Hi Huey, yes this n*(P-S) turns out to be the cost of dilution. Pre-tax, that is. To all parties.
We almost worked it all out on the QCOM thread.
Let's say that the company is worth "A", equal to the present value of all of its future profits, plus its assets. Then a shareholder owns an asset worth A/N where N is the number of shares outstanding. And assuming that the price of a slice is fair, then market price P = A/N
Add n more shares, and one gets diluted to own A/(N+n)
Except that when the dilution is by stock options, the company gets the premium that shareholders contribute. Namely n*S
So we have Value Before = A/N, and Value After = (A+n*S)/(N+n)
Thus the cost of dilution is A/N - (A+n*S)/(N+n)
A bunch of smart people have looked at this and agree fully.
The next step is to re-arrange terms, and reduce to the common denominator, which is n/(N+n). But without skipping steps...
...have Dilution
Cost Per Share = A/N -(A+n*S)/(N+n)
= (N+n)*A/[N*(N+n)]- N*(A+n*S)/[N*(N+n)]
= [(N+n)*A - N*(A+n*S)] /[N*(N+n)]
= [ N*A + n*A -(N*A + N*n*S)] /[N*(N+n)]
= [ n*A - N*n*S ] / [ N*(N+n)]
= n * [A/N - S ] / (N+n)
= n * [P - S ] / (N+n)
Times (n+N) shares = n * [P - S ]
Total cost of dilution to all shareholders is n*[P-S].
Now, this is the case when we assume shares are fairly priced. In actual practice shares trade at some difference to fair price. A bit of rather horrendous math shows that all of the additional cost due to market mispricing is born by the shareholders who buy the shares at this mispriced value. If you hold a $20 bill and I buy one from your brother for $50 that doesn't mean you hold a $20 worth $50. It just means I lost $30.
Anyway, the cost of dilution to shareholders equals n*[P-S].
The benefit to the option holder equals n*[P-S]
This kind of stands to reason, that whoever gets value gets the same value that the person providing loses. There is no free lunch.
And not surprising, the cost reported to the IRS is n*[P-S] too.
Gee... I wonder what the (pre-tax) value of a stock option turns out to be when it is exercised???
John |
