A non-dividend paying stock has a current price of 40. Three European call options on this stock, with three months (0.25 years) to maturity, have strike prices 35, 40 and 45, respectively. The continuously compounding risk-free interest rate is 8% per year. The volatility of the stock is 30%. An option trading strategy, called butterfly spread, involves purchasing one 35-strike call, selling two 40-strike call and purchasing one 45-strike call. 

(a) Without considering the costs of the options, draw the payoff graph of this butterfly spread at maturity. What is the maximum gain and loss of this strategy?

(b) Compute the prices of three call options using the Black-Scholes formula. 

(c) Draw the payoff graph of this butterfly spread at maturity taken into account of the costs of the strategy. What is the maximum gain and loss of this butterfly spread?