Source: https://guthlabs.ai/docs/instruments/ltv-cac-payback-unit-economics/mechanism/

instrument mechanism / verified-with-binding-errata

# LTV / CAC / Payback Unit Economics mechanism

The inspectable method record for LTV / CAC / Payback Unit Economics, kept separate from implementation and qualification.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**

## Model scope

The existing honest label correctly identifies this as a simplified SaaS model, but the UI or specification must explicitly define percentage input encoding, monthly periodicity, the LTV:CAC formula, and zero-denominator behavior before release.

- The LTV:CAC ratio is named but no explicit formula is provided; it should be defined as LTV divided by CAC.

- The LTV formula is valid only as a simplified perpetuity model assuming constant monthly churn, monthly ARPU, and no discounting, expansion, contraction, reactivation, or cohort variation.

- The notation grossMargin% and churnRate is ambiguous: percentage inputs such as 80 and 5 must be converted to decimal fractions 0.80 and 0.05 before calculation.

## Units and conventions

- ARPU is recurring revenue per customer per month.

- Gross margin percentages are entered as percentage points and converted by dividing by 100; for example, 80 means 0.80.

- Monthly churn percentages are entered as percentage points and converted by dividing by 100; for example, 5 means 0.05.

- CAC and ARPU are in the same currency, and CAC is a one-time acquisition cost.

- LTV is expressed in the same currency as ARPU and CAC; CAC payback is expressed in months.

- LTV:CAC ratio is dimensionless and is calculated as LTV/CAC.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "ARPU": 100,
    "ARPU_unit": "USD/month",
    "gross_margin_percent": 80,
    "monthly_churn_percent": 5,
    "CAC": 1200,
    "CAC_unit": "USD"
  },
  "expected_outputs": {
    "LTV": 1600,
    "LTV_CAC_ratio": 1.3333333333,
    "CAC_payback_months": 15
  },
  "working": "Gross margin fraction = 80/100 = 0.80. Monthly churn fraction = 5/100 = 0.05. Monthly gross-profit contribution = 100 × 0.80 = 80 USD. LTV = 80/0.05 = 1,600 USD. LTV:CAC = 1,600/1,200 = 1.3333333333. CAC payback = 1,200/80 = 15 months."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The specification exposes no stated validation behavior for zero churn, so the formula can encounter undefined division. It also does not define any formula branch or explicitly resolve whether percentage inputs are decimal fractions or percentage points, producing a material payback discrepancy under the alternate convention.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/ltv-cac-payback-unit-economics/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/ltv-cac-payback-unit-economics/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/ltv-cac-payback-unit-economics/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`