The person and the choice
Riley Thompson's decision starts before any input is entered
Riley Thompson, a finance manager considering an interstate move, is the fictional decision-maker in this worked example. Riley's household compares its current city with a destination offer, including partner-income timing, housing, recurring expenses, commuting, moving support, deposits, and first-year cash needs. The goal is to turn that situation into a traceable case without pretending the assumptions describe a future that is certain.
The choice is not simply between the largest and smallest displayed values. It is whether the modeled result gives Riley Thompson enough evidence to act, which number affects current cash, which number remains conditional, and which unanswered term could reverse the interpretation.
The profile is deliberately realistic rather than universal. Readers should borrow the method—document facts, normalize units, run the engine, reconcile outputs, vary one assumption, and record omitted risks—not copy Riley Thompson's inputs into a different situation.
What is known
Build the evidence ledger before building the scenario
Current and destination compensation, partner and other income, housing, named expenses, commute, moving quotes, deposits, support terms, eligibility dates, tax assumptions, and employment contingencies must be entered on the proper household timeline. Those items anchor the base case. They receive the label “input” only when a document, record, or current policy supports them; otherwise they remain an assumption even if the value feels likely.
Riley should reconcile the offer, location and schedule policy, partner employment timing, lease or mortgage obligations, destination housing quotes, moving bids, travel and storage needs, support and gross-up terms, clawbacks, benefit dates, and deposit rules. For the worked example, the visible input table highlights the fields that explain the result while the typed fixture supplies the calculator's complete validated object.
That distinction prevents a common reporting problem: showing six attractive inputs while hidden defaults do most of the calculation. The fixture is tested against the schema, and the displayed lead metric is recalculated by the production engine. In this a relocation salary decision analysis, that boundary is applied to Riley Thompson's stated facts and assumptions.
| Field | Value | Role |
|---|---|---|
| Current location | Current city | Input |
| Destination | New city | Input |
| Current salary | $100,000 | Input |
| Destination salary | $120,000 | Input |
| Tax mode | disabled | Assumption |
| Projection | 5 years | Input |
Preparing the inputs
What Riley Thompson has to normalize before pressing calculate
Monthly household flows need annual alignment; already itemized costs must not also receive a broad regional multiplier; recoverable deposits must stay separate from losses; and employer support must be matched to the cost and tax timing it offsets. The normalization step creates a common clock and compatible units, but it does not erase restrictions or uncertainty. Cash remains cash, time remains time, and conditional value remains labeled.
In this case, the three operational layers are household income and after-tax cash, housing, life, commute, and time, and transition costs, liquidity, and cumulative break-even. Each is prepared separately so the engine can connect them in the right order.
A useful preflight check is to ask whether every percentage has a defined base, every annual amount has a recurrence rule, every date belongs to the correct period, and every scenario value has an owner. Ambiguous units are resolved before calculation, not explained away afterward. In this a relocation salary decision analysis, that boundary is applied to Riley Thompson's stated facts and assumptions.
Riley Thompson's result is reproducible because the fixture, engine path, and assumptions remain separate.
Why these assumptions
Choose a base case that can be defended, not one that flatters the outcome
Destination housing, partner-income gap, tax rates, unitemized spending, commute, childcare, moving overlap, employer support, taxable reimbursement, deposits, salary growth, inflation, and projection horizon can each flip the result. The base fixture selects explicit values for those variables so the result can be reproduced. It does not claim they are the most likely values for every reader.
For Riley Thompson, the strongest assumption is the one closest to a written term or recent observed pattern. The weakest is a future outcome controlled by a market, employer, client, schedule, or household event. Those two should never carry the same confidence label.
A conservative case should stress one credible downside without changing unrelated facts. A favorable case should do the same in the other direction. This structure shows which variable causes the spread instead of producing two opaque bundles. In this a relocation salary decision analysis, that boundary is applied to Riley Thompson's stated facts and assumptions.
Calculation walkthrough
Follow one case through the actual PayArith engine
The engine builds current and destination household timelines, applies user-selected tax assumptions, projects housing and recurring expenses, prices commute and time, separates transition costs and cash requirements, and solves salary and cumulative break-even. The audit table below is derived from that engine result. The article does not reimplement the formulas, which prevents prose examples from drifting away from the calculator's validation, ordering, and rounding behavior.
Disposable cash flow subtracts recurring household expenses from modeled after-tax cash. Adjusted economic value can add employer value, while initial cash required remains a liquidity measure because a recoverable deposit is not necessarily a permanent loss. The formula block names the central relationship, while the step rows reconcile how the fixture reaches its displayed output. Each calculated value is labeled separately from the assumption that feeds it.
To audit the calculation, start with the first row and ask where its basis came from. Then carry the output into the next relevant stage. If a value cannot be traced, it should not be used as the reason for Riley Thompson's choice.
| Step | Basis | Calculated result |
|---|---|---|
| Current city | $107,200 household cash − $62,640 recurring costs | $44,560 disposable; $59,560 adjusted |
| New city | $137,700 household cash − $71,940 recurring costs | $65,760 disposable; $71,160 adjusted |
What the outputs mean
Translate every result back into the decision
Disposable cash measures recurring household breathing room; adjusted economic value adds modeled employer value; nonrecoverable transition cost measures economic loss; initial cash required measures timing; cumulative break-even shows when a destination deficit is recovered. For Riley Thompson, those are not interchangeable scorecards. The metric that best describes long-term modeled value may be the wrong metric for a near-term cash constraint.
The headline strip is a navigation aid, not the whole analysis. The audit explains composition, the scenario chart explains conditional range, and the projection explains timing. A decision should cite the specific view that supports it. In this a relocation salary decision analysis, that boundary is applied to Riley Thompson's stated facts and assumptions.
The text alternative under each chart repeats the plotted values in a table. That supports readers who cannot use the visual and also makes the numerical comparison easier to reconcile against the engine audit. In this a relocation salary decision analysis, that boundary is applied to Riley Thompson's stated facts and assumptions.
The next view keeps the fixture constant and exposes the numerical spread. Read it to locate a decision boundary, then use the table to reconcile the plotted values without relying on color or shape.
| Scenario | Calculated value | Reference value |
|---|---|---|
| conservative | 62,271 | 59,560 |
| expected | 71,160 | 59,560 |
| favorable | 75,887 | 59,560 |
The chart does not rank personal outcomes. It shows how the defined engine metrics move; the surrounding article explains whether the spread is liquid, recurring, sensitive, or incomplete.
The counterfactual
Change one condition and explain why the answer moves
The destination may lead after Year 2 but require substantial cash in month one; a later partner start or higher housing cost can delay cumulative break-even without changing the primary salary. That alternative changes the relevant engine inputs while leaving the rest of the case intact. The resulting difference is therefore attributable to a named condition rather than a collection of favorable edits.
If the ranking changes, Riley Thompson has found a decision boundary. The next task is to verify how plausible that condition is and whether the household can tolerate being wrong, not to average the cases into a false point estimate.
If the ranking does not change, inspect the size and timing of the remaining lead. A numerically stable result can still be impractical when its value is illiquid, delayed, reversible, or dependent on staying in the role. In this a relocation salary decision analysis, that boundary is applied to Riley Thompson's stated facts and assumptions.
What matters now
Separate current cash, recurring economics, and later value
Staying avoids most transition outlays. Relocating can require deposits, overlap, travel, storage, and setup before new payroll or reimbursement arrives, even when the destination improves recurring annual value. This is the part of the example most likely to affect an immediate action. A household cannot pay a current obligation with a future scenario value, even when both appear in the same long-term comparison.
A destination advantage compounds if salary growth and recurring costs behave as assumed; a large first-year deficit can take years to recover. Housing tenure, partner career effects, and future moves can extend beyond the selected horizon. The projection makes that sequence visible but does not predict persistence. It repeats the stated growth, schedule, vesting, cost, or availability assumptions across the chosen horizon.
A good decision memo records three numbers: the Year 1 cash consequence, the recurring annual difference after one-time effects, and the cumulative result at a horizon the person may realistically remain. That memo is more informative than one lifetime total. In this a relocation salary decision analysis, that boundary is applied to Riley Thompson's stated facts and assumptions.
A single-year lead can disappear, widen, or reverse. The projection uses the same stated horizon so timing remains visible rather than being compressed into one lifetime total.
| Period | Primary path | Comparison path |
|---|---|---|
| Year 1 | 59,560 | 71,160 |
| Year 2 | 61,016.8 | 76,549.4 |
| Year 3 | 62,517.3 | 78,174.4 |
| Year 4 | 64,062.8 | 79,835.5 |
| Year 5 | 65,654.7 | 81,533.4 |
Use the projection to ask when value appears and which assumption repeats. Do not treat the final point as more certain merely because it is farther to the right.
Outside the output
The engine can be right while the decision is still exposed
Housing, partner income, taxes, support reimbursement, moving overruns, commute, inflation, salary growth, and retention are uncertain. Conservative and favorable destination cases should change named assumptions independently. The worked example isolates those uncertainties rather than hiding them inside a single expected label.
The core risk is timing mismatch: an economically recoverable deposit or reimbursable cost can still create a real liquidity crisis if cash leaves before the household receives support or new income. That risk is not an arithmetic defect; it is information outside or beyond the model. It belongs beside the result because it affects how much confidence Riley Thompson should place in the numerical lead.
Family support, schools, care access, climate, community, partner career, housing stability, commute reliability, culture, and the option value of a new market can outweigh a modest cash-flow difference. None of those factors should be converted into invented dollars merely to force one total. A separate qualitative ledger keeps them explicit and allows Riley Thompson to choose a financially lower path for a stated reason.
Decision takeaway
What Riley Thompson can responsibly conclude from this worked case
This fixture proves how a validated set of a relocation salary decision inputs travels through PayArith's production calculation engine. It proves the arithmetic relationship and the displayed reconciliation; it does not prove that future assumptions will occur.
Before acting, Riley Thompson should ask: Which support is guaranteed, taxable, capped, reimbursed later, clawed back, or tied to receipts, and what happens if the role, move date, or partner-income timeline changes? The answer should update a named input or document an unsupported risk. Either outcome improves the decision more than adding another generic scenario.
The practical takeaway is to choose from the range that the household can fund and tolerate, using the metric tied to the actual objective. The highest modeled value is relevant only after its timing, availability, fragility, and nonfinancial cost are acceptable. In this a relocation salary decision analysis, that boundary is applied to Riley Thompson's stated facts and assumptions.