Answer: USD 2.85

The correct answer to the question is D. USD 2.85. This is determined using the Black-Scholes-Merton (BSM) model for pricing a European-style call option on company CzC's stock. The BSM model is a mathematical model used to calculate the price of European call and put options, which assumes constant volatility and a log-normal distribution of stock prices. In this scenario, the company CzC has announced a dividend payout of USD 0.50 per share on an ex-dividend date one month from now, with no further dividend plans for at least one year. This dividend affects the stock price, and thus, the call option pricing needs to account for it. The formula for the BSM model, adjusted for dividends, 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, which is USD 40. - \( N(d_1) \) and \( N(d_2) \) are the cumulative normal distribution functions for \( d_1 \) and \( d_2 \), respectively. - \( K \) is the exercise price of the call option, which is also USD 40. - \( r \) is the risk-free rate, which is 3% per year. - \( T \) is the time to expiration in years, which is 1 year in this case. However, because of the dividend, the current stock price \( S_0 \) needs to be reduced by the present value of the dividend to be paid: \[ \text{Present value of dividend} = \text{Dividend amount} \cdot e^{-r \cdot \text{time to dividend payment}} \] \[ \text{Present value of dividend} = 0.50 \cdot e^{-0.03 \cdot \frac{1}{12}} = 0.4988 \] So the adjusted stock price \( S_0 \) becomes: \[ S_0 = 40 - 0.4988 = 39.5012 \] Plugging the values into the BSM formula: \[ \text{Call option price} = 39.5012 \cdot 0.5750 - 40 \cdot e^{-0.03 \cdot 1} \cdot 0.5116 \] \[ \text{Call option price} = 22.7132 - 19.8592 = 2.8540 \] This calculation results in a call option price of USD 2.8540, which is rounded to USD 2.85, corresponding to option D.

Author: LeetQuiz Editorial Team