As believers in the singularity are quick (and right) to point out, we don’t do very well as humans when it comes to understanding exponential growth.  This is not a new insight as we can see from the much older story about the peasant who wins a chess game against a king and ask as his reward for simply a single grain of wheat/rice/whatever on the first square to be doubled on every subsequent square.  

It is worth frequently reminding ourselves of our lack of intuitive grasp for exponential growth when we are trying to build or invest in businesses that have exponential growth characteristics. Here is a simple picture to illustrate what happens when we apply linear interpolation to exponential growth:

Admittedly, this is hand drawn, not-to-scale, exaggerated and all that but the basic point holds: the true explosion in exponential growth comes quite a ways out.  If you interpolate value linearly, you will be way, way above the exponential curve almost everywhere.  Also, when you are still on the flat part of the exponential curve, the slope of the linear interpolation will be higher than that of the exponential curve.

What does this mean for entrepreneurs and investors?  If you are valuing a startup based on linear interpolation, you will be way ahead of actual value at the time.  Now if the startup happens to be the next Facebook or Twitter or Zynga or Google investors will still earn an excellent return (although not a crazy return) and entrepreneurs will be even better off because they will own even more of the company.   

Alas, therein lies the problem. 99.99% of startups are not the next Facebook.  They will never grow to multi-billion dollar valuations and they will experience one or more big setbacks along the way and may have to cope with macro shocks to the environment (2008 anyone?).  It’s pretty obvious why investing at “linear interpolation” pricing is not an attractive proposition for investors in those companies.  Why should you care as an entrepreneur though?  Because until you are cash flow positive for good, it is hard to know how much capital you will need (and it will generally be more than you think).

Financing a company over time is orders of magnitude easier if you don’t get too far ahead of your value at any time.  You will be much more resilient to set backs.  You will absorb macro shocks more easily.  At each point you will have more options (extend previous round, small round at a step up, large round a bigger step up, exit, etc).  Your existing investors will be much more likely to be sitting in the same boat.  Financing always seems easy when the business is growing and markets are going up all around.  But that’s not a test of a company or an entrepreneur any more than sailing downwind in 10 knots of steady breeze and sunny weather.  Where your capital structure (and hence financing history) matters is when you need to sail upwind in 30 knots or more with currents and choppy seas. 

As believers in the singularity are quick (and right) to point out, we don’t do very well as humans when it comes to understanding exponential growth.  This is not a new insight as we can see from the much older story about the peasant who wins a chess game against a king and ask as his reward for simply a single grain of wheat/rice/whatever on the first square to be doubled on every subsequent square.  

It is worth frequently reminding ourselves of our lack of intuitive grasp for exponential growth when we are trying to build or invest in businesses that have exponential growth characteristics. Here is a simple picture to illustrate what happens when we apply linear interpolation to exponential growth:

Admittedly, this is hand drawn, not-to-scale, exaggerated and all that but the basic point holds: the true explosion in exponential growth comes quite a ways out.  If you interpolate value linearly, you will be way, way above the exponential curve almost everywhere.  Also, when you are still on the flat part of the exponential curve, the slope of the linear interpolation will be higher than that of the exponential curve.

What does this mean for entrepreneurs and investors?  If you are valuing a startup based on linear interpolation, you will be way ahead of actual value at the time.  Now if the startup happens to be the next Facebook or Twitter or Zynga or Google investors will still earn an excellent return (although not a crazy return) and entrepreneurs will be even better off because they will own even more of the company.   

Alas, therein lies the problem. 99.99% of startups are not the next Facebook.  They will never grow to multi-billion dollar valuations and they will experience one or more big setbacks along the way and may have to cope with macro shocks to the environment (2008 anyone?).  It’s pretty obvious why investing at “linear interpolation” pricing is not an attractive proposition for investors in those companies.  Why should you care as an entrepreneur though?  Because until you are cash flow positive for good, it is hard to know how much capital you will need (and it will generally be more than you think).

Financing a company over time is orders of magnitude easier if you don’t get too far ahead of your value at any time.  You will be much more resilient to set backs.  You will absorb macro shocks more easily.  At each point you will have more options (extend previous round, small round at a step up, large round a bigger step up, exit, etc).  Your existing investors will be much more likely to be sitting in the same boat.  Financing always seems easy when the business is growing and markets are going up all around.  But that’s not a test of a company or an entrepreneur any more than sailing downwind in 10 knots of steady breeze and sunny weather.  Where your capital structure (and hence financing history) matters is when you need to sail upwind in 30 knots or more with currents and choppy seas.