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
Hint: You can use the Excel functions Mduration and Duration to calculate the required durations. For c, you will need to use the Excel function to calculate yield before you can calculate Mduration and Duration).
4. A 5-year bond with a 4.45% coupon sells for $107.48. A 7-year bond with a 5.75% coupon sells for 116.564. The conversion factor for the 5-year bond is 0.933891 while the 7-year bond is 0.98588. Assume that the yields for both bonds are 6% and that coupon payments are semiannual. Which of the two bonds is cheaper to deliver given a T-note futures price of 117.92?