Final answer:
The value of Firm B can be calculated using the dividend discount model by applying the Gordon Growth Model, which requires the last dividend paid, the dividend growth rate, the beta of the firm, the risk-free rate, and the market risk premium. Using the Capital Asset Pricing Model, we can find the required rate of return, which is then used to calculate the current stock price with the Gordon Growth Model. The total value of Firm B is then the stock price multiplied by the number of shares outstanding.
Step-by-step explanation:
The valuation of Firm B using the dividend discount model (DDM) involves calculating the present value of all future dividends, which are expected to grow at a constant rate indefinitely. To find the value of Firm B, we first determine its required rate of return using the Capital Asset Pricing Model (CAPM), which gives us the discount rate by adding the risk-free rate to the product of Firm B's beta and the market risk premium. With a risk-free rate of 2.64%, a beta of 0.72, and a market risk premium of 7.12%, we can calculate the cost of equity for Firm B. Then, the Gordon Growth Model (a version of DDM) is applied using the last dividend paid, the cost of equity, and the dividend growth rate to determine Firm B's share price. Finally, we multiply the share price by the number of shares outstanding to find the total value of Firm B.
The formula for the Gordon Growth Model is P0 = D0 * (1 + g) / (k - g), where P0 is the current stock price, D0 is the most recent dividend payment, g is the growth rate of dividends, and k is the required rate of return (cost of equity).
Using the given numbers for Firm B, we would have:
- Last dividend (D0) = $1.71
- Dividend growth rate (g) = 2.50%
- Risk-free rate = 2.64%
- Market risk premium = 7.12%
- Beta (β) = 0.72
First, we calculate the required rate of return using CAPM:
k = Risk-free rate + (Beta * Market risk premium) = 2.64% + (0.72 * 7.12%)
Then, we calculate the stock price using the Gordon Growth Model:
P0 = $1.71 * (1 + 0.025) / (k - 0.025)
After finding the stock price per share, we calculate the total value of Firm B by multiplying the stock price by the number of shares outstanding:
Total value of Firm B = Stock price * Number of shares
Note that in practice, market conditions and investor perceptions can also affect stock prices, and these models provide theoretical values based on the information provided and assumptions made.