The price of Tara Inc. stock will be either $75 or $95 at the end of the year. C

Question

The price of Tara Inc. stock will be either $75 or $95 at the end of the year. Call options are available with one year to expiration. T-bils currently yield 6 percent. a. Suppose the current price of Tara stock is $85. What is the value of the call option if the exercise price is $65 per share? (Do not round intermediate calculations. Round the final answer to 2 decimal places.) Call value b. Suppose the current price of Tara stock is $85. What is the value of the call option if the exercise price is $70 per share? (Do not round intermediate calculations. Round the final answer to 2 decimal places.) Call value

Explanation / Answer

a)

down node = 75 / 85 = 0.882353

up node = 95 / 85 = 1.117647

Probabaility of up movement = [( 1 + risk free rate) - down node] / up node - down node

Probabaility of up movement = [( 1 +0.06) - 0.882353] / 1.117647 - 0.882353

Probabaility of up movement = 0.177647 / 0.235294

Probabaility of up movement = 0.755

probability of down movement = 1 - 0.755 = 0.245

Value of call option at time 1 when stock goes up = stock price - excercise price

Value of call option at time 1 when stock goes up = 95 - 65 = 30

Value of call option at time 1 when stock goes down = 75 - 65 = 10

Value of call option at time 0 = [ ( 0.755 * 30) + ( 0.245 * 10 ) / ( 1 + 0.06)1

Value of call option at time 0 = [ 22.65 + 2.45 ] / 1.06

Value of call option at time 0 = 25.1 / 1.06

Value of call option at time 0 = $23.68

b)

alue of call option at time 1 when stock goes up = 95 - 70 = 25

Value of call option at time 1 when stock goes down = 75 - 70 = 5

Value of call option at time 0 = [ ( 0.755 * 25) + ( 0.245 * 5 ) / ( 1 + 0.06)1

Value of call option at time 0 = [ 18.875 + 1.225 ] / 1.06

Value of call option at time 0 = 20.1 / 1.06

Value of call option at time 0 = $18.96

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