Part I – Multiple Choice Questions
1) A company’s management believes the shares are undervalued. What is the order
of the financing sources that the company will choose?
A) Retained earnings -> Debt -> Equity
B) Debt -> Retained earnings -> Equity
C) Equity -> Debt -> Retained earnings
D) Retained earnings -> Equity -> Debt
Answer: A
2) Rejecting an investment today forever might not be a good choice because:
(I) The size of the firm will decline.
(II) There are always errors in the estimation of the NPVs.
(III) The option value is negative.
(IV) The company is foregoing future rights or the option to deepen the investment if
economic and industry conditions change for the better.
A) I only
B) II only
C) I, II, and III only
D) IV only
Answer: D
3) An all-equity company has contacted the bank to ask for a loan with a market value
of $160 million. The bank analyst believes that the company’s assets will be worth
$350 million, $170 million, or $100 million. These outcomes are all equally likely, and
this risk is diversifiable. The risk-free rate is 5%. In the event of default, 20% of the
value of the firm’s assets will be lost to bankruptcy costs. What is the face value of
the debt?
A) $160 million
B) $168 million
C) $212 million
D) $288 million
Answer: D
Total Assets
350
136
80
Debt
X
136
80
Equity
350-X
0
0
160
(X+136+80)/3=160*1.05
4) Debt overhang refers to the problem that equity holders prefer not to invest in
positive-NPV projects in highly levered firms because ________.
A) future investments are contingent on debt financing
B) projects are contingent on equity financing
C) gains are evenly shared between all stakeholders
D) most of the gains from the investment accrue to debt holders
Answer: D
5) Consider the following three statements:
(1) A real option is always present if there is uncertainty about the future development
of the market (e.g., demand)
(2) The option to abandon a Project is akin to a call option
(3) Real options are usually easier to identify and value than financial options
Which statements are correct?
A) Only (1) is correct.
B) Only (1) and (2) are correct.
C) All statements are correct.
D) All statements are incorrect.
Answer: D
6) Being the owner of a piece of land near the sea, you decide to purchase insurance
that will pay you 500 million euros in the event the land is destroyed by a tsunami,
knowing the likelihood for this to happen is 0.05%. Given the beta of an insurance for
these cases if -0.2 what is the actuarially fair premium, if the risk-free rate is 3% and
the expected return of the market is 8%?
A) 250 thousand euros
B) 247 thousand euros
C) 245 thousand euros
D) 240 thousand euros
Answer: C
7) For the following two questions, please consider a scenario where all participants are
risk neutral and the risk-free rate of return is 20%. Assuming the initial investment
required is 100 thousand euros and funds can only be raised via new debt, a manager
is considering carrying out one of two projects with the following payoffs, in thousand
euros:
2
Sucess Failure
Probability
0,4
0,6
Opportunity 1
200
200
Opportunity 2
350
80
What is the final cost of the risk-shifting problem and who bears it?
A) The bank bears a cost of 12 thousand euros
B) The manager bears a cost of 12 thousand euros
C) The bank bears a cost of 60 thousand euros
D) The manager bears a cost of 60 thousand euros
Answer: C. Note that the bank anticipates the risk-shifting problem, demanding a face
value of 180: 100=(F*40%+80*60%)/(1+20%). The expected payoff for the entrepreneur
is then 40%*(350-180)=68, lower than what the entrepreneur would get in the absence of
this friction (80, the payoff associated with opportunity 1 while issuing debt with face value
equal to 120)
8) Analysts expect Pineapple Inc. to face increased competition on the beverage
market, which would result in Pineapple Inc. losing 5% of their market share over the
next two years, and then to have stable income with no growth forever. Currently the
company follows a target debt-to-value strategy. Tomorrow it is planning to hold a
press conference, where the CEO will announce that the company will change its
debt structure strategy to permanent debt in three years. How will the value of the
shares change after the press conference? Assume perfect capital markets.
A) The share price will decrease
B) The share price will remain the same
C) The share price will increase
D) The market reaction is not certain
Answer: B
9) Garlic Bread Co. has just paid a dividend of $1.50 per share on its stock. The
dividends are expected to grow at a constant rate of 4% per year indefinitely. If
investors require a 10% return on the Garlic Bread Co. stock, what will the price be
in 5 years?
A) $26
B) $30.42
C) $31.63
D) $32.90
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Answer: C
Explanation: $1.5*1.04^6/(0.1-0.04)=31.63
10) A project has an up-front cost of $100,000. The project's WACC is 12%, and its net
present value is $10,000. Which of the following statements is most correct?
A) The project should be rejected since its return is less than the WACC.
B) The project's internal rate of return is greater than 12 percent.
C) All of the statements above are correct.
D) None of the statements above is correct.
Answer: B
11) You have the following information about BoxLock Inc: PE ratio = 12; EV/EBITDA=6;
Net Debt=$150 Billion. What is your estimate for the share price of LuckyLocks Inc.,
knowing that LuckyLocks has the following characteristics: number of shares: 10 M,
EBITDA=$300M, Net Debt = 0. Assume that BoxLock is an appropriate comparable
for the valuation of LuckyLocks.
A) $165
B) $360
C) $180
D) $195
The right answer is C) 180. We obtain it by multiplying the multiple of 6 with the EBITDA
of $300 M, and then dividing by the number of shares, 10 M.
12) Suppose you have the following four investment opportunities:
Initial Investment
NPV
I
100
30
II
20
7
III
30
12
IV
100
50
If you only use the profitability index method to allocate a budget of 200, which projects
do you select?
A) II, III, and IV.
B) I and IV.
C) I, II, and III.
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D) All projects.
The right answer (which btw is not the optimal allocation) is A) II, III, and IV. The first step
is to compute the profitability index (PI) for each project: I=0.3, II=0.35, III=0.4, and IV=0.5.
So we would start with project IV (highest PI), then go to project III, and then to II. This
would consume 150 of our budget, and so we would not be able to do I.
13) Consider a firm that is evaluating implementing new safety policies that will reduce
the chances of 100 million euros losses next year from 10% to 5%. To do so, it has a
cost of 500 thousand euros upfront. We also know the beta of the loss is 0 and the
risk-free rate is 3%. How much is the NPV of implementing the new policies if the firm
is fully insured?
A) +4.5 million euros
B) + 4.35 million euros
C) + 5 million euros
D) – 500 thousand euros
Answer: D
14) StrongBearings Inc. currently has an equity beta of 2.4. The company currently has a
D/E ratio of 3 and has been using permanent debt. The current debt beta is 0.5 and
the firm faces a tax rate of 35%. Suppose the firm suddenly announces that it will
switch to targeting a D/E ratio of 4. Under the new capital structure, the firm’s debt
beta will jump to 0.6. What is the new equity beta closest to?
A) 3.1
B) 3.3
C) 3.5
D) 1.0
The right answer is B) 3.3. The first step is to compute beta_u. We can use the
expression beta_e=beta_u+D/E(beta_u-beta_d)*(1-tc) and solve it for beta_u:
2.4=beta_u+3(beta_u-0.5)*(1-0.35). After a few algebra steps, you obtain
beta_u=(2.4+3*0.5*0.65)/(1+3*0.65)=1.14. The second step is to insert beta_u in the
expression for levered cost of equity under targeting, being careful to replace D/E and
beta_d by the new values: beta_e=beta_u+D/E*(beta_u-beta_d)=1.14+4*(1.140.6)=3.3.
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Part II: Real options
Sounds of the Earth Inc (“SOE”) is developing a new music app. The firm has already
spent $150 in this project and is considering whether or not it should take its development
to the next stage (spending an additional $200) or abandon the project altogether (payoff
of zero).
a) (1 point) If SOE advances the app to the next development stage, the value of the app
in one year is either $0 (failure) or $400 (success), with equal probability. If this risk is
diversifiable and the risk-free rate 5%, should SOE take the development of the music
app to the next stage? Why?
You should disregard the $150, since it is sunk. SOE should not take the development to
the next stage, since the expected future payoff is just $200 (0.5*$400+0.5*$0) and the
investment is $200 (negative NPV).
b) (1 point) Now assume that instead of the fixed payoffs at t=1 of either $0 or $400, SOE
can invest an additional amount (at t=1). If SOE invests an additional $200, then the
value of the project doubles (immediately). Would this change your previous answer?
Why?
With this expansion option, SOE would invest an additional $200 if the development is a
success. The new payoffs at t=1 are then either $600 (2*$400-$200) or zero. The NPV of
the project at date 0 is then 0.5*$600 / 1.05 - $200 = $85.7. Now the NPV is positive and
SOE should go ahead with the next development stage.
c) (2 points) Redo just question a) knowing that there exists a mispriced twin security
that trades at $40 and has t=1 payoffs of $42 (app success) or $32 (app failure). Does
your answer change? Why? Carefully explain your reasoning/calculations. Assume
perfect capital markets.
Using our standard notation for the replicating portfolio, we can find x and y such that
42x + 1.05y = 400
32x + 1.05y = 0
A few steps of algebra yield x=40 and y=-1,219.1. The value of the replicating portfolio is
40*40-1,219.1=380.9. This implies that SOE can actually create value by doing the
following arbitrage strategy: (i) invest in the project (-$200 at t=0); (ii) short-sell 40 units
of twin security (+40*$40=+$1600 at t=0); and (iii) lend $1,219.1 (-$1,219.1 at t=0). This
strategy generates $0 for sure at t=1 (long project, short replicating portfolio) and a profit
of $180.9 at t=0.
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Part IV: M&M with taxes
New Wine Co (NW) is a publicly traded firm with 10 shares outstanding. The firm’s current
equity value is $150, which is also the market value of its (net) permanent debt. NW’s
current cost of equity is 10% and the cost of debt is 5% (also the risk-free rate). The
company faces a corporate tax rate of 40%. Besides taxes there are no other deviations
from perfect capital markets.
a) (2 points) NW announces that it will stop using debt and that it plans a share issue to
repurchase the full debt amount. Calculate what happens to the share price upon
announcement (before debt repurchase), assuming debt value is unchanged. Explain
your reasoning.
The share price before the announcement is $15 (=$150/10). After the announcement
the firm no longer has tax shields and so the price will come down. Using the MM formula
for tax shields with permanent debt, these are worth $150*0.4=$60. So equity goes down
from $150 to $90. The share price goes down to $9 (-40%).
b) (2 points) Suppose instead that NW announces that it will gradually reduce its current
debt amount by 10% every year (starting next year). Specifically, the amount of debt
Dt+1 will be equal to 0.9*Dt. Calculate what happens to the share price upon
announcement. Explain your reasoning.
Since the tax shields are proportional to debt, they are also growing every year at a
negative rate of -10%. Therefore you can compute the new PVTS as TS1/(5% - - 10%),
where TS1 is the tax shield one year from now: TS1=$150*5%*40%=$3; so the new PVTS
is $20. There is thus a loss of $40 in PVTS relative to before the announcement ($60$20), which means that equity goes to $110 and the stock price to $11 (-26.7%).
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