To determine the value of Firm B, we can use the Gordon Growth Model (also known as the Dividend Discount Model), which states that the value of a stock is equal to the next year's expected dividend divided by the difference between the required rate of return and the dividend growth rate.
Steps to Calculate the Value of Firm B:
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Calculate the required rate of return (r) for Firm B using the Capital Asset Pricing Model (CAPM):
\[ r = \text{Risk-free rate} + \beta \times \text{Market Risk Premium} \]
Here, the risk-free rate is 2.21%, \(\beta\) for Firm B is 0.86, and the market risk premium is 7.30%.
\[ r = 2.21% + 0.86 \times 7.30% \] \[ r = 2.21% + 6.278% \] \[ r = 8.488% \]
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Calculate the next expected dividend (D1) for Firm B. Since Firm B just paid a dividend of $1.52 and dividends are expected to grow at 2.22%, we can calculate D1 as:
\[ D1 = D0 \times (1 + g) \] \[ D1 = 1.52 \times (1 + 0.0222) \] \[ D1 = 1.52 \times 1.0222 \approx 1.5534 \]
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Calculate the value per share (P0) of Firm B using the Gordon Growth Model:
\[ P0 = \frac{D1}{r - g} \]
Using \(D1 = 1.5534\), \(r\) from step 1 (8.488% or 0.08488), and \(g = 2.22% \) or 0.0222, we can substitute these into the formula:
\[ P0 = \frac{1.5534}{0.08488 - 0.0222} \] \[ P0 = \frac{1.5534}{0.06268} \approx 24.758 \]
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Calculate the total value of Firm B by multiplying the price per share by the number of shares outstanding:
\[ \text{Total Value of Firm B} = P0 \times \text{Number of shares} \]
Given that Firm B has 190 million shares outstanding:
\[ \text{Total Value of Firm B} = 24.758 \times 190,000,000 \approx 4,699,020,000 \]
Conclusion:
The estimated total value of Firm B is approximately $4.70 billion.
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