Question

Suppose you know that a company’s stock currently sells for $65 per share and the required return on the stock is 15 percent. You also know that the total return on the stock is evenly divided between a capital gains yield and a dividend yield. If it’s the company’s policy to always maintain a constant growth rate in its dividends, what is the current dividend per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

The current dividend per share is $6.50.

Step-by-step explanation:

To find the current dividend per share, we need to determine the growth rate in dividends. Since the total return on the stock is evenly divided between the capital gains yield and the dividend yield, we can assume that the growth rate in dividends is the same as the growth rate in stock price. The capital gains yield is the difference between the required return and the dividend yield:

Capital gains yield = Required return - Dividend yield

In this case, the required return is 15% and the stock price is $65 per share. Let's assume the dividend yield is x:

Capital gains yield = 0.15 - x

We know that the dividend yield is equal to the dividend per share divided by the stock price:

Dividend yield = Dividend per share / Stock price

Substituting the values, we can solve for the dividend per share:

x = (Dividend per share) / 65

Capital gains yield = 0.15 - (Dividend per share) / 65

Since the total return is evenly divided between the capital gains yield and the dividend yield, the growth rate in dividends is equal to half of the total return:

Growth rate in dividends = (Capital gains yield) / 2

Growth rate in dividends = (0.15 - (Dividend per share) / 65) / 2

Now we can set up an equation to solve for the dividend per share:

Dividend per share = $65 * (0.15 - (Dividend per share) / 65) / 2

Simplifying the equation:

Dividend per share = $65 * (0.15 - (Dividend per share) / 65) / 2

Dividend per share = $9.75 - (Dividend per share) / 2

Dividend per share + (Dividend per share) / 2 = $9.75

3/2 * Dividend per share = $9.75

Dividend per share = ($9.75 * 2) / 3

Dividend per share = $6.50

Answer 2

Answer: Current dividend = $57.35

Step-by-step explanation:

Given:

Company’s stock currently sells for $65 per share

The required return on the stock = 15%

Required return =
`\left [ (Current dividend * (1+growth rate))/(current share price) \right ]+(growth rate)`

Required return = Dividend yield + Capital gains

15% =
`(15)/(2) + (15)/(2)`

`\therefore` Dividend yield = 7.5% , Capital gains = 7.5%

Now we will compute the current dividend as follow:

Dividend yield =
`\left [ (Current dividend * (1+growth rate))/(current share price) \right ]`

`\therefore` Current dividend =
`(65* 7.5)/(1+7.5)`

Current dividend = $57.35