28. Convertible bonds (S25.2) This question illustrates that when there is scope for the firm to vary its risk, lenders may be more prepared to lend if they are offered a piece of the action through the issue of a convertible bond. Liu Zhang is proposing to form a new start-up firm with initial assets of $10 million. She can invest this money in one of two projects. Each has the same expected payoff, but one has more risk than the other. The relatively safe project offers a 40% chance of a $12.5 million payoff and a 60% chance of an $8 million payoff. The risky project offers a 40% chance of a $20 million payoff and a 60% chance of a $5 million payoff.

Ms. Zhang initially proposes to finance the firm by an issue of straight debt with a promised payoff of $7 million. Ms. Zhang will receive any remaining payoff. Show the possible payoffs to the lender and to Ms. Zhang if

(a) she chooses the safe project and

(b) she chooses the risky project. Which project is Ms. Zhang likely to choose? Which will the lender want her to choose?

Suppose now that Ms. Zhang offers to make the debt convertible into 50% of the value of the firm. Show that in this case the lender receives the same expected payoff from the two projects.