Suppose the CEO of a $1 billion all-equity firm personally owns $10 million in company stock. Assume that the risk-neutral CEO makes investment decisions based strictly on the change in value (or expected change in value for risky investments) of her personal holdings, plus private benefits (if any) she gets from the investment.

a. Suppose the CEO is considering a risky investment that will generate a gain with a present value of $100 million with 50% probability, but a loss of $150 million (present value) with 50% probability. Will she invest in the risky project?

b. Now, suppose that the firm recapitalizes by borrowing $950 million and pays a special dividend of $950 million, and suppose that the CEO reinvests her $9.5 million dividend back into the recapitalized firm. (In answering this question, ignore any change in the overall value of the firm resulting from the recapitalization.)

Given the same assumptions as above, will she invest in the risky project?