Problem $23-1$ Employee Stock Options

Cheryl Levin is the chief executive officer of Mountainbrook Trading Company. The board of directors has just granted Cheryl $40,000$ at$-$the$-$money European call options on the company's stock, which is currently trading at $$55$ per share. The stock pays no dividends. The options will expire in five years and the standard deviation of the returns

on the stock is $56$ percent. Treasury bills that mature in five years currently yield a continuously compounded interest rate of $7\mathrm{.}4$ percent. Use the Black$-$Scholes model to calculate the value of the option grant. $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$