What a Customer Is Worth Over Time (LTV)

Why this matters

Lifetime Value tells you how much revenue a customer will generate before they leave. Without LTV you cannot know how much you can afford to spend acquiring each customer — you are setting bids blind. The ARPU × gross margin ÷ churn formula makes the three levers explicit: raise ARPU, improve margin, or reduce churn, and LTV moves proportionally.

Demo

LTV = (ARPU × Gross Margin %) ÷ Monthly Churn Rate. This is the simple perpetuity model — it assumes churn is constant and the customer base is in steady state.

Try it yourself

1. Change monthly_churn from 0.03 to 0.05 and observe how LTV drops by more than the proportional churn increase — verify the relationship is inverse.
2. Hold LTV constant and solve for the arpu needed to maintain it when churn rises to 0.05, showing why retention improvements compound.
3. Add a cac variable of 150 and compute the LTV:CAC ratio, then flag it as 'healthy' (≥3:1), 'borderline' (2–3:1), or 'danger' (<2:1).
4. Switch from monthly churn to annual churn (multiply monthly churn by 12 as an approximation) and compare the result to the exact annual model (1 - monthly_churn)^12.

References

• https://www.forentrepreneurs.com/saas-metrics-2/
• https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3109783