Answer everything on a piece of paper using correct formulas showing all work 1.

Question

Answer everything on a piece of paper using correct formulas showing all work

1. Employee Stock Options Gary Levin is the chief executive officer of Mou Mr. Levin 25,000 at-the- money European call options on the company's stoc $55 per share. The stock pays no dividends. The options standard deviation of the returns on the stock is 61 percent. Treasury five years currently yield a continuously compounded interest rate of 6 percent. a. Use the Black-Scholes model to calculate the value of the stock options. b. You are Mr. Levin's financial adviser. He must choose between the previously men- k, which is currently trading at will expire in five years, and the bills that mature in tioned stock option package and an immediate $750,000 bonus. If he is risk-neutral, which would you recommend? c. How would your answer to (b) change if Mr. Levin were risk-averse and he could not sell the options prior to expiration?

Explanation / Answer

a.) Given that, Current Stock Price, S0=55,

Strike Price, K=55 (At the money option is carrying same strike price as current price)

Risk Free Rate, r=0.06,

Volatility, =0.61,

Time to Maturity, T=5 years

Continuously Compounded Dividend Yield, q = 0

Using relation, d1 = ln (S0/K) + (r+2/2) x T

          T

                          = ln (55/55) + (0.06 + 0.612/2) x 5

                                        0.615

                          = 0.00 + 1.23025

                 1.3640

                = 0.9019

Now, d2 = d1 - T

             = 0.9019 - 0.615

             = 0.9019 - 1.3640

             = -0.4621

European Call Price as per Black-Scholes Merton,

                  = S0 x N(d1) - {Ke-rT x N(d2)}

                  = 55 x N(0.9019) - {55e-0.06 x 5 x N(-0.4621)}

                  = 55 x 0.8164 - {55e-0.30 x 0.3220}

                  = 44.902 - 13.1199

                  = 31.78

Number of Options offered = 25,000

Value of Options offered =$31.78 x 25,000 =$794,500

b.) Immediate Bonus Offered =$750,000

Value of Options offered =$31.78 x 25,000 =$794,500

Since Mr. Levin, is risk-neutral, he will prefer the alternative with a higher payoff i.e. he will prefer going with options.

c.) If Mr. Levin is risk-averse and if the options cannot be sold prior to 5 years holding, the bonus of $750,000 will be preferrred alternative as it is paid immediately and is a more predictable alternative. He can then invest the proceeds in risk-free treasury bills to generate returns rather than remain locked for the next 5 years.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.