Question

Alta shares are currently selling for $24 and have paid a dividend of $1 per share for the most recent year. The risk-free rate is 4%, beta is 1.2, and the equity risk premium is 5%. Based on the above information, determine the constant dividend growth rate that would be required to justify the market price of $24.

Answer 1

The constant dividend growth rate required to justify the current market price of Alta shares at $24, given a dividend of $1 per share, a risk-free rate of 4%, a beta of 1.2, and an equity risk premium of 5%, is 5.83%.

Step-by-step explanation:

To determine the constant dividend growth rate needed to justify the current market price of Alta shares, we can use the Gordon Growth Model (also known as the Dividend Discount Model). This model is expressed as P = D / (r - g), where:

P is the current stock price.

D is the dividend per share.

r is the required rate of return (calculated as the risk-free rate plus beta times the equity risk premium).

g is the constant dividend growth rate.

We have P = $24, D = $1, the risk-free rate = 4%, beta = 1.2, and the equity risk premium is 5%. First, calculate r:

r = risk-free rate + (beta × equity risk premium) = 0.04 + (1.2 × 0.05) = 0.04 + 0.06 = 0.10 or 10%

Now, using the Gordon Growth Model:

$24 = $1 / (0.10 - g)

Solving for g:

g = 0.10 - ($1 / $24)

g = 0.10 - 0.0417

g = 0.0583 or 5.83%

The constant dividend growth rate required to justify the current market price is 5.83%.