Many new entrepreneurs are uncertain about the rules for engaging with venture capitalists. How does a deal benefit a startup? What are the essential calculations involved?

Paul Graham has done an in-depth analysis of this perennial teaser for new business owners.

If a venture capitalist offers you a certain sum of money in exchange for a shareholding in your startup, what are the rules governing these deals and how much of your business should you part with?

The answer apparently is : 1/(1 - n)

Whenever you’re trading stock in your company for anything … the test for whether to do it is the same. You should give up n percent of your company if what you trade it for improves your average outcome enough that the (100 - n) percent 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).

If you are in this scenario, you will have to go through a lot of hoops to get funding. It’s not a decision to take lightly. You will also lose much of your control of your business idea. Equally, a VC company will receive many business plans a year, some as many as 6000. They will probably fund around 20 of them.