This is the stock price multiplied by the dividend yield rate of .05 and multiplied again by 1 + the risk-free rate of .03. This is not the correct way to calculate next year's dividend. To calculate next year's dividend, it is necessary to use the Dividend Growth Model and solve for G, then use that to calculate the next year's dividend.
This is the stock price multiplied by the dividend yield rate of .05 and multiplied again by the stock's beta of 1.2. This is not the correct way to calculate next year's dividend. To calculate next year's dividend, it is necessary to use the Dividend Growth Model and solve for G, then use that to calculate the next year's dividend.
The cost of retained earnings is equal to the investors’ required rate of return. The problem says that the cost of retained earnings is 10.2%, so the investors' required rate of return is 10.2%. (You can confirm this by using the Capital Asset Pricing Model and the stock's beta, the risk-free rate and the return to the market, if you wish. However, it is not necessary to do so, because the investors' required rate of return is given. The information on the stock's beta, the risk-free rate and the return to the market are included as distractors in this problem.) The current year’s dividend is 5% of the stock price, so the current year’s dividend is $1.50. We have everything we need for the Dividend Growth Model except for the growth rate in dividends. To find what next year’s dividend should be, we can use the Dividend Growth Model, solve for the rate of growth, and then multiply the current year’s dividend ($1.50) by 1 + the growth rate. The Dividend Growth Model is (D1 / P0) + G = C, where C is the cost of retained earnings and the investors’ required rate of return. D 1 is next year’s dividend, so it is the current year’s dividend multiplied by 1 + the dividend growth rate. The growth rate in dividends is what we need to find. So the formula will be: (((1.50 * (1 + X)) / 30) + X = .102 ((1.50 + 1.50X) / 30) = .102 – X 1.50 + 1.50X = 30 * (.102 ? X) 1.50 + 1.50X = 3.06 – 30X 1.50 + 31.5X = 3.06 31.5X = 1.56 X = .0495, which is the dividend growth rate Therefore, next year’s dividend should be $1.50 * (1 + .0495), or $1.574 per share.
This is the stock price multiplied by the expected return to the market. This is not the correct way to calculate next year's dividend. To calculate next year's dividend, it is necessary to use the Dividend Growth Model and solve for G, then use that to calculate the next year's dividend.
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