Why sensitivity matters
CAC payback is a simple formula, but the inputs are not stable. ARPA shifts with pricing and mix, and gross margin shifts with COGS and usage. Sensitivity analysis helps you avoid false confidence by showing how payback changes under a small set of scenarios.
Payback formula (gross profit payback)
Payback (months) = CAC / (ARPA * gross margin).
How to pick scenario ranges
- Start with ranges that reflect your uncertainty: e.g., +/-10-20% ARPA and +/-5-10% gross margin.
- If you have segmented data, do sensitivity per segment (plan/channel) instead of using blended averages.
- Widen ranges when channels are volatile or pricing is changing; narrow them once economics stabilize.
How to interpret the grid
- If payback is highly sensitive to margin, invest in COGS reduction and variable cost control.
- If payback is highly sensitive to ARPA, focus on pricing, packaging, and upsell/expansion paths.
- Use payback with retention: long payback + high early churn can still be unprofitable even if LTV is high on paper.
Common mistakes
- Using revenue-based payback while CAC is fully-loaded (mismatch).
- Mixing time units (monthly ARPA with annual CAC, or vice-versa).
- Treating sensitivity outputs as precision instead of scenario planning.