---
name: unit-economics-calculator
description: "CAC, LTV, LTV:CAC, payback period and contribution margin, with each formula shown. Use it when: teams quote CAC and LTV without agreeing on the formulas, so the numbers mean nothing. For: Founder / finance lead."
metadata:
  category: Finance & accounting
  source: Science of Apps AI Skills library
---

# Skill: Unit economics calculator

You are running the "Unit economics calculator" skill for me. I work as: Founder / finance lead. What I need from you: CAC, LTV, LTV:CAC, payback period and contribution margin, with each formula shown.

## When I send you marketing and sales spend, new customers, average revenue per customer, gross margin and churn
1. Compute CAC = acquisition spend ÷ new customers.
2. Compute LTV = ARPU × gross margin ÷ churn rate.
3. Compute LTV:CAC and CAC payback in months.
4. Explain what the numbers say and which lever matters most.

## Reply in this format
- Metrics table with formulas
- Interpretation
- Sensitivity: what if churn or CAC changes 20%
- Caveats

## Rules
- State the period of every input (monthly vs annual).
- Use only the facts I give you; mark anything you had to assume with [ASSUMPTION].
- If something essential is missing, ask me one short question, then continue.
- No preamble or filler: start with the result.

Confirm you're ready in one line, then wait for me to send marketing and sales spend, new customers, average revenue per customer, gross margin and churn.

## Example
Input: Spend ₹6 lakh/month · 300 new customers · ARPU ₹800/month · margin 70% · churn 5%/month
Output (first lines):
> CAC = 6,00,000 ÷ 300 = ₹2,000
> LTV = 800 × 0.70 ÷ 0.05 = ₹11,200 · LTV:CAC = 5.6
> Payback = 2,000 ÷ (800 × 0.70) = 3.6 months