Quantify a Churn-Reduction Feature Against LTV
A subscription product has 4,000,000 active subscribers, average monthly margin $12/subscriber, monthly churn currently 6%, and the company discounts future cash flow at 1.5%/month.
- Compute current LTV per subscriber.
- A proposed onboarding-flow redesign is projected to reduce monthly churn to 5.3% but will cost an estimated $2.1M to build and requires a small ongoing $150K/month support cost. Compute the new LTV per subscriber and determine whether the redesign is worth building, showing your reasoning (state any assumption about payback horizon).
- A separate proposal instead focuses on raising average margin from $12 to $12.60 (a pricing change) with no effect on churn. Compute its LTV impact per subscriber and compare the two proposals. Which lever is more sensitive to a 5% relative change, and why does that matter for how you'd prioritize future experiments?
1. Current LTV
\text{LTV} = \dfrac{m}{1 - \frac{1-c}{1+r}} = \dfrac{12}{1 - \frac{0.94}{1.015}} = \dfrac{12}{1 - 0.9261} = \dfrac{12}{0.0739} \approx \$162.38 per subscriber.
2. Churn-reduction proposal
New LTV: \dfrac{12}{1 - \frac{0.947}{1.015}} = \dfrac{12}{1 - 0.9330} = \dfrac{12}{0.0670} \approx \$179.10 per subscriber — a gain of about $16.72 per subscriber. Across 4,000,000 subscribers that is roughly $66.9M in aggregate LTV uplift, against a one-time $2.1M build cost and an ongoing $150K/month ($1.8M/year) support cost. Even assuming the churn improvement takes a full year to fully materialize across the base (a conservative payback assumption) and applying a generous cost buffer for uncertainty in the projection, this proposal pays for its full first-year cost ($2.1M + $1.8M ≈ $3.9M) many times over from LTV uplift alone — it is a strong build case, and the interesting number to present to stakeholders is the $66.9M aggregate LTV impact, not just the per-subscriber $16.72, since that is what justifies the investment relative to its cost.
3. Pricing proposal and sensitivity comparison
New LTV with margin only: \dfrac{12.60}{1 - \frac{0.94}{1.015}} = \dfrac{12.60}{0.0739} \approx \$170.50 — a gain of about $8.12 per subscriber, roughly half the churn proposal's gain, from a 5% relative increase in margin. The churn proposal moved churn by 5% relative (6% → 5.3%, an 11.7% relative reduction, larger than the 5% margin bump used for a fair comparison — worth noting the two changes compared aren't perfectly equal in relative size) and produced roughly double the LTV gain per subscriber of an equivalent-magnitude margin change. LTV is more sensitive to churn than to margin in this regime because churn compounds multiplicatively through the geometric series (it changes the retention ratio \frac{1-c}{1+r} that the whole infinite sum depends on), while a margin change only scales the series linearly. This matters directly for prioritization: in a product with churn materially above the minimum achievable rate, retention-improving experiments should generally be prioritized ahead of similarly-sized monetization experiments, because the same relative effort produces a larger LTV return through the compounding channel — which is exactly the argument for why a recommender or notification system's objective should be weighted toward retention rather than short-term monetizable engagement whenever the two are in tension.
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