Tender price sensitivity analysis recalculates a defined offer when material inputs change. Start with individual changes, then test combinations that have a credible common cause and any capacity or contractual thresholds they cross. The deliverable is a scenario decision table showing changed inputs, supporting evidence, recalculated contribution and cash needs, the relevant approval limit, and who must decide. It should explain where the offer stops being acceptable, not merely report that the spreadsheet still produces a positive number.
The proposed price passes review at the estimated workload and current staffing rate. Extra work still appears affordable, and a higher hourly rate also appears affordable when tested separately. During mobilisation both occur. The team then discovers that the combined cost crosses its approval limit, while additional volume would require another fixed capacity commitment. A reassuring base case did not answer the question the approver needed to resolve.
Approve an offer against the conditions under which it must be delivered. Use evidenced ranges, recalculate interacting costs and make failed conditions visible. All amounts, rates, quantities and approval limits below are fictional arithmetic examples, not Zephior prices, market forecasts or recommended profit margins. The cited public-sector guides support analytical methods; they do not set a private bidder’s commercial policy or override a procurement’s instructions.
Model boundary
Decide what the price has to cover
A percentage called “margin” is ambiguous until its numerator and denominator are stated. In this example, contract contribution is revenue less the delivery costs explicitly included in the model. The contribution percentage divides that amount by revenue. Corporate overhead, financing and tax are excluded here. A positive contribution is therefore neither statutory profit nor proof that the company can afford the contract. A real approval model must include or separately assess every material excluded cost.
The fictional Westmere offer charges EUR 250 for each delivered unit. At 2,000 units, each requiring three paid hours at EUR 50 per hour, variable cost is EUR 150 per unit. Contract fixed cost is EUR 100,000. Revenue is EUR 500,000; delivery cost is EUR 400,000; contribution is EUR 100,000, or 20%. The illustration uses a 10% contribution approval floor. That floor is an assumed management decision for this case, not an industry standard.
Write the arithmetic before building scenarios: revenue = P × Q; delivery cost = F + Q × h × r; contribution = revenue − delivery cost. P is unit selling price, Q is delivered and billable quantity, F is contract fixed cost, h is paid hours per unit and r is cost per paid hour. This deliberately narrow model assumes uniform units and no other variable charges. Add materials, travel, non-billable work, price tiers and other relevant terms when the actual offer requires them.
Keep the buyer’s prescribed evaluation calculation unchanged. Your internal delivery forecast may test different actual volumes, but those cases do not replace the quantities or formula the buyer requires for scoring. Save the offered price, internal base case and scenario results separately, with a common version reference. Before interpreting any sensitivity result, another reviewer should be able to reproduce the base total and explain how it reconciles to the submitted schedule.
Input evidence
Choose ranges that could change the decision
A supplier quote with an expiry date can support a different hourly-cost case; a delivery rehearsal can support an effort range. Neither supports a universal rule that every input should move by ten percent. GAO’s cost-estimating guide, chapter 11, calls for traceable sources of variation and warns against unsupported percentage changes. The equal ten-percent movements later in this article are stipulated teaching inputs chosen to expose an interaction, not estimates of a real contract’s uncertainty.
For each range, retain its unit, period and applicable conditions. An hourly rate may already contain employer charges and an overtime allowance. Extra effort may already contain a rework cycle. Identify those inclusions before adding a “delay” row that charges the same hours again. Where the evidence is weak, label the range as judgment, explain who supplied it and record what observation would narrow it. An unknown parameter is not automatically zero.
Prioritize investigation where uncertainty could reverse the approval. The IPA’s cost-estimating guidance connects the value of further investigation to material sensitivity. For Westmere, confirming whether extra capacity costs EUR 40,000 may matter more than refining a small stationery estimate. This is a choice about where to spend estimating effort, not permission to omit a known cost because it is small.
A ranked bar chart only ranks the changes you tested. If all inputs move by the same percentage, it shows sensitivity to that convention; it does not establish which input is most uncertain or most likely to cause failure. Show the absolute ranges beside the ranking. Include asymmetric cases where supported, such as a rate held by a valid quote until an expiry date and a different rate afterwards.
| Input | Evidence and boundary | Review owner |
|---|---|---|
| Paid hours per unit | Comparable delivery records; task mix, rework and acceptance conditions | Delivery estimator |
| Cost per paid hour | Dated staffing or supplier quote; included charges and expiry | Finance or purchasing |
| Billable quantity | Buyer information and contract mechanism; distinguish forecast from commitment | Commercial lead |
| Capacity step | Resource plan and incremental commitment; exact trigger and maximum supported volume | Operations lead |
| Cash timing | Payment milestones, acceptance conditions and supplier payment dates | Treasury reviewer |
Separate tests
Recalculate the whole offer for each changed input
In a one-input test, hold the other independent inputs constant, not the outputs that depend on the changed input. Raising hours from 3 to 3.3 must recalculate labour cost. Reducing quantity must recalculate both revenue and variable cost. Freezing total cost while changing its driver would produce a misleading sensitivity result, even if the spreadsheet contains no formula error.
For Westmere, ten percent more hours costs another EUR 30,000 and reduces contribution to 14%. A ten percent higher hourly cost produces the same result when tested alone. A five percent selling-price reduction leaves delivery cost unchanged and reduces contribution to EUR 75,000, or 15.79% of the new revenue. Do not divide by the old revenue or confuse a five percent price reduction with five percentage points of contribution.
The volume case also passes the illustrative floor: 1,600 units generate EUR 400,000 of revenue against EUR 340,000 of cost, leaving EUR 60,000, or 15%. It assumes every unit has the same effort and rate, and fixed cost remains EUR 100,000. A lower order quantity with a less favourable service mix would require another case. These rows diagnose specific changes; none establishes the worst possible outcome.
Use units that describe the operational change accurately. Ten percent more hours per unit is an effort increase. It is not the same as a ten percent reduction in productivity measured in units per hour. If units per hour fall by 20%, hours per unit rise by 25%, because the reciprocal changes from 1 to 1 ÷ 0.8. A mislabeled productivity input can understate cost before any approval rule is applied.
| Case | Revenue | Delivery cost | Contribution | Contribution / revenue |
|---|---|---|---|---|
| Base | 500,000 | 400,000 | 100,000 | 20.00% |
| Hours per unit +10% | 500,000 | 430,000 | 70,000 | 14.00% |
| Hourly cost +10% | 500,000 | 430,000 | 70,000 | 14.00% |
| Unit selling price −5% | 475,000 | 400,000 | 75,000 | 15.79% |
| Billable quantity −20% | 400,000 | 340,000 | 60,000 | 15.00% |
Approval boundary
Check the cost band before trusting a break-even quantity
A switching value identifies where a decision changes. The Green Book 2026 uses this concept for public appraisal and value for money; here it is applied to a separately chosen commercial contribution limit. For a constant fixed cost F, unit variable cost v, price P and contribution fraction m, the quantity reaching the floor is Q = F ÷ [P × (1 − m) − v]. This expression needs a positive denominator and must be checked within the cost band used to derive it.
At the Westmere base costs, zero contribution occurs at 1,000 units. Reaching 10% requires 100,000 ÷ (225 − 150) = 1,333.33 units, so at least 1,334 whole units under the stated assumptions. Those are different boundaries. Now stipulate that existing capacity covers at most 2,200 units and that serving 2,201 through 3,500 units requires an additional EUR 40,000 fixed commitment. Variable cost is assumed unchanged by this capacity purchase. A real capacity arrangement needs its own evidence.
Under the original effort and rate, contribution at 2,200 units is EUR 120,000. At 2,201 it falls to EUR 80,100: the extra unit earns EUR 100 before the new EUR 40,000 commitment. Contribution is not continuously increasing with quantity across that boundary. Test immediately below and above every step, including minimum purchases, support tiers, extra supervision and any contractual rebate that applies retrospectively.
For the combined effort-and-rate case, the old fixed cost gives an apparent 10% threshold of 2,298.85 units, rounded up to 2,299. That answer lies outside the band where EUR 100,000 is valid. At 2,299 units with the required EUR 140,000 fixed cost, contribution is only EUR 17,481.50, or 3.04%. Recalculate within the second band: 140,000 ÷ (225 − 181.50) = 3,218.39, requiring 3,219 whole units. This lies below the stipulated 3,500-unit capacity ceiling; 3,218 units still fall short of 10%. The calculation does not establish that the buyer will order 3,219 units.
| Test | Quantity | Applicable fixed cost | Interpretation |
|---|---|---|---|
| Base-cost zero contribution | 1,000 | EUR 100,000 | Covers modelled delivery cost only |
| Base-cost 10% floor | 1,334 whole units | EUR 100,000 | Valid in the first capacity band |
| Joint-cost root using old fixed cost | 2,299 whole units | EUR 140,000 is actually required | Reject the old formula’s conclusion |
| Joint-cost 10% floor after capacity step | 3,219 whole units | EUR 140,000 | Mathematically valid; demand remains unconfirmed |
Other limits
A contribution pass cannot fund an early payment
Run a dated cash schedule alongside the contribution analysis. Put customer receipts after the relevant invoice, acceptance and payment conditions, not at the date revenue appears in the commercial model. Place payroll, deposits, taxes and supplier payments when they must be funded. Calculate the largest cumulative cash deficit during the contract and compare it with funds actually available to this offer, after other commitments.
If EUR 90,000 must be paid before any customer receipt and only EUR 70,000 is available for that interval, the immediate gap is EUR 20,000. Later contribution does not pay that earlier bill. This small example identifies one interval only, not the contract’s peak funding requirement. Extend the schedule across the full delivery and collection period, including a supported late-acceptance case. Do not count an unapproved credit facility as available cash.
Service feasibility needs its own test. The fixed-cost step above assumes capacity can be bought in time and can support the required work. Money alone does not establish that qualified staff, equipment or access slots exist before the deadline. A quantity that restores the contribution percentage may exceed a daily throughput constraint even when it sits within an annual capacity band. Preserve the timing and skill mix, not just the total units.
An analyst should show a failed constraint beside the financial result, without converting it into a convenient penalty estimate. Finance can assess the funding gap; operations must confirm resources; the authorized commercial reviewer decides what the business may accept. The Orange Book’s risk-treatment guidance connects chosen responses to responsible people, resources and timing. Its government governance rules are not private-bid approval authority.
Decision record
Give the approver the failing condition and the available response
Issue a scenario table with enough information to reproduce the decision: offer version, scenario name, changed independent inputs, evidence, cost-band rules, calculated outputs, approval limits and unresolved facts. Attach the calculation rather than hiding its assumptions in a slide. The AQuA Book’s 2025 guidance supports documenting analytical sources, assumptions, ownership, limitations and review. Approval of analytical quality and acceptance of commercial exposure remain different decisions.
For Westmere’s joint case at 2,000 units, the decision is whether the business accepts a 7.4% contribution or changes the offer through an allowed, approved route. Investigate whether the staffing reservation can be secured, whether a delivery change actually reduces hours, and what either response costs. If a control requires a deposit or paid rehearsal, include it before rerunning the model. An unfunded intention to work faster is not a corrected case.
A calculated selling-price floor is an analytical output, not an instruction to quote it. At the base volume and cost, the mathematical price for 10% contribution is EUR 400,000 ÷ (2,000 × 0.9), or about EUR 222.22 per unit before considering price granularity and excluded costs. That calculation says nothing about buyer scoring, competition or the right to revise a submitted price. Round and retest an actual proposed price, and obtain the required authority before changing it.
Close each failed case with an explicit disposition: obtain missing evidence, fund a feasible control, seek a permitted clarification, accept the residual exposure within authority, or do not release the bid. Record the owner and deadline. Reopen the decision when an input crosses its trigger, a quote expires or the buyer changes the requirement. The finished artifact is a reviewed commercial decision tied to the final offer, with the unacceptable conditions still visible.
| Condition | Finding | Required decision and owner |
|---|---|---|
| More hours with higher hourly cost | 7.4% contribution, below the illustrative 10% floor | Commercial approver: require a costed response or authorized acceptance |
| Volume proposed as the cure | At least 3,219 units needed in the revised cost band | Commercial and operations leads: verify demand basis and deliverability |
| EUR 90,000 outflow before receipts | EUR 20,000 gap against EUR 70,000 available | Treasury: establish funding or escalate before commitment |
| Supplier reservation expires | The tested rate may no longer be obtainable | Purchasing and pricing: refresh the quote and rerun affected cases |
What good looks like
Useful outcomes from tender price sensitivity analysis
- The tested offer and its included costs are identifiable and reproducible.
- Individual changes and plausible combinations have separate results.
- Every calculated switching value is checked against its valid capacity band.
- Contribution, liquidity and delivery constraints receive distinct decisions.
- The price approver receives unresolved conditions and costed responses before release.
Operating model
How to run the work
- 01
Freeze the reference offer
Record the scope, pricing file, delivery period, price date, currency and cost boundary. Reproduce the approved base calculation before changing inputs.
- 02
Select supported variations
Link material inputs to observations, quotes or documented expert judgment. State ranges, expiry dates, missing information and dependencies without inventing probabilities.
- 03
Run separate and combined cases
Change one independent input at a time while recalculating dependent formulas. Then test coherent joint conditions, including changes in cost bands and resource availability.
- 04
Find the decision boundary
Solve for the input that reaches the authorized contribution limit. Check the formula’s domain, integer quantities and both sides of any discontinuity; assess cash and service limits separately.
- 05
Choose a funded response
Present failed cases with the proposed control, its cost, responsible owner and remaining exposure. Obtain authority for acceptance, an allowed offer change or stopping the bid.
- 06
Reopen on material change
Assign review triggers for supplier expiry, schedule movement, revised demand and buyer amendments. Retest the final offer rather than attaching an obsolete scenario sheet to it.
Evaluation
Questions that change the decision
- Which changed assumption reaches an approval limit first?
- Can the tested conditions occur together?
- Does the calculation cross a new cost or capacity band?
- Would a profitable case still exceed available funding or delivery capacity?
- Is the proposed response feasible, funded and permitted?
- Who accepts the remaining exposure before submission?
Failure modes
Where teams lose control
A uniform percentage substitutes for evidence about the input range.
Separate cost impacts are added despite a multiplicative relationship.
A solver returns a quantity outside the fixed-cost band it assumed.
Estimated demand is treated as committed revenue.
An average result hides an individually unacceptable outcome.
A modelled price adjustment is mistaken for authority to change the offer.
Measurement
Measure the finished job
Measure the completed workflow, including review effort and exceptions. Output volume on its own is not evidence of a better process.
- Material assumptions with a dated range and evidence owner
- Unapproved threshold breaches by scenario
- Switching values checked against valid model ranges
- Peak funding gaps under dated payment cases
- Offer changes awaiting a repeated sensitivity review
Questions
Common questions
Is changing every input by ten percent enough?
No. Use ranges supported by the input’s evidence and conditions. An equal percentage can illustrate sensitivity, but it cannot establish plausible uncertainty. Record why each actual range is appropriate and include material step changes.
Why can two passing sensitivity tests fail together?
Inputs can interact. More hours multiplied by a higher hourly cost produces an extra interaction cost that adding the two separate impacts misses. A joint case also needs a credible explanation of why the changes could coincide.
Is break-even the same as the approval threshold?
Only if the organization has explicitly chosen zero contribution as that threshold on the same cost basis. A positive contribution floor, liquidity limit or delivery constraint can be breached well before modelled contribution reaches zero.
What if the switching-value denominator is zero or negative?
With positive fixed cost in this model, increasing quantity cannot reach the chosen contribution floor within that band when P × (1 − m) − v is zero or negative. Check the model and permitted alternatives; do not report a negative or infinite quantity as a viable target.
Can a higher order volume always repair the economics?
No. Additional capacity, retrospective rebates or a changed work mix can reduce contribution at a threshold. Solve separately within each applicable band and verify any proposed demand level rather than treating it as an order commitment.
Should failed cases be combined into an expected average?
Keep them individually visible. An expectation requires supported probabilities and answers a different question from whether a specific outcome exceeds authority. Averaging does not fund a cash gap or authorize an unacceptable delivery obligation.
Does this analysis authorize a changed tender price?
No. It supplies evidence for an authorized commercial decision. Any price revision, qualification, buyer communication or submission must follow the actual procedure and the customer’s approval boundaries.
Sources
Primary references
- Cost Estimating and Assessment Guide, chapter 11: sensitivity analysis (2020) U.S. Government Accountability Office
- The Green Book 2026: sensitivity analysis and switching values HM Treasury
- Cost Estimating Guidance: input evidence and material uncertainty (2021) Infrastructure and Projects Authority
- The AQuA Book: documentation, review and analytical limitations (2025) Government Analysis Function
- The Orange Book, section D: risk evaluation and treatment HM Treasury
About the author
Tony Kim
Tony writes about applied AI, dependable product engineering and the systems that turn complex response work into controlled delivery.
Zelius
Managed tender intelligence and bid execution for teams that want the commercial outcome.
Suppliers, founders and commercial teams pursuing public or private opportunities. Start with the workflow, constraints and evidence you already have.