Suppose that a firm always announces a yearly dividend at the end of the first quarter of the year, but then pays the dividend out as four equal quarterly payments. If the next such "annual" dividend has been announced as $2, it is exactly one quarter until the first quarterly dividend from that $2, the effective annual required rate of return on the company's stock is 15 percent, and all future "annual" dividends are expected to grow at 10 percent per year indefinitely, how much will this stock be worth?

Question

Quizplus · Accepted Answer

The stock price can be calculated using the Gordon Growth Model (Dividend Discount Model for a growing perpetuity). The quarterly dividend is $0.50 ($2/4). The first dividend is received in one quarter, so we discount it accordingly. The formula is P = D1 / (r - g), where D1 is the dividend in the next period, r is the required rate of return, and g is the growth rate. Adjusting for quarterly payments and growth, the stock price is approximately $42.09.

Suppose That a Firm Always Announces a Yearly Dividend at the End