Diluted shares and the treasury stock method
Why options add fewer shares than there are options, and why dilution grows as the share price rises.
- Calculate diluted shares with the treasury stock method
- Explain why only in-the-money options count, and why RSUs count in full
- Work back from net new shares to the strike price
- Explain why a higher share price means more dilution
The intuition
Ten employees each hold an option to buy one share at $15. The shares trade at $20, so every one of them will exercise: they pay the company $15 and receive a share worth $20.
The company issues ten new shares, but it also receives $150 of cash. The treasury stock method assumes it spends that cash buying its own shares back at $20: that buys 7.5 shares. So the real dilution is only 2.5 new shares, not ten.
Options only dilute by the part the strike money cannot buy back. That part is 1 − strike ÷ price of the options, so the further in the money they are, the more they dilute.
Why it works
- Only in-the-money options count. If the strike is above the share price nobody would pay it, so those options add nothing.
- Exercise brings cash in. Options × strike is the cash the company receives.
- That cash buys shares back at the market price: proceeds ÷ price.
- Net new shares are the options less the shares bought back.
- Restricted stock units have no strike and bring in no cash, so these questions add every one in full.
- Diluted shares = basic shares + net new shares from options + RSUs. Equity value in the bridge uses this count.
| Exercise proceeds: 10M × $15 | $150M |
| Shares bought back: $150M ÷ $20 | 7.5M |
| Net new shares: 10M − 7.5M | 2.5M |
| + RSUs, in full | 2.0M |
| = Diluted shares: 100M + 2.5M + 2.0M | 104.5M |
| If the price were $30: $150M ÷ $30 buys back 5M | 107.0M |
Net new shares are 25% of the options, which is 1 − $15 ÷ $20.
The formulas
The cash holders pay in when they exercise.
What that cash buys back at the market price.
The dilution the proceeds cannot undo.
Every share that would exist if in-the-money claims turned into shares.
The share of options bought back, times the price, is the strike.
Worked example
A full diluted share count. Check the options are in the money before you do anything else.
See it move
Same company. Change the share price, the strike, the number of options and the RSUs.
- Slide the strike up toward the share price. The proceeds grow, more shares are bought back, and net new shares shrink toward zero.
- Slide the strike down. The lower the strike, the closer net new shares get to the full number of options.
- Raise the share price. The same proceeds buy back fewer shares, so dilution rises.
- Compare the +20% bars: net new shares are always higher at the higher price, because the buyback always shrinks.
Run it backwards
Same company, reversed: you know the price, the options and how many net new shares they add. What is the strike?
Options less net new shares is the number bought back. Bought back × share price is the cash that paid for them, which is the exercise proceeds. Divide by the options and you have the strike.
In a real filing the stock compensation note gives the weighted average strike directly. Running it backwards is how you check a diluted share count someone else built.
Traps
Say it in the interview
“How does the treasury stock method work?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- Only in-the-money options count.
- Net new shares = options − (options × strike ÷ price).
- RSUs are added in full.
- A higher share price means more dilution: rerun at the offer price.