Question

(a)       Consider a 14-year, 9.5% corporate bond with face value $10,000. Assume that the bond pays semi-annual coupons. Compute the fair value of the bond today if the nominal yield-to-maturity is 11% compounded semi-annually.

(b)       Consider a 11-year, corporate bond with face value $1,000 that pays semi-annual coupon. With the nominal yield-to-maturity equal to 10%, the bond is selling at $802.5550. Find the coupon rate for this bond. Assume that the market is in equilibrium so that the fair value of the bond is equal to the market price of the bond.

(c)        Consider a 4-year, 5% annual coupon bond with a face value of $10,000, which was issued three years ago. The bond just paid the coupon. Therefore, this bond has one year to maturity, and the next payment of the face and coupon will be made in exactly one year, after which the bond will cease to exist. If the bond defaults before next year, it will pay total of $8,000 in one year. The effective 1-year risk-free rate is 3.55%. If the bond is currently selling at $9,501.50, compute the risk-neutral probability that the bond will default within one year.

Answer 1

a)