Using the Merton model, the equity of a firm is valued as a European call option on the firm's assets, where the strike price is the face value of the debt. Given parameters:

• Value of the firm ($V$) = $200 million
• Face value of debt ($D$) = $180 million
• Time to maturity ($T$) = 3 years
• Risk-free interest rate ($r$) = 5% or 0.05
• Volatility of firm value ($\sigma$) = 10% or 0.10

First, calculate $d_1$ and $d_2$: $d_1 = \frac{\ln(V / D) + (r + \frac{\sigma^2}{2})T}{\sigma \sqrt{T}}$ $d_1 = \frac{\ln(200 / 180) + (0.05 + \frac{0.10^2}{2}) \times 3}{0.10 \times \sqrt{3}}$ $d_1 = \frac{0.10536 + (0.055) \times 3}{0.1732} = \frac{0.10536 + 0.165}{0.1732} = \frac{0.27036}{0.1732} \approx 1.561$

$d_2 = d_1 - \sigma \sqrt{T} = 1.561 - 0.1732 \approx 1.388$

Next, find the standard normal cumulative probabilities: $N(d_1) = N(1.56) \approx 0.9406$ $N(d_2) = N(1.39) \approx 0.9177$

Now, compute the value of the equity ($E$): $E = V \cdot N(d_1) - D \cdot e^{-rT} \cdot N(d_2)$ $E = 200 \times 0.9406 - 180 \times e^{-0.15} \times 0.9177$ $E = 188.12 - (180 \times 0.8607 \times 0.9177)$ $E = 188.12 - 142.17 = 45.95 \text{ million}$

Rounding to the nearest million, the value of the equity is approximately $46 million.