You are considering the purchase of Miller Manufacturing's ordinary shares.The shares are selling for $21.00 per share.The next dividend is expected to be $2.10, and you expect the dividend to keep growing at a constant rate.If the shares are returning 15%, calculate the growth rate of dividends.

Question

Quizplus · Accepted Answer

The growth rate of dividends can be calculated using the Gordon Growth Model (Dividend Discount Model for a perpetuity with growth), which is given by the formula: $ P_0 = \frac{D_0 \times (1 + g)}{r - g} $, where $P_0$ is the current price of the stock, $D_0$ is the most recent dividend, $g$ is the growth rate of the dividend, and $r$ is the required rate of return. Rearranging the formula to solve for $g$, we get: $ g = \frac{P_0 \times r}{D_0} - 1 - \frac{D_0}{D_0} $. Plugging in the given values ($P_0 = $21$, $D_0 = $2.10$, and $r = 15\%$), we find that the correct calculation actually follows the rearranged formula: $ g = r - \frac{D_1}{P_0} $, where $D_1 = D_0 \times (1 + g)$. Given the mistake in the rearrangement, the correct approach is to use the original formula: $ P_0 = \frac{D_1}{r - g} $, where $D_1 = D_0 \times (1 + g)$ or simply $D_1 = $2.10$ as the next dividend. Solving for $g$ gives us: $ 21 = \frac{2.10}{0.15 - g} $, leading to $ g = 0.10 - 0.15 = -0.05 $ or a 5% growth rate when correctly solved. The correct calculation without the mistake is: $ 21 = \frac{2.10}{0.15 - g} $, solving for $g$ correctly gives $ g = 0.15 - \frac{2.10}{21} = 0.15 - 0.10 = 0.05 $ or 5%.

You Are Considering the Purchase of Miller Manufacturing's Ordinary Shares