Question

6. Suppose you believe that the price of Stock X is going to increase from its current level of $18 during the next several months. For $4 you buy a call option giving you the right to buy 1 share at a price of $24 per share. [12 points] a. What is the exercise value of the option now? X is going to increase from its curent level of 18 during b. What is the time value of the option? c. Calculate the net profit (dollars) if the option is purchased and the stock price rises to $30? d. Calculate the net profit percentage (rate of return) on the option. e. Calculate the breakeven price of the stock--the stock price that would produce neither a net profit nor a net loss for the buyer of the call option. (Ignore any option time value.) f. Suppose you are the writer of this call option. If the price of the stock is $24 at the expiration date, calculate the dollar amount of income you earned by writing the option.

Answer 1

Current market price of stock X = 18 $ , Option Price = 4 $ , Strike Price = 24 $

a) Since the current market price is less than the strike price the option holder will not choose to exercise the call option. Hence the exercise value is 0 $.

b) Time value of option = Option premium - Intrinsic value

= 4 - (18-24) = 4 + 6 = 10 $

c) Market price = 30 $ , Strike Price = 24$ , Option Price = 4 $

Hence the net profit at a market price of 30 $ is = 30 - (24+4) = 30 - 28 = 2 $

d) Rate of return of the option is = 2/4 * 100 = 50 %

e) Since the total value of the option including option price is 24 + 4 = 28 $ at this price option will neither produce a profit or loss.

f) Since the call option was brought with a strike price of 24 $ and the price at expiration is also 24 $ the net difference is 0. Hence the option writer will not lose any money if the option is exercised and his/her gain is the entire option price which is 4 $.