In a Dutch auction of 10,000 options, bids are as follows: A bids $30 for 3,000; B bids

Why was it attractive for companies to grant at-the-money stock options prior to 2005? What changed in 2005?

What are the main differences between a typical employee stock option and an American call option traded on an exchange or in the over-the-counter market?

Explain why employee stock options on a non-dividend-paying stock are frequently exercised before the end of their lives, whereas an exchange-traded call option on such a stock is never exercised early.

Stock option grants are good because they motivate executives to act in the best interests of shareholders. Discuss this viewpoint.

Granting stock options to executives is like allowing a professional footballer to bet on the outcome of games. Discuss this viewpoint.

Why did some companies backdate stock option grants in the US prior to 2002? What changed in 2002?

In what way would the benefits of backdating be reduced if a stock option grant had to be revalued at the end of each quarter?

Explain how you would do the analysis to produce a chart such as the one in Figure 16.2.

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?

The notes accompanying a companys financial statements say: Our executive stock options last 10 years and vest after 4 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

In a Dutch auction of 10,000 options, bids are as follows: A bids $30 for 3,000; B bids $33 for 2,500; C bids $29 for 5,000; D bids $40 for 1,000; E bids $22 for 8,000; and F bids $35 for 6,000. What is the result of the auction? Who buys how many at what price?

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 4 years. The company decides to value the options using an expected life of 5 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?

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.

What is the (risk-neutral) expected life for the employee stock option in Example 16.2? What is the value of the option obtained by using this expected life in BlackScholes Merton?

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 2 years. The company decides to value the options using an expected life of 6 years and a volatility of 22% per annum. Dividends on the stock are $1 per year, payable halfway 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?

A company has granted 1,000,000 options to its employees. The stock price and strike price are both $20. The options last 10 years and vest after 3 years. The stock price volatility is 30%, the risk-free rate is 5%, and the company pays no dividends. Use a four-step tree to value the options. Assume that there is a probability of 4% that an employee leaves the company at the end of each of the time steps on your tree. Assume also that the probability of voluntary early exercise at a node, conditional on no prior exercise, when (a) the option has vested and (b) the option is in the money, is 1 expaS=K 1=T where S is the stock price, K is the strike price, T is the time to maturity, and a 2. 1

(a) Hedge funds earn a management fee plus an incentive fee that is a percentage of the profits, if any, that they generate (see Business Snapshot 1.3). How is a fund manager motivated to behave with this type of compensation package? (b) Granting options to an executive gives the executive the same type of compensation package as a hedge fund manager and motivates him or her to behave in the same way as a hedge fund manager. Discuss this statement.