The price of Tara, Inc., stock will be either $79 or $101 at the end of the year

Question

The price of Tara, Inc., stock will be either $79 or $101 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 4 percent a. Suppose the current price of the company's stock is $90. What is the value of the call option if the exercise price is $75 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Call value b. Suppose the current price of the company's stock is $90. What is the value of the call option if the exercise price is $85 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Call value

Explanation / Answer

Solution :

a) The value of the call option = stock price - the present value of the exercise price of the stock hence

at option expiration the expected value of the stock = $90 =.5 (101) + .5 (79)

hence = 90 - 75/1.05 = 90 - 71.42 = $18.58

b) Here we will have the call option = 1/2 the leverage equity portfolio

2C = 90 - 79/1.05 = 90 - 75.23 = 14.77

hence 2C = 14.77 = C = 14.77/2 = $7.38

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