Lifetime value with geometric retention
With monthly churn c, the chance a subscriber is still active in month m is (1−c)ᵐ. Expected active months within a horizon of H months:
E[months] = ( 1 − (1−c)ᴴ ) / c · → 1/c as H → ∞
LTV = order value × deliveries/month × margin × E[months]
The horizon cap keeps the model honest: an uncapped 1/c at 4% churn claims 25 months of revenue, most of it far in the future. The default 24-month cap limits how much the distant tail can inflate today's decision. Churn is assumed constant, which slightly overstates early-month retention for most programs (real churn is highest in months 1–3), so treat results as mildly optimistic.
The exchange rate
1 subscriber = LTV / (one-off AOV × margin) one-off orders
Computed per scenario. This is the single number that changes how a subscription test is read.
Test valuation
Per arm, per scenario:
value per visitor = ( one-offs × AOV × margin + subscribers × LTV ) / visitors
The verdict compares arms in all three scenarios. If the same arm wins in all three, the decision is robust to the churn assumption. If the winner flips between scenarios, the tool says so — that means the decision genuinely depends on a number you don't have, and the break-even below is the honest way to present it.
Break-even lifetime — inverting the unknown
When one arm has fewer one-off orders but more subscribers, the value tie-point is the subscriber lifetime that exactly cancels the one-off deficit:
E*[months] = − Δone-offs × AOV / ( Δsubscribers × monthly value )
Reported in months, with the implied churn rate solved numerically from the capped-geometric formula. The claim "the variant wins if subscribers stay at least 4.2 months" requires no subscription data at all — it's a threshold, not an estimate, and the room can judge whether 4.2 months is a safe bet for your product.