The person and the choice
Maya Chen's decision starts before any input is entered
Maya Chen, a product manager at a public software company, is the fictional decision-maker in this worked example. Maya contributes from every paycheck, receives a 15% purchase discount with a lookback, and must decide what to do when each six-month offering closes. 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 Maya Chen 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 Maya Chen's inputs into a different situation.
What is known
Build the evidence ledger before building the scenario
Her compensation, elected contribution percentage, offering dates, purchase dates, discount, lookback rule, price observations, and sale instruction are facts only when they match payroll and the governing plan. 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.
The plan prospectus, enrollment confirmation, payroll statements, offering and purchase calendars, brokerage lot records, discount and lookback clauses, refund rules, sale restrictions, and tax forms should all tell the same operational story. 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.
| Field | Value | Role |
|---|---|---|
| Annual compensation | $120,000 | Input |
| Payroll contribution | 10% | Input |
| Plan discount | 15% | Input |
| Lookback | offering-start | Assumption |
| Share rounding | Fractional shares | Assumption |
| Sale strategy | hold | Assumption |
Preparing the inputs
What Maya Chen has to normalize before pressing calculate
Contributions must be aligned to each offering period, capped in the same units used by the plan, and paired with the correct beginning and ending market prices before a purchase price can be calculated. 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 payroll cash and eligibility, purchase-price and share mechanics, and sale, tax, and concentration consequences. 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.
Maya Chen'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
Lookback eligibility, purchase-date price, the contribution election, compensation-based caps, fractional-share treatment, sale timing, and tax assumptions can each change the result without any change to salary. 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 Maya Chen, 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.
Calculation walkthrough
Follow one case through the actual PayArith engine
The engine builds purchase lots in date order, applies contribution and share limits, calculates the eligible purchase price, rounds shares under the selected rule, carries unused cash, and then models sale or holding treatment by lot. 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.
A discounted purchase is based on eligible market value rather than the amount withheld. Keeping the cash ledger separate from the share ledger prevents a cap or whole-share rule from silently turning uninvested payroll cash into stock. 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 Maya Chen's choice.
| Step | Basis | Calculated result |
|---|---|---|
| Purchase 1 | $6,000 at $85/share | 70.59 shares; $0 unused |
| Purchase 2 | $6,000 at $85/share | 70.59 shares; $0 unused |
What the outputs mean
Translate every result back into the decision
Accepted contributions describe cash that reached purchases; purchased shares describe the acquired position; after-tax proceeds describe modeled liquidity; ending paper value describes unsold exposure; and unused cash explains the reconciliation between deductions and stock. For Maya Chen, 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.
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.
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 | 13,754.1 | — |
| expected | 14,961.7 | — |
| upside | 16,649.4 | — |
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
If the purchase-date price rises above the offering-date price, lookback can deepen the effective discount; if it falls, the purchase price may reset lower while an immediate post-purchase recovery remains uncertain. 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, Maya Chen 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.
What matters now
Separate current cash, recurring economics, and later value
Immediate sale restores liquidity soon after payroll deductions but may create a different tax treatment; holding preserves exposure while leaving household cash tied to a volatile and employment-linked asset. 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.
Repeated holding can turn modest semiannual purchases into a large single-company position. Repeated selling can reduce concentration but also gives up future gains and may not satisfy every tax holding-period objective. 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.
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 | 2,961.7 | 14,961.7 |
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
Future prices, sale access, tax rates, employment continuity, contribution interruptions, and plan amendments are unknown. Scenarios therefore describe conditional outcomes, not a forecast or a promise of discount-sized profit. The worked example isolates those uncertainties rather than hiding them inside a single expected label.
The key risk is not merely a lower share price. Job income, unvested equity, retirement holdings, and purchased shares can all respond to the same company event, concentrating several household risks at once. 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 Maya Chen should place in the numerical lead.
Automation, trading-window friction, comfort with volatility, existing company equity, emergency savings, and the cognitive burden of managing lots matter even when two strategies show similar modeled values. None of those factors should be converted into invented dollars merely to force one total. A separate qualitative ledger keeps them explicit and allows Maya Chen to choose a financially lower path for a stated reason.
Decision takeaway
What Maya Chen can responsibly conclude from this worked case
This fixture proves how a validated set of an employee stock purchase plan 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, Maya Chen should ask: Which plan limits, holding rules, trading restrictions, and payroll refund mechanics apply to this exact offering and purchase lot? 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.