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      "unit": "USD/customer",
      "detail": "12 months; excludes acquisition cost and fixed costs."
    },
    {
      "key": "ratio",
      "label": "Contribution LTV / CAC",
      "value": 2.4875951239358742,
      "unit": "×",
      "detail": ""
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    {
      "key": "payback",
      "label": "CAC contribution payback",
      "value": 5,
      "unit": "months",
      "detail": "First cumulative expected contribution recovery, checked with exact canonical decimal inputs."
    },
    {
      "key": "cash",
      "label": "Additional opening cash for trough",
      "value": 58025.462072332506,
      "unit": "USD",
      "detail": "Keeps modelled cash at or above zero."
    }
  ],
  "tables": [
    {
      "title": "Monthly operating and cash reconciliation",
      "columns": [
        {
          "key": "month",
          "label": "Month",
          "unit": ""
        },
        {
          "key": "customers",
          "label": "Active customers",
          "unit": ""
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        {
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          "unit": "USD"
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        {
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        {
          "key": "cashFlow",
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          "unit": "USD"
        },
        {
          "key": "cash",
          "label": "Closing cash",
          "unit": "USD"
        }
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    },
    {
      "title": "One-customer contribution and retention curve",
      "columns": [
        {
          "key": "age",
          "label": "Customer age",
          "unit": "months"
        },
        {
          "key": "survival",
          "label": "Retention probability",
          "unit": "%"
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        {
          "key": "price",
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          "unit": "USD/month"
        },
        {
          "key": "expectedContribution",
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          "unit": "USD/month"
        },
        {
          "key": "discountedContribution",
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          "unit": "USD"
        },
        {
          "key": "cumulativeContribution",
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          "unit": "USD"
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      ],
      "rows": [
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        {
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    {
      "title": "Acquisition cohort contribution ledger",
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          "unit": ""
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            5996.073382734373,
            5815.141868410363
          ],
          "contribution": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            4575,
            4445.634375,
            4319.868382734373,
            4197.604043410363
          ],
          "totalRevenue": 24368.849626144736,
          "totalContribution": 17538.106801144735
        },
        {
          "startMonth": 10,
          "acquired": 75,
          "customers": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            75,
            72.375,
            69.841875
          ],
          "revenue": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            6375,
            6182.634375,
            5996.073382734373
          ],
          "contribution": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            4575,
            4445.634375,
            4319.868382734373
          ],
          "totalRevenue": 18553.707757734373,
          "totalContribution": 13340.502757734372
        },
        {
          "startMonth": 11,
          "acquired": 75,
          "customers": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            75,
            72.375
          ],
          "revenue": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            6375,
            6182.634375
          ],
          "contribution": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            4575,
            4445.634375
          ],
          "totalRevenue": 12557.634375,
          "totalContribution": 9020.634375
        },
        {
          "startMonth": 12,
          "acquired": 75,
          "customers": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            75
          ],
          "revenue": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            6375
          ],
          "contribution": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            4575
          ],
          "totalRevenue": 6375,
          "totalContribution": 4575
        }
      ]
    }
  ],
  "warnings": [
    "Illustrative cash falls below zero. An additional 58,025.46 USD opening cash would cover the modelled cash trough, before any unmodelled financing or contingencies.",
    "Price expansion compounds for surviving customers. It is a supplied assumption, not a forecast, and may dominate longer-horizon economics.",
    "Payables exceed inventory days, creating a negative inventory/payable working-capital component. Review whether the operating terms support this cash benefit."
  ],
  "summary": "Expected new customers are 75 per month. The 12-month contribution LTV is 597.02 USD/customer, or 2.49× CAC. CAC contribution payback occurs in month 5. Closing cash is -54,942.09 USD; the lowest cash balance, including opening cash, is -58,025.46 USD.",
  "methods": [
    "Expected new customers each month = acquisition spend / CAC. Acquisition occurs at the beginning of the month, with first revenue in that month.",
    "For cohort age a: active customers = cohort size × (1 − churn)^a; price = initial price × (1 + expansion)^a.",
    "Contribution = revenue − active customers × variable cost. Monthly operating profit subtracts acquisition spend and fixed costs.",
    "Working capital = revenue × receivable days / 30 + variable cost total × (inventory days − payable days) / 30. Cash flow = operating profit − change in working capital.",
    "Finite-horizon contribution LTV discounts one customer’s expected contributions at ages 0 to horizon − 1. CAC payback uses undiscounted cohort contribution. Its first recovery crossing is evaluated from exact canonical JSON-number decimals, without a numerical tolerance."
  ],
  "limitations": [
    "Expected fractional customers and constant acquisition, churn, expansion and cost assumptions. Months have 30 days for working capital.",
    "Finite-horizon LTV is not infinite lifetime value. No taxes, capex, financing, terminal value, seasonality or saturation.",
    "Customers surviving at horizon generate no terminal value; working capital is not released at horizon.",
    "Numerical input precision: use zero or absolute values of at least 0.000000001. Smaller nonzero inputs are rejected explicitly."
  ]
}