Final answer:
The lower bound for the price of the four-month call option is at least the intrinsic value, which is the in-the-money amount of $2. To accurately calculate this, one must use the Black-Scholes model considering factors like the risk-free interest rate, but the question provides insufficient data for a precise figure.
Step-by-step explanation:
The question asks for the lower bound for the price of a four-month call option on a non-dividend-paying stock. Using financial theory, specifically the Black-Scholes model and option pricing principles, we can establish that the lower bound or the intrinsic value of an European call option is the maximum of zero or the difference between the stock price and the strike price discounted back to present value at the risk-free rate. In this case, since the stock price is $47 and the strike price is $45, the call option is in the money. Therefore, the intrinsic value, ignoring time value, is at least $47 - $45 which is $2. However, we must also consider the present value of the strike price given the risk-free interest rate of 7.9% per annum.
The exact mathematical formulation would require us to apply the Black-Scholes model which takes into account other factors such as time to maturity and volatility, but the provided information is not sufficient for this calculation. Nevertheless, we understand that the intrinsic value is a lower bound for the price of the call option, which can be adjusted higher depending on time value and other market factors.