Question

Gotard Processing's stock currently sells for $42.00. It just paid a dividend of $1.75. The required rate of return on the stock, rs​, is 9.25%. What dividend growth rate, g, is assumed here?

Answer 1

The assumed dividend growth rate for Gotard Processing's stock is calculated using the Dividend Growth Model. Given a current stock price of $42.00, a dividend of $1.75, and a required rate of return of 9.25%, the growth rate is determined to be approximately 5.08%.

Step-by-step explanation:

The question is asking to calculate the assumed dividend growth rate for Gotard Processing's stock using the given stock price, dividend, and required rate of return. This involves the Dividend Growth Model (also known as the Gordon Growth Model), which establishes a relationship between these variables. The formula to compute the growth rate (g) is derived from the model's equation:

P = D₁ / (rs - g)

Where P is the current stock price ($42.00), D₁ is the dividend just paid plus the growth rate ($1.75), rs is the required rate of return (9.25%), and g is the dividend growth rate we need to calculate.

Rearranging the formula to find g yields:

g = rs - (D₁ / P)

Substituting the values:

g = 0.0925 - ($1.75 / $42.00)

g = 0.0925 - 0.0417

g ≈ 0.0508 or 5.08%

Therefore, the assumed dividend growth rate for Gotard Processing's stock is approximately 5.08%.