Question

Suppose the risk-free rate is 2.41% and an analyst assumes a market risk premium of 5.94%. Firm A just paid a dividend of $1.06 per share. The analyst estimates the β of Firm A to be 1.22 and estimates the dividend growth rate to be 4.22% forever. Firm A has 289.00 million shares outstanding. Firm B just paid a dividend of $1.78 per share. The analyst estimates the β of Firm B to be 0.71 and believes that dividends will grow at 2.54% forever. Firm B has 188.00 million shares outstanding. What is the value of Firm A?

Answer 1

To determine Firm A's value, the Gordon Growth Model is applied using the dividend payment, the calculated required rate of return (CAPM), and the dividend growth rate. The resulting stock price per share is then multiplied by the number of shares outstanding to obtain Firm A's total value.

Step-by-step explanation:

To calculate the value of Firm A, we need to use the Gordon Growth Model (also known as the Dividend Discount Model), which is a method used for valuing a stock based on the theory that a stock is worth the present value of all of its future dividend payments, discounted back to their present value. In this case, the formula is P = D / (k - g), where P equals the price per share, D equals the dividends per share, k equals the required rate of return, and g equals the growth rate of the dividends.

The required rate of return (k) for Firm A is calculated using the Capital Asset Pricing Model (CAPM) as follows: k = risk-free rate + (beta * market risk premium). Thus, for Firm A, k = 2.41% + (1.22 * 5.94%) = 9.63%. Now we can calculate the price per share for Firm A using the Gordon Growth Model: P = $1.06 / (9.63% - 4.22%) = $21.70. To find the total value of Firm A, we multiply the price per share by the number of shares: $21.70 * 289 million shares = $6,271.3 million.