Consider a firm whose 1-year zero-coupon bonds currently yield 5%. The yield on 1-year zero-

coupon Treasury bonds is 2%. Assume periodicity of 1 (i.e. annual compounding).

a. What is this firms implied probability of default if the recovery rate expected by

bondholders is zero?

b. What is this firms implied probability of default if the recovery rate expected by

bondholders is $0.50 on the dollar?

c. Bondholders are unsure as to the recovery rate in the case of default. They believe that

they would either recover $0.30, $0.40, or $0.50 on the dollar with probability 0.25, 0.50,

and 0.25 respectively. What is this firms implied probability of default?

d. The same firms 2-year bonds currently yield 7%, while the yield on 2-year zero-coupon

Treasury bonds (i.e. the 2-year spot rate) is 3.5%. What is this firms implied cumulative

probability of default if bondholders do not expect to recover anything in the case of

default?