Consider a five year corporate bond with a face value of $1,000. The bond currently pays a coupon of 5% per annum, but there is a chance the bond's issuer may default in five years time (just before the final payments on the bond are paid to bondholders).

 

There is a 80% chance that the bond will repay all of its cash flows in full, as promised. However, there is a 20% chance that the bond will default, and bondholders will only receive a fraction of the cash flows they were promised. Specifically, if the issuer defaults just before the maturity date of the bond, then bondholders will only receive $0.30 per $1 of cash flows they were promised on the maturity date. Given this default risk, the appropriate discount rate is 9% per annum. 

 

What is the fair price of this corporate bond?