Question 1: The Debt Cost of Capital
In mid-2012, Ralston Purina had AA-rated, 10-year bonds outstanding with a yield to maturity of 2.05%.
a. What is the highest expected return these bonds could have?
b. At the time, similar maturity Treasuries have a yield of 1.5%. Could these bonds actually have an expected return equal to your answer in part (a)?
c. If you believe Ralston Purina's bonds have 0.5% chance of default per year, and that expected loss rate in the event of default is 60%, what is your estimate of the expected return for these bonds?
Question 2: The Behavior of Individual Investors
Your brother Joe is a surgeon who suffers badly from the overconfidence bias. He loves to trade stocks and believes his predictions with 100% confidence. In fact, he is uninformed like most investors. Rumors are that Vital Signs (a startup that makes warning labels in the medical industry) will receive a takeover offer at $20 per share. Absent the takeover offer, the stock will trade at $15 per share. The uncertainty will be resolved in the next few hours. Your brother believes that the takeover will occur with certainty and has instructed his broker to buy the stock at any price less than $20. In fact, the true probability of a takeover is 50%, but a few people are informed and know whether the takeover will actually occur. They also have submitted orders. Nobody else is trading in the stock.
a. Describe what will happen to the market price once these orders are submitted if in fact the takeover will occur in a few hours. What will your brother's profits be: positive, negative, or zero?
b. What range of possible prices could result once these orders are submitted if the takeover does not occur? What will your brother's profits be: positive, negative, or zero?
c. What are your brother's expected profits?
Question 3: The Efficiency of the Market Portfolio
Davita Spencer is a manager at Half Dome Asset Management. She can generate an alpha of 2% a year up to $100 million. After that her skills are spread too thin, so cannot add value and her alpha is zero. Half Dome charges a fee of 1% per year on the total amount of money under management (at the beginning of each year). Assume that there are always investors looking for positive alpha and no investor would invest in a fund with a negative alpha. In equilibrium, that is, when no investor either takes out money or wishes to invest new money,
a. What alpha do investors in Davita's fund expect to receive?
b. How much money will Davita have under management?
c. How much money will Half Dome generate in fee income?