CFA Level 1: Dividend Growth Rate, Payout Ratio, and Required Rate of Return Calculation

Return on Equity Calculation

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Question

A firm has a dividend growth rate of 4.3%. It typically pays out 45% of its earnings as dividends. Recently, it paid out $1.2 per share dividend and the required rate of return on its stock is 12.6%. The firm's return on equity equals ________.

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Explanations

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A. B. C. D.

A

The dividend growth rate equals the product of ROE and the earnings retention ratio. The earnings retention in this case equals 1 - 0.45 = 0.55. Hence, the ROE equals 4.3%/0.55 = 7.82%.

To calculate the firm's return on equity (ROE), we need to use the dividend growth model and the payout ratio.

The dividend growth model is given by the formula:

ROE = (Dividend per Share / Stock Price) + Dividend Growth Rate

First, let's calculate the dividend per share using the information provided. We know that the firm paid a dividend of $1.2 per share. Since the payout ratio is 45%, we can calculate the earnings per share (EPS) as follows:

EPS = Dividend per Share / Payout Ratio

EPS = $1.2 / 0.45 = $2.67

Now, let's calculate the stock price using the dividend growth model formula:

Stock Price = Dividend per Share / (Required Rate of Return - Dividend Growth Rate)

Stock Price = $1.2 / (0.126 - 0.043) = $1.2 / 0.083 = $14.46

Next, we can calculate the return on equity (ROE) using the dividend growth model formula:

ROE = (Dividend per Share / Stock Price) + Dividend Growth Rate

ROE = ($1.2 / $14.46) + 0.043

ROE = 0.083 + 0.043

ROE = 0.126

The firm's return on equity (ROE) is 12.60%.

Therefore, the correct answer is D. 12.60%.

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