Unit economics that survive scrutiny

Work out the unit economics for {{business}}. Inputs: {{price, COGS components, CAC by channel, churn, expansion, gross margin, payback expectations}}.

1. Define each metric explicitly before computing — especially CAC (which costs are in?), gross margin (is support in COGS?), and churn (logo or revenue, monthly or annual, and how you annualise it).
2. Compute contribution margin per customer, CAC payback in months, and LTV using a method you justify — and show why the naive LTV formula overstates it here.
3. Break it down per acquisition channel and per segment; the blended number usually hides the truth.
4. Identify which single input the model is most sensitive to and by how much.
5. Stress test: what happens at 1.5x CAC, at 1.5x churn, and at a 10% price cut with 20% more volume?
6. State plainly whether this business works at current numbers, at what scale it starts to, and the one metric that has to move.

Call out any input that looks implausible for this kind of business.