Final answer:
The value of Firm B is calculated using the Gordon Growth Model, with inputs including a dividend of $1.51 per share, a beta of 0.72, and a growth rate of 2.31%. Using the required rate of return from the CAPM, the per-share value is found to be $32.99, which gives Firm B a total value of approximately $6.565 billion.
Step-by-step explanation:
To calculate the value of Firm B, we use the Gordon Growth Model (also known as the Dividend Discount Model), which values a stock by assuming dividends grow at a constant rate indefinitely. The model is represented by the formula P = D / (k - g), where P is the price of the stock, D is the dividend per share, k is the required rate of return, and g is the dividend growth rate.Given that Firm B just paid a dividend (D) of $1.51 per share, has a beta (β) of 0.72, and an expected dividend growth rate (g) of 2.31%, we can find the required rate of return (k) using the Capital Asset Pricing Model (CAPM). CAPM is k = risk-free rate + (β * market risk premium), which in this case is k = 1.24% + (0.72 * 6.47%) = 6.8884%. With these figures, we can plug into the Gordon Growth Model:
P = $1.51 / (0.068884 - 0.0231) = $1.51 / 0.045784 = $32.99 per share
To find the total value of Firm B, we multiply the price per share by the number of shares outstanding (199.00 million):
Total Value of Firm B = $32.99 per share * 199.00 million shares = $6,565.01 millionThus, using the risk-free rate of 1.24%, the market risk premium of 6.47%, and the respective forecasts and assumptions about Firm B's dividends and growth, we calculate the total value of Firm B to be approximately $6.565 billion