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Compute LTV with Churn, Margin and Discounting, Then Judge a CAC of 150 USD
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A subscription product charges $20 per month at a 60 percent contribution margin. Monthly churn is 5 percent (constant, for this exercise). The finance team uses an annual discount rate of 12 percent and payments arrive at the start of each month. Paid acquisition costs $150 per customer.
- Compute LTV with the simple formula on revenue and on contribution margin.
- Compute the discounted LTV with the closed form m(1+d)/(c+d), where d is the monthly discount rate.
- Compute the naive payback period (\text{CAC}/m) and the payback period for the cohort, undiscounted and discounted, accounting for churn.
- Is this a good acquisition channel? What else would you check before spending more?
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