Question

Problem 23-2 Employee Stock Options Jared Lazarus has just been named the new chief executive officer of BluBell Fitness Centers, Inc. In addition to an annual salary of $632,500, his three-year contract states that his compensation will include 29,250 at-the-money European call options on the company's stock that expire in three years. The current stock price is $50 per share and the standard deviation of the returns on the firm's stock is 60 percent. The company does not pay a dividend. Treasury bills that mature in three years yield a continuously compounded interest rate of 3 percent. Assume that the annual salary payments occur at the end of the year and that these cash flows should be discounted at a rate of 12 percent Use the Black-Scholes model to calculate the value of the stock options. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Determine the total value of the compensation package on the date the contract is signed. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Stock options Compensation package

Answer 1

a) answer:

i am sharing the excel working and the formula and how i use excel to solve this formula is given here.

C D E 632500 29250 50 salary no. of call options time in years (T) current stock standard deviation risk free rate discount rate strike price Formula: 0.6 0.03 0.12 50 11 12 13 15 c=S, N(d)-Ke-N(d) p=Ke " N(-d,)-S, N(-d.) where d. - In(S, /K)+(r+02/2) OVT In(S,/K)+(r-62/2) OT

=((LN(C6/C10)+(C8+C712/2)*C5)/C7*SQRT(C5)) =H2-C7*SQRT(C5)) Call Price =C6*NORMSDIST(H2)-C10*EXP(-C8*C5)*NORMSDIST(H3) Value of options 29250 * 12.535= =H5*29250

solution:

1.818653348 0.779422863 d2 Call Price 12.53502837

b) compensation package value =

Value of options 29250 * 12.535= 366649.5797

present value of his salary =

cashflows/(1+r)

= 632500 /(1.12)^1+632500/(1.12)^2+632500/(1.12)^3

= 1519158.277

total compensation = 1519158.277 + 366649.5797 = 1885807.857

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