Question $3$

Leona Motel$$s debt has a face value of $$40$ million, a coupon rate of $14\%($paid semiannually$),$ and expires in $12$ years $($at t $=12).$ The current annual yield$-$to$-$maturity $($stated$)$ for all bonds of the company is $15\%.$

Leona wishes to conserve cash for the next few years. To do this, Leona decides to issue new equity and use the proceeds to purchase the existing debt at the market price. The current stock price of Leona is $$60$ and there are $2$ million shares outstanding.

a$.$ How many shares should Leona issue to purchase the existing debt? Assume the decision to purchase the bond does not change the stock price.

Instead, the company decides to issue a zero$-$coupon bond that matures at year $5,$ and use the proceeds to purchase the existing debt at the market price.

b$.$ What is the face value of the zero$-$coupon bond that Leona needs to issue?