Consider a corporate bond with face value $$1,000,$ maturing in $2$ years, $6\%$ annual coupon rate, and

semi$-$annual coupon payments. The fair discount rate that compensates investors in the bond is $4\%$

per semester. Assume that when the corporation defaults, bondholders receive a recovery value

equal to $40\%$ of face value at the time of default.

a$)$ If the probability of default is constant and equal to $1\%$ per semester, what is the fair price

of the bond?

b$)$ What is the yield to maturity for this bond?

c$)$ What is the expected holding period return of buying the bond for its fair price $($calculated

in item a$)$ today and selling it for its expected fair price after one semester?