project.
a) Assume initially that all firm types issue equity and invest. What fraction of the
firm’s equity has to be offered to the public to raise $3 million in the equity offering?
The firm type is known only to the manager. This means that the outside
investors who are supposed to purchase the issue will not know whether an
individual firm is good, bad, or ugly. They will have to act based on the
assumption that they deal with the “average” firm.
The average firm value after the offering is equal to 7 + 3 + 0 = 10 ($ million).
This means that the new shareholders will demand at least 3/10 (or 30%) of
the firms’ equity in order to break even, in expectation.7
b) Based on your answer in part a), which firms will find it profitable to undertake the
equity offering?
To see whether it is profitable to undertake the equity offering we have to
compare the original shareholders’ wealth after the offering (70% of the total
firm value after the investment), with their wealth if no offering takes place
(100% of the assets in place):
Good: 7/10 * (8 + 3 + 2) = 9.1 > 8 Issue and invest!
Bad: 7/10 * (10 + 3 - 1) = 8.4 < 10 Don’t issue!
Terrible: 7/10 * (3 + 3 – 1) = 3.5 > 3 Issue and invest!
Only the Good and the Ugly type are going to issue and invest. The
shareholders of the Bad type are better off without the new investment.
c) Now suppose that managers decide whether to issue equity or not. Based on your
answer in part b), what fraction of the equity will the issuing firms now have to give
to the outside investors in order to be able to raise $3 million? (10 POINTS)
Investors will realize that the Bad type will not issue. This means that the
“average” firm that issues equity now consists to 50% of the Good, and to 50%
of the Ugly type.
After the issue, this average issuing firm will therefore be worth
0.5 * (8 + 3 + 2) + 0.5 * (3 + 3 -1) = 0.5 *(13 + 5) = 9
In order to raise $3 million, the issuing firms will therefore have to offer
3/9 = 1/3 = 33.3% of the equity to the new shareholders.8
d) Based on your answer(s) in part b) and/or c), what will be the market value of an
issuing firm be AFTER the announcement of the equity offering, but BEFORE the
actual equity issue takes place?
Only G and U issue. After the announcement, but prior to the offer the market
value of these firms will be equal to the sum of the average value of the assets in
place, and the average project NPV.
0.5 * (8 + 3) + 0.5 * (2 - 1) = 6 ($ million)
e) You may have found that certain firm types in this example will over invest
(undertake negative NPV-projects), or under invest (forego positive-NPV projects).
For each firm type, provide a short intuitive explanation for why this type firm does
or does not invest. (10 POINTS)
Good: The equity issue is very costly since shares can be issued only at a price
below their true value. This creates an incentive to under invest. However, the
new investment is profitable enough, so that the Good type will invest anyway.
Bad: The firm has a negative NPV project. In addition, because of its high
value of assets in place, its equity issue would be undervalued (the true value of
the firm after the issue would be $12, compared to an average of $10). The firm
therefore has no reason to (and will not) invest.
Ugly: Firm type has only a negative NPV project. However, the value of its
assets in place is very low, so that issuing overvalued equity is sufficiently
profitable for the old shareholders to more than offset the negative NPV of the
new investment. The ugly type will therefore overinvest
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