Social Opportunity Cost of Capital

Social Opportunity Cost of Capital in Public and Health Appraisal

The social opportunity cost of capital, usually shortened to SOC, is a kind of opportunity cost that values the money a government puts into a project at the social return those funds would have earned had they stayed in private investment. It is one of the two classic bases for the discount rate in public appraisal, the other being social time preference. Health economists meet it when a long-lived investment such as a new hospital is judged by cost-benefit analysis across government rather than inside a fixed health budget. A higher rate shrinks the present value of benefits that arrive late, so the basis chosen for the rate can decide whether prevention with slow returns passes or fails.

Where the idea sits in welfare economics

In welfare economics a public project raises welfare when the social value it creates exceeds the social value of whatever it displaces. Zhuang and colleagues (2007), surveying social discount rates for the Asian Development Bank, start from the investor's version of this test. Funds placed in one project could earn a return elsewhere, so the project should yield at least the return on the next best investment, and without market distortions that rate is the marginal social rate of return on private investment, which they call the marginal social opportunity cost of capital.

The survey traces the case for discounting public projects at this rate to Mishan and Baumol in the late 1960s and to Diamond and Mirrlees in 1971. Government and private firms compete for the same pool of funds, public investment is assumed to displace private investment pound for pound, and a public project that earns less than the private return lowers total welfare. The SOC is, in effect, the crowding out of private investment written into a discount rate.

Social opportunity cost and social time preference as rival rates

HM Treasury's October 2026 supplementary guidance on discounting names two broad ways of deriving a discount rate. Under social time preference the rate reflects how far society is willing to trade consumption today for consumption tomorrow, which ties it to time preference. Under the SOC approach the rate reflects the cost of capital drawn from the different sources of government funding and the return on the private investment that spending displaces.

With perfect competition and no distortions the two rates coincide, as the supply and demand prices of investible funds meet at one market interest rate. Taxes on company income and on interest earnings drive a wedge between them, the time preference rate is generally the lower of the two, and the survey reports that decades of debate have produced no consensus on which to use.

Freeman and Groom (2026), who led the independent review of the Green Book discount rate, draw the line slightly differently. A time preference rate comes from a model that explicitly maximises a social welfare function, whereas an SOC rate is taken from financial market returns or observed returns on real private investment, matched for maturity and systematic risk.

Weighted average and shadow price methods

A pure SOC rate assumes that every pound of public spending displaces private investment, and a pure time preference rate assumes that it all comes from postponed consumption. The weighted average approach, associated with Harberger, treats public funds as drawn partly from displaced investment, partly from extra household saving and, in an open economy, partly from foreign borrowing.

$$\rho = \alpha \, r_{SOC} + \beta \, r_{STP} + (1 - \alpha - \beta) \, i_f$$

where $\rho$ is the social discount rate, $r_{SOC}$ is the social opportunity cost of capital, $r_{STP}$ is the social rate of time preference, $i_f$ is the government's real long-term foreign borrowing rate, $\alpha$ is the share of funds obtained at the expense of private investment, $\beta$ is the share obtained at the expense of current consumption, and $(1 - \alpha - \beta)$ is the share raised abroad.

In a closed economy, if the supply of funds is perfectly inelastic, the rate equals the SOC, and if the demand for funds is perfectly inelastic, it equals the time preference rate. Harberger argued that investment responds strongly to interest rates while evidence that saving does is scanty, so the weighted average should lie close to the SOC. Critics reply that the method treats benefits as consumed at once and ignores their reinvestment, which can bias appraisal against long-term projects.

The shadow price of capital approach answers that criticism. Costs and benefits that displace or generate private investment are multiplied by a shadow price of capital, the present value of the future consumption lost when one unit of private investment is displaced, and the adjusted streams are discounted at the time preference rate. Zhuang and colleagues report that the shadow price is very sensitive to the two rates, to depreciation and reinvestment assumptions and to project life, and that no adjustment is needed when a least-cost analysis, which the survey equates with cost-effectiveness analysis, compares similarly financed ways of producing the same output.

How governments have used SOC rates

Early United Kingdom practice was close to an SOC rate. Freeman and Groom, citing Spackman, record that a 1967 Treasury document set a test discount rate for nationalised industry investment at 8 per cent in real terms, presented as broadly consistent with the return private firms sought on low-risk projects. By 1980 a reassessed 5 per cent public sector rate was described as a projection of the pre-tax return on assets achieved by private companies, and the Green Book of 2003 then based its 3.5 per cent rate on social time preference through the Ramsey rule.

The 2026 review kept that framework but used SOC evidence to set the number. HM Treasury's response confirms a social time preference approach informed by SOC evidence, and in the supplementary guidance real gilt yields of around 2 per cent in June 2026, the SOC evidence it weighs with surveys and international comparisons, lift the Ramsey risk-free rate from 1.875 to 2.00 per cent. A systematic risk premium of 1.00 per cent then gives 3.00 per cent for the first 30 years of a proposal, replacing 3.50 per cent.

Freeman and Groom put the central SOC risk premium for the average public project at 1.9 per cent before recommending 1 per cent, and judge the gap between the two approaches to be commonly overstated. The 2003 Circular A-4 of the United States Office of Management and Budget leaned the other way. It described its 7 per cent rate as an estimate of the average before-tax return to private capital that approximates the opportunity cost of capital, for use when a regulation mainly displaces private capital, with about 3 per cent where effects fall mainly on consumption.

Why a fixed health budget changes the question

In health technology assessment the agency usually fixes the rate. The NICE manual for technology appraisal and highly specialised technologies (PMG36), in its version last updated on 13 October 2026, requires reference-case costs and health effects to be discounted at the same rate of 3.5 per cent a year, with 1.5 per cent allowed only when set criteria are met. That is now higher than the Green Book's 3.00 per cent.

Attema, Brouwer and Claxton (2018) show why the SOC logic only partly carries over to health technology assessment. For health interventions in general, opportunity costs reflect the chance that resources used for health care could have earned a positive return in another sector. A body such as NICE, however, can be viewed as an agent given a budget to improve health, so the budget is treated as fixed and new spending comes at the expense of other health care. The opportunity cost is then the health forgone, the extra cost divided by the marginal cost-effectiveness of current spending that a cost-effectiveness threshold tries to capture.

Here the welfarist and extra-welfarist traditions part company, and Attema and colleagues frame the choice as whether the objective is broader welfare or health alone from a given budget. A welfarist cost-benefit analysis values health in money and asks whether funds should leave the private economy at all, so the SOC is a natural benchmark. An extra-welfarist appraisal measures opportunity cost in QALYs displaced within the system, and the return on private capital drops out. The Green Book likewise excludes the costs of raising public funds, because most proposals are paid for from budgets set in advance.

Worked example with a diagnostic centre funded by public capital

The figures are illustrative. A health department weighs a diagnostic centre that costs GBP 10 million now and yields net social benefits, including monetised QALY gains and cost savings, of GBP 0.8 million a year for 20 years in real terms, with the Green Book's 2 per cent uprating of health effects set aside for simplicity. Its net present value depends on the rate chosen.

$$NPV = -C + B \times \frac{1 - (1 + r)^{-n}}{r}$$

where $NPV$ is the net present value in GBP million, $C$ is the capital cost of 10, $B$ is the annual net benefit of 0.8, $n$ is the life of 20 years, and $r$ is the real discount rate.

At the Green Book rate of 3.00 per cent, $(1.03)^{20} = 1.8061$ and the annuity factor is $(1 - 1/1.8061)/0.03 = 14.8775$. The present value of benefits is $PV = 0.8 \times 14.8775 = 11.902$, so $NPV = 11.902 - 10 = 1.902$, a gain of about GBP 1.9 million.

At a pure SOC rate of 7 per cent, the before-tax private return in the 2003 United States guidance, $(1.07)^{20} = 3.8697$ and the annuity factor is $(1 - 1/3.8697)/0.07 = 10.5940$. Then $PV = 0.8 \times 10.5940 = 8.475$ and $NPV = 8.475 - 10 = -1.525$, a loss of about GBP 1.5 million.

For a weighted average, suppose 60 per cent of the funds displace private investment earning 7 per cent, 30 per cent come from consumption valued at 3 per cent and 10 per cent are borrowed abroad at 4 per cent. The rate is $\rho = 0.6 \times 7 + 0.3 \times 3 + 0.1 \times 4 = 5.5$ per cent. Then $(1.055)^{20} = 2.9178$, the annuity factor is $(1 - 1/2.9178)/0.055 = 11.9504$, $PV = 0.8 \times 11.9504 = 9.560$ and $NPV = 9.560 - 10 = -0.440$.

The internal rate of return is about 4.96 per cent, so the centre passes under social time preference and fails under both SOC-based rates. Much of the 7 per cent reflects the systematic risk of private capital, so a low-risk public service needs a benchmark matched on risk. A NICE appraisal of the centre's tests would weigh discounted QALYs and costs against the threshold instead.

Boundaries with neighbouring ideas

Opportunity cost is the general principle, and the SOC is one measure of it for capital funds. The social discount rate is the rate a government applies, with the SOC as one candidate basis. The market interest rate equals the SOC only in an undistorted capital market.

Capital cost in a costing study is the cost of the buildings and equipment an intervention uses, a cost item rather than a rate of return. The marginal cost of public funds measures the extra burden of raising tax revenue, and Freeman and Groom argue that it belongs among a project's costs rather than in the discount rate. Differential discounting, the use of different rates for health effects and costs, is a separate question.

Limitations and common misreadings

A frequent error is to treat an observed private return as a riskless SOC. Freeman and Groom note that a core reason the United States rates of 7 and 3 per cent differ is the very different systematic risk of private capital and Treasury bonds, and they call it a simple error to compare a long-term, safe public project with a short-term, high-risk private one. Zhuang and colleagues add that the marginal return, which is lower than the average, is the right measure.

The displacement assumption is also fragile. The survey reports the argument of Dasgupta, Marglin and Sen that pound-for-pound crowding out holds only in a two-period model with a fixed stock of capital, so the rate should fall below the SOC when consumers fund part of a project by postponing consumption. The 2026 review also warns against overworking the rate, which should reflect only maturity and systematic risk, and the Green Book now uprates future health effects by 2 per cent a year instead of using a separate health discount rate. In health appraisal a common slip is to treat the SOC as the opportunity cost of NHS spending, when within a fixed budget that cost is health displaced elsewhere.

Sources

• Attema AE, Brouwer WBF, Claxton K. 2018. Discounting in economic evaluations. PharmacoEconomics 36(7): 745-758. https://doi.org/10.1007/s40273-018-0672-z
• Freeman MC, Groom B. 2026. Green Book Discount Rate Review: Summary of Findings and Recommendations. London: HM Treasury. https://assets.publishing.service.gov.uk/media/6a43915e7ac6fd9c6a94abbe/Findings_and_Recommendations_-_Green_Book_Discount_Rate_Review.pdf
• Freeman MC, Groom B. 2026. Green Book Discount Rate Review: Technical Annexes. London: HM Treasury. https://assets.publishing.service.gov.uk/media/6a439175db380b085e94abc4/Technical_Annexes_-_Green_Book_Discount_Rate_Review.pdf
• HM Treasury. 2026. The Green Book (2026). https://www.gov.uk/government/publications/the-green-book--2/the-green-book-2026
• HM Treasury. 2026. Green Book supplementary guidance: discounting. October 2026. https://assets.publishing.service.gov.uk/media/6ae0b34016428df537606216/Green_Book_supplementary_guidance_-_discounting.pdf
• HM Treasury. 2026. Green Book Discount Rate Review 2026: HM Treasury response. October 2026. https://assets.publishing.service.gov.uk/media/6ae0b3a97cf9b2248904678e/Green_Book_Discount_Rate_Review_2026_-_HM_Treasury_response.pdf
• National Institute for Health and Care Excellence. 2022, last updated 13 October 2026. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). https://www.nice.org.uk/process/pmg36/chapter/economic-evaluation
• Office of Management and Budget. 2003. Circular A-4, Regulatory Analysis. Washington DC: Executive Office of the President. https://obamawhitehouse.archives.gov/omb/circulars_a004_a-4/
• Zhuang J, Liang Z, Lin T, De Guzman F. 2007. Theory and practice in the choice of social discount rate for cost-benefit analysis: a survey. ERD Working Paper No. 94. Manila: Asian Development Bank. https://www.adb.org/sites/default/files/publication/28360/wp094.pdf