To determine the value of Firm A, we will use the Gordon Growth Model (also known as the Dividend Discount Model), which is defined as follows:
\[ P_0 = \frac{D_0 (1 + g)}{r - g} \]
Where:
- \( P_0 \) = price of the stock today
- \( D_0 \) = most recent dividend paid
- \( g \) = growth rate of the dividend
- \( r \) = required rate of return
To calculate \( r \) (the required rate of return), we can use the Capital Asset Pricing Model (CAPM):
\[ r = r_f + \beta (r_m - r_f) \]
Where:
- \( r_f \) = risk-free rate
- \( \beta \) = beta of the stock
- \( (r_m - r_f) \) = market risk premium
Given that:
- The risk-free rate (\( r_f \)) = 1.86%
- The market risk premium = 5.84%
- \( \beta \) of Firm A = 1.32
We can calculate \( r \) as follows:
\[ r = 1.86% + 1.32 \times 5.84% \]
Calculating the excess return from the market risk premium:
\[ = 1.86% + (1.32 \times 5.84%) \] \[ = 1.86% + 7.7088% \] \[ = 9.5688% \]
Thus, \( r \approx 9.57%\).
Now we can apply this to calculate the present value of Firm A’s stock using the Gordon Growth Model.
Given:
- \( D_0 = 1.46 \)
- \( g = 4.28% \) or 0.0428
First, calculate \( D_1 = D_0 \times (1 + g) \):
\[ D_1 = 1.46 \times (1 + 0.0428) \approx 1.46 \times 1.0428 \approx 1.5249 \]
Now we can calculate \( P_0 \):
\[ P_0 = \frac{D_1}{r - g} = \frac{1.5249}{0.095688 - 0.0428} \]
Calculating the denominator:
\[ r - g = 0.095688 - 0.0428 = 0.052888 \]
Finally,
\[ P_0 = \frac{1.5249}{0.052888} \approx 28.84 \]
Now we can calculate the total value of Firm A by multiplying the price per share by the number of shares outstanding.
Number of shares outstanding for Firm A = 284 million
Thus, the total value of Firm A is:
\[ \text{Value of Firm A} = P_0 \times \text{Shares Outstanding} = 28.84 \times 284,000,000 \approx 8,187,760,000 \]
The value of Firm A is approximately $8.19 billion.
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