# Unit economics

> ARPA, churn, customer acquisition cost (CAC), lifetime value (LTV), LTV to CAC and CAC payback: whether each customer is worth what it costs to win.

## The building blocks

- **ARPA**, average revenue per account: monthly recurring revenue divided by customers.
- **Churn rate**: customers lost in a month divided by customers at the start of the month.
- **Gross margin**: the share of revenue left after the direct cost of serving customers.
- **CAC**, customer acquisition cost: sales and marketing cost divided by new customers.

## Lifetime value

**LTV** is what a customer is worth over their life, in gross margin:

$$\mathit{LTV} = \frac{\text{ARPA} \times \text{gross margin}}{\text{churn rate}}$$

A customer who leaves with a 2 % chance each month stays $1 / 0.02 = 50$ months on average; LTV is the gross margin
they bring over those months. It holds when churn is above zero and stays roughly constant.

With an ARPA of 100, a gross margin of 80 % and a monthly churn of 2 %, LTV is 100 × 0.8 / 0.02 = 4,000.

## Is a customer worth winning?

- **LTV to CAC** compares that value with the cost to win the customer. With a CAC of 1,000 it is 4: each customer
  brings back four times what it cost.
- **CAC payback** is how many months of gross margin repay the CAC:

  $$\text{CAC payback} = \frac{\mathit{CAC}}{\text{ARPA} \times \text{gross margin}} = \frac{1{,}000}{100 \times 0.8} = 12.5 \text{ months}$$

The shorter the CAC payback, the less cash growth needs.

## The exact formulas

[Forecast formulas: KPIs and unit economics](/learn/formulas/forecast#9-kpis-and-unit-economics)