Chapter 16, Problem 29PS

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 dividends.” (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:

$P_0=\frac{\text{DIV}}{r-g}=\frac{2}{.12-.08}=50$

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.