C15.0008 Corporate Finance Topics
Mid-Term Exam
Name:______
Signature:______
Answer all of the questions on the exam. Write your answers in the space provided. Show your work, including intermediate calculations, and formulas. Incorrect answers, with no work shown, will receive no credit. Be explicit about any assumptions that you make. There exam are 4 questions, each with sub-questions. The exam will last 90 minutes. Make sure to read the questions carefully. Good luck!
Question 1 (20 points)
Check the correct alternative out of the ones provided:
1. The higher the stock price,
A) the higher the call price.
B) the lower the call price.
C) has no effect on call price.
D) the higher the put price.
E) the lower the exercise price.
2. The equity of the firm is like
A) a call option on the firm with the exercise price equal to the firm's after-tax cash flow.
B) a call option on the firm with the exercise price equal to the promised payments to the bondholders.
C) a put option on the firm with the exercise price equal to the promised payments to the bondholders.
D) a put option on the firm with an exercise price equal to the firm's after-tax cash flow.
E) None of the above.
3. The biggest difference in the tax-treatment of debt and equity is:
A) Dividends payments are tax-deductible, while interest payments are not.
B) Interest expense is tax-deductible and thus debt has a tax shield.
C) Dividends are not taxed in the hands of the shareholder
D) Interest expense is not taxed in the hands of the bond-holder.
4. AJN inc. announces an IPO of $100 million. On the first day of trading of the stock, its price rises 10% above the offering price. Which of the following is an explanation for this?
A) Announcement effects
B) IPO under-pricing
C) EPS dilution
D) Over-valued stock.
5. There are 3 directors seats up for election. If you own 1,000 shares of stock and you can cast 1,000 votes with three unique names each, this is illustrative of
A) cumulative voting.
B) absolute priority voting.
C) sequential voting.
D) straight voting.
E) None of the above.
6. Based on historical experience, which of the following best describes the "pecking order" of long-term financing strategy in the U.S.?
A) Long-term debt first, new common equity, internal financing last.
B) Long-term debt first, internal financing, new common equity last.
C) Internal financing first, new common equity, long-term borrowing last.
D) Internal financing first, long-term borrowing, new common equity last.
E) None of the above.
7. Seniority of debt refers to
A) The preference that is accorded to bond-holders in terms of dividends.
B) The time when the debt becomes due
C) The order in which bond-holders get paid in the event of default.
D) The amount of collateral that is included in the bond-indenture.
8. A warrant gives the owner
A) the obligation to sell securities directly to the firm at a fixed price for a specified time.
B) the right to purchase securities directly from the firm at a fixed price for a specified time.
C) the obligation to purchase securities directly from the firm at a fixed price for a specified time.
D) the right to sell securities directly to the firm at a fixed price for a specified time.
E) None of the above.
9. The price of a 1-year European call option with exercise price 50 on a stock that is trading at 45 is 10. If the risk-free rate is 10%, what is the price of a 1-year put option with exercise price 50?
A) $10
B) $10.45
C) $9.45
D) Cannot be determined.
E) None of the above.
10. The reason Discounted Cash Flow does not work with real options if you use the discounting rate of the project for the option’s cash flow is
A) The wrong discounting rate is used because options do not have the same risk as the underlying project.
B) The wrong probabilities are used. The probabilities of the option are different from the probabilities of the underlying asset.
C) The assumptions of Black-Scholes cannot be applied to many Real Options
D) It is the correct approach. Binomial valuation is just another way of doing it.
Question 2: (30 points)
Your friend Larry W. has plans for a new futuristic movie about human beings cultivated in giant farms to produce energy for a civilization of super-intelligent acrobatic cows that rule the earth. He plans to call the movie “Moo-tricks”. The movie will be expensive to produce. Expected cash flows are going to be 20 million per year in perpetuity starting year 1 of the movie. The investment required to produce the first movie is 110 million. The discounting rate applicable to the first movie is 20%. On the basis of this, Larry thinks that the net present value of the movie is -5 million.
Larry is not sure if he should go ahead with his movie. He is discussing his options with you. If “Moo-tricks” is successful, he can produce a sequel called “Moo-tricks: Rotations” after 1 year. If the first movie is successful, the sequel will produce cash flows of 10 million per year (starting year 2) in perpetuity. If it is unsuccessful, the sequel will only produce 1 million per year (starting year 2) in perpetuity. Success and failure both have probabilities of 0.5. Because a lot of the development work will already have been done, the sequel will require an initial investment of only 30 million dollars. The discounting rate for the sequel is 10%. Harry suspects that there is some value in the sequel that he is not considering, and wants you to help out. Because you took C15.0008, you recognize that the option to produce a sequel is an expansion option. (The risk free rate is 2%.)
Questions:
a. Look at Harry’s estimate of the NPV of the first movie without the sequel. Is it correct? If not, what is the correct NPV?
b. What is the underlying asset for the expansion option?
c. Draw the binomial tree for the underlying asset. What is the present value of the underlying asset?
d. What is the exercise price of the expansion option?
e. What are the pay-offs from the expansion option? Draw the Binomial tree.
f. Using replication in the underlying, find the value of the option to produce a sequel. What is H? What is B? What is the value of the option?
g. What is the NPV of the movie project including the value of the expansion option? (Use the ‘correct’ NPV for the movie without the sequel option, which is not necessarily Harry’s estimate.)
h. Zero Credit Question in case you have some time left over: Think of a possible name for a second sequel.
Question 3: (25 points)
You are at a job interview for Sherryl Finch & Co., a reputed investment bank. Your interviewer is an option trader, and he wants to test you on your understanding of options. He asks you to consider a stock that is trading at a price of 50 dollars. In a year, the price can go up by 10%, or it can go down by 10%. There is a risk free bond of that can be used to borrow or lend, and the risk-free rate is 2%.
- Consider a European-style call option with an exercise price of 52 expiring at the end of 1 year. Draw the pay-off from the option on a binomial tree.
- Find the value of the call-option using replication. What is H? What is B? What is the value of the option?
- Now consider a European style put option with an exercise price of 52 expiring at the end of 1 year. Draw the pay-off from the option on a binomial tree.
- What is the value of the put option by replication?
- In the context of parts a to d above, show that put-call parity is true in terms of the current prices of the call and the put options. (You get the job if you answer this question.)
- Is there a difference between the put value you get from part d and part f? If yes, why? If not, what fundamental principle of finance is the reason?
- What are the risk-neutral probabilities for the up move and the down move of the stock? Recall that risk-neutral probabilities are probabilities in a binomial tree such that the expected value discounted at the risk-free rate give the price of the stock.
Question 4. (25 points)
Black stripes inc. decides to issue convertible bonds of a total face value of 30 million dollars. The face value of each bond is 1000 dollars. The bonds have no coupons and have a maturity of 2 years. The discounting rate on straight debt issued by the firm is 6%. Each bond is convertible to 20 shares on maturity if the holder of the bond so decides. The company is currently purely equity financed and is worth 40 million dollars. The company’s stock currently trades at a price of 40 dollars. The volatility of the stock is 30% and its beta is 1.1. Options on the company’s stock trade on the Chicago board of trade. Based on the inputs into the Black-Scholes model, you have the following information about a European call option with an exercise price of 50 and expiration of 2 years.
N(d1) = 0.4131, N(d2) = 0.2598, Call option price = 4.04.
a. What is the total number of bonds being issued? What is the total number of shares outstanding of the company? How many new shares will be created if the bond-holders exercise their warrants?
b. What is the conversion price of the bond?
c. What is the value of the straight debt part of each bond?
d. What is the value of the warrant part of each bond?
e. What is the total value of each convertible bond?
f. How many shares do you need to replicate each call option?
g. How many shares do you need to replicate the convertible bond?
i. What is the approximate increase in the value of the convertible for a 1% increase in the price of the stock?