## Answered) Exam 2 - Economics 134 Professor Madhav Chandrasekher Directions: This exam consists of 8 questions, with point allocations as noted. Please write...

Finish this question. (Corporate Finance) Â  Â  Â Â

1. What are the perfectmarket assumptions?
2. Explain whether the following statements are true or false. In each case,
â€¢ In a perfect capital market, expected returns on all bonds must be
equal to the risk-free (T-bill) rate.
â€¢ In a perfect capital market with risk-neutral investors, expected returns
on all bondsmust equal the risk-free rate.
3. Write down the CAPM formula. What are the economy-wide inputs and
what are the firm-specific inputs?
II. The table below describes the return rates for a stock X and a market index
fund, call itM. Find the (true, as opposed to estimated) beta of stock X. Assume
the probability of the â€œgoodâ€ state is 1/3 (â€œbadâ€ has probability 2/3).
M 10% 6%
Asset X 4% 10%
III. Suppose Intelâ€™s stock has an expected return of 10%and a volatility (standard
deviation) of 5%, while Coca-Colaâ€™s has an expected return of 5% and volatility
of 2%. Assume these two stocks have correlation coefficient âˆ’1.
1. Calculate the portfolio weights that remove all risk.
2. If there are no arbitrage opportunities, what is the risk-free rate of interest
in this economy?
IV. A biotech company has a drug in development that will allow you to sell your
firm for \$10 billion next year. Assume your boss wants you to use the CAPM.
Your firm has a beta of 4, the risk-free rate is 5% per year, and the equity premiumis
2% per year. What do you think the firmis worth today?
V. Your borrowing rate is 15% per year. Your lending rate is 5% per year. The
project costs \$1,000 and has a rate of return of 10%.
1. Assume you have \$500 of your own money to invest. Should you invest in
this project?
1
2. Find themaximal amount the investor would bewilling to borrow in order
to invest in the project?1
VI. Option pricing:
1. Consider a European call option on a single share of stock in company
X. The strike price is \$25 and the maturity date is 1 year. Call this a â€œ25-
callâ€ for simplicity (and, generally, a â€œKâ€-call, where K is the strike price).
Draw the payoff diagram in the two cases where (i) an investor goes long
on a single 25-call, and (ii) an investor shorts both a 25-call and a 20-call.
2. Consider (European) call and put options on a single share of stock in
company X. Each has a strike price of \$25 and matures in 1 year. Assume
the (per share) stock price at the time the options are written is \$22 and
that the cost of the put is \$2. Also assume that the risk-free rate is 10%.
Find the price of the call.

Exam 2 - Economics 134
Directions: This exam consists of 8 questions, with point allocations as noted.
You have 80 minutes. Good luck.
1. (5 pts) List the conditions under which a market is considered â€œperfectâ€.
2. Explain whether the following statements are either true or false. Provide brief
i. (3 pts) In a perfect capital market, the expected return rate on all bonds must
be equal to the risk-free (T-bill) rate.
ii. (2 pts) In a perfect capital market with risk-neutral investors, expected return
rate on all bonds must equal the risk-free rate.
3. (5 pts) Write down the CAPM formula. What are the economy-wide inputs and
what are the firm-specific inputs?
4. (5 pts) A Fortune 100 firm is initially financed by 20 billion dollars debt and
20 billion dollars equity, i.e. a debt/equity ratio of 1. It has a historical equity beta
of 4. Assume the firm never defaults on its debt. Say the firm repurchases some
shares by issuing more debt, with the result being that the new debt/equity ratio is
2/1. Find the beta of (levered) equity under this new capital structure.
5. (5 pts) A corporate zero-bond promises to pay \$100 in one year. The bond
has a default probability of .3 and its market beta is 0.3. The equity premium is
4%; the equivalent Treasury rate is 3%. Assume that the bonds pays out nothing in
the default state. Find the appropriate bond price today.1
6. The table below describes the return rates for a stock X and an equivalent
to the S&amp;P 100 index fund, call it M. Assume both â€œgoodâ€ and â€œbadâ€ states are
equally likely. M
8%
4%
4%
8% i. (3 pts) Find the beta of stock X.
1 Maintain the assumption that capital markets are perfect. 1 2
ii. (2 pts) For a random variable X, we let ÂµX , ÏƒX
denote (resp.) its mean and
variance. Assume an investorâ€™s preferences over random variables (bets) is a
function only of their mean and variance and takes the following functional
form,
1 2
2
.
u(ÂµX , ÏƒX
) = ÂµX âˆ’ ÏƒX
4
Assume that the investor has a dollar to invest and that the price of one
share of X or of the index fund M is equal to \$1. Find the utility-maximizing
(affordable) portfolio choice of the investor.2 7. Your borrowing rate is 20% per year. Your lending rate is 10% per year. The
project costs \$2,000 and has a rate of return of 15%.
i. (3 pts) Assume you have \$500 of your own money to invest. Should you invest
in this project?
ii. (2 pts) Find the maximal amount the investor would be willing to borrow in
order to invest in the project?3
8. (5 pts) You are in the 10% tax bracket.4 A project will return \$30,000 next year
for a \$20,000 investment today. The equivalent tax-exempt bond yields 15%, and
the equivalent taxable bond yields 20%. What is the NPV of this project? 2 The set of budget-feasbile portfolios in this problem is the set of shares, {Î±, 1 âˆ’ Î±} in (resp.)
stocks X and M , where 0 â‰¤ Î± â‰¤ 1.
3
An equivalent way to phrase this turns out to be: Find the threshold wealth level such that
the investor would select the project whenever his(her) wealth is at or above this level.
4
As in the examples from lecture 10, this is a capital gains tax. 2

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