# Word Problems, or How to Shaft Your CTO

Issuing equity to an employee may seem like a simple process. Slap a title on him, give him some equity and a desk, if he hits a milestone, give him another chunk of equity.

Easy, right? OK. Here’s a word problem.

A founder hires a CTO and promises to give him 10% of the company’s stock. If the company hits a certain milestone, the CTO will get an additional 10%. There are currently 100 shares outstanding. Assuming the company hits the milestone, how many shares will the CTO have?

Is the answer: a) 23.45, b) 25 or c) 20?

Like all contractual matters, the right answer is whatever the parties agreed to. The problem is that reasonable parties can reach different conclusions. However, there is only one right answer.

Answer c) is a rookie mistake. A first-timer would multiply 100 x 20% and come up with 20. There’s a problem with that formula: if the CTO received 20 shares, he would actually only have 16.67% of the company (20/120 = 16.67%).

Answer b) is better, but it assumes everything will go according to plan, which rarely happens. You get 25 if you do a little algebra:  x/(100+x) = .8, or x = 25. That’s a better attempt, but what happens if the company doesn’t hit the milestone? Then the CTO presumably ends up with only 12.5 shares. In that case, however, the CTO would end up with 11.11% of the company. That’s probably not what anyone had in mind.

Answer a) is the number a judge would probably come up with. And because judges are always right, that’s the right answer. To get to 23.45, you assume that the CTO will get 10% on his start date (x/(100+x)=.1, or x=11.11), and then another 10% when the milestone is hit (x/(111.11+x)=.1, or x=12.34. Using that analysis, if the milestone is never hit, then the CTO receives only 10% of the company. If the milestone is hit, then he ends up with a total of 23.45 shares, which is 18.995% of the company. Why? Because the second 10% grant actually dilutes the first 10%.

None of the numbers in any of the situations is probably what anyone anticipated when the CEO and CTO shook hands. That’s one of the many reasons to get things in writing as quickly as possible.

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### 3 Responses to Word Problems, or How to Shaft Your CTO

1. Mike F. says:

Great post to highlight the complexities of compensation and cap tables. What do you think about elements of time and dilution protection? For example, somewhere between the initial grant and hitting the milestone the company has an event that greatly improves the value (and/or the # of shares).

• Joel Nied says:

There’s no hard and fast rule. If I were representing the company, I would tell the grantee that dilutions are expected and his equity will be worth a lot more post-investment/dilution due to the added value of the investment, etc. If I were representing the grantee, I would be most concerned about a self-dealing investment that substantially dilutes the grantee, or an investment at a very low valuation. Ultimately, it’s all about negotiating leverage. If a hotshot comes in and says he doesn’t want to be diluted by the next investment round, agreeing to it might be the right thing to do. If a company gives out dilution-proof equity to one person, however, keep in mind the dilution effect will be amplified for everyone else. And it’s impossible for everyone to have dilution-proof equity.

• Ned Lilly says:

Agreed. We’ve found that one class of stock, everybody gets diluted equally, is the easiest to manage. Someone who’s more concerned with keeping his nest feathered, than growing the company, is probably not the right hire for a startup anyway.