During the past 10 years, Saturn's common stock dividends have grown from $0.24 to $0.62. If the past growth of dividends is expected to continue at the same rate in the future, what is the current value of Saturn's common stock to an investor who requires an 18% rate of return?

Question

Quizplus · Accepted Answer

The growth rate of dividends can be calculated using the formula for the growth rate (g) in dividends, which is $g = \left( \frac{D_1}{D_0} \right)^{\frac{1}{n}} - 1$, where $D_1$ is the future dividend, $D_0$ is the current dividend, and $n$ is the number of periods. Here, $D_1 = 0.62$, $D_0 = 0.24$, and $n = 10$. This gives us $g = \left( \frac{0.62}{0.24} \right)^{\frac{1}{10}} - 1 = 0.1$ or 10%. The value of the stock (V) can then be calculated using the Gordon Growth Model (also known as the Dividend Discount Model for a perpetuity with growth), which is $V = \frac{D_0 \times (1 + g)}{r - g}$, where $D_0$ is the current dividend, $g$ is the growth rate, and $r$ is the required rate of return. Substituting the values gives us $V = \frac{0.62 \times (1 + 0.1)}{0.18 - 0.1} = \frac{0.62 \times 1.1}{0.08} = \frac{0.682}{0.08} = 8.525$, which rounds to $8.53, matching choice C.

During the Past 10 Years, Saturn's Common Stock Dividends Have