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Walter Maxim, the CEO of Digital Storage Devices has been granted options on 300,000 shares. The stock is currently trading at $27 a share and the options are at the money. The volatility of the stock has been about .15 on an annual basis over the last several years. The options mature in five years, become exercisable in three years, and the risk free rate is 4%.What is the value of Mr. Maxim's options? S=Current stock priceE=Exercise price of callR=Annual risk free rate of return,continuously compounded σ^2=Variance per year of the continuous return on stock t=Time (in years)to expiration dated_1=[In(S/E)+(R+σ^2/2)t ]/√(σ^2 ) td_2=d_1-√(σ^2 ) tC=S ×N (d_1 )-K ×N (d_2)C=2 (.74668)-27e^-×20(.41992)C=1.49336-27e^- (9.89176)C=$10.88Total value=Shares×CTotal value=300,000×$10.88Total value=$3,264,000
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