Question

A company’s stock price is $50 and 10 million shares are outstanding. The company is considering giving its employees three million at-the-money five-year call options. Option exercises will be handled by issuing more shares. The stock price volatility is 25%, the five-year risk-free rate is 5% and the company does not pay dividends. Estimate the cost to the company of the employee stock option issue.

Answer 1

Given stock price S= $50

Strike price K = $50

Risk free rate r = 0.05 = 5%

Volatility = standard deviation = s= 25% = 0.25

Time period t= 5 years

Firstly, let us calculate price of option using Black Scholes model

Option price = [S *N (d1)] –[ N (d2)*K*e^-rt]

Here N (d1) and N(d2) are normal distribution variables.

d1 = [log (S/K) + (r + s^2/2) *t]/ s * sqrt (t)

d2 = d1 - s * sqrt(t)

d1 = [log (50/50) + (0.05 + 0.25^2/2) *5]/ 0.25 * sqrt (5)

= [0 + 0.40625]/0.559016 = 0.7267

d2 = 0.7267- 0.25 * sqrt (5) = 0.1677

N(d1) = NORMSDIST (0.7267) = 0.7663 (where NORMSDIST is the excel function for cumulative probability density function)

N(d2) = NORMSDIST (0.1677) = 0.5666

Option price = [S *N (d1)] –[ N (d2)*K*e^-rt]

= (50*0.7663) – (0.5666* 50*e^-0.05*5)

= 38.315 – 22.06342618= 16.2515

Price = $16.252

Cost to company per option = [10 million/(10 million + 3 million)] * 16.252 = $12.5015

Cost to company per option = $12.5. The total cost = 3million times $12.5 = $37.5 million

Therefor total cost to company due to employee stock option issue = $37.5 million