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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 24-month contribution LTV is 971.94 USD/customer, or 4.05× CAC. CAC contribution payback occurs in month 5. Closing cash is 218,526.01 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."]}}