A company issues a \(10 \%\) coupon bond that matures in 5 years. However, this company is in trouble, and it is estimated that each year there is a probability of .1 that it will default that year. (Once it defaults, no further coupons or principal are paid.) What is the value of the bond?

(a) Assume the term structure of interest is flat at \(10 \%\).

(b) Assume that the short rate is currently \(10 \%\) and the short rate is multiplied by either 1.2 or 9 each year with risk-neutral probabilities of .5. Default risk is independent of the interest rate.