A one-year call option contract on Cheesy Poofs Co. stock sells for $1,260. In o

Question

A one-year call option contract on Cheesy Poofs Co. stock sells for $1,260. In one year, the stock will be worth $58 or $79 per share. The exercise price on the call option is $71. What is the current value of the stock if the risk-free rate is 4 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

A one-year call option contract on Cheesy Poofs Co. stock sells for $1,260. In one year, the stock will be worth $58 or $79 per share. The exercise price on the call option is $71. What is the current value of the stock if the risk-free rate is 4 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Explanation / Answer

p=(e^(0.04*1)-58/S)/(79/S-58/S)=(S*e^(0.04)-58)/21

1-p=1-(S*e^(0.04)-58)/21

Call price=e^(-rt)*(p*max(79-71,0)+(1-p)*max(58-71,0))=p*8*e^(-rt)=p*8*e^(-0.04)

So, 1.260=(S*e^(0.04)-58)/21*8*e^(-0.04)

=>(e^(0.04)*21/8+58)/e^(0.04)*1.26=S

=>S=73.52199

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