Two entrepreneurs, Kevin and Mike, operate shoe shining businesses on identical, opposite street corners in a major city. Although each of their annual incomes varies unpredictably due to the effects of weather, consumer preferences, and the disposable income of their customers, each young man's annual income is gov- erned by a simple probability distribution. Specifically, each year is either a good year or a bad year. In a good year, each man's income is equal to $700; in a bad year each man's income is only $300. Good years and bad years each occur with a probability of .50, and the outcome for any year is independent of the outcomes for the preceding years. The two young gentlemen differ in their willingness to substitute between the average level of their income and the unpredictable variability of that income. Specifically, Kevin is more risk-averse than Mike.
(a) Explain, by creating a hypothetical numerical example, how the two men can create a mutually beneficial exchange by merging their businesses into a single firm and issuing a bond and a share of stock against the firm's earnings.
(b) Using your answer to question (a), calculate the prices of the bond and the share of common stock, assuming the risk-free interest rate is .10 per year and the risk-adjusted rate of return on the stock is .13 per year. What is the value of the firm?