1. Suppose you bought a five-year zero-coupon Treasury bond for $800 per $1000 face value
a. What is the rate of return on the bond?
b. Assume the yield on a three-year zero-coupon bond with face value $1000 is the same as the yield on the five-year bond. What is the price of the three-year bond?
2. Which of the following investments do you prefer?
a. Purchase a zero-coupon bond which is sold at a price of $550 with a face value of $1,000 with a maturity of 10 years
b. Invest $550 for ten years in Chase at a guaranteed annual interest rate of 4.5%
3. Nat-T Cat Enterprises has decided to go public. After getting feedback from some experts in the kitty litter business, the firm's underwriter decided that the true value of the Nat-T-Cat's equity will be a star IPO: $200 million with probability 0.65 and average IPO: $100 million with probability 0.35. The underwriter has decided to sell 4 million shares, and it needs to compute the appropriate offer price. There is a group of uninformed investors willing to submit bids for 6 million shares as long as their expected profit is not negative. These uninformed investors know the probability distribution of firm values as given above but do not know the true value of Nat-T-Cat as informed investors do. These informed investors are willing to order 10 million shares of the IPO if the offer price is lower than the true value.
a. Compute the equilibrium offer price that the underwriter should charge for each share so that uninformed investors are willing to participate in the offering.
b. What is the total expected profit in dollars to the informed investors if the investment bank sets the offer price at the value computed in part (a)?
c. How much money will the firm raise in this IPO?
d. What is the expected true per share value of Nat-T-Cat?
e. Why are the answers to part (c) and (d) different (i.e. who pockets the difference?)
4. Suppose that the maximum initial margin as established by the Federal Reserve is 45 percent. The maintenance margin is 30 percent. Suppose that you have $10,000 in cash that you wish to invest in stock XYZ, which currently sells for $45 per share. This stock does not pay dividends.
a. If you buy on margin, what is the maximum number of shares that you can purchase?
b. Ignoring interest expenses, at what stock price will you get a margin call?
c. Suppose that the share price falls to the value computed in part (b) and that instead of depositing additional cash into your brokerage account, you decide to sell your stock and take the loss. What percentage loss would you take if this bad scenario occurred?
d. Instead of going down, the stock price actually goes up from $45 to $55 per share over a one-year holding period. For your margin account, interest costs are 6 percent annually. What is the percentage return on your initial $10,000 investment in this case?
5. Consider the four stocks in the following table. P1 represents closing price in day 1, Q1 represents the total shares outstanding at the market close of day 1.
Stock P0 Q0 P1 Q1 P2 Q2
A 92 137 87 137 89 137
B 23.25 58 24.25 58 23.25 58
C 145 102 153 102 54 306
D 90 70 85 70 65 70
a. Calculate the rate of return on the price-weighted index of four stocks at the end of day 1.
b. Calculate the rate for return on a value-weighted index of four stocks for the two-day period starting on day 0 and ending on day 2.