We’ve gotten a ton of great feedback on these posts and are really excited that it’s providing a useful and valuable set of tools with which to understand your business. Feel free to email me at email@example.com if you have questions. I can’t guarantee that I’ll respond, but I’ll certainly try!
In the first two parts of this series we described how growth accounting can be applied to understand the sub-components of both user growth and recurring revenue growth. We mentioned that growth accounting has a shortcoming in that it doesn’t give us a sense of the lifecycle of a customer. In particular it doesn’t help answer questions such as: “Do customers spend more early vs. later in life?” Or perhaps “Does churn occur abruptly at some point or does it steadily occur through the life of a customer?”
To get started, let’s pretend we have a business that sells something to customers. The following description is indifferent with regards to whether the revenue is subscription or transaction based. We are interested in the lifetime value of customers in our business i.e. the cumulative revenue realized per customer.
Most descriptions of lifetime value (LTV) use a model which ends up with a formula based on a combination of contribution margin (m), retention rate (r) and discount rate (d) which encapsulates the infinite time horizon LTV (e.g. the wikipedia article).
LTV = m * r / (1 + d - r)
This model turns out to be of limited usefulness for understanding early stage companies because of the following assumptions that are built into it’s derivation:
- Retention is constant both across cohorts and, perhaps more importantly, throughout the lifetime of a customer (i.e. it assumes that if you have a probability r of being retained from month 1 to 2 then you also have a the same probability r of being retained from month 20–21)
- Constant unit economics throughout cohorts and customer lifetime which leads to a constant contribution margin.
- It assumes that these quantities are sufficiently constant over long enough time spans such that including the discount rate is sensible.
When we look at a company, it’s usually the case that none of these assumptions hold. Early stage companies have only a few month- or week-sized cohorts that usually vary significantly in retention as the underlying product is changing across cohorts. Early stage companies also usually haven’t settled on unit economics. These uncertainties are large enough that it’s not sensible to forecast so far into the future where discounting would matter.
We strongly prefer to look at empirically realized cohort LTV as opposed to imputed LTV based on a formula.
Getting back to our fictional revenue generating company, let’s look at some sample LTV curves.
The parenthetical number is the size of the cohort in week zero. Note that younger cohorts appear as shorter lines because we don’t know much about their LTV yet. Also note that there is inherent ambiguity in a quantity such as “9 month (36 week) LTV”. In this data set it’s anywhere between $160-$280, which is quite a large range. The older cohorts appear to have been higher and the more recent ones lower. Also note that the 2014–03–24 cohort is unusually strong, possibly due to some unusually large customers in that cohort who are spending a lot. Overall, these LTV curves are linear which is to say that customers are consistently spending as they age. If customers were not getting value out of the product they would presumably slow their spend leading to a flattening of the LTV curve. Of course, any single LTV curve is always increasing. Also note that we decided to show only a few cohorts as showing them all would make the graph unreadable. We also indexed against the week of first spend rather than registration because different products encourage/require registration at different times relative to convincing customers to spend actual money.
Something to watch out for, the LTV for a given cohort at age T is computed as the total revenue realized by that cohort up to T divided by the total number of customers in the cohort including customers who may have churned out. Sometimes we see companies exclude churned customers and compute LTV at T based only on customers who are still paying at time T. This is not the way to go because you had to pay to acquire all those customers up-front (via marketing, etc.) and that expenditure doesn’t disappear when the customers churn out.
Also note that we typically only look at the top-line revenue LTV per cohort and leave out the contribution margin/unit economics discussion to a separate conversation. There’s the question of how customers are reacting to your proposed offering which is separate from your ability to deliver that offering with reasonable unit profitability. For the purposes of this discussion, we are only seeking to understand the first part of this question.
There are four types of behavior that any cohort can exhibit:
- Flat LTV: The cohort spent once up-front and never spent again. The cohort is generating no further incremental revenue. Not necessarily bad if the flat LTV is at a value high enough to be very profitable. For example, eBay Motors probably exhibits this behavior.
- Sub-linear LTV: The cohort continues to spend as time goes on although the spend decreases over time. Such cohorts approach Flat LTV after some time. Most businesses are in this category. Customers spend initially and then spend less and less as time goes on.
- Linear LTV: The cohort consistently spends the same amount per user in the cohort. This is probably what Spotify looks like. There is likely some fall-off in the first month but after that their cohorts probably evolve to linear or just under sub-linear assuming that the core Spotify user doesn’t intend to ever cancel their subscription. Truly linear LTV would be something like your relationship with a utility such as PG&E which is extremely high retention. Also note that there are different classes of linear LTV growth. A business can be linear with a large positive slope or linear with a smaller positive slope. If a business has a core of recurring customers in each cohort that continue to spend indefinitely then the LTV will be linear. The magnitude of the slope will be determined by how many non-core customers are in each cohort diluting the LTV of those core customers.
- Super-linear LTV: Customers spend more as they age. For example, this is almost surely what Amazon sees. In your first month on Amazon you spend some money and in later months you spend much more. For another example, consider Slack. Each paying customer is a company that pays for some number of seats. In successive months a customer may purchase more seats as more people adopt the service in the company. These cases are the most exciting. They suggest the possibility of almost limitless LTV per customer.
Needless to say, what we really want to see are businesses that exhibit some strong evidence of linear to super-linear LTV in at least some of the cohorts of customer.
The visualization above of the LTV curves is good and easy to understand but it doesn’t give a good sense of whether the LTVs are getting better or worse. If all the LTV curves looked the same and everything was stable then we’d just use the formula above to compute full LTVs. However, we’re usually looking at companies that are fluctuating a lot in their early days so we’re really interested in the trends of LTV. Here’s how we prefer to look at LTVs to get a sense of those trends.
This image is a bit tricky at first so we’ll describe it in detail. In this image, the x-axis is the calendar week of the cohort. The bars in the background are the sizes of the cohorts. They’re included for reference purposes. The lines show successive LTV points as the cohort ages. For instance, the 2014–11–03 cohort (arrow 1 in the above figure) had about 350 customers and spent an average of $44 per customer in the initial week. After a month, the 4-week LTV for that cohort was a bit higher at $55 (on the green line). This cohort just passed 6 months (24 weeks) of age and thus the 24 week LTV for this cohort was just determined at $125. We do not yet know the 36 week LTV for this cohort because the cohort is not yet 36 weeks old and the above image does not attempt to extrapolate it for us (recall, that’s essentially the problem with the formula based approach which mixes in extrapolation with actual observation). Note that the lines in this figure can never cross each other because for every cohort the N+1 week LTV is greater or equal to the N week LTV. Also note that any given line is made up of different customers on successive data points. The N week LTV line measures this quantity for each successive cohort which are made up of distinct customers.
This visualization is good because it shows us trends in the LTV. For instance, you can see that the 12 week LTV started trending down a bit as the cohorts got larger starting in late 2014 (arrow 2). The earliest cohorts in early 2014 had very high LTVs (arrow 3). This is pretty common as early adopters are usually more inclined to use a product. The 2014–03–24 cohort that appeared oddly in the original LTV graph appears here as a clear spike (arrow 4). Note that the spike didn’t occur until sometime between 24 and 36 weeks in the lifetime of that cohort (arrow 5). That is also apparent in the original LTV figure where that cohort started growing strongly at around 28 weeks.
In terms of what we want to see when we look at the LTV trends of a company:
We want to see increasing LTV both for later larger cohorts and later in the customer lifecycle.
As the business attracts larger cohorts of customers it’s often the case that LTV degrades because the larger cohorts are made up of later adopting customers who are less inclined to use the product. If the product has truly great product-market fit then the later larger cohorts will monetize at even higher rates both as the cohorts get larger and as the cohorts age.
Another view that is sometimes useful is the heatmap view.
For this figure, the cohort week of first spend is on the y-axis. The x-axis along the top is weeks since first spend and the color is the cumulative LTV of that cohort. So the topmost row is the 2013–12–30 cohort which has 110 customers and whose LTV goes up as one goes to the right. The bars on the left are the sizes of each successive cohort. More recent cohorts have not yet revealed their LTV. As time passes diagonal lines are added to this figure. This is showing only the first few cohorts as if time stopped in March 2014 for readability. The full heatmap for all the cohorts looks like this:
Note that you can see the outlier 2014–03–24 cohort here as the green horizontal stripe. Fixed calendar phenomena (such as holidays or sales) manifest themselves as diagonal features in this image. Phenomena that affect fixed cohorts (such as customers gained via a burst of paid acquisition expenditure) appear as horizontal features. If there was a significant drop in, say, N-week retention, it would make itself apparent as a change in the color where cohorts would be taking longer to reach the color yellow for instance.
Each of the above visualizations has a strength and a weakness. The LTV curves give you a good sense of the shape of the curves but it starts becoming unreadable after a small handful of cohorts and it doesn’t show trends well. The LTV trends gives a good sense of the trend and shows all cohorts, but only gives a hint of the shape of the LTV curve via the spacing between the lines for each cohort (it’s essentially a contour plot). Also, the LTV trends doesn’t show the LTV at all points in the cohort age but rather at selected age milestones. The heatmap allows you to see all the cohorts at all points in their lifecycle, but does not give a good sense of how the values are increasing as it’s encoded in the color change. The heatmap also does a good job of showing seasonal effects. When we do diligence we typically prefer to see the curves themselves and the LTV trends and only occasionally use the heatmap view. If you’re coming to pitch your company to us you’d do well to make these graphs ahead of time.
So that’s the story for revenue lifetime value. Next time we’ll take this framework and use it to understand cohort level engagement and retention.
Edit: For reference, here’s the full table of contents.
- Accounting for user growth
- Accounting for revenue growth
- Empirically observed cohort lifetime value (revenue)
- Empirically observed cohort lifetime value (engagement)
- Depth of engagement and quality of revenue
- Epilogue: The 8-Ball and GAAP for Startups
Published in #SWLH (Startups, Wanderlust, and Life Hacking)