Tags: LTV, model, retention, subscription
We’ve posted before about how to estimate lifetime value (“LTV”) for an ecommerce business and for a subscription business, and have provided a sample cohort analysis for each (ecommerce and subscription). This is one of the most important factors in understanding unit economics.
Recently, Eric Liaw sent us a very interesting May 2006 paper entitled “How to Project Customer Retention”, authored by marketing professors Peter Fader (Wharton) and Bruce Hardie (London Business School) and published in the Journal of Interactive Marketing in 2007. In it, the professors explain how previous attempts to project retention rates using line-fitting regression models failed, even after introducing quadratic or exponential functions. Since we had advocated essentially using an exponential line fit for subscription LTV estimation, we figured it was worth reading. The authors show that exponential form fitting is too conservative and underestimates actual retention rates.
Professors Fader and Hardie decide to start from scratch with a simple assumption: what if each customer has a fixed probability of renewing his or her contract at the end of each period? So if I’m a big movie fan, let’s say I’m 80% likely to renew Netflix each month, but you’re caught up on Breaking Bad and only 30% likely to renew each month going forward. Probability varies by customer, but each customer’s rate remains constant over time.
It turns out that, based on probability theory, this simple assumption implies that the distribution of renewal rates can be characterized by a statistical model. Over time, the difference in each individual’s probability to renew suggests that individuals with lower renewal probabilities will generally drop out before those with higher probabilities. Incidentally, this also explains why incremental retention may appear to improve over time, when it’s actually a likely side effect of the remaining customer mix.
After some mathematical gymnastics, the authors unveil the model they’ve derived: the shifted-beta-geometric distribution. The authors tested the model by using the first seven years of data from a given sample to project renewal rates at the end of the final five years in the sample. The model proved to be quite accurate, within 3% of actuals, and much better than linear or exponential form fitting.
A few quick caveats: this model is appropriate only when the data reflects a discrete renewal period, such as a defined monthly or annual cycle. Also, the model should be reserved for projecting behavior in contractual settings, such as subscription renewals and other observable customer exit points, rather than ecommerce or other businesses where the customer can remain dormant for long periods between orders.
We’ve uploaded a spreadsheet here, along with directions for how to use it yourself.
Hope this is helpful. We look forward to hearing from you regardless, but especially if:
1) You use the model and have any feedback on results
2) Your company uses any other methods to capture, analyze, and project customer retention
3) Your innovative company achieves valuable unit economics. As previously mentioned, we like to see LTV / Customer Acquisition Cost > 2.5 and payback periods under 12 months.
If you found this post useful, follow us @lightspeedvp on Twitter.
I’ve been asked several times how the analysis would differ for an ecommerce business, so I finally got around to uploading a sample cohort analysis for an ecommerce business. Please note that this is a SAMPLE only. Data is dummy data, so you should not use it for benchmarking purposes. I have not allowed editing to the google doc so that the spreadsheet will be useful to anyone who finds it, but you can download it and edit it offline as you see fit.
For an ecommerce business, rather than focusing on the percentage of retained subscribers per cohort, instead you focus on the net revenue (after discounts, returns and refunds) from that cohort in a given period. This revenue has to be normalized by dividing by the number of (original) buyers in each cohort so that you can make meaningful comparisons. You should focus on revenue per (original) buyer in each period for each cohort as the raw data from which you can build a lifetime value analysis. Then you should average across cohorts to understand “typical” revenue per sub in period 1, 2, 3 etc, where period 1 is the first month (quarter/ year) when you see a buyer make a purchase.
You still typically see a steep drop off in revenue per buyer after the initial period. But a well run ecommerce business that does a good job of retention marketing and line expansion should see stable revenue per buyer after the initial drop off. This is in contrast to subscription businesses which typically continue to see attrition over time. If you do see continued drop off, you should model that in a similar way that I do it for subscription screen sharing businesses, but if you see relatively stable out month revenues per buyer, it’s OK to model that in the out months.
Lifetime Value is calculated as the cumulative contribution of an average customer, so you have to multiply lifetime revenue by contribution margin. Contribution margin should include all variable costs except one time acquisition costs. This typically includes COGS, packaging, shipping and handling, reverse logistics, inventory obsolescence/write offs, customer service, credit card charges, hosting costs, fraud accruals etc. It would not include fixed costs such as photography, production, site development, merchandising or other overhead.
The two most importnat metrics that I look at to gauge the health of an ecommerce business are LTV/Customer Acquisiton Cost ratio and payback period. This is why i highlighted these two metrics in the spreadsheet.
I like to see LTV/CAC > 2.5 (which tells you that you have a robust long term business with enough margin to cover overhead) and Payback periods under 12 months.
If you found this post useful, follow Lightspeed on Twitter @lightspeedvp
How to estimate Lifetime Value; Sample cohort analysis July 19, 2010Posted by jeremyliew in Ecommerce, ltv, subscription.
In many businesses, repeat purchase behavior is a key driver of value. Many companies track % of repeat purchases as a key business metric. This is useful in steady state, but can sometimes be quite misleading if the company is showing substantial growth. By definition, growth implies many first time customers, and the mix of these new customers can distort the view into how much repeat purchase behavior is actually occuring.
I prefer to try to analyze repeat pruchase behavior, and hence, estimate lifetime value, by doing cohort analysis. This is approximate by definition, but it can give you some sense of lifetime value well before you actually see a full customer lifetime, which can help in accelerating decisions about marketing and customer acquisition. I recently posted about how you can improve LTV and CAC for your subscription or repeat purchase business. But how do you estimate Lifetime value?
I’ve uploaded a spreadsheet with a sample cohort analysis, using representative but dummy data to illustrate how to do this.
In this particular example, I look at a hypothetical subscription business. Assume that the business has been in operation for one year. First, divide the users into cohorts depending on when they initially subscribed to the service. I calculate retention at the end of month N by dividing the number of subscribers still subscribing after month N by the total number of subscribers that started in each cohort. These are the numbers in blue. Obviously, for the subscribers that started in month 1, we have 12 months of retention data, for the subscribers that started in month 2 we have 11 months of retention data, and so on.
By averaging across the cohorts, you can get an average retention rate at the end of one month, two months and so on. As the cohorts age, there are fewer datapoints to average over, and hence the potential for error is greater. However, it is still a useful exercise to get an early indication of how the business looks.
A typical pattern found in subscription businesses is that after a steep drop off after an initial period, month-on-month attrition rates tend to level off. You can see a similar pattern in this example, where after the first month, month-on-month attrition rates are around -6% (ie month N subs ~ 94% of month [N-1] subs).
If you see a pattern like this, you can extrapolate forward using the same month-on-month attrition across several years. As you can see in the model, we extrapolate an average lifetime of 9.77 months by extrapolating forward over 5 years of data.
So if you were a subscription business charging $20/month with 90% gross margins (after accounting for customer service costs for example), then you would attribute a lifetime value for a new customer of 9.77 x $20 x 90% = $176. This sets an upper bound of what you would be willing to pay to acquire a customer (although in practice, you would prefer to see a ratio of CAC/LTV in the 25-35% range).
This example is for a subscription business where the key value driver is the number of active subscribers. However, you can conduct similar analysis on any type of repeat behavior business. In a social business the metric might be activity (e.g. how many users posted a photo this month), and in a social game the metric might be dollars spent in virtual goods that period. The measurement periods may vary according to the tempo of the business. Many social games do their cohort analysis on a daily or weekly basis, whereas some ecommerce companies whose purchases are less frequent may do their cohort analysis on a quarterly basis. This will dictate how long you have to collect data before you have enough data to project forward.
Different billing mechanisms can complicate this (e.g. an annual billing system will by nature skew average lifetime upwards) and while these can be important levers, it is usually helpful to hold billing constant and compare cohorts on a same-billing basis, at least initially. However, this cohort analysis is also useful tool to see what the impact of changes in billing, registration flow, product features etc can have on retention as you can often see an increase in early month retention from later cohorts.
The spreadsheet for the sample cohort analysis is read only but you can download it to play with it yourself.
I’d love to hear from others how they estimate lifetime value.
UPDATE: June 2012 – I have a new post describing how to estimate lifetime value for an ecommerce business using cohort analysis.
How can you improve LTV and CAC? June 15, 2010Posted by jeremyliew in CAC, ltv.
A lot of the startups that have quickly reached millions in monthly revenue rely on the arbitrage of being able to acquire customers through paid marketing for less than the lifetime value of that customer.
CAC < LTV
As a reminder, lifetime value, or lifetime contribution as it should perhaps more accurately be named, is given by the formula:
LTV = Expected Life x ARPU x Gross Margin
where Arpu = average revenue per user in each time period. This equation can hold whether you are in a subscription business or an ecommerce business with repeat purchase behavior. Although you need to be a bit more nuanced with non subscription businesses, the same cohort analysis techniques still allow you to approximate LTV in this manner. I’ll post more about this later.
Both LTV and CAC are key metrics that the management teams should be focused on improving.
Usually CAC is a blended average of several customer acquisition costs from several different channels. Each of these channels typically can be optimized by better targeting, better copy and creative on the advertising, better landing pages,optimization ofthe flow through to checkout, more and better payment options, and increased viral pass along.
Some of the tools that can be used to improve LTV include retention programs to extend life, cross sell and upsell campaigns to increase ARPU, and improving gross margin.
Both metrics are very important. However, if resource constraints force a choice between focusing on one or the other (it can be hard enough to do one thing at a time at a startup!), I would choose to focus on lifetime value. There are two reasons for this. Firstly, most of the improvements that can be made to LTV will improve LTV for all users, both current and future, and regardless of channel of acquisition. In contrast, many of the improvements that can be made to CAC are channel specific (e.g. copy of a particular ad) and none of them improve the economics of existing customers, only new customers. You get more leverage out of your efforts on LTV.
Secondly, because LTV is typically already higher than CAC, an x% increase in LTV has more impact to the company than an x% reduction in CAC.
I’d love to hear what others think about this choice, and about other ways to improve both CAC and LTV