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?
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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.
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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.