We create financial models for all sorts of reasons, but one of the most common is to answer the question: "How quickly will our business grow?"

Sounds simple, right? In reality though, there's a lot for us to consider. First, we need to ask some more questions, such as:

• How novel is our product category?
• Is there already significant take-up of our product category in the market?
• What is the competitive environment?
• What is our current market share?
• Does our product add to the total market size, or can we only gain share by taking it off others?

And depending on our answers to these (and some other) questions, we usually end up taking one of 3 approaches:

1. Straight-line or Exponential growth
2. Churn-based growth
3. S-Curve (Bass model) growth

Each of these suits a different situation and has its pros and cons - let me walk you through them:

1. Straight-line / Exponential

✅ Easy to model ❌ Risk of growing to unrealistic sizes over time

These two techniques are often the first we reach for when building our models. And why wouldn't we, they're so easy to implement!

Quick recap of why they're easy to model:

• Straight-line = Constant # of additions in each period of the model
• Exponential = Constant rate of growth in each period of the model

These are great in a couple of situations:

• When we're in the early stages of growing a highly scalable business with low initial market penetration (think web software-as-a-service in a new field).
• When we have a stable market share in a mature market (the overall market might grow at a low % each year in line with overall economic growth, so our business follows that trajectory)

If either of those does not apply, it's probably not a good idea to use these methods though. Exponential growth in particular can lead to unrealistic sizes over time - if we try to adjust for this by reducing the growth rate over time, we quickly start getting into trouble. How do you justify your growth assumptions? Are they completely made up in order to get to a target market size? Is that reasonable? What happens if we want to shift our product launch out by one model period? (answer: we now have to move all of our assumptions out by one period as well - an ingredient for making spreadsheet errors!)

In those cases, we may want to consider one of our alternative approaches...

2. Churn-based Growth

✅ Keeps growth rates realistic in a competitive market ❌ Involves several steps so can be complex

What is churn-based growth? Well, churn is simply the customers who leave a company over a certain period of time. So let's imagine that our business is entering a mature, competitive market (maybe we've entered a new geography) - the only way to grow our company is by taking customers from our competitors.

But customers are unlikely to just suddenly abandon competitors for the new entrant - what if they're locked into contracts, for instance? In this case, we need to model a few things: How many customers are likely to leave one of our competitors in each period? How many new customers are likely to enter the market in each period? For each of these, how many customers can we win vs. our competitors?

Model each of these correctly, and we get a nice curve like the one shown above, peaking at a share of market consistent with how likely we are to win customers vs. the rest of the market.

But this approach works best in mature markets - what do we do when we want a sophisticated method of modelling new markets?

3. S-Curve (Bass Diffusion Model) growth

✅ Incredibly powerful and flexible ❌ Involves a bit of math!

I'm just going to say it: I love modelling growth with Bass Model Curves!

Bass curves are based on a mathematical model (the Bass diffusion model) of how new products gain penetration in markets, with growth rate accelerating to a peak, and then slowing down again over time. I won't go into the details here - an internet search will quickly give you the background if you want to read more...

With one formula, you can easily move the start of growth to any period you want, and flex the rate of growth over time with just a couple of inputs, all while ensuring that growth follows a realistic trajectory for both new and mature products. Sounds too good to be true, right?

Well, there's just one snag: it involves some pretty convoluted formulae. Below is the one I use:

Eek. A quick translation:

• Sales = % of maximum sales of your product (outputs a number between 0 and 1, which you can multiply by the eventual sales volume you think you can achieve over time)
• t = Number of years from launch
• p = Coefficient of innovation (usually a number between 0.01 and 0.03)
• q = Coefficient of imitation (usually a number between 0.3 and 0.5)

This formula is pretty painful to type into a spreadsheet (each of your p and q values needs to be referenced 3 times) - that's why I'd strongly advise using a LET formula in Excel, or better yet, creating a bespoke LAMBDA function which you can do quite easily in Excel (and even more easily in Google Sheets!).

Give it a try and let me know how you get on!