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Choose a route or read from the beginning. All teaching chapters stay open; the grouped index below is expandable.
Name the funding promise
Chapters 1–2. Define the amounts and translate the percentage.
Practise and continue
Chapters 11–12. Solve changed cases and choose connected reading.
Full chapter index · Practice and worked checks · Public Policy subject root
“The funder contributes 40%” sounds clear until someone asks: 40% of what? A share of the whole eligible project, a percentage added to the applicant’s contribution and a share of an approved grant are different rules. The same printed percentage can produce different budgets.
This guide develops the arithmetic behind matching grants and co-financing. Every budget below is fictional, expressed in currency units, and conditional on the stated model. None describes a Singapore entitlement, an open funding offer or an approved award. Start with the Public Policy subject root for the wider connection between purpose, delivery and evaluation.
Chapter index
Name the funding promise · Chapters 1–2
1. Name the amounts before using a percentage
2. Translate a matching ratio into a cost share
Work the budget · Chapters 3–5
3. Work one project through three different promises
4. Separate eligible cost from the whole project
5. Apply a cap to the specified base
Follow delivery · Chapters 6–8
6. Test what an applicant can actually afford
7. Distinguish contribution from cash-flow timing
8. Keep pledges, in-kind support and other funding visible
Check the public purpose · Chapters 9–10
9. Ask what behaviour the rule encourages
10. Build a calculation someone else can check
Practise and continue · Chapters 11–12
11. Practise with changed conditions
12. Choose your next reading route
CHAPTER 1 OF 12 · Name the funding promise
1. Name the amounts before using a percentage
Let G be the grant, L the applicant’s contribution to eligible expenditure, and E the total eligible cost. In the simplest two-source budget, E = G + L. Let I be expenditure outside that eligible budget. The whole project then costs C = E + I, and the applicant must also finance I if no other source covers it.
These are accounting boundaries, not judgements about whether an item is worthwhile. A useful activity can be outside a particular award’s rules. Keep its cost in the whole-project ledger even when it is excluded from the grant calculation.
Write the proposed rule as a sentence with its denominator: “The grant covers 40% of approved eligible cost.” Then write G/E = 0.40. This small step prevents the later calculation from quietly changing the promise.
CHAPTER 2 OF 12 · Name the funding promise
2. Translate a matching ratio into a cost share
Suppose the rule matches each unit of eligible applicant contribution with m grant units. Then G = mL, E = (1 + m)L, and the grant share of eligible cost is s = m/(1 + m).
A one-for-one match has m = 1 and s = 1/2. Two grant units for each applicant unit give m = 2 and s = 2/3, about 66.7%. “Two-to-one” needs the order of the two parties stated; reversing it changes the result.
The inverse calculation is m = s/(1 − s), for 0 ≤ s < 1. A 40% grant share corresponds to 0.40/0.60 = 2/3 grant units per applicant unit. It is not the same as adding 40% to the applicant’s contribution. A 100% grant share is the boundary case with no required applicant contribution in this simple model; the finite matching-ratio formula does not apply there.
CHAPTER 3 OF 12 · Work the budget
3. Work one project through three different promises
Take an eligible project costing 60,000 units. Assume approval, no cap and no excluded expenditure for this comparison. Calculate the applicant contribution as well as the grant, then add them to check the budget.
| Written rule | Grant G | Applicant L | Grant share G/E |
|---|---|---|---|
| Grant covers 40% of eligible cost | 24,000 | 36,000 | 40% |
| Grant adds 40% of applicant contribution | 17,142.86 | 42,857.14 | About 28.57% |
| Grant matches applicant one for one | 30,000 | 30,000 | 50% |
For the second row, E = 1.40L. Therefore L = 60,000/1.40 and G = 0.40L. The difference arises before any rounding. Rounding to minor currency units should follow a declared rule and preserve the required reconciliation.
The mistaken move is applying “40%” before identifying its base. Repair it by placing the funding statement beside the equation. A calculator cannot resolve wording that never specified the denominator.
Now a fictional project costs 75,000 units, but only 60,000 is eligible. The award covers 40% of eligible cost, with no cap. Grant G is 24,000; eligible applicant share L is 36,000; the excluded 15,000 brings the applicant’s total financing requirement to 51,000.
| Cost category | Project cost | Eligible amount under the invented rule |
|---|---|---|
| Approved equipment | 45,000 | 45,000 |
| Approved training | 15,000 | 15,000 |
| Other project expenditure | 15,000 | 0 |
| Total | 75,000 | 60,000 |
The grant is 40% of eligible cost but only 24,000/75,000 = 32% of whole-project cost. Both statements are correct when labelled. Calling it “40% of the project” would misstate the financing.
Evidence matters here: retain the cost schedule, eligibility decision and rule version. Do not move an excluded cost into an eligible label merely to make the desired grant total appear. If the classification is uncertain, resolve it before treating the scenario as approved funding.
Under a fictional rule with share s and maximum grant H, a simple maximum calculation is G = min(sE, H). Actual approval can still be lower or conditional. With s = 0.40, E = 60,000 and H = 20,000, the model grant is 20,000, not 24,000. The applicant finances the remaining 40,000 of eligible cost.
The cap begins binding when E exceeds H/s, assuming s > 0. Here that boundary is 50,000. Up to that eligible cost, the uncapped share applies. Beyond it, the grant stops increasing under this rule even though the project may become more expensive.
For the 75,000-unit whole project in the previous chapter, a 20,000 grant leaves 55,000 to finance. The effective grant share becomes one third of eligible cost and about 26.67% of whole-project cost. The headline maximum percentage remains a ceiling, not the achieved percentage for every project.
Turn the calculation around. An applicant has 18,000 units available for eligible costs. With a 40% grant share and no binding cap, L = 0.60E, so E = 18,000/0.60 = 30,000 and G = 12,000. Under a different rule that adds 40% of L, the same applicant contribution instead supports E = 25,200, with G = 7,200.
These are maximum model budgets under the stated contribution constraint. They do not prove that the grant is approved, that prices are reliable or that the applicant can meet payment timing. Any excluded expenditure uses additional resources and may reduce the affordable eligible scope.
This is a useful public-policy question. A matching offer can encourage local commitment while being difficult for organisations with little unrestricted money to use. Examine actual take-up and unmet need before concluding that low applications mean low demand.
CHAPTER 7 OF 12 · Follow delivery
7. Distinguish contribution from cash-flow timing
An applicant can ultimately bear 60% of eligible cost yet need to pay more than 60% temporarily. Suppose the fictional 60,000-unit project requires full payment before a 24,000 reimbursement. The final net contribution is 36,000, but the applicant needs a permitted way to meet the earlier 60,000 payment.
Draw a dated cash ledger: opening available cash, supplier payments, approved advances if any, reimbursement and restrictions on each balance. A favourable final total does not ensure that every intermediate balance is feasible. Conversely, an advance changes timing without necessarily changing the final cost share.
Avoid assuming every programme reimburses after payment. The operative award determines evidence, release conditions, instalments and eligible dates. A fictional cash-flow illustration should not become a claim about an unrelated real scheme.
CHAPTER 8 OF 12 · Follow delivery
8. Keep pledges, in-kind support and other funding visible
“Contribution” may mean different things under different agreements. Some accept specified in-kind support; others require qualifying cash. A pledge, an eligible contribution, an authorised award and a payment received are separate stages. Do not count one receipt twice because two funders both ask for a matching contribution.
The literacy-campaign matching case develops the pledge-versus-eligible-receipt problem. Carry that distinction into the budget here rather than assuming that any announced fundraising total is usable match.
For a practical check, annotate every financing line with amount, source, restriction, availability date and evidence. Where the agreement allows non-cash support, keep its accepted valuation method separate from bank cash. A balanced funding table is insufficient if the promised resources cannot perform the job assigned to them.
CHAPTER 9 OF 12 · Check the public purpose
9. Ask what behaviour the rule encourages
Arithmetic clarifies a mechanism; it does not decide whether the mechanism serves the public purpose. A uniform match can favour applicants with greater fundraising capacity. A cap can spread resources among more recipients while leaving large projects with a smaller effective share. Eligibility exclusions can protect a purpose while creating costs that weaker applicants struggle to finance.
Compare alternatives against the same objective. Options might include a base grant, different contribution rates or support for preparation. Each has trade-offs and requires its own authority and evidence. Do not infer an ideal design from a single worked budget.
The intergovernmental education-finance guide examines how matching conditions interact with fiscal capacity. The school fundraising guide connects voluntary contributions with educational access and governance.
CHAPTER 10 OF 12 · Check the public purpose
10. Build a calculation someone else can check
A useful funding note identifies the exact rule, eligible cost, excluded cost, grant share or matching ratio, cap, other funding and payment stage. Show the formula, unrounded result and final reconciliation. Someone reviewing the note should be able to reproduce the answer without guessing which percentage applies to which subtotal.
Check the actual agreement when a cost is changed. If eligible expenditure falls, a percentage-based award may change; the rule decides what happens. If costs rise, a cap may leave the entire increase with the applicant. Neither direction should be hidden by copying an old headline grant amount into a revised budget.
Does a 50% match mean half the project is funded?
Only if it means a grant covering 50% of the relevant project-cost base. Adding grant equal to 50% of applicant contribution produces a one-third grant share. Ask for the equation.
Does meeting the calculation guarantee payment?
No. The arithmetic describes a funding scenario. Eligibility, approval, evidence and release conditions remain separate questions.
First, a fictional award provides three grant units for every two eligible applicant units. What share of eligible cost is grant-funded? Here m = 3/2, so s = 1.5/2.5 = 0.60. For E = 50,000, G = 30,000 and L = 20,000 before any cap.
Now add a grant cap of 24,000 and excluded expenditure of 8,000. The grant becomes 24,000. The applicant finances 26,000 of eligible expenditure plus 8,000 excluded expenditure: 34,000 in total. Whole-project cost is 58,000, and the effective grant share is 24,000/58,000 ≈ 41.38%.
Finally, change only the wording to “grant equals 60% of applicant contribution”, with no cap and E still 50,000. Then L = 31,250 and G = 18,750. Explain the difference in a sentence before checking the calculation. Transfer is recognising the changed denominator without being prompted by a chapter label.
Funding mechanisms and public judgement
Return to Public Policy for purpose, evidence and evaluation. Continue with budget-capped awards when the question concerns distributing one shared pool, and eligibility cliffs when a threshold changes support.
Delivery and education
Use the matching-donation case to trace evidence through approval. Use education fiscal transfers and school fundraising governance for the wider distributional questions.
Source and learning transfer
The official England Water Management round-two application guidance, updated 12 November 2025 and marked closed, provides a real example of specifying a percentage of eligible cost and separate match funding. It is an archived jurisdiction-specific illustration, not an available offer or a rule for our invented cases.
Connect the method to The Gold Standard of Education and the How X Works hub. The transferable skill is identifying the base, conditions and timing before interpreting a percentage.
Sources checked 21 October 2026. Worked examples are educational models with the assumptions stated above.