Question

A company has granted 2,000,000 options to its employees. The stock price and strike price are both $70. The options last 8 years and vest after 2 years. The company decides to value the options using an expected life of 6 years and a volatility of 30% per annum. Dividends on the stock are $1.50 per year, payable halfway through each year, and the risk-free is 5%. What will the company report as an expense for the options on its income statement?

1) $44,648,028.58
	2) $44,082,648.58
	3) $44,028,648.58
	4) $44,028.468.84

Answer 1

The answer is 3) $44,028,648.58.

We need to Black-Scholes -Merton model to calculate value of the option. first we need to calculate present value of dividend and adjusted the stock price with the present value of dividend.

Dividend is  payable halfway through each year.

Present value of dividend = $1.5*e^-0.05*0.5 + $1.5*e^-0.05*1.5 + $1.5*e^-0.05*2.5 + $1.5*e^-0.05*3.5 + $1.5*e^-0.05*4.5 + $1.5*e^-0.05*5.5 = $1.5*e^-0.025 + $1.5*e^-0.075 + $1.5*e^-0.125 + $1.5*e^-0.175 + $1.5*e^-0.225 + $1.5*e^-0.275 = $1.5*0.9753 + $1.5*0.9277 + $1.5*0.8825 + $1.5*0.8395 + $1.5*0.7985 + $1.5*0.7596 = $1.463 + $1.392 + $1.324 + $1.259 + $1.198 + $1.139 = $7.775

Stock price after adjustment = $70 - $7.775 = $62.225

Value of the option

Call Option input data		Output data
Stock price	$62.23	d1	0.6155
Strike price	$70.00	d2	-0.1194
Time (in years)	6.0000	N(d1)	0.7309
Interest rate	5.00%	N(d2)	0.4525
Volatility	30.00%
Dividend yield	0.00%
Call option value	$22.014

Formula and calculation

the company will report 2,000,000*$22.014 = $44,028,000 as an expense for the options on its income statement.

The small difference of $648.58 is due to rounding-off.