To calculate the price of a 1-year call option with an expected dividend, we use the dividend-adjusted Black-Scholes-Merton model.

Step 1: Calculate the present value of the expected dividend. $PV(D) = D \times e^{-r \times t_1} = 2 \times e^{-0.05 \times 0.25} = 2 \times e^{-0.0125} \approx 1.9752$

Step 2: Calculate the adjusted stock price ($S^*$). $S^* = S_0 - PV(D) = 50 - 1.9752 = 48.0248$

Step 3: Calculate $d_1$ and $d_2$. $d_1 = \frac{\ln(S^*/K) + (r + \sigma^2/2)T}{\sigma \sqrt{T}} = \frac{\ln(48.0248/50) + (0.05 + 0.20^2/2) \times 1}{0.20 \times \sqrt{1}}$ $d_1 = \frac{-0.04032 + 0.07}{0.20} = \frac{0.02968}{0.20} \approx 0.1484$ $d_2 = d_1 - \sigma \sqrt{T} = 0.1484 - 0.20 = -0.0516$

Step 4: Determine $N(d_1)$ and $N(d_2)$. $N(d_1) = N(0.1484) \approx 0.5590$ $N(d_2) = N(-0.0516) \approx 0.4794$

Step 5: Calculate the call option price. $c = S^* N(d_1) - K e^{-rT} N(d_2)$ $c = 48.0248 \times 0.5590 - 50 \times e^{-0.05 \times 1} \times 0.4794$ $c = 26.8459 - 50 \times 0.95123 \times 0.4794 = 26.8459 - 22.8009 = 4.045 \approx \text{USD } 4.04$