Still, it is common for people to want ‘financial forecasts’ even for start-up companies!

Once I was in a start-up company. I had written some software that had “Solved the most important problem” facing the start of the company, then, mostly was struggling with some ‘operational’ NP-complete problems, which actually in practice have a reasonably easy solution, but around the HQ it became well known that the Board very much wanted a ‘revenue growth curve’.

Of course, there were hopes, intentions, goals, etc. With something so indefinite, and that really would not contribute directly to earnings or revenue (!), I tried not to get involved, but, for a curve, no one had anything much beyond just ‘art work’!

So, I started with, “What do we know?”. Well, we knew what the revenue was then. But, since we were less than six months into any revenue at all, compared with the goals, the revenue was quite small.

Also we had in mind what we regarded as the ‘potential’ of the market, that is, what our revenue should be once we were successful and mature (don’t laugh yet — it actually did become both successful and mature!). Further, we didn’t yet have any clever ads, but we had one heck of a case of ‘viral marketing’ with a ‘network effect’.

So, basically we had to ‘interpolate’ between the customers we had and the full collection of customers we were going to get.

So, I assumed, from the ‘viral’ effect, that a customer not yet being served heard about us at a rate proportional to the number of customers we were serving.

So, the rate, in, say, new customers per day, would be proportional to both the number of customers being served and the number of customers yet to be served. And we had the start — the number of customers currently being served.

So, here’s the ‘dynamics’ — it’s nearly all determined, in this theory, quite precisely.

So, again, the rate of revenue growth is proportional to the product of the current revenue and the revenue yet to be achieved. So, that’s an initial value problem for a ordinary differential equation. Ah, calculus! Yes, the equation has a closed form solution. Yes, the solution is some exponentials (which are what keep me from typing the solution here).

Yes, from the calculus there is one free parameter; otherwise the calculus gives a full curve. Yes, the curve is a lazy S that initially can grow like a ‘hockey stick’ but then flattens out and approaches the ‘total market’ asymptotically from below.

Yes, as I learned later, the solution is commonly called the ‘logistic’ curve. Yes, it does somewhat well describing several old cases of technology growth, e.g., TV sets. Yes, in applying this curve, it’s important to know the asymptote since otherwise what the curve does can be an unstable extrapolation of the beginning of the curve.

So, from this calculus — I was the only one around who remembered that sin’ = cos — there was some interest. My boss, SVP Planning, decided to be the ‘point man’ on getting the answer for the Board and wanted my answer.

So, on a Friday, the two of us got out some graph paper, picked some candidate constants, drew some curves, picked a ‘reasonable’ curve, and drew its graph. Easy enough. Not really good but better than just hoping.

The next day, Saturday, was the Board meeting. The SVP was traveling. I was in my office struggling again with NP-complete when the phone rang and I was asked, “Do you know anything about these revenue growth projections? Could you come over?”

When I arrived, two Board members from our lead investor were standing at the door with their bags packed and reservations on the next plane out intending not to return.

It seemed that the graph had been presented to the Board early that morning, and the two investors, one in finance, the other in engineering, had asked how the graph was calculated. People kept trying to reproduce points on the curve but were unsuccessful. “Dance ’round and ’round and suppose …”, and, yet, there it was, a nice, smooth curve. The investors lost patience, got plane reservations, went to pack their bags, and only returned a little before I arrived as the last chance.

I was asked to reproduce one point on the curve. With just my calculator, I punched in the numbers, carefully, and reproduced the point. After about three more such successes, the two investors unpacked their bags and stayed after all.

Yes, I should have been invited to the Board meeting or at least asked to stand by, available. That I was not came close to killing the company and might be called a particularly egregious case of dysfunctional “goal subordination”.

So, the ‘assumptions’, the ‘analysis’, and some calculus reduced the question of the whole curve, with its infinitely many numbers, to a question of just the one free constant. In the context, that was progress.

So, that was a case of being able to do something mathematical with the ‘dynamics’ of growth of a start-up company.

Did the company achieve the curve I drew? For the short term covered by the graph, I don’t have the details; but, in the long term, the company did MUCH better than the curve — the initial assumptions about the ‘potential’ of the market were too small by some factors of 10. Right: It’s important to be clear on the assumptions!

You’ve heard of the company; extra credit for knowing the name. Hint: The investors were from General Dynamics. Hint: The company is one of the most successful venture funded start-ups of all time.

Yes, asking for the revenue projections was a bit silly; but the projections were fully ‘serious’ at least in the sense that fumbling with them nearly killed the company. Further, as silly as the projections were, it was possible to make some possibly serious progress on the ‘growth dynamics’.

]]>The Fled Blog has it right. It’s just awkward to fathom the first time you see it presented as he has (so well).

Read and apply it, you’ll be ahead of the rest of the crowd. Then your unfair advantage will stand out.

]]>When people ask why we’ve succeeded at Eyeris, I love to tell them that 90% of what was in our original business plan was wrong. But, the 10% that dealt with organic issues like how this is connected causally to that, like who needs what and why — those things are the building blocks of the intuitive improvisation that is the REAL pre-req for success in a venture.

]]>would you please explain when you perceive forecasts may be valid even when the numbers are wrong ?

]]>On the other hand, I recently attended an event where a VC-turned-entrepreneur said his first investor go-round showed modest early growth. He said (to VCs he knew) “come on, everyone knows the hockey stick almost never actually happens.”

He was declined, revised the model to show higher, faster growth and prospective investors sat up and said “now this sounds interesting”. So perhaps there’s a certain amount of “playing the game” involved as well- at least with a portion of the investor community.

]]>You can’t debate numbers, only assumptions.

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