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Case Math & Quant Fluency · Lesson 5

Unit economics: CAC, LTV, and churn

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Intuition

Unit economics asks one brutally simple question: do you make money on a single customer? A company can have soaring revenue and still be doomed if each customer costs more to win and serve than they ever pay back. It's like a leaky bucket — pouring in more water (growth) doesn't help if the hole (bad unit economics) is bigger than the inflow.

Get the unit economics right and growth multiplies profit. Get them wrong and growth multiplies losses. That's why investors and case interviewers obsess over them.

Framework

  • CAC (Customer Acquisition Cost) = total sales & marketing spend / new customers won. The cost to land one customer.
  • LTV (Lifetime Value) = (average revenue per customer per period × gross margin) × average lifetime. The total profit a customer delivers over their life.
  • Churn = % of customers lost per period. Average lifetime ≈ 1 / churn rate.
  • The test: LTV must comfortably exceed CAC (rule of thumb ~3:1). And payback period — how many months of margin to recover CAC — should be short.

Worked Example

A streaming app spends $6M on marketing to win 200,000 subscribers, so CAC = $30. Each pays $10/month at 70% gross margin = $7 contribution/month. Monthly churn is 5%, so average lifetime ≈ 1/0.05 = 20 months. LTV = $7 × 20 = $140. LTV:CAC = 140:30 ≈ 4.7:1 — healthy. But if churn doubled to 10%, lifetime halves to 10 months, LTV drops to $70, and the ratio falls to ~2.3:1. Same business, churn quietly decides whether it thrives.

Pitfalls

  • Using revenue instead of margin in LTV — you only keep the margin, not the whole price.
  • Ignoring payback period: a great LTV that takes five years to earn back can still sink a cash-strapped startup.
  • Treating churn as a footnote when it's the single biggest lever on LTV.