First, which 1%. Here it means one percentage point: monthly churn from 5% to 4%. A cut of 1% of the churn rate itself takes 5% to 4.95%, and the one-point cut is 20 times larger. Both get written as “1%”, and the academic estimate further down means the second kind.
Everything below is revenue. Margin and what the cut costs to get come at the end: they decide whether the cut is worth buying.
One customer
When the same share of customers leaves every month, the average customer stays for one divided by that share: 20 months at 5% churn, 25 at 4%. At €29 a month, the average customer is worth €580 of revenue as things stand and €725 with the cut. That is the lifetime-value answer, and it is correct as far as it goes; it says nothing about when the money arrives. The formula, and the corrections it needs before you spend against it, are on customer lifetime value.
The whole customer base, month by month
Let’s take the invented subscription company that runs through this site’s demos, and its entry plan, Starter, on its own: 2,400 customers at €29 a month, so €69,600 of revenue a month. Each month 5% of them leave, 120 customers. To keep the arithmetic simple, say 120 new ones join, so the plan holds steady. The whole company, with its other plans and the customers who come back, grows a little; the revenue forecast demo, further down, models that.
In the first month at 4% churn, 96 customers leave instead of 120. The 24 kept bring in €700 more that month, and they stay on into the next, when another 24 are kept. The gap grows every month. By month 24 the plan has 2,775 customers instead of 2,400 and bills €10,900 a month more. Added up over the two years, the cut is worth €156,800 of revenue.
Kept customers pile up: 2,775 against 2,400 by month 24, on the way to 3,000
The same data as a table
| Month | Churn at 5% | Churn at 4% | Extra revenue that month |
|---|---|---|---|
| 1 | 2,400 | 2,424 | €700 |
| 6 | 2,400 | 2,530 | €3,800 |
| 12 | 2,400 | 2,632 | €6,700 |
| 17 | 2,400 | 2,700 | €8,700 |
| 24 | 2,400 | 2,775 | €10,900 |
| 36 | 2,400 | 2,862 | €13,400 |
| 48 | 2,400 | 2,915 | €14,900 |
| 60 | 2,400 | 2,948 | €15,900 |
After that the gain keeps growing, more slowly. With 120 new customers a month and 4% leaving, the plan settles where leavers match new customers, at 3,000 customers, worth €17,400 a month more than today. It takes its time getting there: half of the way in 17 months.
With the same 120 joining, a slower drain fills the plan to 3,000 customers
The lifetime-value answer, multiplied out, gives €145 for each of 2,400 customers: €348,000 from today’s customers alone. That total is right if every future month counts at full value, but less than a third of it, €107,000, arrives in the first two years. (A calculator that prints the €348,000 is not wrong, only patient.)
Why the answer is a range
Everything above divides by churn, so a one-point cut is worth more the lower churn already is. From 4% to 3%, a customer’s average stay grows by 8.3 months, from 25 to 33.3; from 6% to 5%, by 3.3 months, from 16.7 to 20.
Where churn starts moves the long-run gain 2.5 times, and one month of data cannot pin the start down
The same data as a table
| Churn a month | Cut to | Average stay, months | Extra revenue, first two years | Extra revenue a month, long run |
|---|---|---|---|---|
| 4% | 3% | 25 to 33.3 | €178,800 | €29,000 |
| 5% | 4% | 20 to 25 | €156,800 | €17,400 |
| 6% | 5% | 16.7 to 20 | €137,800 | €11,600 |
Over two years the spread is moderate, €137,800 to €178,800, because every row starts by keeping the same 24 customers in month 1 and the paths take time to part. In the long run it opens to €11,600 to €29,000 a month.
So how well do you know your churn? With 2,400 customers and a true rate of 5%, one month’s leavers land anywhere from 100 to 141 in 95 months out of 100: a measured churn of 4.2% to 5.9%, by chance alone. Twelve months together narrow that to 4.8% to 5.3%, but only if churn held still all year. Seasons, price changes and the mix of new and old customers all move it. So a single month’s 5% pins churn down only to about a point either side, close to the 4% and 6% of the chart above.
My read: quote the two-year figure, as a range. The long-run figure moves 2.5 times across about the range one month of data leaves open, so I would not put it in a business case without a year of churn history behind it, checked for seasons and for changes in the customer mix.
Listed companies show the same pattern. Gupta, Lehmann and Stuart valued the customers of five companies (Amazon, Ameritrade, Capital One, eBay and E*Trade) from public data as of March 2002, and found that a 1% improvement in the retention rate raised customer value by 2.45% to 6.75%. Their 1% is the relative kind: a yearly retention rate of 70% becoming 70.7%. The effect was largest at Ameritrade, which kept about 95% of its accounts a year, and smallest at Amazon, at about 70%. Their customer value is the discounted margin of current and future customers over an unlimited horizon, and the retention rates were the authors’ own estimates, so read the figures as a pattern in five companies in 2002, not as a rate for yours.
What the figure leaves out
It is revenue. At the invented company’s 80% gross margin, €156,800 of revenue is €125,400 of margin, which is the most a programme delivering the cut could cost over the same two years and still pay for itself.
It assumes the programme delivers the point. Whether it does is measured by holding a random group of customers back from the programme and comparing the two groups’ churn, and that takes months: in a group of 1,000 customers at a true 5%, one month’s churn lands anywhere from 3.7% to 6.4% by chance alone, a wider swing than the point you are trying to see.
A month of a 1,000-customer group swings further by chance than the one point you want to see
The same data as a table
| What is measured | Out of | Leavers | Measured churn |
|---|---|---|---|
| One month, all 2,400 customers | 2,400 customers | 100 to 141 | 4.2% to 5.9% |
| Twelve months pooled, if churn held still | 28,800 customer-months | 1,368 to 1,513 | 4.8% to 5.3% |
| One month, a holdout group of 1,000 | 1,000 customers | 37 to 64 | 3.7% to 6.4% |
It counts every month at full value, with no discounting, and every kept customer as an average one paying €29. A programme keeps the customers it reaches and persuades, who may pay more or less than that. And it takes one plan on its own, so nobody moves up to a dearer plan and nobody comes back.
The same question, simulated
The revenue forecast demo runs this question on the whole company: three plans, customers moving between them, lapsed customers coming back, and the churn level drawn afresh in each of 1,000 runs, so the range comes out of the simulation itself. You can change the cut, its churn, how steady that churn has been, and its sign-ups: Where is revenue heading, and what would lower churn add?
How FinDaS does it
On a real company nothing is invented: churn comes from your own history, by plan and by how long customers have stayed, and the range from how much it has actually moved. AI agents build the model, and a review round checks it before you see a number. A decision to fund a retention programme rests on a memo; a panel of reviewer agents reads it, and then I sign it. How the model is built is on churn prediction, and the review on how it works.
Sources
- Sunil Gupta, Donald R. Lehmann and Jennifer Ames Stuart, Valuing Customers, Journal of Marketing Research 41(1), February 2004, pp. 7-18. The figures here are from the authors’ version, hosted by Columbia Business School.