UST recently issued a consol bond. The market currently
charges a one time price equal to p to provide investors with $1 of perpetual
credit protection in the event of default by UST on this debt [that is, the holder
of such insurance is entitled to receive exactly $1 at the first passage to default].
Letting r denote the risk-free interest rate, derive an analytical expression for
the debt yield in terms of p and r.