November 15, 2011

The Geometry of Startup Valuations.

Posted in Category: Tech,Work — Amr Awadallah @ 10:40 pm | link | | comments (1)

I frequently find that I have to explain to candidates joining Cloudera (and existing employees) how not to be overly concerned about dilution of their percent ownership when a company is experiencing strong growth.

Towards that end I created the chart below to illustrate how percent ownership is just a small part of the total equation. The core concept is that the “paper” valuation of your stock options is equal to twice the area of your sector under the pie, and the area of your sector is proportional to your angle (i.e. your percent ownership) multiplied by the radius squared (where radius is the stock price). Hence if a startup raises a new round of funding at a large radius then that quickly out weighs any shrinkage in the angle of ownership due to the to the squaring of the stock price. I am not saying that you shouldn’t worry about dilution at all, you should obviously try to get the best deal and keep dilution low, but don’t be overly obsessed by dilution, it is just one factor in the grand scheme of things.

Fortunate startups that demonstrate repeatability/efficiency of their business model raise additional funds at a large radius so that they can fuel further growth thus making the pie larger for everyone. On the other hand startups that get overly concerned by dilution and avoid raising money (depsite being in a growth market) can fall in a penny-wise pound-foolish trap where they end up being a zombie company that goes nowhere (I know many such startups, and by the time they realize their mistake it is usually too late).


— amr

PS: For stock options, the “paper” value is (area of sector) minus (cost of sector), where cost of sector is angle * strike-price^2.

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1 Comment »

  1. (Reposting as the scripts messed up the previous post)

    Interesting geometry, adding some more logic to it:

    Assuming: O2 – % ownership after dilution, O1 – % ownership before dilution, r2 – new stock value, r1 – old stock value

    Stockholders would like:

    O2 * sqrd(r2) > O1 * sqrd (r1), where O2 sqrd (r1/r2)

    This means value is increased if on 50% increase in stock valuation, dilution is less than 55% (higher dilution is generally unusual unless stock valuation increased 10-fold at a very early stage)

    Comment by S Agarwal — November 16, 2011 @ 5:39 am

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