Customer lifetime value

Customer Lifetime Value (LTV)

Four modeling tiers from descriptive to Monte Carlo simulation. Always outputs an inline HTML dashboard + exec recommendation. Reference book: Katsov §3.5.7 (pp. 113–120).

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Core LTV Formula (Berger & Nasr, 1998 — Katsov eq. 3.23)

LTV(u) = Σ_{t=1}^{T}  (R − C) · r^(t−1) / (1 + d)^(t−1)

Parameters:

• R — average revenue per customer per period
• C — average cost per customer per period
• r — retention rate (probability of staying one more period)
• d — discount rate (cost of capital per period)
• T — projection horizon (periods)

Key insight: LTV is the upper bound on acquisition spend. Customer equity = Σ LTV(u) across all customers.

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Model Selection

Scenario	Model	Script
Quick estimate, segment-level	Descriptive (eq. 3.23–3.24)	ltv_descriptive.py
Multi-state customer journey (recency/frequency states)	Markov Chain (eq. 3.25–3.28)	ltv_markov_chain.py
Individual-level with churn survival function	Regression + Survival (eq. 3.30–3.31)	ltv_survival.py
Confidence intervals + uncertainty quantification	Monte Carlo on Markov	monte_carlo_ltv.py
Portfolio-level metric	Customer Equity	customer_equity.py

→ Read references/model_selection_ltv.md for deeper guidance.

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Workflow

Step 1 — Gather Parameters

Minimum viable inputs:

• Net margin per period m₀ = R − C
• Retention rate r (historical cohort analysis or survival model output)
• Discount rate d (WACC or cost of capital; 8–15% annually typical)
• Horizon T (typically 24–60 months)

For Markov: define states (recency buckets), transition matrix P, gain vector G.
For Survival: requires transaction history with churn events or heuristic lapse rule.

Step 2 — Run Model

# Descriptive
python scripts/ltv_descriptive.py --m0 100 --mM 150 --tau 3 --r 0.9 --d 0.1 --T 5

# Markov chain
python scripts/ltv_markov_chain.py --transitions data/transitions.csv \
       --gains "75,-5,-5,0" --discount 0.001 --horizon 24

# Survival regression
python scripts/ltv_survival.py --transactions data/txns.csv --horizon 36

# Monte Carlo
python scripts/monte_carlo_ltv.py --transitions data/transitions.csv \
       --gains "75,-5,-5,0" --n-sims 10000 --horizon 36

Step 3 — Export Dashboard JSON

python scripts/export_ltv_dashboard_json.py --results results/ltv_output.csv \
       --model-type descriptive --output dashboard_data.json

Step 4 — Render Inline Dashboard

Load references/ltv_dashboard_template.html, inject JSON, call show_widget.

Output sequence:

1. [bash_tool] Run model script → capture output
2. [bash_tool] export_ltv_dashboard_json.py → JSON
3. [show_widget] Render HTML dashboard
4. [text] 3–5 line exec recommendation
5. [text] Model caveats / sensitivity notes

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Scripts Reference

Script	Key Inputs	Key Outputs
ltv_descriptive.py	m0, mM, tau, r, d, T	LTV table + LTV curve JSON
ltv_markov_chain.py	transitions CSV, gains, d, T	LTV vector per initial state
ltv_survival.py	transaction history CSV	Per-customer LTV with survival function
monte_carlo_ltv.py	transitions CSV, gains, n_sims, T	LTV distribution: mean, p10, p50, p90
customer_equity.py	scored customers CSV	Total customer equity + segment breakdown
export_ltv_dashboard_json.py	any LTV output CSV	JSON for HTML dashboard

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Output Format — Visualization First

Primary output: inline HTML dashboard (show_widget). Always render before text.

Dashboard panels (see references/ltv_dashboard_template.html):

1. KPI bar — LTV (base state), customer equity, payback period, breakeven retention rate
2. LTV curve over time — discounted cumulative LTV vs. horizon (shows saturation)
3. Retention sensitivity — LTV as function of r from 0.5→0.99
4. Discount rate sensitivity — LTV as function of d from 0→0.3
5. Monte Carlo distribution — histogram with p10/p50/p90 bands (if MC model)
6. Segment comparison table — LTV by customer state / segment

Fallback (if show_widget unavailable): Katsov Table 3.6 format — year | net_profit | retention_rate | expected_profit | discount_multiplier | discounted_profit | cumulative_ltv

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Key Equations Reference

# Descriptive with growing net profit (eq. 3.24):
m_t = m0 + (mM − m0)(1 − e^{−kt})    where k = ln(2)/τ

# Regression/Survival LTV (eq. 3.30–3.31):
LTV(u) = Σ_t p(u,t) · m(u,t)
LTV(u) = Σ_t S_u(t) · m(u,t)         [survival function replaces retention]

# Markov LTV (eq. 3.28):
V = Σ_{t=1}^{T} [1/(1+d)^{t−1}] P^t G

# Customer equity:
CE = Σ_u LTV(u)

# Retention budget optimization (eq. 3.49–3.52):
r = r_max(1 − e^{−k_r R})            [retention as function of spend R]
argmax_{A,R} N_p(a·LTV(r) − c) + N_c·LTV(r)   s.t. A + R ≤ budget

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Key Caveats

• Retention rate is the dominant driver. A 5pp improvement in r has larger LTV impact than a 10% increase in margin. Always run sensitivity.
• Discount rate encodes risk. Higher d → lower LTV → lower acquisition bid ceiling. Use WACC or sector-appropriate rate.
• Descriptive model ≠ causal model. Changing a marketing action changes r, which changes LTV — the feedback loop requires eq. 3.49.
• Survival model requires lapse definition. Must define churn event heuristically (e.g., 5 months without purchase = lapsed). Results are sensitive to this.
• Monte Carlo provides variance, not bias correction. Use MC to communicate uncertainty to CMO/CFO, not to correct model specification.

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Integration with Agency Growth OS

Skill	Handoff
response-uplift-modeling	Savability × LTV → retention targeting score (eq. 3.40)
audience-segmentation-brief	Segment-level LTV inputs (R, C, r per persona)
crm-journey-architect	LTV payback period → journey trigger timing
margin-simulation	Customer equity → business valuation input
measurement-incrementality	LTV uplift as campaign success metric

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Reference Files

• references/model_selection_ltv.md — Descriptive vs Markov vs Survival decision guide
• references/katsov_ltv_excerpts.md — Key equations, Table 3.6, and Markov example
• references/ltv_dashboard_template.html — Reusable HTML dashboard. Inject SKILL_DATA_JSON