The four inputs
ARPA is average revenue per account per month; if 100 customers pay you $5,000 in total, ARPA is $50. Gross margin is what remains after hosting, APIs, and support, typically 70 to 85 percent for SaaS. Monthly churn is the percentage of customers who cancel each month. CAC is total sales and marketing spend divided by new customers acquired in the same period, and it must include ad spend, tools, and contractor costs, not just the ads.
The worked example
Take a $50 per month product with 80 percent gross margin, 4 percent monthly churn, and $300 CAC. Average customer lifetime is 1 divided by 0.04, so 25 months. LTV is ARPA times gross margin divided by churn: 50 x 0.80 / 0.04 = $1,000. LTV to CAC is 1,000 / 300, about 3.3 to 1. CAC payback is 300 / (50 x 0.80) = 7.5 months, meaning each customer is underwater for their first 7.5 months.
How to read the results
An LTV:CAC of 3:1 or better is the standard health bar; below 1:1 you lose money on every customer. CAC payback under 12 months is the target for a bootstrapped company, because you cannot float long payback periods without outside capital. Churn dominates everything: the same example at 8 percent churn halves LTV to $500 and drops the ratio to 1.7. Fix churn before you spend more on acquisition.
Where founders get the math wrong
The most common error is skipping gross margin and using raw revenue, which flatters LTV by 20 to 30 percent. The second is measuring churn over one lucky month instead of a 3 to 6 month average. The third is counting only ad spend in CAC while ignoring tools, contractors, and your own time. With under 100 customers, treat all of these numbers as rough sketches, not truth.