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.;7.64%). 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 As 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 bonds market price is $936.25. Its 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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