In addition to the five factors, dividends also affect the price of an option. The Black-Scholes Option Pricing Model with dividends is: C = S times e^-at times N(d_1) - E times e^-kt times N(d_2) d_1 = [ln(S/E) + (R - d + sigma^2/2) times t] (sigma - squareroot t) d_2 = d_1 - sigma times squareroot t All of the variables are the same as the Black-Scholes model without dividends except for the variable d, which is the continuously compounded dividend yield on the stock. The put-call parity condition is also altered when dividends are paid. The dividend-adjusted put-call parity formula is: S times e^-dt + P = E times e^-kt + C where d is again the continuously compounded dividend yield. A stock is currently priced at $82 per share, the standard deviation of its return is 56 percent per year, and the risk-free rate is 3 percent per year, compounded continuously. What is the price of a put option with a strike price of $78 and a maturity of six months if the stock has a dividend yield of 3 percent per year? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)