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ECON 138 Summer 2010
Final
Maximum possible score is 40.
I.
Multiple Choices—choose the best answer (1 points each. Total 7 points)
1. Which of the following is true?
A. Forwards are handled through clearinghouses.
B. Binomial pricing of option is an example of pricing by replication.
C. The Black-Scholes formula assumes that the movement of asset price, measured in
dollars, follows a Brownian motion with drift.
D. The Black-Scholes formula prices European put options.
2. Which of the following are false?
i. Issuing stocks to management can reduce the empire-building problem, but will
not be able to completely eliminate it.
ii. With asymmetric information, good managers will always promise a fixed return
to investors to price bad projects out of the market.
iii. With the principle-agent model we discussed , unpaid existing debt makes it
harder to obtain financing from all investors.
A. i. and ii. only
B. i. and iii. only
C. ii. and iii. only
D. All three
3. In the free-rider model of mergers and acquisitions,
i. Strategic response of shareholders might affect a merger’s the chance of success if
the acquirer offers a price
ƒ above the target’s current value, but
ƒ below the target’s current value plus expected synergy
ii. To solve the free-rider problem with a post-merger transfer, the acquirer must
threaten to transfer enough value from the hold-out shareholders so that they
would receive less than the target’s current value.
iii. The free-rider problem can be solved if we allow shareholders to have different
beliefs.
A. i. and ii. only
B. i. and iii. only
C. ii. and iii. only
D. All three
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4. Which of the following is neither an assumption nor an implication of Modigliani-Miller
Theorem?
A. No transaction cost.
B. The Theorem does not hold whenever there is tax.
C. With all the assumptions holding, amount of dividend does not matter.
D. All parties hold the same beliefs on the firm’s prospect.
5. If investors incorrectly valuate firms in the short run, which of the following is true?
i. The acquirer always prefers stock mergers because it can take advantage of the
incorrect valuation.
ii. The acquirer’s short-run payoff of using cash and stock are the same.
iii. The target’s short-run payoff of receiving cash and stock are the same.
A. i. and ii. only
B. i. and iii. only
C. ii. and iii. only
D. All three
6. Which of the following are false about overconfidence?
i. Overconfident managers are more likely to make acquisitions.
ii. Overconfident managers prefer stock mergers over cash mergers.
iii. If Vinci believes he teaches better than the average summer instructor, he could be
making an error of overprecision.
A. i. and ii. only
B. i. and iii. only
C. ii. and iii. only
D. All three
7. [Challenge Question – Attempt only when you finish everything else]
Which of the following is false?
A. This is false.
B. There are statements in this final that are false.
C. I have no idea, and I bet Vinci doesn’t have any too.
D. None of the above.
(Note: Don’t worry, you get credit for this question no matter what you chooses.)
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II.
Long Questions—show all your steps! (Total 33 points)
1. (8 points) A European call option is set to expire in two more days. The current stock price
is 10, and on each day the stock price could either go up by 3 or down by 2. Name today as
= 0, tomorrow as = 1 and the last day as = 2.
a.
Draw a tree diagram representing the possible price movements. (2 points)
16
13
11
11
10
8
6
b.
Calculate the price of the option if the exercise price is 11. (6 points)
Solving the upper case,
16 +
11 +
Yields = 1 and
the lower case,
=5
=0
= −11. Cost of such a portfolio would be 13 ∙ 1 + −11 = 2. Solving
11 +
6 +
=0
=0
Yields = 0 and = 0. Cost of such a portfolio would be 8 ∙ 0 + 0 = 0. Now we can
combine what we obtained above and go back to the first stage,
13 +
8 +
Yields
= 0.4 and
=2
=0
= −3.2. The cost of such a portfolio is the price of the option,
= 10 ∙ 0.4 + −3.2 = 0.8
2. (13 points) Consider the empire building model, where the manager maximizes
+
′
[ + ( )] + [ + ( )]
with being the number of existing shares, ′ the number of shares to be issued to new
investors and the manager’s preference for firm size. Return to investment ( ) is
concave, so ′ ( ) > 0 and ′′ ( ) < 0.
Now we add in a twist—suppose a tax is imposed on any return new investors receives.
The budget constraint the manager faces is then
′
(1 − )
a.
[ + ( )] = −
+ ′
Solve for amount that the manager will invest in. Your answer should be in the form
′
( ) = ⋯. (4 points)
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With the stock issuance/repurchase constraint,
′
(1 − )
′
+
[ + ( )] = −
Rearranging gives
−
=
1−
+
− +
Plugging into the maximization and simplify gives,
max
+
−
+
+
1−
+
Taking derivative with respect to I and set it to zero,
1
+
1−
1
1
=
1− 1+
−
b.
=0
Does the amount invested go up or down with ? (2 points)
increases with so the amount invested goes down with .
c.
[Challenge Question] Suppose
= ln + 10. If the government’s goal is to
maximize the tax revenue it receives, what should it set? (7 points)
Rearrange the budget constraint
′
(1 − )
[ + ( )] = −
+ ′
′
[ + ( )] =
+ ′
−
1−
Amount invested is given by
1
=
1
1
1− 1+
=
1
1
1− 1+
= 1−
1+
So tax revenue is
−
=
1−
+
Taking derivative with respect to t and set to zero,
+
1+
−
=
1−
1−
4
−
1−
1+
1+
−
=0
= 1−
+
1−
1−
=
1+
=1−
1+
is rejected because 1 − = −
1+
<0
(Not required: Intuitively the government is balancing between higher tax rate and lower
new stock issuance. Optimal tax rate thus increases with , which increases firm size, and
decreases with cash, which reduces number of new stock issued)
3. (12 points) In the noise trader model the rational traders’ demand for the risky asset is
+ [ +1 ] − (1 + )
=
[ +1 ]
2
while the noise traders’ demand is
+ [
=
where
d.
∗
~ ( ,
+1 ]
−
2
(1 + ) +
[ +1 ]
2 ).
Suppose there are noise traders and 1 − rational traders. What will the equilibrium
price of the risky asset be if the supply of the asset is fixed at 1? The price you find
should be a function of , , , ,
[ +1 ]. (4 points)
+1 and
Price is determined by requiring the market for the risky asset to clear,
+ 1−
+
−
1+
=1
+
=1
2
=
1
1+
+
−2
+
e. [Time-Consuming Question] What will the price be in steady state? The price you
find should be a function of , , , , ∗ and 2 . (8 points)
Price in period depends on the expected price in period + 1. To find that we assume
that the economy is in steady state, so that
We can then apply the pricing formula to
=
=
1
1+
+
1
1+
=
+2
and
+1 ,
−2
+
5
+1
−2
+
+
+1
=
+2
.
=
1
1+
+
−2
+
=
1
1+
+
−2
+
∗
Rearranging the terms we have
=1−
∗
2
+
As for the variance, notice that interest rate/dividend, expectations and variances are all
numbers. Numbers are not random and thus have zero variance. Therefore,
1
1+
=
=
=
+
−2
1+
1+
Plugging everything back to the pricing formula for
=
1
1+
+
+1−
=1+
2
∗
1+
−
1+
+
∗
−2
∗
+
End of Final
(See ya!)
6
we have
−
2
1+
1+
+