Answer: USD 2.85

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).

Author: LeetQuiz Editorial Team