To determine Firm A's market capitalization, we first need to calculate the expected price per share using the Gordon Growth Model (also known as the Dividend Discount Model). The formula for the Gordon Growth Model is:
\[ P_0 = \frac{D_1}{r - g} \]
Where:
- \( P_0 \) = Current price per share
- \( D_1 \) = Expected dividend next year
- \( r \) = Required rate of return
- \( g \) = Growth rate of dividends
- Calculate \( D_1 \): Given that the last dividend paid, \( D_0 \), is $4.51 and the growth rate \( g \) is 1.85%, we calculate the expected dividend next year \( D_1 \):
\[ D_1 = D_0 \times (1 + g) = 4.51 \times (1 + 0.0185) = 4.51 \times 1.0185 \approx 4.601435 \]
- Calculate \( r \): The required rate of return \( r \) 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 = 2.50%
- \( \beta \) = Beta of Firm A = 1.75
- \( r_m - r_f \) = Market risk premium = 4.51%
Substituting the values:
\[ r = 0.025 + 1.75 \times 0.0451 = 0.025 + 0.078925 = 0.103925 \approx 10.39% \]
- Calculate \( P_0 \): Now we can calculate the expected price per share \( P_0 \):
\[ P_0 = \frac{D_1}{r - g} = \frac{4.601435}{0.103925 - 0.0185} = \frac{4.601435}{0.085425} \approx 53.96 \]
- Calculate Market Capitalization: Market capitalization is calculated as the price per share multiplied by the total number of shares outstanding:
\[ \text{Market Capitalization} = P_0 \times \text{shares outstanding} = 53.96 \times 280,000,000 \]
Calculating this gives:
\[ \text{Market Capitalization} \approx 15,117,136,000 \text{ USD} \]
Therefore, Firm A's market capitalization is approximately $15.12 billion.
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