1. Unit cost
call cost = uncached input tokens × input rate + output tokens × output rateRates are normalized to one million tokens. Cache hit rate reduces modeled input tokens only; output remains fully billed in this local formula.
Trust center / methodology
Every report starts with the same open formulas.
The workbench uses deterministic Decimal arithmetic, explicit validation, and versioned scenario exports. It is decision support—not a provider bill estimator or a forecast guarantee.
Return to workbench2. Retry and success
successful task cost = submitted task cost ÷ (1 − failure rate ^ total attempts)Expected attempts are a bounded geometric series from the first attempt through the retry cap. A failure rate of 100% is rejected instead of producing an invalid denominator.
3. Scale
monthly AI cost = successful task cost × tasks / user × active usersThe typical-user estimate and total workload stay separate from conversion. Heavy-use behavior should be modeled as an alternative rather than hidden in an average.
4. Margin and allowance
gross margin = (price − AI cost − payment fee − other variable cost) ÷ priceSustainable allowance solves the same equation for the maximum whole task count that preserves the entered target margin.
5. Break-even
paid users = ceiling(monthly fixed cost ÷ contribution per paid user)If contribution is zero or negative, the result is unbounded rather than a misleading finite audience target.
Precision contract
Calculate at full Decimal precision. Round only for display and exported decision fields.
The report fingerprint identifies the canonical scenario and derived projection. It is not a cryptographic signature and does not prove the assumptions are true.