Solutions fundamentals of futures and options markets 7e by hull chapter 14

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CHAPTER 14 Employee Stock Options Practice Questions Problem 14.8 Explain how you would 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 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 company’s 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 executive’s exercise decision Problem 14.10 The notes accompanying a company’s financial statements say: “Our executive stock options last 10 years and vest after four years We valued the options granted this year using the Black–Scholes–Merton model with an expected life of years and a volatility of 20% ”What does this mean? Discuss the modeling approach used by the company The notes indicate that the Black–Scholes–Merton model was used to produce the valuation with T , the option life, being set equal to 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 using Black–Scholes–Merton with S0 = 40 , K = 40 , T = , σ = 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 company’s 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 once—on 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 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, σ =0.22, r =0.05 The present value of the dividends during the six years assumed life are 1×e-0.05×0.5+1×e-0.05×1.5+1×e-0.05×2.5+1×e-0.05×3.5+1×e-0.05×4.5+1×e-0.05×5.5 = 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 2,000,000×5.183 or \$32.984 million \ ... 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 years and. .. 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... current rules the options are valued only once—on 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
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