In recent years, Sears, Roebuck & Co.has paid out only 32% of its earnings in dividends.Retained earnings have been invested in expansion projects that have yielded an average ROE of 20%.If Sears' cost of equity capital is 16% and next year's expected dividend is $1 per share, compute the value of Sears' shares using the constant dividend growth model as interpreted through the sustainable growth model.

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Quizplus · Accepted Answer

The value of Sears' shares can be calculated using the constant dividend growth model, which is $ P_0 = \frac{D_0 \times (1 + g)}{k - g} $, where $ P_0 $ is the price of the stock today, $ D_0 $ is the current dividend, $ g $ is the growth rate of dividends, and $ k $ is the cost of equity. The growth rate $ g $ can be calculated using the retention ratio (b) and the return on equity (ROE) as $ g = b \times ROE $. Since Sears pays out 32% of its earnings as dividends, it retains 68% (100% - 32% = 68%). Therefore, $ g = 0.68 \times 20\% = 13.6\% $. Using the given next year's expected dividend of $1 (which implies $ D_0 $ is approximately $0.884 based on the growth rate since $ D_1 = D_0 \times (1 + g) $), and a cost of equity capital of 16%, the value of Sears' shares is calculated as follows:$$ P_0 = \frac{1}{0.16 - 0.136} = \frac{1}{0.024} = \$41.67 $$This calculation assumes the dividend grows at a constant rate indefinitely, and the cost of equity is greater than the growth rate.

In Recent Years, Sears, Roebuck & Co