Customer Lifetime Value (LTV)

By the end of this article, you should be able to: define LTV, compute it two ways, connect it to acquisition spend, and explain why you can't just measure it directly.

Step 1: Meet the problem

A subscription app wants to know how much it can afford to spend on ads to acquire one new paying customer. "They paid $5 this month" isn't the right number to compare against an ad cost, because that customer will likely keep paying for months to come. What matters is the total value they'll generate over their whole relationship with the product, and that number simply isn't observable on day one.

Step 2: The quick version

For a subscription-style product, there's a shortcut. If a customer pays a steady amount each period and churns at a constant rate, their expected lifetime, in periods, is just one over the churn rate:

$\text{LTV} \approx \text{ARPU} \times \frac{1}{\text{churn rate}}$

Quick check. A payer spends about $5 a month, and about 11% of payers churn each month. Roughly what's their LTV?

Where "1 / churn" actually comes from

This isn't an arbitrary shortcut. If a customer survives each period with probability $r = 1 - \text{churn}$, their expected number of remaining periods is $1 + r + r^2 + r^3 + \dots = \frac{1}{1-r} = \frac{1}{\text{churn}}$, a geometric series. Multiply that expected lifetime by the revenue earned each period, and you get $\text{ARPU} / \text{churn}$.