In addition to the five factors discussed in the chapter, dividends also affect the price of an option. The Black-Scholes 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 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 altered when dividends are paid. The dividend-adjusted put-call parity formula is:

Sedt+P=EeRt+CSedt+P=EeRt+C

where d is the continuously compounded dividend yield.

A stock is currently priced at $84 per share, the standard deviation of its return is 60 percent per year, and the risk-free rate is 5 percent per year, compounded continuously. What is the price of a put option with a strike price of $80 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.)