John considers investing his hard-earned cash in either a $1,000 bond which pays off $1,300 (utility: 70) for certain in one year OR the stock of a risky company, X Co. If the economy is good, the stock in X Co. will be worth $4,000 in one year (utility: 100); if the economy is bad, the stock will be worth only $500 (utility: 40). Through diligent research, John learns that the economy has been good only 20% of the time.
a. What is the expected value of the stock?
b. What is the expected utility of the stock?
c. Which investment should he make?
d. Is he risk-averse, risk-neutral, or risk-seeking? How can you tell?
John also happens to be an avid reader of the financial statements of X Co. and wonders whether the information in the Management Discussion and Analysis section has any usefulness. He investigates and learns that when the economy has been good, management has forecast good prospects for the firm 95% of the time. When the economy has been bad, management has forecast good prospects 50% of the time. These predict good times ahead.
e. What is John's revised belief that the economy will be good?
f. Should he buy the stock?
g. Does the financial information have "decision usefulness?"