1. Suppose a company's $50 stock pays an 8% continuous dividend and the continuously compounded risk-free rate is 6%. Calculate the following:
a. The price of a prepaid forward contract that expires 1 year from now
b. The price of a forward contract that expires 1 year from now
(Hint: You will need a scientific calculator.)
2. Suppose the gold spot price is $1700/oz, the 1-year forward price is 1760.54, and the continuously compounded risk-free rate is 4%. Calculate the following:
a. The lease rate
b. The return on a cash-and-carry if gold cannot be loaned
c. The return on a cash-and-carry if gold is loaned and it earns the lease rate
(Hint: You will need a scientific calculator.)
3. Compute Macaulay and modi?ed durations for the following bonds:
a. A 5-year bond paying annual coupons of 3.322% and selling at par
b. An 8-year bond paying semiannual coupons with a coupon rate of 9% and a yield of 8%
c. A 10-year bond paying annual coupons of 5% with a price of $96 and a maturity value of $100