Calculating Present Value of Credit Risky Bonds

In the context of credit analysis and valuation using reduced form models, it is essential to understand the implications of hazard rates and default probabilities on the pricing of credit risky securities. Consider a corporate bond with an assumed constant hazard rate of 2% per annum. This bond has a face value of $1,000 and a mature in 5 years. The risk-free rate is 3%. What is the present value (PV) of the expected payoff at maturity, taking into account the likelihood of default?

To determine this, we must first calculate the probability of survival over the 5-year period using the constant hazard rate and then compute the expected payoff. Note that the expected payoff is the product of the face value and the survival probability, discounted back to present value using the risk-free rate.