LTV / CAC / Payback Unit Economics implementation

Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

Record owner

Guth Instruments

Lifecycle

verified-with-binding-errata

Evidence ID

t4-281

Effect

Computation or source lookup only

Input and validation requirements

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.

Required corrections

[
  {
    "stress_correction": {
      "vector_inputs": {
        "ARPU_cents_per_month": 10000,
        "gross_margin_percent": 80,
        "monthly_churn_percent": 5,
        "CAC_cents": 24000
      },
      "wrong_outputs": {
        "LTV_cents": 16000,
        "LTV_CAC_ratio": 6.6666666667,
        "CAC_payback_months": 3
      },
      "corrected_outputs": {
        "LTV_cents": 160000,
        "LTV_CAC_ratio": 6.6666666667,
        "CAC_payback_months": 3
      },
      "method": "LTV = ARPU*margin/churn = 10000*0.8/0.05 = 160000 cents; only LTV_cents was wrong, ratio/payback were already correct (self-consistent with the $-denominated vectors in the same instrument)"
    }
  }
]

Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

{
  "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."
}

Other records

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
• STRESS_TEST_CORRECTIONS_APPLIED.json