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"key": "ratio", "label": "Contribution LTV / CAC", "value": 0.25416666666666665, "unit": "×", "detail": "" }, { "key": "payback", "label": "CAC contribution payback", "value": null, "unit": "months", "detail": "First cumulative expected contribution recovery, checked with exact canonical decimal inputs." }, { "key": "cash", "label": "Additional opening cash for trough", "value": 695795, "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": "" }, { "key": "revenue", "label": "Revenue", "unit": "USD" }, { "key": "variableCosts", "label": "Variable costs", "unit": "USD" }, { "key": "contribution", "label": "Contribution", "unit": "USD" }, { "key": "acquisitionSpend", "label": "Acquisition spend", "unit": "USD" }, { "key": "fixedCosts", "label": "Fixed costs", "unit": "USD" }, { "key": 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"customers": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 75, 0, 0, 0, 0, 0, 0, 0 ], "revenue": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6375, 0, 0, 0, 0, 0, 0, 0 ], "contribution": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4575, 0, 0, 0, 0, 0, 0, 0 ], "totalRevenue": 6375, "totalContribution": 4575 }, { "startMonth": 18, "acquired": 75, "customers": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 75, 0, 0, 0, 0, 0, 0 ], "revenue": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6375, 0, 0, 0, 0, 0, 0 ], "contribution": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4575, 0, 0, 0, 0, 0, 0 ], "totalRevenue": 6375, "totalContribution": 4575 }, { "startMonth": 19, "acquired": 75, "customers": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 75, 0, 0, 0, 0, 0 ], "revenue": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6375, 0, 0, 0, 0, 0 ], "contribution": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4575, 0, 0, 0, 0, 0 ], "totalRevenue": 6375, "totalContribution": 4575 }, { "startMonth": 20, "acquired": 75, "customers": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 75, 0, 0, 0, 0 ], "revenue": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6375, 0, 0, 0, 0 ], "contribution": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4575, 0, 0, 0, 0 ], "totalRevenue": 6375, "totalContribution": 4575 }, { "startMonth": 21, "acquired": 75, "customers": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 75, 0, 0, 0 ], "revenue": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6375, 0, 0, 0 ], "contribution": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4575, 0, 0, 0 ], "totalRevenue": 6375, "totalContribution": 4575 }, { "startMonth": 22, "acquired": 75, "customers": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 75, 0, 0 ], "revenue": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6375, 0, 0 ], "contribution": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4575, 0, 0 ], "totalRevenue": 6375, "totalContribution": 4575 }, { "startMonth": 23, "acquired": 75, "customers": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 75, 0 ], "revenue": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6375, 0 ], "contribution": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4575, 0 ], "totalRevenue": 6375, "totalContribution": 4575 }, { "startMonth": 24, "acquired": 75, "customers": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 75 ], "revenue": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6375 ], "contribution": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4575 ], "totalRevenue": 6375, "totalContribution": 4575 } ] } ], "warnings": [ "CAC is not recovered by one expected customer’s contribution within the supplied horizon.", "Illustrative cash falls below zero. An additional 695,795 USD opening cash would cover the modelled cash trough, before any unmodelled financing or contingencies.", "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 24-month contribution LTV is 61 USD/customer, or 0.25× CAC. CAC contribution payback is not reached. Closing cash is -695,795 USD; the lowest cash balance, including opening cash, is -695,795 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." ] }