A3 · Comparison · FAQPage schema
Naive LTV vs Corrected LTV (Fader-Hardie sBG)
At a glance
| Dimension | Naive LTV | sBG LTV |
|---|---|---|
| Formula | ACV × gross_margin / monthly_churn_rate | Probabilistic survival model fitted to cohort churn data |
| Churn assumption | Constant hazard rate for all customers | Heterogeneous — customers have different churn probabilities |
| Typical overstatement | 20–60% above true LTV in B2B SaaS | Baseline (correct by construction) |
| Data required | Single aggregate churn rate | Cohort-level survival curves (monthly retention by cohort) |
| Computational complexity | Arithmetic | Maximum likelihood estimation (Excel-solvable) |
| Use case | Quick heuristic, board deck shorthand | Unit economics, CAC payback, pricing, M&A due diligence |
| Sensitivity to early churn | Understates: spreads early losses across full life | Correctly weights early-period churn more heavily |
| Academic validation | None — folk formula | Fader & Hardie (2007, 2010), peer-reviewed |
When to use Naive LTV
Naive LTV is acceptable for rapid, directional estimates in early-stage companies where cohort data is insufficient to fit a survival model (fewer than 3 complete cohort years of data). It is also acceptable as a shorthand metric in board decks when everyone in the room understands its limitations. Never use naive LTV for M&A valuations, pricing optimization, or any decision where a 20-40% error in customer lifetime value would change the decision.
When to use sBG LTV
Use Fader-Hardie sBG LTV whenever the stakes justify the additional modeling effort: CAC budget setting (spending to a 3:1 LTV:CAC ratio requires an accurate denominator), cohort-level profitability analysis, pricing tier optimization, and investor or acquirer due diligence. The sBG model requires only monthly retention data by cohort, which any CRM or billing system can export. The estimation itself can be done in Excel using Solver. Peter Fader and Bruce Hardie have published free Excel templates on their faculty pages.
Trade-offs
The naive formula LTV = ARPU / churn treats all customers as statistically identical and assumes that the cohort's churn rate today will remain constant forever. Both assumptions are wrong in practice. Real B2B SaaS churn is heterogeneous: some customers are structurally more likely to churn (wrong-fit, budget-constrained, low-activation) while others are deeply embedded and will retain for a decade. When you observe a cohort over time, the high-risk customers churn early, leaving a progressively more retained 'survivor' population. This means the apparent churn rate of a cohort declines over time — it looks like you are getting better at retention, but you are actually observing the natural filtering of the population. Naive LTV ignores this dynamic and projects the current aggregate churn rate forward indefinitely, creating the overstatement. For a company with 5% monthly churn, naive LTV implies a 20-month average customer life. The sBG model, fitted to the same data, will typically produce a 12–15 month average life — enough to change a funding decision or a CAC ceiling. The business implication: if you have been making CAC investment decisions based on naive LTV, you may have been overpaying for customer acquisition. The corrected number produces a lower LTV:CAC ratio, which argues for tighter CAC discipline or higher gross margin targets.
Frequently asked questions
What is the shifted Beta-Geometric (sBG) model?
Developed by Peter Fader and Bruce Hardie at Wharton, the sBG model assumes that each customer has a fixed (but unobserved) churn probability drawn from a Beta distribution, and that churn can occur at each renewal period. Maximum likelihood estimation fits the two Beta distribution parameters (alpha, beta) to observed cohort retention curves. The result is a per-customer survival probability at any future period, and a closed-form expected LTV.
By how much does naive LTV typically overstate in practice?
In Fader and Hardie's analysis of subscription datasets — and in subsequent practitioner replications on SaaS cohorts — naive LTV overstates corrected LTV by 20-40% at a 5% monthly churn baseline, and by 40-60% at a 2-3% monthly churn baseline (longer-lived cohorts accumulate more survivor bias over time). The overstatement is largest for companies with low churn and long average customer life.
Do I need a data science team to implement sBG LTV?
No. Fader and Hardie have published Excel workbooks with Solver configurations that fit the sBG model to a standard retention curve table (% of cohort surviving at months 1, 2, 3, etc.). The input is a single cohort survival curve from your billing system. Implementation takes 2–4 hours for an analyst comfortable with Excel Solver. Python implementations are also available in the lifetimes open-source library by Cam Davidson-Pilon.
How does corrected LTV affect LTV:CAC ratio targets?
If your naive LTV is $30,000 and your CAC is $10,000, you report a 3:1 ratio. If the sBG-corrected LTV is $20,000, your true ratio is 2:1 — below the 3:1 floor most investors use as the minimum healthy threshold. This gap is material for fundraising conversations and for setting CAC budgets. Companies that discover this discrepancy typically need to either reduce CAC (improve efficiency) or increase gross margin and ARPU to restore the ratio.
Should I use LTV with or without gross margin?
Always report LTV net of gross margin (i.e., LTV = expected revenue × gross margin %, not expected revenue alone). Gross-margin-adjusted LTV is the economically correct numerator for LTV:CAC because CAC is a cash cost that must be recovered from gross profit, not revenue. The industry convention is 70-75%+ gross margin for SaaS. Using revenue LTV inflates the ratio and overstates the business's economics.
Where this sits in the GTM World Model
Corrected LTV is a foundational input to the GTM World Model's CAC Efficiency framework — the LTV:CAC ratio is only a reliable decision variable when LTV uses a survival-model estimate rather than the naive constant-churn approximation.
How to cite this
@misc{shalvi_gtm_naive_ltv_vs_corrected_ltv_2026,
author = {Singh, Shalvi},
title = {Naive LTV vs Corrected LTV (Fader-Hardie sBG) — GTM World Model Comparison},
year = {2026},
url = {https://shalvisingh.com/gtm/vs/naive-ltv-vs-corrected-ltv}
} Singh, Shalvi. "Naive LTV vs Corrected LTV (Fader-Hardie sBG) — GTM World Model Comparison." shalvisingh.com, 2026. https://shalvisingh.com/gtm/vs/naive-ltv-vs-corrected-ltv