Thursday, June 12, 2008

Sally Jameson: Valuing Stock Options in a Compensation Package

Executive summary

Jameson needs to choose either stock option compensation package or cash compensation package if she joins Telstar. If she can sell her options during 5-year vesting period, the stock option package is worth more than the cash package. If she is not allowed to sell her option during 5-year vesting period, cash package is worth more than stock option package. In considering option liquidity, taxes and transaction costs, we conclude that cash package is worth more than stock option package and therefore, Jameson should choose cash package. If Jameson decided to choose stock option package, she should untie her wealth to the fortunes of Telstar by either entering a forward contract on stocks or using bull spread strategy to insure her long call position. In doing so, the value of her options will not totally depend on Telstar’ stock price. As a result, she can get some benefits even if her options turn to be worthless at expiration.

1. Options or cash compensation

a. Cash compensation:

If Jameson chose cash compensation package and if there is no tax, she will receive $5000 today. If she used this money to invest in 5-year T-bills, the future value of her compensation would be worth: $5000 x 1.0602 = $5301 in 5 years (5-year T-bills’ interest rate is 6.02% in the Exhibit 4).

b. Stock option compensation:

If Jameson chose stock options, she would hold European 3000 call options (early exercise is impossible) on stocks without dividends which give her the right to buy Telstar stocks at the strike price $35 per share in the 5th year from the date she joins Telstar. The option price is $2.65 (please refer to Appendix 01 for detailed option price calculation). Total value of 3000 call options that Jameson would receive is 3000 x $2.65 = $7943 (taxes and transaction costs are ignored), which is option premiums that Jameson can receive if she sells her 3000 granted options.

c. Cash or stock options?

If Jameson holds options until maturity:

- If Telstar’s stock price is below strike price ($35 per share), Jameson will not exercise her options and therefore will get nothing (she does not pay option premiums by cash).

- If Telstar’s stock price is above strike price, Jameson will exercise her options, sell shares and get profits = 3000 x (stock price – strike price).

- In order to have the same profit as that of cash compensation, the stock price must rise up to $5301/3000 + $35 = $36.767 per share.

- From the Exhibit 2, we see that Telstar’s stock price only rose to $35 per share in 1990 during the last 10 years. It means that the chance of the rise of stock price to above $35 par share is very rare. Therefore, if Jameson holds options until maturity, she will risk receiving nothing from the stock option compensation package.

If Jameson sells options after she joins Telstar:

- The profit from selling 3000 call options is $7943, assuming that there is no transaction costs, no taxes and it is easy to sell such options. As $7943 is greater than profit of cash compensation, we would say that stock option compensation is worth more than cash compensation.

d. Conclusion

If Jameson is free to sell her options at any time after she joins Telstar, and if there is no taxes and no transactions costs, stock options package is worth more than cash compensation.

2. Choosing the compensation package

It seems that option package is better than cash package. However, Jameson needs to consider other factors before choosing the best package.

- Options liquidity: Most companies granting stock options compensation packages do not allow their employees to sell options in the vesting period. There is no information in the case about the right to sell options. If Jameson is not allowed to sell her options at any time after she joins Telstar, she risks receiving nothing from option compensation package at the expiration time of options as discussed above. In other words, if she has to hold options until expiration, the value of her options would be easily zero at expiration.

- Early exercise: As options granted to Jameson are European calls, she can not exercise them before expiration. If she left Telstar before her 5th year with Telstar, she would get nothing. Her options will be, therefore, worthless to her.

- Taxes: If taxes are considered, Jameson will receive $5000 x (1-0.28) = $3600 today and $3600 + {$3600 x 6.02% x (1-0.28)} = $3769.04 in 5 years from cash package. In order to have the same profit as that of cash compensation, the stock price must rise above $3769.04/3000 + $35 = $36.256 per share. In such case, the value of her options must be at least ($36.256-$35) x 3000 = $3769.04. However, the chance of rise in stock price above $36.256 is even rare. As a result, taxes make the options be worthless easier. Besides, there is no advantage of tax treatment to her between cash package and option package as tax on Jameson’ salary would equal to tax on capital gains (28%).

- Conclusion: From the above analysis, we see that it is very easy that Jameson receives nothing if she chooses stock option package. Hence, she would better to choose cash compensation package. By doing so, she will have cash right after joining Telstar and will be free to leave the company if she finds a better opportunity.

3. Stock options compensation package from the view of granting companies

Employee stock options are the same as call options. Unlike call options, employee stock options are corporate securities issued by corporations. Corporations are the option writers and employees are option holders. Option holders pay strike prices to corporations when they exercise options. As a result, corporations will receive cash and issue new shares. At expiration, corporations will have more cash and more outstanding shares.

Granting stock options costs companies the value for which options are sold. In fact, companies do not pay for such value directly. Instead, this value will be deducted in employees’ cash compensation. In other words, employees pay for options value by receiving less cash compensation by an amount equivalent to options value. From the accounting view, this options value can be regarded as non-cash operating expenses to corporations.

Executive stock option plans create some incentives for their recipients:

- Tax reduction: as tax on individual income is higher than tax on capital income, stock options can help executives avoid tax payment on their high income and pay less tax on capital gains by converting part of their income to capital gains.

- Feeling of ownership: By granting stock options, the firm creates the feeling of ownership in the mind of its executives so they take actions in the interests of shareholders.

The purpose of creating incentive plans is to lure talented employees, keep excellent employees and motivate them to act consistently with the interests of shareholders with less cost to the firm. Stock option compensation plans have become popular nowadays because these incentive plans provide firms with several advantages:

- Minimize the firm’s compensation costs

- Conserve cash because the firm does not pay cash through option granting

- Avoid the limits on the tax deductibility of cash compensation

- Solve agency problems by aligning managers’ incentives with shareholders’ interests

While stock option packages bring granting firms with the above advantages, they are somehow worth for executives with high salaries but not worth for employees with low salaries. The biggest incentive of such compensation plans to receivers is to decrease tax payment on incomes. As discussed through the case of Jameson, it is very rare that employees can exercise options because the vesting period is long and options risk being worthless at expiration. It is, therefore, better that companies can create cash compensation programs that motivate employees and cost less.

4. Recommendations for Jameson

If Jameson accepts option package and works for Telstar, she should untie her wealth from the fortunes of Telstar by using bull spread strategy, which is to sell identical call options (option A) with higher strike price, for instance $40, to insure her long call position. Buy selling option A at $40 strike price, she can get option premiums. If Telstar’s stock price will not rise to $35, she will not exercise options granted by Telstar but can get option premiums to compensate her losses from not being able to exercise options. If stock price rises above $35, she will exercise options granted by Telstar and gain profits = stock price – $35. If stock price rises above $40, she will exercise options granted by Telstar and gain profits = stock price – $35 while delivering stocks to the holders of option A and get a loss = $40 – stock price. However, the overall profit when stock price is greater than $40 is positive. As a result, she can insure the benefits of her options regardless of increase or decrease in Telstar’s stock price.

The second way to untie her wealth to Telstar is to enter a forward contract in which she will pay a certain amount of money if stock price rises above $35 and receive a certain amount of money if stock price is below $35. If stock price is above $35, she has to give up a portion of the benefits from exercising options to pay the counterparty of the forward contract. If stock price will not rise above $35, she still gets money from the counterparty. By doing so, she can receive a certain amount of money regardless of increases or decreases in Telstar’s stock price.

Appendix 01: Option price calculation

1. Binomial Model


1. Single date: time 0 and time 1.

2. Stock price can go up or down.

3. Perfect market: there is no transaction costs, borrowing and lending at

interest rate, no taxes.

4. Volatility on stock return is historical volatility that is assumed 30% based on Exhibit 3.


Current stock price (s) $ 18,75
Divident yield (di) 0
Volatility of stock return (sd) (historical volatility) 0,3
Strike price (x) $ 35
Time to expiration (t) years 5
Risk-free rate (rf) % 0,0602
Number of steps (n) 1000

Price of European call option ($) 2,92
Total value of 3000 options granted to Jameson 8.760

VBA codes:

Function Euro_call(s, di, sd, x, t, rf, n)

'calculate price of a Europeran call option by Binomial tree model'

Dim u As Double

Dim d As Double

Dim p As Double

Dim bicomp As Double

Dim sumbi As Double

Dim h As Double

Dim j As Integer

'calculate u,d,p'

h = t / n

u = Exp(sd * Sqr(h))

d = Exp(-1 * sd * Sqr(h))

p = (Exp((rf - di) * h) - d) / (u - d)

'calculate expected call payoff at time t'

For j = 1 To n

bicomp = Application.Combin(n, j) * (p ^ j) * ((1 - p) ^ (n - j)) * Application.Max(s * (u ^ j) * (d ^ (n - j)) - x, 0)

sumbi = sumbi + bicomp

Next j

'calculate call price = PV of expected payoff'

Euro_call = sumbi * Exp(-1 * rf * t)

End Function

2. Black-Scholes Model


1. Risk-free rate at 6.02% (Exhibit 4) is assumed to be known and constant in the next 5 years.
2. There are no transactions costs and no taxes.

3. It is possible to short-sell the options and and to borrow at the risk-free rate.
4. Stock pays no dividend during the option life (5 years).

5.Markets are efficients.

6. Implied volatility is calculated by opserving market prices of the option. However, in this case
report, I assumed that implied volatility is equal to historical volatility at 30% and I ignored the
computation of implied volatility on stock return based on the information given in Exhibit 1.
This is because of the complexity of calculating and predicting implied volatility from information
given in the case.


Current stock price (s) $ 18,75
Strike price (k) $ 35
Volatility of stock return (v) (implied volatility) 0,3
Risk-free rate (rf) % 0,0602
Time to expiration (t) years 5
Divident yield (d) 0

Price of European call option ($) 2,65

Total value of 3000 call options granted to Jameson, $ 7.943

VBA codes:

Function Euro_callBS(s, k, v, r, t, d)

'calculate price of a Europeran call option by Black-Scholes model'

Dim d_1 As Double

Dim d_2 As Double

Dim nd1 As Double

Dim nd2 As Double

'Calculate N(d1) and N(d2)'

d_1 = (Application.Ln(s / k) + (r - d + 0.5 * (v ^ 2) * t)) / (v * (t ^ 0.5))

d_2 = d_1 - v * (t ^ 0.5)

nd1 = Application.NormSDist(d_1)

nd2 = Application.NormSDist(d_2)

'Calculate option price'

Euro_callBS = s * Exp(-d * t) * nd1 - k * Exp(-r * t) * nd2

End Function

3. Option price

The option price by Binimial model is higher than the price obtained from Black-Scholes model.
Because it is very difficult to estimate accurately future implied volatility of returns on Telstar's
stocks in 5 years, the price by Black-Scholes model seems to be less reliable.

However, to be conservative, I chose the option price $2.65 by Black-Scholes model for the analysis
of the case.


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