Question

Suppose the risk-free rate is 1.09% and an analyst assumes a market risk premium of 6.81%. Firm A just paid a dividend of $1.18 per share. The analyst estimates the β of Firm A to be 1.38 and estimates the dividend growth rate to be 4.78% forever. Firm A has 255.00 million shares outstanding. Firm B just paid a dividend of $1.51 per share. The analyst estimates the β of Firm B to be 0.83 and believes that dividends will grow at 2.33% forever. Firm B has 197.00 million shares outstanding. What is the value of Firm A?

Answer 1

The value of Firm A, calculated using the Gordon Growth Model, is approximately $5.2683 billion, considering its dividends, growth rate, risk-free rate, beta, and market risk premium.

Step-by-step explanation:

To estimate the value of Firm A, we can use the Gordon Growth Model (also known as the Dividend Discount Model) which calculates the present value of an infinite series of dividends that grow at a constant rate. The formula for the model is:

P = D / (k - g)

where:

• P is the price per share
• D is the dividend per share
• k is the required rate of return (calculated as the risk-free rate plus the product of the beta (β) and the market risk premium)
• g is the dividend growth rate

For Firm A, we have the following information:

• D = $1.18
• β = 1.38
• Risk-free Rate = 1.09%
• Market Risk Premium = 6.81%
• g = 4.78%

Let's calculate the required rate of return (k) for Firm A:

k = Risk-free Rate + (β * Market Risk Premium)

k = 1.09% + (1.38 * 6.81%)

k ≈ 1.09% + 9.3998%

k ≈ 10.4898%

Now we use the Gordon Growth Model to calculate P for Firm A:

P = D / (k - g)

P = $1.18 / (10.4898% - 4.78%)

P ≈ $1.18 / 5.7098%

P ≈ $20.66

The estimated value of Firm A is then the price per share multiplied by the number of shares outstanding:

Value of Firm A = P * Number of shares

Value of Firm A ≈ $20.66 * 255 million

Value of Firm A ≈ $5,268,300,000

Therefore, the calculated approximate value of Firm A, based on the Gordon Growth Model, is $5.2683 billion.