Respond to the following questions:
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
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
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
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?