Problem $3$: Expected returns vs$.$ yields to maturity $(3$ points$)$

A zero$-$coupon bond maturing in $2$ years with a face value of $$1,000$ has a $20\%$ chance of

defaulting. Regardless of when the company defaults, any recovery payments made to debt

holders will be at maturity in two years. Assume the recovery rate will be $60\%$ in the event

of default.

$($a$)$ What is the expected payment for bondholders at maturity?

Expected payment:

$($b$)$ Assuming the company's default is uncorrelated with the market, and the yield on a

zero$-$coupon US treasury expiring two years is $2\mathrm{.}5\%,$ what is the price of the company's

bond today? Assume that all assets' expected returns follow the CAPM.

Bond price:

$($c$)$ Given the price you computed in part $($b$),$ what is the yield to maturity for this bond?

Yield to maturity: