A startup Black & Scholes

PART1: why should you manage Uncertainty?

In the startup world, the financial forecast is definitely uncertain. As a consequence, some people see the forecast as a reflexion of the entrepreneurial dreams only.

But I remember a question I asked to an experienced consultant: “What is the best advice in the B2B world?”

He answered “benchmarking“.

And the more I look at the entrepreneurial world, the more I think he is right. Benchmarking means to internalize external world realities and reduce execution risk. Similarly, your budget is an ambitious but realistic benchmark. Forecasts are not made to be 100% correct. Forecasts are showing a direction. They are translating a vision in clear metrics. They are an incredible alignment tool.

By knowing the average trajectory to hit the center (an IPO?), you can increase the probability to reach it. Most of the time, you will miss your target. That’s why a deterministic forecast have a limited value in the startup world. Startup budgeting needs to be lean. Startup budgeting needs to embed uncertainty: it needs to be stochastic…

PART2: how we simulated Go-To-Market trajectories?

Knowing a distribution of startup revenues as they grow, we can deduct the volatility of their go-to-market strategies. The difference with Black & Scholes is that the trajectory is sigmoidal and not exponential.

Here we simulated 100 sigmoidal random walks with 1 potential IPO outcome.

The average revenue generated by the simulations is realistic. In developed countries, we observe between 10 and 15 employees per company. Multiply by a revenue per person and you get an average revenue per company.

PART3: how Value creation is linked to these trajectories?

By dividing the previous revenue trajectories with your average revenue per customer, you get the potential trajectories of paying customers.

Cash flow is King and all your cash flow could be deducted from your number of customers.

The number of customers is the main “operating cash flow driver”: your selling and marketing expenses are related to the variation of your number of customers. Your contribution margin (Recurring revenue less recurring costs) depends on your total stock of acquired customers.

Moreover your customers are driving your balance-sheet: your fixed assets and your working capital will scale proportionally.

After you have calculated the sum of the cash in (operating and investing expenses less revenue), the magic of this kind of forecast is that you could estimate the cash out (the Exit value). Why?

Future traction determines future free cash flow. And we often value exits with future free cash flow: sometimes indirectly through multiples.


Mathematical technics, as random walks, help to manage uncertainty. It will give you a distribution of potential developments.

Based on them, you will be able to set ambitious and realistic goals. You will be able to plan your fundraising needs (cash in).

And by calculating the expected value of discounted future free cash flow (Exit valuation or cash out), you can estimate the Multiple On Invested Capital (MOIC) of your venture project:

NB: the closed form valuation (like in Black & Scholes) is not displayed here. Would you like to comment or be interested by a future collaboration, I look forward to hearing from you.

About the author


Hello! I am Damien.