Finite and uncapped LTV
Planning LTV sums the contribution from each month the subscriber is expected to stay, up to the observation period. It stops at a date, which makes it usable for planning and cash decisions.
Uncapped LTV is contribution ÷ churn. It assumes the churn rate continues forever. It is a useful comparison, but it is not a promise and it explodes as churn approaches zero.
The formula
Monthly contribution = monthly ARPU − monthly variable cost. Planning LTV = contribution × (1 − (1 − churn)^months) ÷ churn. When churn is 0, it is contribution × months.
CAC payback = CAC ÷ monthly contribution. Retained months = 1 ÷ churn. LTV:CAC uses the planning LTV, not the uncapped number.
Worked example
ARPU $30, variable cost $12, monthly churn 5%, CAC $54, 36-month observation. Monthly contribution is $18.
Planning LTV is $303.20 over 36 months. Uncapped LTV is $360. CAC payback is 3 months, retained months are 20 and LTV:CAC is 5.61x.
Churn sensitivity
At 2% churn, planning LTV over 36 months is $465.11. At 5% it is $303.20. At 10% it is $175.94. A five-point churn change moves LTV by roughly 40–50%.
That is why retention experiments can be worth more than acquisition discounts. A small churn improvement compounds across every future month.
When churn is zero
Zero churn makes the uncapped formula infinite. The calculator caps planning LTV at the observation period and hides uncapped LTV, with a warning that the result is period-bound.
No subscription business has zero churn forever. Use the observation cap as a sanity check, not as evidence of infinite retention.
Where the model stops
It assumes a constant churn rate, constant ARPU and constant cost. Real subscriptions have cohort curves, seasonality, price changes, expansion revenue and win-backs.
Use the result as a planning baseline. Validate it against cohort retention, then test a shorter observation period and a higher churn rate to see how fragile the conclusion is.