LTV / CAC

Compute LTV, CAC payback, and LTV/CAC ratio with the four canonical formulas side by side. Anchor the verdict on Skok's 3:1 rule, layer on a16z NDR, Sequoia contribution-margin, and Tunguz AI-inference adjustments. Output a styled Excel workbook with a sensitivity heatmap and a 36-month synthetic cohort projection.

Step 1: Ask the user up to 6 inputs

Ask in order. The first 3 are required; the rest have defaults.

1. ARPU (monthly revenue per customer, $), e.g. 200
2. Customer churn rate (monthly, decimal), e.g. 0.03 for 3%/mo
3. CAC (customer acquisition cost, $), e.g. 1500
4. Net revenue expansion (monthly, decimal, optional), e.g. 0.005 for 0.5%/mo. Default 0. If they have NDR > 100%, this is positive.
5. Gross margin (decimal, optional), e.g. 0.78. Default 0.78 (78%, typical SaaS).
6. Inference / variable cost per customer per month ($, optional), only relevant for AI products. Default 0.

If the user is hesitant on inputs, suggest they start with the example fixture (examples/inputs.json).

Step 2: Run

python skills/ltv-cac/run.py \
  --arpu 200 \
  --churn 0.03 \
  --cac 1500 \
  --expansion 0.005 \
  --gross-margin 0.78 \
  --inference-cost 0 \
  --out-dir /tmp/ltv-cac-<client>-<date>

Or load all inputs from a JSON file:

python skills/ltv-cac/run.py --inputs path/to/inputs.json --out-dir /tmp/ltv-cac

Step 3: KPIs the user gets

Verdict sheet (the headline)

• Skok basic LTV: ARPU × GM / churn (the canonical 3:1 reference)
• NDR-adjusted LTV: ARPU × GM / (churn − expansion) (a16z framework)
• AI-adjusted LTV: (ARPU × GM − inference) / churn (Tunguz inference erosion)
• Sequoia contribution-margin LTV: combines the above two: (ARPU × GM − inference) / (churn − expansion)
• CAC Payback: months to recover CAC from gross profit. Basic and AI-adjusted.
• LTV/CAC ratio: color-coded: red <1, yellow 1-3, green 3-5, blue >5
• Verdict statement: plain-English read with Skok 3:1 anchor + AI flag if inference erodes LTV >20%
• NDR: monthly and annual-compounded
• Citations: every formula tagged with its source

Sensitivity sheet

• LTV/CAC heatmap across monthly churn (1% to 10%) × gross margin (50% to 90%)
• Same color coding as the verdict
• Lets the founder see "if I cut churn from 5% to 3% at the same GM, where does my LTV/CAC land?"

Cohort Projection sheet

• Synthetic 100-customer cohort projected forward 36 months with the user's churn + expansion + inference inputs
• Columns: customers retained, MRR, cumulative gross profit, vs cohort CAC
• Line chart of cumulative GP vs CAC
• Payback callout: "Cohort breaks even at lifetime month N" or "Doesn't break even within 36mo"

Step 4: Output

Default output (--output all) writes to /tmp/ltv-cac-<client>-<date>/:

• ltv_cac_workbook.xlsx: the 3-sheet styled Excel file
• summary.md, markdown digest with the verdict + tables, paste-able into a doc
• inputs.json, the inputs you used (re-runnable: pass with --inputs)
• ltv_summary.csv, every formula's LTV + ratio
• cac_payback.csv, basic and AI-adjusted payback months
• ndr.csv, monthly + annual NDR
• sensitivity.csv, full heatmap data
• cohort_projection.csv, month-by-month projection

Step 5: After running

Show the user 4-5 lines:

1. The headline verdict (one of: Underwater 🔴 / Tight 🟡 / Healthy 🟢 / Possibly under-investing 🟦)
2. Skok basic LTV/CAC ratio
3. CAC payback months
4. NDR (annual)
5. Path to the workbook

If the AI-adjusted LTV diverges from the basic LTV by >20%, flag inference cost as a key sensitivity.

When to use

• A founder asks "is my SaaS healthy?" / "should I scale paid acquisition?"
• An investor wants LTV, CAC payback, NDR for a deck
• Modeling unit economics for a new pricing tier
• Comparing scenarios: "what if I raise prices 10%?" / "what if I cut churn from 5% to 3%?"

When NOT to use

• The user has actual cohort data and wants observed retention curves → use /cohort-analysis instead. This skill is for forward-looking modeling from assumptions.
• Pre-revenue product with no churn data → there's nothing to compute. Suggest gathering 3-6 months of data first, then running both /cohort-analysis (observed) and /ltv-cac (modeled) side by side.

Try it without thinking

The examples/inputs.json ships with a typical mid-stage B2B-SaaS profile (ARPU $200, 3% churn, $1,500 CAC, 78% GM, no inference cost). Run:

python skills/ltv-cac/run.py --inputs skills/ltv-cac/examples/inputs.json --out-dir /tmp/ltv-cac-demo
open /tmp/ltv-cac-demo/ltv_cac_workbook.xlsx

Frameworks referenced

• David Skok / Matrix Partners: "SaaS Metrics 2.0", origin of the 3:1 LTV/CAC rule and the canonical LTV = ARPU × GM / churn formula.
• a16z: "The 16 Startup Metrics", introduced NDR (Net Dollar Retention) as a first-class LTV input.
• Sequoia Capital: argues for contribution-margin LTV (deduct variable costs from GM) over headline gross-margin LTV.
• Tomasz Tunguz / Theory: "Unit Economics of LLMs", showing how variable inference costs erode AI-product LTV in ways the traditional formulas miss.

The skill computes all four side by side so the user sees where they agree (and where AI economics break the textbook).