Customer Lifetime Value (LTV)

By the end of this article, you should be able to: define LTV and compute it from a retention curve, explain why the "revenue ÷ churn" shortcut undervalues customers, project retention beyond the data you have, and turn LTV into an acquisition decision.

What LTV measures

Customer lifetime value (LTV) is the total profit you expect a customer to bring in over their whole relationship with the product. It's the number to compare with what it costs to win that customer, because a customer who pays $10 this month may keep paying for years.

Three pieces go into it:

Margin per period, $m$ : what the customer pays each month or year, minus the cost of serving them. Revenue overstates value for any product with real running costs.
Survival, $S(t)$ : the share of customers still active $t$ periods after joining. $S(0) = 1$ .
A discount rate, $d$ : money next year is worth less than money today.

Add up the margin from each period, weighted by the chance the customer is still there to pay it:

$\text{LTV} = \sum_{t=0}^{\infty} \frac{m \cdot S(t)}{(1+d)^t}$

Everything difficult about LTV is in $S(t)$ . You know it for the periods you've seen, and you have to project it for the ones you haven't.

The shortcut, and where it comes from

The version most people learn is shorter:

$\text{LTV} \approx \frac{m}{\text{churn}}$

It comes from assuming every customer leaves with the same probability each period, the churn rate. Then survival after $t$ periods is $(1 - \text{churn})^t$ , and the expected number of periods a customer stays is a geometric series:

$1 + (1-\text{churn}) + (1-\text{churn})^2 + \dots = \frac{1}{\text{churn}}$

Multiply by the margin per period and you get the shortcut.

Now try it on real data. Peter Fader and Bruce Hardie published 12 years of survival for one segment of a subscription business (they call it "Regular"). In year 1, 36.9% of customers left. The shortcut says the average customer stays 1 ÷ 0.369 = 2.7 years, so at $100 margin a year they're worth $271.

The real customers paid $441 each in the first 12 years alone, and 17.3% of them were still subscribed at year 12. The shortcut missed by more than a third, and the gap was still growing.