OV = PV + EV ...
Option value = promise value + exercise value ...
John, the reason you believe that OV does not equal PV+EV is because you ignored the time variable. I replaced the EV term with an IV term, because I redefined the time of valuation of this term. (Note: This proof is for non-qualified stock options.)
We start assuming the general equation, PV(t) = OV(t) - IV(t). The equation will be validated by showing it properly defines values at option grant and option exercise. Showing both PV(t) and IV(t) as positive non-zero values, not necessarily simultaneously, at some point during the option life will prove that the option value can be expressed as a sum of those terms.
Between the grant and exercise dates:
By definition, the conditional "promise value" is the option value minus the intrinsic value of the option. The employee stock option cannot be converted to cash on the open market, so the only relevant dates are the grant date and the exercise date.
[For t >= grant date and t <= exercise date, PV(t) = OV(t) - IV(t) = OV(t) - (P(t) - S)]
On the exercise date:
The exercise value is the intrinsic value of the option. The intrinsic value is, by definition, a positive non-zero value. Thus the "promise value" equals zero, i.e., the promise value immediately before exercise, if any, is forfeited. This agrees with the stock-based employee compensation deduction reported to the IRS, resulting in a tax benefit.
[When t = exercise date, OV(t) = IV(t), thus PV(t) = 0]
On the grant date:
The strike (exercise) price equals the stock price, making the intrinsic value of the stock option equal to zero. (This is the result of the "intrinsic value method" of SFAS 123.) Since the intrinsic value is zero, we see the value of the "conditional promise itself" is equal to the option value. This is the result of the "fair value method" of SFAS 123. This result can be shown to be a positive non-zero value.
[When t = grant date, IV(t) = P(t) - S = 0, thus PV(t) = OV(t)]
Therefore, PV(t) = OV(t) - IV(t) is a valid equation, and the option value can be said to be the sum of the "promise value" and the intrinsic value.
QED
The observant will notice the "promise value" as the time value of an option.
Ron
P.S.
Definitions:
Option Value, OV(t), current option value. Also present value of expected future difference between option strike price and stock price upon exercise.
Intrinsic Value, IV(t), current difference between option strike price (S) and stock price (P(t)).
Promise Value, PV(t), difference between option value and intrinsic value on current date.
Neither OV, nor IV, nor PV can be a negative value. |
