Benefit-cost ratio with averted costs counted gross or netted

Gives the two ratios that arise when averted treatment costs are counted as a benefit (gross) or subtracted from programme costs (netted). Net present value, H plus S minus C, is the same under both, but the ratios differ, and the netted ratio is undefined or negative when averted costs reach or exceed programme costs.

Signature

BCR_gross = (H + S) / C; BCR_net = H / (C - S)
Inputs
InputsDefinitionUnit
HPresent value of the monetised health gain of the programmecurrency in the stated price year, £ million in the examples
SPresent value of treatment costs averted by the programmethe same currency basis as H
CPresent value of the costs of delivering the programmethe same currency basis as H, above zero
Output
BCR_grossRatio of monetised health gain plus averted costs to programme costsratio
BCR_netRatio of monetised health gain to programme costs less averted 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

    Gross and netted benefit-cost ratios in two cells

    With named cells HealthGain, AvertedCosts and ProgrammeCost, the first formula returns the gross ratio and the second the netted ratio, or #N/A when averted costs reach programme costs.

    =(HealthGain+AvertedCosts)/ProgrammeCost; =IF(ProgrammeCost>AvertedCosts,HealthGain/(ProgrammeCost-AvertedCosts),NA())

Assumptions

  • Positive programme cost and a stated classification of savings

    C is greater than zero and the analysis states which classification it reports. The netted ratio reads as a return per pound of net cost only when C exceeds S.

  • Each averted cost counted once

    Each averted cost appears either in the numerator or in the denominator, never in both and never left out, so that net present value is the same under either ratio.

Worked examples

  • Routine vaccination option X counted gross and netted

    Option X costs £4.0 million, averts £3.0 million of treatment costs and yields a monetised health gain of £5.0 million. Its gross ratio is 2.0 and its netted ratio 5.0, with the same net present value of £4.0 million.

    H = 5.0; S = 3.0; C = 4.0; BCR_gross = 2.0; BCR_net = 5.0

  • Catch-up vaccination option Y counted gross and netted

    Option Y costs £9.0 million, averts £5.0 million of treatment costs and yields £9.0 million of health gain. Its gross ratio is about 1.56 and its netted ratio 2.25; net present value is £5.0 million under both.

    H = 9.0; S = 5.0; C = 9.0; BCR_gross = 1.56; BCR_net = 2.25

  • Cost-saving vaccination option with a negative netted ratio

    If option X averted £4.5 million of treatment costs, its gross ratio would be 2.375 and its netted denominator minus £0.5 million, giving a netted ratio of minus 10 for a programme that saves money and improves health.

    H = 5.0; S = 4.5; C = 4.0; BCR_gross = 2.375; BCR_net = -10

Common errors

  • Comparing a gross benefit-cost ratio with a netted one

    Option X reads as £2 of benefit per pound counted gross and £5 per pound netted, with no change in its net value. Ratios from studies that classify savings differently are not on the same scale and cannot be compared.

  • Reading a negative netted ratio as a loss

    A netted ratio of minus 10 in the cost-saving variant describes a programme with a net present value of £5.5 million that both saves money and improves health. When averted costs reach programme costs, net present value or the gross ratio is reported instead.

Sources

  • Green Book on classification affecting the BCR but not net value

    HM Treasury. The Green Book (2026): UK government guidance on appraisal. Updated 5 February 2026. Chapter 6, paragraph 6.95, which notes that counting an effect as a benefit in the numerator or as a cost in the denominator affects the BCR but not the NPSV or RPSC, and asks practitioners to explain the choice.

    View source →

Canonical Identity

Persistent URI
https://healtheconomics.wiki/formula/benefit-cost-ratio-with-averted-costs-counted-gross-or-netted

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