Systems Engineering Laboratories (SEL) sells an issue of $300 million face value of subordinated debentures with a coupon rate of 9.375% (assume coupons are paid annually). Each bond in the issue has a face value of $1,000 and matures in 15 years. The bonds were originally sold at par. The 15-year risk free interest rate is 4.5%. The expected market risk premium (remember, this is rm-rf), is 7%.
a. What is the yield to maturity on the SEL subordinated debentures?
b. Suppose the market believes that, if SEL were to default, the subordinated debenture holders would receive a recovery rate of 40%. Suppose also, in each year of the bond’s life, if the bond is still alive, that there is a 5% probability of default. Calculate the expected rate of return on SEL subordinated debenture bond.
c. Given your answer to parts a and b, estimate the beta of the SEL subordinated debenture.
d. The 5% probability of default on the SEL bond stated in part b is a conditional probability of default (i.e., it is the probability of default in any year, conditional on never having defaulted prior to that year). What is the unconditional probability that the SEL bond will default in year 2?
e. What is the unconditional probability that the SEL bond will not default in year 2?