14
Employee CHAPTER Stock Options
Practice Questions
Problem 14.8.
Explain how you would do the analysis to produce a chart such as the one in Figure 14.2.
It would be necessary to look at returns on each stock in the sample (possibly adjusted for the
returns on the market and the beta of the stock) around the reported employee stock option
grant date. One could designate Day 0 as the grant date and look at returns on each stock each
day from Day 30 to Day +30. The returns would then be averaged across the stocks.
Problem 14.9.
On May 31 a companys stock price is $70. One million shares are outstanding. An executive
exercises 100,000 stock options with a strike price of $50. What is the impact of this on the
stock price?
There should be no impact on the stock price because the stock price will already reflect the
dilution expected from the executives exercise decision.
Problem 14.10.
The notes accompanying a companys financial statements say: Our executive stock options
last 10 years and vest after four years. We valued the options granted this year using the
BlackScholesMerton model with an expected life of 5 years and a volatility of 20%. What
does this mean? Discuss the modeling approach used by the company.
The notes indicate that the BlackScholesMerton model was used to produce the valuation
with T , the option life, being set equal to 5 years and the stock price volatility being set equal
to 20%.
Problem 14.11.
A company has granted 500,000 options to its executives. The stock price and strike price are
both $40. The options last for 12 years and vest after four years. The company decides to
value the options using an expected life of five years and a volatility of 30% per annum. The
company pays no dividends and the risk-free rate is 4%. What will the company report as an
expense for the options on its income statement?
The options are valued BlackScholesMerton using with S0 = 40 , K = 40 , T = 5 , = 0.3
and r = 0.04 . The value of each option is $13.585. The total expense reported is
500, 000 $13.585 or $6.792 million.
Problem 14.12.
A companys CFO says: The accounting treatment of stock options is crazy. We granted
10,000,000 at-the-money stock options to our employees last year when the stock price was
$30. We estimated the value of each option on the grant date to be $5. At our year end the
stock price had fallen to $4, but we were still stuck with a $50 million charge to the P&L.
Discuss.
The problem is that under the current rules the options are valued only onceon the grant
date. Arguably it would make sense to treat the options in the same way as other derivatives
entered into by the company and revalue them on each reporting date. However, this does not
happen under the current rules in the United States unless the options are settled in cash.
Further Questions
Problem 14.13
A company has granted 2,000,000 options to its employees. The stock price and strike price
are both $60. The options last for 8 years and vest after two years. The company decides to
value the options using an expected life of six years and a volatility of 22% per annum. The
dividend on the stock is $1, payable half way through each year, and the risk-free rate is 5%.
What will the company report as an expense for the options on its income statement?
The options are valued using Black--Scholes with K=60, T=6, =0.22, r =0.05. The present
value of the dividends during the six years assumed life are
1e-0.050.5+1e-0.051.5+1e-0.052.5+1e-0.053.5+1e-0.054.5+1e-0.055.5 = 5.183
The stock price, S0, adjusted for dividend is therefore 60 5.183=54.817. The Black--Scholes
model gives the price of one option as $16.492. The company will therefore report as an
expense 2,000,0005.183 or $32.984 million.
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