CHALLENGE 29. Dividend policy and the dividend discount model Consider the following two statements: "Dividend policy is irrelevant," and "Stock price is the present value of expected future divi- dends." (See Chapter 4.) They sound contradictory. This question is designed to show that they are fully consistent. The current price of the shares of Charles River Mining Corporation is $50. Next year's earnings and dividends per share are $4 and $2, respectively. Investors expect perpetual growth at 8% per year. The expected rate of return demanded by investors is r = 12%. We can use the perpetual-growth model to calculate stock price: DIV 2 Po = = 50 r-8 .12 - .08 Suppose that Charles River Mining announces that it will switch to a 100% payout policy, issuing shares as necessary to finance growth. Use the perpetual-growth model to show that current stock price is unchanged. 30. Dividends and taxes Suppose that there are just three types of investors with the following tax rates: Individuals Corporations Institutions 50% Dividends Capital gains 5% 35 0% 0 15 Individuals invest a total of $80 billion in stock and corporations invest $10 billion. The remaining stock is held by the institutions. All three groups simply seek to maximize their after-tax income. These investors can choose from three types of stock offering the following pretax payouts per share: Low Payout Medium Payout High Payout Dividends Capital gains $5 15 $5 5 $30 0 These payoffs are expected to persist in perpetuity. The low-payout stocks have a total market value of $100 billion, the medium-payout stocks have a value of $50 billion, and the high- payout stocks have a value of $120 billion. a. Who are the marginal investors that determine the prices of the stocks? b. Suppose that this marginal group of investors requires a 12% after-tax return. What are the prices of the low-, medium-, and high-payout stocks? c. Calculate the after-tax returns of the three types of stock for each investor group. d. What are the dollar amounts of the three types of stock held by each investor group