Appendix: calculation and unit dictionary

Reproduction begins with a dimensional statement, not with the preferred bid. The procurement workbench reports costs in thousands of the supplied currency. Its electricity quantity is annual megawatt-hours; its electricity price is thousands of currency per megawatt-hour. Their product is therefore an annual cost in the same cost unit as acquisition and operating expense. Downtime uses annual hours multiplied by thousands of currency per hour. A reviewer should verify those relationships before deciding whether a number is plausible. An unnoticed currency-scale difference can dominate a ranking without producing a software error.

The input dictionary describes a common comparison horizon in whole annual periods, a discount rate entered as a percentage, and an electricity-price escalation rate entered as a percentage. Each bid has a name, acquisition amount, whole-year service life, annual operating amount, annual electricity quantity, electricity price, annual downtime hours, downtime loss rate and terminal residual amount. The common fields are shared across alternatives. Their shared position is a modelling convention for comparable service, not evidence that the buyer has established comparability. A different duty or commercial perimeter must be resolved before the fixture is interpreted.

Acquisition is a base-date payment. It enters present cost without discounting and does not appear in the annual operating cash-cost rows. That distinction explains why summing the annual ledger alone does not reproduce total lifecycle present cost. The ledger describes subsequent costs and the terminal credit. To reconcile the displayed total, add acquisition to the discounted annual ledger for each bid. A reviewer who mistakes the ledger for a complete payment schedule may incorrectly conclude that acquisition has been omitted. Conversely, adding acquisition to both the ledger and the separate base-date field would duplicate it.

Uniform operating expense is incurred at the end of every annual period through the common horizon. Uniform downtime cost uses the same dates. The workbench does not model monthly cash, seasonality, working capital or the distinction between accounting expense and a payment date. Those exclusions are important when a procurement has a material mobilisation burden or a concentrated maintenance cycle. The simple engine can still explain a lifecycle mechanism, but its annual convention must not be presented as the buyer's detailed liquidity forecast. A separate dated model is needed where timing affects execution.

Replacement occurs at each supplied service-life multiple strictly before the common horizon. The cost is the same acquisition amount used at the base date. A replacement falling exactly at the horizon is excluded because the current comparison does not require a further operating period. This discrete rule is a visible boundary, not a claim about the actual physical condition of an asset. A real replacement policy may respond to inspection, obsolescence, usage or maintenance history rather than a fixed annual life. The supplied life must therefore be defended as a comparison assumption.

The replacement rule assumes that a purchase restores the required service without a separate commissioning delay, disposal cost or changed duty. The annual rows include replacement cash alongside operating costs in that year. They do not infer whether the replacement and operation could physically coexist under the buyer's plan. A reviewer should identify any required outage or transition service outside the engine and decide how the comparison should recognise it. The deterministic timing convention should make the missing mechanism visible rather than encourage the evaluator to bury it in a longer life input.

Electricity cost begins with the input annual quantity and the input first-year price. Subsequent prices compound by the supplied escalation rate. The engine holds electricity quantity constant and does not escalate operating expense or downtime loss. This asymmetric convention is deliberate and published. It can represent a specific comparative test, but it should not be mistaken for a comprehensive nominal forecast. If other costs should escalate, the analytical team must use a model that represents them explicitly or explain why the current comparison remains faithful to the decisive differential.

Discounting converts each dated amount to the common base date through the supplied annual rate. The engine converts percentage inputs to fractional rates internally. The analytical team remains responsible for the meaning of the rate and the monetary convention. A real-dollar operating amount should not be mixed casually with a nominal rate or an escalation input copied from a nominal forecast. Currency, price date, inflation treatment and rate basis belong in the case record. Correct arithmetic can preserve an economically incoherent set of inputs just as faithfully as a coherent one.

The terminal residual is a supplied nonnegative credit at the common horizon. It is not computed from asset age, accounting depreciation or remaining service life. The workbench therefore allows the evaluator to test a documented terminal convention while also exposing the danger of an unsupported credit. The analyst must explain what event produces the value, which costs are netted and whether the buyer can execute the assumed transfer or continued use. A terminal credit without a credible route can create a preferred bid from a speculative amount that the organisation will never receive.

The ordinary annuity factor is the present value of a uniform end-of-year unit payment across the common horizon. Equivalent annual cost divides the full lifecycle present cost by that factor. It therefore annualises acquisition, replacement and residual as well as recurring cost. It is not the supplier's annual invoice and does not represent a funding arrangement. Because admissible bids use the same horizon and rate, their annuity factor is common. Annualisation preserves their present-cost ordering while making the scale easier to compare with a recurring operating differential.

At a zero discount rate, the annuity factor is the number of annual periods and each dated amount retains its undiscounted value. This branch avoids division by a rate that is zero; it does not remove the economic question of whether a zero rate is appropriate. The fictional replacement-end case uses it to isolate the timing boundary. The case's lower-cost bid has a base acquisition, a common recurring operating component and no inside-horizon replacement. Its displayed lifecycle present cost can be reconciled directly without any claim about an actual buyer's cost of capital.

The negotiation hurdle separates the fixed lifecycle differential from the operating differential. Fixed present cost comprises acquisition and replacement less residual. For each nonleading bid, the workbench subtracts the leader's fixed present cost and divides the difference by the common annuity factor. A positive hurdle describes the uniform annual operating saving required to recover that premium within the current convention. A negative hurdle describes a fixed-cost advantage that can accommodate some operating disadvantage. The metric does not mean that a supplier has agreed to deliver the required saving.

The displayed operating saving is the leader's recurring present cost minus the alternative's recurring present cost, divided by the same factor. It therefore has a sign that matters. A negative value means that the alternative carries a larger annualised operating burden. The model does not relabel that disadvantage as a positive saving. An analyst should read the hurdle and the supplied operating differential together, then reconcile them with the lifecycle gap. A fixed-price concession can also change future replacement cost under the same-acquisition convention, so its impact requires a complete rerun.

The stress outputs use deterministic energy and downtime multipliers already encoded in the canonical engine. They are intervention cases, not assigned probabilities or empirical confidence intervals. A combined case can reveal whether an apparent advantage survives concurrent pressure, but it cannot establish the likelihood of that pressure or whether the mechanisms are independent. The analyst should name the changed inputs and retain unchanged controls. When a supplier's operating quantity changes as well as the price, that is a different intervention and needs its own case rather than an ambiguous stress label.

Sorting uses lifecycle present cost and then names when costs tie. Name ordering is a display convention, not an inferred preference between economically equal offers. The output warns when the leading pair has exactly equal computed lifecycle costs under the disclosed finite numerical precision. It uses no additional near-tie tolerance. Exactly equal computed costs receive literal code unit name order independent of browser language. That warning does not establish practical materiality because the importance of a difference depends on the decision and its evidence. Displayed rounding can also make different underlying amounts look equal. A reviewer should compare canonical raw outputs and the applicable uncertainty before giving a rounded result any role in an award or negotiation.

Reproduction should use the complete exported input and the current model version, not copied headline metrics. Imported output is recalculated by the app; it is not trusted as an instruction. The paper's fixtures, outputs and reciprocal scalar bindings identify the exact cases used in its exhibits. A verifier can execute the same pure computation, compare every field and trace each printed quantity to an input or output pointer. Full-precision computation and display rounding have different purposes. The former supports reproduction; the latter makes a readable publication without pretending to greater certainty.

Cross-runtime floating-point calculations can differ in their least significant digits. A valid verification records its tolerance and compares numeric values within that explicit bound while requiring exact structure, names and nonnumeric meanings. It should not suppress a substantive discrepancy as rounding or require an impossible byte identity from differently encoded numerical exports. Publication rendering must still bind the actual displayed rounding to the canonical value. The tolerance cannot rescue an altered rate, changed replacement rule or missing cost category, all of which change the meaning of the comparison.

The dictionary supports a placement-error diagnostic. A hypothetical recurring amount placed in acquisition receives base-date treatment instead of annual discounting; an exit expense netted into residual can conceal a retained obligation; an interruption consequence counted in both operating expense and loss per hour is duplicated. A service-life input equal to the common horizon produces no replacement strictly within the model's service window, whereas a shorter life can introduce a discrete purchase event. Trace the disputed amount through its date, category and incidence before challenging a total. This instrument uses the implemented conventions to identify errors of meaning while leaving input truth and commercial commitment for their separate reviews.