The required return on a stock is equal to which one of the following if the dividend on the stock decreases by a constant percent per year? a. Dividend yield - Capital gains yield b. Dividend yield + Capital gains yield c. Dividend yield $$ imes $$ Capital gains yield d. $$ \left(D_{1} / P_{0} ight) / g $$ e. $$ \left(P_{0} / D_{1} ight)-g $$

Question

The required return on a stock is equal to which one of the following if the dividend on the stock decreases by a constant percent per year? a. Dividend yield - Capital gains yield b. Dividend yield + Capital gains yield c. Dividend yield $$ 	imes $$ Capital gains yield d. $$ \left(D_{1} / P_{0}ight) / g $$ e. $$ \left(P_{0} / D_{1}ight)-g $$

UpStudy AI · Accepted Answer

To determine the required return on a stock when the dividend decreases by a constant percent per year, we can use the Gordon Growth Model (also known as the Dividend Discount Model). The model states that the required return $$ r $$ can be expressed as:

$$
r = \text{Dividend Yield} + \text{Capital Gains Yield}
$$

In this case, since the dividend is decreasing, the capital gains yield will be negative. Therefore, we can express the required return as:

$$
r = \left(\frac{D_1}{P_0}\right) + g
$$

Where:
- $$ D_1 $$ is the expected dividend next year,
- $$ P_0 $$ is the current price of the stock,
- $$ g $$ is the growth rate of the dividends (which will be negative in this case).

Given that the dividend is decreasing, we can conclude that the capital gains yield $$ g $$ will be negative, leading to the required return being the sum of the dividend yield and a negative capital gains yield.

Thus, the correct answer is:

**b. Dividend yield + Capital gains yield**
The required return on the stock is the sum of the dividend yield and the capital gains yield.

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