The Mathematical Formula for Exponential Growth and Equity

In mathematics, the formula for infinite exponential progress is defined by the Taylor Series, one of the first series one learns in college level calculus: 1/(1-x) is the summation of x^n. This formula takes on a particularly applicable notion in startups, when one ascertains to jive for exponential growth, when all organizations essentially are, are the sum of their peoples.

Paul Graham, the founder of Y Combinator notes that the amount of equity a co-founders should be given should correspond with the formula 1/(1-n) to break even, where n equals the amount of progress one expects the new hire to contribute to the company. For instance if you anticipate that having a second cofounder will receive half your company, they should will accelerate your business 200%.

However, this is seldom clear-cut and the case with most startups whereinwhic employees expect to be paid in salary and stock. Typically, employees cost 1.5x of what is anticipated by the formula to account for the overhead costs. For instance, if one wishes to give the new hire 6% in equity , then the formula denotes 1/(1-0.06) that the new hire should increase the company by 6.4% stock. However, in actuality one should account for the new hire taking 1.5x of the stock for the same amount of company growth of 6% due to overhead, or 6.4*1.5= 9.6%. If the company is at a 1 million valuation and the employee is supposed to be paid 60k per year, that would be 90k in 1.5x overhead, that would equal 90,000/1,000,000 or 9%. Thus, the total compensation package would be 90k + 0.6% equity.

It turns out that this formula can also be utilized for not only employees, but investors, advisers, and any business partners who essentially wants a chunk of your company. After all, we are all investors, and some just have more time than money. If business incentives and people are the fount of a company’s core principles and culture, it is best for progress of the summation of these small parts to negotiate them well.