Posted: September 16th, 2017

Finance 741 Midterm Exam Fall 2014

For problems on this exam involving semiannual payments or discounting, use the convention (1+r/2)t where r is the simple annual interest rate and t refers to the number of semiannual periods.
Report all interest rates as a percentage with two digits to the right of the decimal place (e.g., .64%). Report dollar values to the nearest penny.

1. You have the following information on two companies.
Company A: 2,000,000 shares outstanding, market price = $40 per share
Company B: 1,500,000 shares outstanding, market price = $100 per share
Company A owns 60% of the shares of Company B. Assuming that Company A’s other assets generate positive cash flow, does it look like there is an arbitrage opportunity here? If so, what would you buy and what would you sell, and in what proportions? If not, why not.
2. A recent study reported that in 2005, there were 4,960 actively managed U.S. equity funds. Of that group, 23 funds managed to beat their benchmark in each of the five years from 2005 to 2009. Is that evidence consistent or inconsistent with the notion that markets are efficient?
3. Given the following spot rates, calculate the price of a bond with a $1,000 par value, a coupon rate of 4.5%, and a maturity of 4 years. Assume annual payments.
1-year

3.5%

2-year

3.75%

3-year

4.25%

4-year

4.55%

4. Refer to the spot rates given in question 3. Calculate the following forward rates.

f

1 1

f

1 3

f

3 1

5. A zero-coupon bond’s market price is $936.25. It’s face value is $1,000 and it matures in 18 months. What is the 18-month spot rate? As always, state your answer as an annual rate. Use the semiannual discounting convention.
6. A bond pays a $50 coupon once per year. The bond has a face value of $1,000 and matures in 5 years. Spot rates are as follows.

1-year

2%

2-year

2.25%

3-year

3%

4-year

4%

5-year

5%

a. What is the market price of this bond today?

b. Under the expectations hypothesis, what is the expected price of this bond in two years, just after it has made its 2nd coupon payment?

c. Assume that you buy the bond today. After you receive the first $50 payment, you reinvest that in a 1-year, zero-coupon bond. After you receive the second $50 payment, you liquidate your investments. How much cash do you expect to have, and what is your expected compound annual rate of return over those two years?

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