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This answer results from using the investors' required rate of return in place of the return to the market in the Capital Asset Pricing Model. The return to the market is what we are solving for, so that would be represented by an "X" in the CAPM formula.
The first step in solving this is to use the Dividend Growth Model to find the investors' required rate of return. The second step is to use the Capital Asset Pricing Model to solve for the expected return to the market. The Dividend Growth Model is: C = (D1 / P0) + G Where C is the cost of retained earnings, which is also the investors' required rate of return. D1 is the next dividend to be paid. The problem tells us that the next annual dividend will be $1.25. It is not necessary to multiply $1.25 by 1 + the growth rate to get the next dividend, because $1.25 is already the next dividend. Therefore, the calculation of the investors' required rate of return (C) is: C = ($1.25 / $31.25) + .05 C = .09 The formula for the Capital Asset Pricing Model is: r = RF + β(RM ? R F) Where r is the cost of retained earnings, which is also the investors' required rate of return. Using the investors' required rate of return calculated in the first step by means of the Dividend Growth Model, we can solve the CAPM for RM, or the return to market, as follows: .09 = .03 + 1.2(X ? .03) .09 = .03 + 1.2X ? .036 .096 = 1.2X X = .08 or 8%
This answer results from using the wrong amount for the next annual dividend in the Dividend Growth Model. The problem states that $1.25 is the next annual dividend. Therefore, that amount does not need to be increased by 1 plus the annual growth rate to get next year's dividend, because it is already next year's dividend. If the problem had stated that the dividend amount given was the current year's dividend, it would be appropriate to multiply it by 1 plus the annual growth rate to get next year's dividend to use in the Dividend Growth Model.
This is the investors' required rate of return. However, the problem asks for the expected return to the market.