The city of Detroit filed for bankruptcy in mid-2013. After this filing, promised yields on Detroit bonds skyrocketed to approximately 15.8 percent. Lenders ultimately received about 25.2 percent of the cash flows they were promised by Detroit because of the bankruptcy. Suppose that it is late 2013 and Detroit wants to issue $13M worth of one-year bonds. Also suppose that potential lenders still demand a promised yield of 15.8 percent, and believe that they will receive 25.2 percent of the cash flows they are promised if Detroit again. Assume that the expected return on risky debt is 7 percent. What is the probability of default implied by this information?

 

(Hint: your first step should be to obtain the promised cash flow using the promised yield equation. Your second step should be to calculate the default cash flow by taking the promised cash flow and multiplying it by the recovery rate of 25 percent. You can then solve for the probability of default using the expected return on debt equation.)