Question

Consider two firms which differ with respect to asset risk and financial leverage. Firm 1 owns assets worth $10,000,000, and has issued zero coupon bonds with a face value of $4,500,000. On the other hand, Firm 2 owns assets worth $25,000,000, and has issued zero coupon bonds with a face value of $15,000,000. The standard deviation of the return on firm 1’s assets is 40%, whereas the standard deviation of the return on firm 2’s assets is 50%. Assume that both firms will be liquidated one year from today and that the rate of interest is 3%. 1. What is the fair market value for the bonds issued by Firm 1? What is the dollar value of Firm 1’s limited liability put option? What is the yield to maturity, credit risk premium, and (risk neutral) probability of default for Firm 1’s bonds?

Answer 1

Fair Market Value should be obtained by calculating as below:

                                                       FV/((1+r)^n)

Hence the current value of the Bond issued by Firm 1 should be: 4,500,000/((1+0.03)^1) = 4,368,932.04.

Assumption: Firm 1 liquidates after 1 year hence the bond will get redeemed after 1 year.

Yield to maturity: This should be the required rate of return, which shall be 3.0% since the maturity is not valid, and bond is getting redeemed after 1 year which is during the term of the bond. After 1 year yield to maturity should be 0, since after the bond defaults the rate of return is 0.

Credit Risk Premium: As the rate of return s same as risk-free rate, the Credit Risk Premium is nil.

(Risk neutral) probability of default: Since the Credit Risk premium is 0, the risk neutral probability of default is same as the real probability of default.