Consider a zero$-$coupon corporate bond, with one year to maturity, priced at $$873$ per $$1000$ face value.

a$)$ What is the Yield to Maturity $($BEY$)$ of the bond?

b$)$ Assume an expected return of $12\%($Effective Annual Rate$)$ and a default probability of $6\%.$ What is the implied recovery rate?

c$)$ Assume an expected return of $6\%($Effective Annual Rate$)$ and a recovery rate of $50\%.$ What is the implied default probability?