The price of Tara, Inc., stock will be either $68 or $90 at the end of the year.

Question

The price of Tara, Inc., stock will be either $68 or $90 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 6 percent.

Suppose the current price of the company's stock is $79. What is the value of the call option if the exercise price is $64 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Suppose the current price of the company's stock is $79. What is the value of the call option if the exercise price is $74 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

The price of Tara, Inc., stock will be either $68 or $90 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 6 percent.

Explanation / Answer

Answer : a) Expected % Return = (% increase in rise in price * probability of increase) - (% decrease in price *probability of price decrease)

Let Probabilty of price increase is P ,

1 = 11 P - 11(1- P)

P = 0.45 Hence ,Probility of price increase is 0.45 & probability of price decrease is 1 - 0.45 = 0.55

;,Value of call at high price, Max[(S-X),0] Here, S = 90$ & X = 64$ ,S-X = 26$ , value of call at low price = Max[(S-X),0] Here, S = 68$ & X = 64$ = S-X = 4$

Expected value of call on expiry ; 0.45*26+0.55*4 = 13.9 $

= 13.9$/1.06 = 13.11 $

b) Here, S = 79$ & X = 74$

Expected % Return = (% increase in rise in price * probability of increase) - (% decrease in price *probability of price decrease)

Let Probabilty of price increase is P ,

1 = 11 P - 11(1- P)

P = 0.45 Hence ,Probility of price increase is 0.45 & probability of price decrease is 1 - 0.45 = 0.55

;,Value of call at high price, Max[(S-X),0] Here, S = 90$ & X = 74$ ,S-X = 16$ , value of call at low price = Max[(S-X),0] Here, S = 68$ & X = 74$ = S-X = 0

Expected value of call on expiry ; 0.45*16+0.55*0 = 7.2

= 7.2/1.06 = 6.79 $

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