Stop Confusing Retention with “Months Stayed”: The Break‑Even Trick Interviewers Want

When you switch a customer from a one‑time purchase to a subscription, the core interview question is: how long does the subscriber need to stay to break even? The clean way to answer is to convert the one‑time profit into "months of profit," then translate months into a monthly retention rate — and avoid the common inversion mistake.

The step‑by‑step method (with numbers)

1. Compute the one‑time sale profit (the contribution you'd lose by moving the customer to a subscription).

   • Example: one‑time price = $29, margin = 50% → one‑time profit = 29 × 0.50 = $14.50.

2. Compute the subscription monthly contribution (revenue — the same cost basis as before, if you assume cost per customer is unchanged).

   • Example: subscription price is 20% off → 29 × 0.80 = $23.20 monthly revenue.
   • If you assume the per‑month cost basis equals the original one‑time profit's cost structure, monthly contribution = 23.20 − 14.50 = $8.70.

3. Find break‑even months (how many months of that monthly contribution equal the one‑time profit):

   • break_even_months = one_time_profit / monthly_contribution
   • Example: 14.50 / 8.70 ≈ 1.67 months.

4. Convert months to a monthly retention rate using the geometric retention model.

   • With constant monthly retention r, expected tenure (in months) = 1 / (1 − r).
   • Solve for r: r = 1 − 1 / expected_months.
   • Example: 1 / (1 − r) = 1.67 → 1 − r = 1 / 1.67 ≈ 0.5988 → r ≈ 0.4012 → ~40% monthly retention.

Important: do NOT compute retention by inverting break_even_months (i.e., don't do r = 1 / months). That inversion is wrong — the correct algebra gives r = 1 − 1 / months. For the example above, the correct monthly retention is ~40% (not 60% or 66.7%).

Quick formulas cheat‑sheet

• monthly_contribution = subscription_price − assumed_cost_base
• break_even_months = one_time_profit / monthly_contribution
• monthly_retention r = 1 − 1 / break_even_months (assuming geometric retention)

Or, in terms of churn c = 1 − r: expected_months = 1 / c.

Assumptions and caveats

• We used a geometric model (constant monthly retention). Real cohorts may not follow constant retention.
• The "cost basis" used to compute monthly contribution must be consistent with how you computed the one‑time profit (same margin/cost assumptions).
• Small differences in rounding or initial assumptions can change practical recommendations; call out assumptions in an interview.

TL;DR (what to say in an interview)

"Compute one‑time profit and monthly contribution, divide to get break‑even months, then convert months to retention using r = 1 − 1 / months. In this example break‑even ≈ 1.67 months → required monthly retention ≈ 40%."

One‑sentence tip

Don't confuse "months stayed" with "monthly retention" — months is the expected tenure (1/(1−r)), and retention is 1 − 1/tenure, not 1/tenure.