C4 · Economics & metrics · model-dependent

Customer Lifetime Value

Also: LTV

Definition. Contribution LTV is the expected present value of customer contribution before acquisition cost: survival-weighted revenue less relevant service and retention costs. Estimate contribution conditional on the customer being active. Customer survival is distinct from revenue retention. A fitted sBG model can address churn heterogeneity, but has no universal downward haircut or guaranteed accuracy.

model-dependent — survival, contribution, timing, discount, censoring and tail assumptions must be validated Last updated 2026-06-18 Source: Fader & Hardie (2007), How to Project Customer Retention, https://www.brucehardie.com/papers/021/. Older methodological foundation; not evidence for a universal B2B SaaS LTV haircut.

Formula

Customer Lifetime Value model-dependent

L T V_{t_{0} : H} = t = t_{0} \sum H \frac{S ( t ) E [ c _{t} ∣ active _{t} ]}{( 1 + d ) ^{t}}, S (0) = 1

Plain English: LTV = sum over the declared horizon of S(t) × expected contribution at t given active / (1 + period discount rate)^t

Notation: LTV_0:H = Σ_{t=t0}^{H} S(t) × E[contribution_t | active at t] / (1+d)^t; S(0)=1, with t0=0 for an initial payment or t0=1 for future payments only

Benchmark by stage

Source: Fader & Hardie (2007), How to Project Customer Retention, https://www.brucehardie.com/papers/021/. Older methodological foundation; not evidence for a universal B2B SaaS LTV haircut.

Stage	Customer Lifetime Value	Notes
Geometric scenario	c/(1-p)	Zero discount, constant contribution and survival, initial payment included; finite only for p<1.
Future payments only	c×p/(1-p)	Same assumptions; excludes the initial payment. Use matching period units.
Heterogeneous churn	Fit and validate	sBG does not imply a universal reduction. Forecast differences depend on matched hazards, cohort age and model fit.
Economic decision	Contribution LTV / CAC	Subtract acquisition cost once for net value. Include uncertainty, cash timing and capacity constraints.

Naive vs corrected

Version	Formula
Naive	For constant contribution c, constant customer survival p and zero discount: initial-payment LTV = c/(1-p); future-only LTV = c×p/(1-p). These are conditional scenarios, not laws for aggregate revenue churn.
Corrected	For churn probability q ~ Beta(α,β), sBG cohort survival is S(t)=B(α,β+t)/B(α,β), S(0)=1. Fit to observed cohort survival with censoring and validate on held-out periods. State the horizon, contribution costs, timing and discount; no fixed cohort age guarantees a reliable fit.

Common errors

Using annual ACV with monthly churn or discount
Substituting GRR or NRR for customer survival
Applying a universal 20–60% haircut for churn heterogeneity
Ignoring initial versus future-only payment timing, censoring or the unobserved tail
Treating sBG fit as guaranteed truth or ignoring conditional contribution and changing costs

Where this sits

Part of the Economics & metrics (C4) cluster in the GTM World Model. Related to the model's "With constant contribution c and zero discount, sBG Σ_{t=0}∞S(t)=(α+β-1)/(α-1), so initial-payment LTV=c×(α+β-1)/(α-1); future-only LTV=c×β/(α-1), for α>1, β>0. For α≤1 the positive-contribution undiscounted infinite sum diverges. A finite horizon or positive discount changes this result." equation.

cac →ltv cac ratio →nrr →grr →

How to cite this

@misc{shalvi_gtm_metric_ltv_2026,
  author = {Singh, Shalvi},
  title  = {Customer Lifetime Value — GTM World Model Metrics},
  year   = {2026},
  url    = {https://shalvisingh.com/gtm/metrics/ltv}
}

Singh, Shalvi. "Customer Lifetime Value — GTM World Model Metrics." shalvisingh.com, 2026. https://shalvisingh.com/gtm/metrics/ltv