You were recently having a family dinner with your uncle who is a Senior Vice-Pr

Question

You were recently having a family dinner with your uncle who is a Senior Vice-President at one of the companies that produces auto parts. He told you, during the dinner, that he has received an offer to be the CEO of another auto part manufacturing company. He has been told that in addition to his annual salary,
he would be given option to purchase 10,000 shares of the company's stock with strike price of RM90 per share where the option will expire in 2 years. The option will be his signing bonus. Your uncle wants to know the monetary value of this option? You told him that you need to do some analysis and will get back to him about the monetary value of the option.
After a careful study you found the following information:
The last trading price of the stock was RM100 a share. You estimated the annual return volatility of the stock to be 20 percent. The ringgit effective annual risk-free interest rate is 4 percent per annum.
What would be your estimate of the value of the option to buy 10,000 shares?

Explanation / Answer

Using Black-Scholes model

C=SN(d1) – N(d2)Ke-rt

d1 = [ln(S/K) + (r+s2/2)t] s.t

d2= d1-s.t

where;

C= Call Premium

S= Current Stock Price = RM100

T = time to expiration = 2 years

K = Strike Price = RM90

r= Risk-Free Interest rate = 4%

N= Cumulative Standard Normal Distribution

e= Exponential term

s= Annual volatility = 20%

ln= Natural Log

Plugging in the numbers, we get,

C = 20.868 i.e. the value of one option

Therefore, the value of 10,000 stock options = 10,000*20.868 = RM208,680

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