Question 3

(a)Consider a 12-year, 6% corporate bond with face value $4,000. Assume that the bond pays semi-annual coupons. Compute the fair value of the bond today if the nominal yield-to-maturity is 10% compounded semi-annually.

(b)One of the ways to value bonds issued by a corporation is to use the risk-neutral valuation model. Consider a 1-year zero-coupon bond issued by a pharmaceutical firm called Designer Drugs with a face value of $1,000 that is currently trading at $950.50. Suppose that if Designer Drugs defaults, the recovery rate of the bond is 65 percent. Assume that the annual risk-free interest rate is 3.5 percent.

(i)Find the risk-neutral probability of default.

(ii)Bloomberg just released news that a new drug to treat COVID-19 from Designer Drugs got approved by the government for large scale human testing. This event decreased the risk-neutral probability of default by 1 percent.In other words, if the probability of default was x percent in part (a), now it is going to be (x - 1) percent.At what price will the bond be trading after the news?

(iii)In addition to the information given in part (b) above, assume now that the risk-free interest rate is decreased from 3.5 percent to 3.0 percent. Find the price of the bond.