Risk Latte - Pricing Employee Stock Options (ESOP) as Forward Start Options

Pricing Employee Stock Options (ESOP) as Forward Start Options

Rahul Bhattacharya
Aug 01, 2005

One corporate finance chief of a large Asian IT corporation, whose stock price was publicly traded, recently confessed to one of our team members over a weekend beer conversation that he is battling hard with the issue of employee stock options (ESOP). His main problems were two fold: a) should he expense the cost of these options in his P & L account as is now becoming the rule (rather than exception and much more importantly, 2) how does he go about valuing these options.


Problem


His problem was as follows: his company is offering stock options to senior programmers and managers who complete 3.5 years of work (employment) in the company and these options could then be exercised into the common stock of the company after 5 years of the completion of work by the employee. This means, if a senior IT manager joins this company, he gets stock options – call options on the stock of the company - today which get vested in him only after he completes three and a half years of employment with the company and he can only exercise these options after another year and a half of remaining employed with the company. And the company has designed the option in such a way that these call options are vested in the employee after 3.5 years with a strike price which is 10% out of the money at that time. This was apparently done so that the economic benefit is not transferred from the existing shareholders to the new shareholder-employees.


The company, strangely enough (after all the bad publicity that stock options have received in the press after the dot com bubble burst) was issuing truck loads of these options to attract relatively junior, but talented IT professionals to senior and responsible positions. The CFO also said that the company had hired a payroll consultant as well as a management consultant to advise the senior management on this issue.


Solutions Suggested by the Consultants


Both these consultants have strongly suggested that the company use a Black-Scholes option pricing model for vanilla call options on the company’s stock to value these options. As for the volatility figure that should go as an input to the model, the consultants were divided over that issue, and ultimately it was decided that since there were no liquid single stock options on the company that were traded hence the 60 day implied volatility of the relevant (country) stock index should be used as a proxy for the volatility of the company. The cost of these options thus calculated should then be taken to the P & L account as an expense.


Our Thoughts on the Issue


Since the CFO didn't ask us for our opinion, none was offered to him. But we believe the company may soon have a big problem on its hand.


There are two major problems with what the consultants suggested to the company:


  1. First and foremost, the employee stock options that the CFO described to us is not a vanilla call option on the stock of a company, but rather a forward starting option, whose strike price is not fixed;


  2. And secondly, why the 60-day implied volatility of the index should go as an input to the BS model (as suggested by the consultants) to calculate the price of the forward starting call? Why not the 100 day EWMA historical volatility of the company stock returns? Or why not some other forecast is made of the long term volatility, which in our opinion would be a better measure as these employee stock options had five year maturity.


Anyway, we don't want to dwell on the second point too much. People have earned Ph.D.s dwelling on this problem and still scratch their heads when asked about it.


On point number one: the employee stock options described above are actually forward start call options and not vanilla call options. This simple, yet fundamental mistake in classification and eventual valuation, can ultimately cost a company millions of dollars in expenses!


In the forward start option with time to maturity T starts at the money or proportionally in or out of the money after a known elapsed time t in future such that 0 < t < T. The ESOP call option has a forward start feature since its strike price is not fixed when the employee begins to work. Rather, at that time, he is promised that he will receive stock options at a date in the future – three and a half years - conditional upon his continued employment. The strikes of these options are currently unknown, but will be set to be out of the money on the subsequent grant date, t, which is 3.5 years. The employee can exercise the options after 5 years from today, i.e. T is 5 years.


The value of a forward start call option is given in a closed form solution as:


CallESOP = CallForward Start = Se(b-r)*t{e(b-r)(T-t)N(d1)-α*e-r(T-t)N(d2}


Where,




α = moneyness of the option = 1.1 in our example
r = risk free rate
q = dividend yield
b = r-q
T = option maturity = 5 years in the example
t = option start date = 3.5 years in the example


Thus if we assume that the company's stock is trading at $100 currently and the 60-day implied volatility of the index is currently at 12% with risk free rate at 4% and the dividend yield at 3% the value of one 5year 110% forward start call starting after 3.5 years is $2.417.


If the company has issued 10 million such options (we are making an educated guess) then the total cost to be taken to the Profit and Loss account should be $24.17 million. The volatility input is very important as you can see from the following table. The table shows the value of the option and the charge to P & L for different levels of volatility:


Total number of Forward Start Call
options issued by the Company
10,000,000
Volatility
Price
Charge to P & L
8%
1.018
$ 10,180,000
9%
1.342
$ 13,420,000
10%
1.687
$ 16,870,000
11%
2.046
$ 20,460,000
12%
2.417
$ 24,170,000
13%
2.797
$ 27,970,000
14%
3.185
$ 31,850,000
15%
1.018
$ 35,790,000
16%
3.977
$ 39,770,000
17%
4.379
$ 43,790,000
18%
4.785
$ 47,850,000
19%
5.194
$ 51,940,000
20%
5.604
$ 56,040,000


Now suppose that the company uses a Black-Scholes-Merton model to price a 5 year vanilla call on the stock of the company with the same parameters. The price of 5-year vanilla call - using BS model - on a stock trading at $100 with strike $100 and volatility 12% is $7.537. Thus the company will have to take a charge of around $75 million for the 10 million options. This is significantly higher than $24 million charge that, according to us, is the fair value of the options under constant volatility assumption.


Therefore, thanks to the management consultants the company would be expensing roughly $50 million more in its P & L account on account of the ESOPs. We wonder how much the consultant would be charging the company for his advice.



Note: No matter how complex the mathematics or how difficult the concept the last word in option trading and valuation, according to us, is Nassim Taleb's book Dynamic Hedging. If you want to forget the math and yet understand all that is there to know about options valuation and trading then Nassim Taleb is the last word.

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