The price of the 1-year call option on the stock is calculated using the Black-Scholes-Merton (BSM) model, which is adjusted for the dividend payout. The formula for a European call option price, when dividends are considered, is:

$\text{Call option price} = S_0 \cdot N(d_1) - K \cdot e^{-rT} \cdot N(d_2)$

Where:

• $S_0$ is the current stock price.
• $N(d_1)$ and $N(d_2)$ are the cumulative normal distribution functions for $d_1$ and $d_2$, respectively.
• $K$ is the call option exercise price.
• $r$ is the risk-free rate.
• $T$ is the time to expiration in years.

However, since the stock pays a dividend, the current stock price $S_0$ must be reduced by the present value of the dividend. The present value of the dividend is calculated as:

$\text{Present value of dividend} = \text{dividend amount} \cdot e^{-r \cdot \frac{T_{\text{dividend}}}{T}}$

Where:

• $T_{\text{dividend}}$ is the time until the dividend is paid, expressed as a fraction of the total time to expiration $T$.

Given:

• $S_0 = USD 40$
• Dividend amount = USD 0.50
• $r = 3\%$ per year
• $T_{\text{dividend}} = 1/12$ (since the dividend is paid 1 month from now, and there are 12 months in a year)
• $T = 1$ year
• $K = USD 40$
• $N(d_1) = 0.5750$
• $N(d_2) = 0.5116$

The present value of the dividend is:

$\text{Present value of dividend} = 0.50 \cdot e^{-0.03 \cdot \frac{1}{12}} = 0.50 \cdot e^{-0.0025} \approx 0.4988$

So the adjusted stock price $S_0$ is:

$S_0 = 40 - 0.4988 = 39.5012$

Now, we can calculate the call option price:

$\text{Call option price} = 39.5012 \cdot 0.5750 - 40 \cdot e^{-0.03} \cdot 0.5116$

$\text{Call option price} = 22.7132 - 19.8592 = USD 2.8540$

Thus, the correct answer is USD 2.85 (Option D).