6. Ms. Blavatsky is proposing to form a new start-up firm. She can invest in one of two projects. The relatively safe project offers a 40 percent chance of a $9 million payoff and a 60 percent chance of an $8 million payoff. The risky project offers a 20 percent chance of a $20 million payoff and a 80 percent chance of a $5 million payoff. Ms. Blavatsky initially proposes to finance the firm by an issue of straight bonds with a promised payoff of $7 million. Show the possible payoffs to the lender and to Ms. Blavatsky if:

(a) she invests in the safe project

(b) she invests in the risky project

(c) suppose now that Ms. Blavatsky offers to make the debt convertible into 3/4 of the firm's equity. Show that the convertible bondholder receives the same expected payoff from the two projects.

(d) Which project should Ms. Blavatsky choose if she finances the firm with convertible debt?