Benefit-cost ratio with a transfer counted on both sides

Gives the ratio when a transfer, such as an incentive payment, is counted as a cost to the payer and an equal benefit to the recipient. The transfer cancels in net present value but moves the ratio towards one: a ratio above one falls and a ratio below one rises.

Signature

BCR_T = (PVB + T) / (PVC + T)
Inputs
InputsDefinitionUnit
PVBPresent value of monetised benefits excluding the transfercurrency in the stated price year, £ million in the examples
TPresent value of a payment from one party to another, such as incentive payments to families, counted once as a cost and once as an equal benefitthe same currency basis as PVB, zero or above
PVCPresent value of costs excluding the transferthe same currency basis as PVB, above zero
Output
BCR_TBenefit-cost ratio after the transfer is added to both benefits and costsratio

Function

Benefit-cost ratio comparison and classification function

Maps the present values of monetised benefits and costs of one or more options, split where needed by how consequences are classified and by who bears the costs, to ratio summaries and to their link with net present value. The basic ratio and net present value are given under cost-benefit analysis (HE-FM-CBA-002 and HE-FM-CBA-001); PVB and PVC on this page are the same quantities as PV_B and PV_C there. The formulas below relate the ratio to net present value, apply it between mutually exclusive options, and show how the classification of savings, transfers and costs outside the public sector changes it.

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Implementations

  • Excel

    Benefit-cost ratio with a two-sided transfer in one cell

    Excel adds the transfer to present-value benefits and to present-value costs before dividing, using named cells PVBenefits, PVCosts and Transfer.

    =(PVBenefits+Transfer)/(PVCosts+Transfer)

Assumptions

  • Equal transfer amounts on both sides of the ratio

    The same present value T is added to benefits and to costs, so net present value is unchanged. The Green Book also allows transfers to be left out of the analysis altogether, which leaves the ratio at PVB divided by PVC.

Worked examples

  • Incentive payments added to routine vaccination option X

    Adding £2.0 million of incentive payments to families lowers the gross ratio of option X from 2.0 to about 1.67, while its net present value stays at £4.0 million.

    PVB = 8.0; PVC = 4.0; T = 2.0; BCR_T = 1.67

  • Transfer added to an option with a ratio below one

    For an illustrative option with benefits of £3.0 million and costs of £4.0 million, the same transfer raises the ratio from 0.75 to about 0.83, again towards one, and net present value stays at minus £1.0 million.

    PVB = 3.0; PVC = 4.0; T = 2.0; BCR_T = 0.83

Common errors

  • Counting a transfer on the cost side only

    Recording incentive payments as a cost to the authority without the matching benefit to families cuts the net present value of option X from £4.0 million to £2.0 million and its ratio from 2.0 to about 1.33, although the payment only moves money between parties.

Sources

  • Green Book on transfers pushing the BCR towards one

    HM Treasury. The Green Book (2026): UK government guidance on appraisal. Updated 5 February 2026. Chapter 6, paragraph 6.38, which gives the two approaches to economic transfers and notes that transfers counted as both a cost and a benefit cancel in net present social value but push the benefit-cost ratio artificially towards one.

    View source →

Canonical Identity

Persistent URI
https://healtheconomics.wiki/formula/benefit-cost-ratio-with-a-transfer-counted-on-both-sides

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