## The Equity Equation

Thursday, July 19th, 2007

Paul Graham gives The Equity Equation:

An investor wants to give you money for a certain percentage of your startup. Should you take it? You’re about to hire your first employee. How much stock should you give him?

These are some of the hardest questions founders face. And yet both have the same answer:

1/(1 – n)

Whenever you’re trading stock in your company for anything, whether it’s money or an employee or a deal with another company, the test for whether to do it is the same. You should give up n% of your company if what you trade it for improves your average outcome enough that the (100 – n)% you have left is worth more than the whole company was before.

For example, if an investor wants to buy half your company, how much does that investment have to improve your average outcome for you to break even? Obviously it has to double: if you trade half your company for something that more than doubles the company’s average outcome, you’re net ahead. You have half as big a share of something worth more than twice as much.

In the general case, if n is the fraction of the company you’re giving up, the deal is a good one if it makes the company worth more than 1/(1 – n).

For example, suppose Y Combinator offers to fund you in return for 6% of your company. In this case, n is .06 and 1/(1 – n) is 1.064. So you should take the deal if you believe we can improve your average outcome by more than 6.4%. If we improve your outcome by 10%, you’re net ahead, because the remaining .94 you hold is worth .94 x 1.1 = 1.034. [1]

One of the things the equity equation shows us is that, financially at least, taking money from a top VC firm can be a really good deal. Greg Mcadoo from Sequoia recently said at a YC dinner that when Sequoia invests alone they like to take about 30% of a company. 1/.7 = 1.43, meaning that deal is worth taking if they can improve your outcome by more than 43%. For the average startup, that would be an extraordinary bargain. It would improve the average startup’s prospects by more than 43% just to be able to say they were funded by Sequoia, even if they never actually got the money.