Problem 17-30 BlackScholes and Dividends

In addition to the five factors discussed in the chapter, dividends also affect the price of an option. The BlackScholes option pricing model with dividends is: C=SedtN(d1)EeRtN(d2)C=SedtN(d1)EeRtN(d2) d1=[ln(S/E)+(Rd+2/2)t](t)d1=[ln(S/E)+(Rd+2/2)t](t) d2=d1td2=d1t All of the variables are the same as the BlackScholes model without dividends except for the variable d, which is the continuously compounded dividend yield on the stock. A stock is currently priced at $81 per share, the standard deviation of its return is 50 percent per year, and the risk-free rate is 4 percent per year, compounded continuously. What is the price of a call option with a strike price of $77 and a maturity of six months if the stock has a dividend yield of 2 percent per year? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Price of call option $