A company’s shares are expected to pay a dividend of $9.42 per share in one year. The dividend is expected to grow at a real rate of 1.6% per year indefinitely. The required real rate of return on the company’s shares is 7% per year. Calculate the stock price (to the nearest cent). Your answer should be to the nearest cent and you should not include a dollar sign or commas. If your answer is $12.187, you should enter your answer as 12.19. If your answer is $12.183, you should enter your answer as 12.18.

Question

BlackTom AI · Accepted Answer

To start, we identify the key inputs: the dividend one year from now is 9.42, the dividend is expected to grow at a real rate of 1.6% per year indefinitely, and the required real rate of return is 7% per year. We’ll use the Gordon Growth Model, which applies to perpetuities with constant growth: P0 = D1 / (r - g). Next, we compute D1, the dividend one year from now, which is given as 9.42 (the problem already specifies the amount for the next period). Then we determine the denominator by subtracting the growth rate from the required return: r − g = 0.07 − 0.016 = 0.054. With these pieces in place, we plug them into the formula: P0 = 9.42 / 0.054. Performing the division, 9.42 ÷ 0.054 equals 174.444... . Rounding to the nearest cent, we obtain 174.44.

It is important to verify units and assumptions: both the dividend and growth are treated in real terms, and the required return is a real rate as well, so the Gordon model is applicable without additional inflation adjustments. If any of these inputs were misinterpreted—for example, if D1 were misread as the current dividend rather than the one-year-ahead dividend or if the growth rate were nominal rather than real—the resulting price would be incorrect. Additionally, ensure you use r and g with the same time basis (both annual) and keep precise arithmetic before rounding to avoid small rounding biases.

In summary, the calculation path is straightforward: apply the Gordon Growth Model with D1 = 9.42, r = 0.07, and g = 0.016, compute the denominator as 0.054, divide 9.42 by 0.054, and round the result to two decimals, yielding 174.44.

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