The Equity Equation
Paul Graham presents a simple equity equation 1/(1-n) for founders to evaluate whether accepting investment, hiring an employee, or making a deal is worth giving up a percentage of the company. The rule: a deal is good if it improves the company's average outcome by more than 1/(1-n). Examples include Y Combinator's typical 7% deal and Sequoia's 30% deal. The article also derives the formula for granting stock to employees (n=(i-1)/i) and discusses adjusting for salary and overhead. While real decisions require judgment, the equation provides a rational framework.
July 2007
2007年7月
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)
投资者想用一笔钱换取你初创公司的某个百分比，该接受吗？你正准备招聘第一位员工，该给他多少股票？
这些都是创始人面临的最棘手问题。然而，它们的答案相同：
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 7% of your company. In this case, n is .07 and 1/(1 - n) is 1.075. So you should take the deal if you believe we can improve your average outcome by more than 7.5%. If we improve your outcome by 10%, you're net ahead, because the remaining .93 you hold is worth .93 x 1.1 = 1.023.
当你用公司股票交换任何东西——无论是资金、员工还是与其他公司的交易——判断是否该做的标准是一样的。如果交换来的东西能足够提升你的平均结果，使得你剩下的 (100 - n)% 比之前整个公司更值钱，那么你就应该放弃 n% 的公司股份。
例如，如果投资者想买你一半的公司，那么这笔投资需要将平均结果提升多少才能让你不亏不赚？显然需要提升一倍：如果用一半公司换来让公司平均结果翻倍不止的东西，你就净赚了。你拥有了一半股份，但公司价值超过原来的两倍。
一般情况下，如果 n 是你放弃的公司股份比例，那么这笔交易是否划算，取决于它能否让公司价值超过 1/(1 - n)。
例如，假设 Y Combinator 提出用资金换取你公司 7% 的股份。此时 n 为 0.07，1/(1 - n) 为 1.075。所以，如果你相信我们能将你的平均结果提升 7.5% 以上，就该接受。如果我们将结果提升 10%，你就净赚了，因为剩下的 0.93 股份相当于 0.93 × 1.1 = 1.023。
[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.
The reason Sequoia is such a good deal is that the percentage of the company they take is artificially low. They don't even try to get market price for their investment; they limit their holdings to leave the founders enough stock to feel the company is still theirs.
The catch is that Sequoia gets about 6000 business plans a year and funds about 20 of them, so the odds of getting this great deal are 1 in 300. The companies that make it through are not average startups.
Of course, there are other factors to consider in a VC deal. It's never just a straight trade of money for stock. But if it were, taking money from a top firm would generally be a bargain.
[1]股权公式告诉我们的一件事是，至少从财务角度看，接受顶级风投公司的资金可能是一笔非常划算的交易。红杉资本的 Greg Mcadoo 最近在 YC 的一次晚宴上说，红杉单独投资时通常要拿走公司约 30% 的股份。1/0.7 = 1.43，意味着只要他们能将你的结果提升 43% 以上，这笔交易就值得。对于一家普通初创公司来说，这绝对是超值。光是能说“我们得到了红杉的投资”这一点，就能将普通初创公司的前景提升超过 43%，哪怕实际上根本没拿到钱。
红杉之所以如此划算，是因为他们要的股份比例被人为压低。他们甚至不试图按市场价获取投资回报；他们限制持股比例，让创始人觉得公司仍然是自己的。
但问题是，红杉每年收到大约 6000 份商业计划书，只投资其中约 20 家，所以获得这笔好交易的概率是 1/300。那些通过筛选的公司并非普通初创公司。
当然，VC 交易中还有其他因素需要考虑。它从来不是简单的用股票换资金。但如果真是这样简单，从顶级风投拿钱通常是一笔划算的买卖。
You can use the same formula when giving stock to employees, but it works in the other direction. If i is the average outcome for the company with the addition of some new person, then they're worth n such that i = 1/(1 - n). Which means n = (i - 1)/i.
For example, suppose you're just two founders and you want to hire an additional hacker who's so good you feel he'll increase the average outcome of the whole company by 20%. n = (1.2 - 1)/1.2 = .167. So you'll break even if you trade 16.7% of the company for him.
That doesn't mean 16.7% is the right amount of stock to give him. Stock is not the only cost of hiring someone: there's usually salary and overhead as well. And if the company merely breaks even on the deal, there's no reason to do it.
给员工股票时也可以使用同一个公式，但方向相反。如果 i 是公司增加某位新人后的平均结果，那么他价值 n，满足 i = 1/(1 - n)。这意味着 n = (i - 1)/i。
例如，假设你们只有两位创始人，想再雇一位非常出色的黑客，你认为他能将整个公司的平均结果提升 20%。则 n = (1.2 - 1)/1.2 = 0.167，所以用公司 16.7% 的股份换他来，你刚好保本。
但这并不意味着 16.7% 就是给他股票的合适数量。股票并不是雇佣一个人的唯一成本：通常还有薪水和日常开销。如果公司只是在这笔交易上保本，那也没有理由去做。
[2]I think to translate salary and overhead into stock you should multiply the annual rate by about 1.5. Most startups grow fast or die; if you die you don't have to pay the guy, and if you grow fast you'll be paying next year's salary out of next year's valuation, which should be 3x this year's. If your valuation grows 3x a year, the total cost in stock of a new hire's salary and overhead is 1.5 years' cost at the present valuation.
How much of an additional margin should the company need as the "activation energy" for the deal? Since this is in effect the company's profit on a hire, the market will determine that: if you're a hot opportunity, you can charge more.
Let's run through an example. Suppose the company wants to make a "profit" of 50% on the new hire mentioned above. So subtract a third from 16.7% and we have 11.1% as his "retail" price. Suppose further that he's going to cost $60k a year in salary and overhead, x 1.5 = $90k total. If the company's valuation is $2 million, $90k is 4.5%. 11.1% - 4.5% = an offer of 6.6%.
Incidentally, notice how important it is for early employees to take little salary. It comes right out of stock that could otherwise be given to them.
[2]我认为将薪水和开销转换为股票时，应该将年费乘以大约 1.5。大多数初创公司要么快速增长，要么死掉；如果死了，你就不用付工资；如果增长很快，明年的薪水将从明年的估值中支付，而明年的估值应该是今年的 3 倍。如果估值每年增长 3 倍，那么新员工的薪水和开销在股票中的总成本相当于当前估值下 1.5 年的费用。
公司需要多少额外的利润作为交易的“激活能量”？由于这实际上是公司从雇佣中获得的利润，市场会决定：如果你是一个热门机会，你可以收取更多。
我们来举个例子。假设公司想从上面提到的新员工身上获得 50% 的“利润”。那么从 16.7% 中减去三分之一，得到 11.1% 作为他的“零售”价格。进一步假设他的薪水和开销每年 6 万美元，乘以 1.5，总共 9 万美元。如果公司估值是 200 万美元，那么 9 万美元占 4.5%。11.1% - 4.5% = 报价 6.6%。
顺便提一句，早期员工拿低薪有多重要。低薪直接转化为原本可以给他们的股票。
Obviously there is a great deal of play in these numbers. I'm not claiming that stock grants can now be reduced to a formula. Ultimately you always have to guess. But at least know what you're guessing. If you choose a number based on your gut feel, or a table of typical grant sizes supplied by a VC firm, understand what those are estimates of.
And more generally, when you make any decision involving equity, run it through 1/(1 - n) to see if it makes sense. You should always feel richer after trading equity. If the trade didn't increase the value of your remaining shares enough to put you net ahead, you wouldn't have (or shouldn't have) done it.
显然，这些数字有很大的弹性。我并不是说股票授予现在可以简化为一个公式。最终你总是需要猜测。但至少要知道你在猜什么。如果你根据直觉或风投公司提供的典型授予规模表来选择数字，要明白这些数字是对什么的估计。
更一般地说，当你做出任何涉及股权的决定时，用 1/(1 - n) 检验一下是否合理。交易股权后你应该总是感觉更富有。如果交易没有让你的剩余股份增值到净赚的程度，你就不会（或不应该）去做。
Thanks to Sam Altman, Trevor Blackwell, Paul Buchheit, Hutch Fishman, David Hornik, Paul Kedrosky, Jessica Livingston, Gary Sabot, and Joshua Schachter for reading drafts of this.
感谢 Sam Altman、Trevor Blackwell、Paul Buchheit、Hutch Fishman、David Hornik、Paul Kedrosky、Jessica Livingston、Gary Sabot 和 Joshua Schachter 阅读本文初稿。