Question

The price of Tara, Inc., stock will be either $82 or $104 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 3 percent.

  

a.	Suppose the current price of the company's stock is $93. What is the value of the call option if the exercise price is $78 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 $93. What is the value of the call option if the exercise price is $88 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Call value

$

Answer 1

a). C0 = S0 - PV(X)

= $93 - [$78/1.03] = $93 - $75.73 = $17.27

b). Step 1: Calculate the option value at expiration based upon your assumption of a 50% chance of increasing to $104 and a 50% chance of decreasing to $82.

The two possible stock prices are:

S+ = $104 and S– = $82. Therefore, since the exercise price is $109, the corresponding two possible call values are:

Cu= $11 and Cd= $0.

Step 2: Calculate the hedge ratio:

(Cu– Cd)/(uS0– dS0) = (11 – 0)/(104 – 82) = 11/22 = 0.5

Step 3: Form a riskless portfolio made up of one share of stock and two written calls. The cost of the riskless portfolio is:

(S0– 2C0) = 88 – 2C0

and the certain end-of-year value is $82.

Step 4: Calculate the present value of $82 with a one-year interest rate of 3%:

$82/1.03 = $79.61

Step 5: Set the value of the hedged position equal to the present value of the certain payoff:

$88 – 2C0= $79.61

2C0 = $88 - $79.61

C0 = $8.39 / 2 = $4.19