The textbook formula divides by churn, and when cohorts expand churn is negative: the answer then depends entirely on the horizon or the rate you choose, so state it.
When net revenue retention is above 100 per cent, the textbook LTV of gross margin divided by churn fails, because churn is negative. Replace it with a discount rate: LTV = gross margin / (r + 1 − NRR), which is finite only while NRR is below 1 + r. With an 80 per cent margin, 115 per cent NRR and a 20 per cent rate, one unit of new ARR is worth 16.00, an LTV:CAC of 4.00x on a CAC of 4.00. At 25 per cent the same company shows 2.00x.
Worked in full in The Venture Capital Associate by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
LTV to CAC is one of the first numbers a venture associate is handed in a pitch deck and one of the least comparable. For a company whose cohorts shrink, the formula behaves. For a company whose customers spend more each year, which is exactly the company investors want, the formula either explodes or produces whatever the chosen horizon allows. The arithmetic below shows how far apart the honest answers are.
| Input | Expanding cohorts | Decaying cohorts |
|---|---|---|
| Net revenue retention | 115% | 70% |
| Gross margin | 80% | 80% |
| CAC per unit of new annual revenue | 4.00 | 4.00 |
| Discount rate (base) | 20% | 20% |
Textbook: LTV = gross margin / (1 − NRR)
Horizon: LTVH = Σt=1..H gross margin × NRRt−1 / (1 + r)t
Perpetuity: LTV = gross margin / (r + 1 − NRR), valid while NRR < 1 + r
In Excel, a row of years with =GM*NRR^(t-1)/(1+r)^t summed to the horizon; the perpetuity is =GM/(r+1-NRR). The ratio is =LTV/CAC.
Step 1, the textbook formula. For the decaying company, revenue churn is 30 per cent: 0.80 / 0.30 = 2.67, an LTV:CAC of 0.67x. For the expanding company churn is minus 15 per cent and the formula gives minus 5.33, which means nothing. A customer whose spend grows 15 per cent a year has no undiscounted lifetime value; the sum keeps rising.
Step 2, the horizon. Count the gross profit year by year. Undiscounted, a unit of revenue at the expanding company is worth 2.78 over three years, 10.98 over eight and 81.95 over twenty. The decaying company converges on 2.67 and goes no further.
Step 3, the discount rate. Discounting at 20 per cent turns the expanding company's sum into a geometric series with ratio 1.15 / 1.20, and it converges: 0.80 / (0.20 + 1 − 1.15) = 0.80 / 0.05 = 16.00, which is 4.00x the CAC. For the decaying company, 0.80 / 0.50 = 1.60 and 0.40x.
| Horizon | 115% NRR, undiscounted | Ratio | 115% NRR, at 20% | Ratio | 70% NRR, at 20% | Ratio |
|---|---|---|---|---|---|---|
| 3 years | 2.78 | 0.69x | 1.92 | 0.48x | 1.28 | 0.32x |
| 5 years | 5.39 | 1.35x | 3.07 | 0.77x | 1.49 | 0.37x |
| 8 years | 10.98 | 2.75x | 4.62 | 1.15x | 1.58 | 0.39x |
| 10 years | 16.24 | 4.06x | 5.55 | 1.39x | 1.59 | 0.40x |
| 20 years | 81.95 | 20.49x | 9.17 | 2.29x | 1.60 | 0.40x |
| No cap | unbounded | 16.00 | 4.00x | 1.60 | 0.40x |
The same company, the same customers and the same CAC produce an LTV:CAC anywhere from 0.48x to 20.49x depending on two choices nobody prints on the slide. The decaying company is robust to those choices: discounted, its ratio sits between 0.32x and 0.40x at any horizon, and undiscounted it can never pass 0.67x, because its customers leave before the horizon matters. Expanding cohorts are more valuable and harder to measure.
| Discount rate | Denominator, 115% NRR | LTV | LTV:CAC | Denominator, 70% NRR | LTV:CAC |
|---|---|---|---|---|---|
| 20% | 0.05 | 16.00 | 4.00x | 0.50 | 0.40x |
| 25% | 0.10 | 8.00 | 2.00x | 0.55 | 0.36x |
| 30% | 0.15 | 5.33 | 1.33x | 0.60 | 0.33x |
Five points of discount rate halve the expanding company's LTV, because the denominator is the small gap between the rate and the growth in spend. When NRR approaches 1 + r the number becomes a statement about the rate, not the customer. A venture-stage rate is a reasonable choice; a cost-of-capital rate of 10 per cent with 115 per cent retention gives no answer at all.
A practical convention: report LTV:CAC discounted and capped at five years, and show the uncapped figure beside it. Here that is 0.77x and 4.00x. A business that needs year six onwards to repay its acquisition cost is relying on retention data that a young company does not yet have.
The common mistake is to plug a blended churn rate into margin over churn and report a ratio above 3x as if it were comparable with another company's. Taking revenue per customer with expansion built in for the numerator and logo churn for the denominator mixes two bases and flatters the result. The second is to read the ratio without the payback period: a 4.00x LTV:CAC earned over decades is a weaker business than a 2x earned in two years, which is why CAC payback belongs on the same page.
For expanding cohorts, use LTV = gross margin / (r + 1 − NRR) or a stated horizon, and always print the rate and the cap: 4.00x at 20 per cent, 2.00x at 25, 0.77x over five years. The two companies of chapter 6, and the acquisition cost at which growth starts destroying value, are computed in the free unit economics workbook for this case. Retention itself is measured in how to calculate net revenue retention.
LTV = gross margin / churn assumes revenue per customer shrinks each year. With 115 per cent net retention, revenue churn is minus 15 per cent and the formula returns minus 5.33 per unit of revenue, which is meaningless. The undiscounted sum of an expanding cohort never converges: 2.78 over three years, 10.98 over eight and 81.95 over twenty.
The conventional benchmark is 3x, but the ratio is only comparable if the horizon and discount rate are stated. The same illustrative company with 115 per cent retention shows 4.00x discounted at 20 per cent without a cap, 2.00x at 25 per cent and 0.77x over five years. Ask for the method before comparing the number.
Only with very cheap acquisition. At 70 per cent retention and an 80 per cent margin a unit of new revenue is worth at most 2.67 undiscounted, 1.60 at 20 per cent. At a CAC of 4.00 the ratio is 0.40x discounted; to reach 3x over five years discounted at 20 per cent, CAC would have to fall to 0.50 per unit.
Chapter 6 of The Venture Capital Associate asks whether a single customer is worth more than it costs to acquire; the free companion workbook computes it for two companies. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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