To find the value of Firm A, we will use the Gordon Growth Model (also known as the Dividend Discount Model), which is suited for valuing a stock that pays dividends that are expected to grow at a constant rate. The formula for the Gordon Growth Model is:
\[ P_0 = \frac{D_0 \times (1 + g)}{r - g} \]
Where:
- \( P_0 \) = price of the stock today
- \( D_0 \) = most recent dividend paid
- \( g \) = growth rate of dividends
- \( r \) = required rate of return
1. Calculate the required rate of return (r) for Firm A
The required rate of return can be calculated using the Capital Asset Pricing Model (CAPM):
\[ r = r_f + \beta \times (r_m - r_f) \]
Where:
- \( r_f \) = risk-free rate = 3.96% (or 0.0396)
- \( \beta \) = beta of Firm A = 1.29
- \( r_m - r_f \) = market risk premium = 5.34% (or 0.0534)
Substituting in the values:
\[ r = 0.0396 + 1.29 \times 0.0534 \] \[ r = 0.0396 + 0.0688836 \] \[ r = 0.1084836 \text{ or approximately } 10.85% \]
2. Substitute values into the Gordon Growth Model for Firm A
- \( D_0 = 1.44 \)
- \( g = 4.44% = 0.0444 \)
Now substituting these values into the formula:
\[ P_0 = \frac{1.44 \times (1 + 0.0444)}{0.1084836 - 0.0444} \] \[ P_0 = \frac{1.44 \times 1.0444}{0.0640836} \] \[ P_0 = \frac{1.505856}{0.0640836} \approx 23.48 \]
3. Calculate the total market value of Firm A
To find the total value of Firm A, we multiply the stock price by the number of shares outstanding:
\[ \text{Total Value of Firm A} = P_0 \times \text{Number of Shares} \]
Number of shares outstanding for Firm A = 259 million:
\[ \text{Total Value of Firm A} = 23.48 \times 259,000,000 \approx 6,086,420,000 \]
Conclusion
The estimated total value of Firm A is approximately $6.09 billion.
0 answers