Sally Jameson Valuing Stock Option in a Compensation Package-Result

Financial Engineering Case

Study

Sally Jameson: Valuing Stock Option in a

Compensation Package

2012/5/31

CASE REVIEW

Ms. Jameson was facing a choice when she got her first job after the graduation of her MBA degree. When she found a wonderful job in the company Telstar, she can get bonus besides the regular salary. Now she had the choice of either $5,000 in cash or 3,000 options on Telstar’s stocks.

The detailed information can be as follows:

Each option granted the owner to buy one share of Telstar stock at $35 on the exact 5 years later. The spot price of that stock is $18.75.

But the option will be rejected if Sally leaves the company during the first five years. Now the problem Sally faced with is whether she should get bonus in case or bonus as options. Also some market data are given in the case.

QUESTION ANSWER

QUESTION 1

What is the implied volatility of the Telstar call with a strike price of $20 and an expiration date of January 22, 1994?

ANSWER

Using Excel, we form the Black-Scholes Formula, so that we can use the function of single variable solution to get the implied volatility.

We have already known stock price, exercise price and option price.

From May 27, 1992 to Jan 22, 1994, there are 604 days left, so it’s nearly 1.65 years. In addition, we have got the table of Treasury Bonds’ BEY (Bond Equivalent Yield), so all we need to do is to change them into continuous compounded rates.

∵BEY=1000?P

×

1

∴(1+r)T=1000

P

=BEY×T+1

∴r=BEY×T+1

T?1

And cc = ln(1+r)

BEY r cc 1year 4.02% 4.02% 3.94% 2year 5.25% 5.12% 4.99%

Then we can input these variables to the spreadsheet, and get the implied volatility of this call option to be 38.4%

Current price of underlying common

stock

S = 18.75 Exercise price K = 20

Risk-free rate (continuously compounded) r=

4.63%

Time to expiration t = 1.65 Volatility (continuously compounded) σ= 38.40%

QUESTION 2

If we ignore tax considerations and assume that Sally Jameson is free to sell her options at any time after she joins Telstar, which compensation package is worth more?

ANSWER

First of all, we should find out the characteristics for the stock options in that compensation package.

From the sentence “the options represent the right to buy Telstar stock at a set price, after a set period of time”, we can know that the options are European Options.

Its strike price is $35, its maturity is 5 years. The current stock price is $18.75. And we also calculate the continuously compounded interest rate of a five-year treasury bond to be 5.26%.

So, the only thing unknown is the volatility. Since we have got the implied volatility of the options sold in the market, we could reasonably guess the implied volatility of Sally’s options.

In the reality, the volatility smile for equity options should be like this:

So, with a strike price of $35, which is much higher than the current price of $18.75, we guess the implied volatility should be lower than 38%.

Current price of underlying common stock S =

18.75

Exercise price

K = 35

Risk-free rate (continuously compounded)

r=

5.26%

Time to expiration t = 5

Volatility (continuously compounded) σ=

?

From different scenarios assuming different σ, we can calculate different option prices and total values as shown in the table below.

σ

23.34%

25%

30%

35%

38%

c X 3000 5000 5760 8160 10650 12180

We don’t think the volatility can be lower than 23%, so, we suggest Sally to select the stock options.

QUESTION 3

How should we factor in the complications ignored in the above question? How would they affect the value of the options to Ms. Jameson? What should she do? Why?

ANSWER

Assume that Sally accepts cash, invests it and reinvests the interest with 5-year T-bond rate 5.4%. Considering the tax, the future value in year5 will be $4357.

1 2 3 4 5

3600 3740 3886 4037 4194 beginning

balance

interest 195 202 210 218 227

tax 54 57 59 61 63

ending balance 3740 3886 4037 4194 4357

What about accepting the options? Since they’re European options, the current option price is the present value of the expected future payoff. Thus

E(π)＝c * e rT=$3.57

38%

σ23.34% 25% 30% 35%

2.17 2.50

3.54

4.62

5.28

Expected

payoff

So, even if the volatility is so low as 23%, the expected income is still higher than the future value of cash compensation.

However, Sally should also consider the likelihood that she might not stay at Telstar that long. To calculate the breakeven point, we think a volatility of 30% is reasonable and we suppose the probability she leaves before year 5 is k. Let 7724*(1-k)=4357, the solution is k=44%, which means if Sally has a probability of leaving the company before year 5 larger than 44%, she should select cash compensation. Otherwise, she should select stock options.

What if Ms. Jameson decided that the option was a better deal, but that she didn’t want all of her financial wealth (as well as her human capital) tied to the fortunes of Telstar? Assuming she works at Telstar and accepts the option grant, is there anything she can do to “untie” some of her wealth from Telstar?

ANSWER

The idea to “untie”the wealth is that to “transfer”some or all of option value to reinvest in other assets including cash.

a)Though usually not the case in reality, if Ms. Jameson can sell the options, trading

part of the options in the market is one way to untie the signing bonus from The Telstar, she can reinvest the money she will get in other assets.

b)Ms. Jameson can also short the stocks or stock futuresof Telstar. Since stock

futures often have higher prices, we suggest a short position of stock futures. Assuming 30% volatility, Δ=0.39, which means if we choose stock as hedging derivative, to completely “untie”the stock option, Ms. Jameson only needs 0.39*3000=1170 shares of stock. To partly untie, she can short an amount like 500 shares.

Does granting stock options cost companies anything? If so, who pays? What incentives do executive stock option plans create for their recipients?

ANSWER

About Cost:

a)Now both in America and in China, stock options to employees are required to be

expensed in company’s financial statements by accounting rules. Therefore, though not affected financially, stock options draw down the income numbers in financial reports of the company, which

b)If eventually the employees exercise the options, since the company usually issue

new stocks to the employees instead of purchasing in the market, there will be dilution effect, resulting in lower price of the stock in the whole market, which means the other stockholders are paying for the exercising of stock options.

Incentives:

Stock options connect the benefits of the company and the executives by directing them to work for the goal of the company: if the executives want to realize the possible capital gain of exercising the stock options, they need to work hard to boost the value of the firms.