Chap24 - Chapter 24: Options and Corporate Finance:...

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Chapter 24: Options and Corporate Finance: Extensions and Applications 24.1 a. The inputs to the Black-Scholes model are the current price of the underlying asset (S), the strike price of the option (K), the time to expiration of the option in fractions of a year (t), the variance of the underlying asset ( σ 2 ), and the continuously-compounded risk-free interest rate (r). Mr. Levin has been granted 20,000 European call options on Mountainbrook’s stock with 4 years until expiration. Since these options were granted at-the-money, the strike price of each option is equal to the current value of one share, or $50. Therefore, the Black-Scholes inputs are: S = $50 σ 2 = 0.25 K = $50 r = 0.06 t = 4 After identifying the inputs, solve for d 1 and d 2 : d 1 = [ln(S/K) + (r + ½ σ 2 )(t) ] / ( σ 2 t) 1/2 = [ln(50/50) + {0.06 + ½(0.25)}(4) ] / (0.25*4) 1/2 = 0.7400 d 2 = d 1 - ( σ 2 t) 1/2 = 0.7400 - (0.25*4) 1/2 = -0.2600 Find N(d 1 ) and N(d 2 ), the area under the normal curve from negative infinity to d 1 and negative infinity to d 2 , respectively. N(d 1 ) = N(0.7400) = 0.7704 N(d 2 ) = N(-0.2600) = 0.3974 According to the Black-Scholes formula, the price of a European call option (C) on a non- dividend paying common stock is: C = SN(d 1 ) – Ke -rt N(d 2 ) = (50)(0.7704) – (50)e -(0.06)(4) (0.3974) = $ 22.8897 The Black-Scholes Price of one call option is $ 22.8897. Since Mr. Levin was granted 20,000 options, the current value of his options package is $457,794 (= 20,000 * $ 22.8897). 24.2 Kimberleigh’s total compensation package consists of an annual salary of $500,000 for 3 years in addition to 10,000 at-the-money stock options. Answers to End-of-Chapter Problems B-111
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First, find the present value of the salary payments. Since the payments occur at the end of the year, the payments can be valued as a three-year annuity, discounted at 10%. PV(Annual Salary Payments)
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This note was uploaded on 11/02/2011 for the course ACTSC 371 taught by Professor Wood during the Fall '08 term at Waterloo.

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Chap24 - Chapter 24: Options and Corporate Finance:...

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