Arts and Crafts, Inc. will pay a dividend of $3 per share in 1 year. It sells at $30 a share, and firms in the same industry provide an expected rate of return of 16%. What must be the expected growth rate of the company's dividends?

Answer: The growth rate of the company's dividend is 6%.

Explanation:

GIVEN the following;

Dividend per period (D) = $3

price per share (P) = $30

Rate of return (r) = 16% = 0.16

Expected growth rate (g) = ?

Using the relation:

P = D : (r - g)

30 = 3 : (0.16 - g)

30 (0.16 - g) = 3

4.8 - 30g = 3

4.8 - 3 = 30g

1.8 = 30g

g = 1.8 : 30

g = 0.06

g = 6%

Therefore, to have a current stock price of $30, yielding a constant dividend of $3 per annum at a rate of return of 16%, Then the growth rate of the company's dividend is 6%.

The expected growth rate is 6%

Explanation:

The constant growth model of DDM calculates the price of a stock today based on the dividends that grow at a constant rate in future.

The formula for the Price of a stock using the constant growth model is,

P0 = D1 / r - g

Where,

P0 is the price of stock today D1 is the dividend expected for the next period r is the required rate of return g is the growth rate in dividends

Plugging in the values provided in the question, the growth rate is:

30 = 3 / (0.16 - g)

30 * (0.16 - g) = 3

4.8 - 30g = 3

4.8 - 3 = 30g

1.8 / 30 = g

g = 0.06 or 6%