Discount Rate

Discount Rate: Present-Value Formula, NICE 3.5% Rule and Differential Discounting

The discount rate decides how much weight an economic evaluation gives to costs and health outcomes that arrive years after the decision, so it can change incremental results and sometimes the preferred option. This page sets out the present-value formula with an illustrative worked example, the rates required by the NICE manual (PMG36), the HM Treasury Green Book and the Dutch guideline, and the debate over equal versus differential discounting of costs and health effects. It also separates discounting from the time horizon, inflation adjustment and timing conventions, and shows how to apply and report the rate correctly in a model.

The discount rate is an analytical input rather than a universal constant. The appropriate rate normally comes from the reference case or guidance used by the relevant decision-making institution.

Why future costs and health outcomes are discounted

Economic evaluations may include costs and health outcomes that occur many years apart. Discounting converts those future quantities into present values so they can be compared at a common reference point.

Discounting reflects the importance of timing, including time preference and the opportunity cost of committing resources. It does not mean that future health or future patients are unimportant, and it should not be used to remove consequences that belong within the analysis.

• Discounting assigns less present value to a quantity occurring further in the future when the discount rate is positive.
• Discounting allows costs and outcomes occurring at different times to be compared on a consistent basis.
• Discounting is distinct from inflation adjustment and from selection of the time horizon.
• The applicable discount rate should come from the relevant reference case or institutional guidance.

How a future value is converted into a present value

The present value calculation uses the future amount, the annual discount rate and the time between the reference point and the future event. A higher rate or a longer delay produces a smaller present value when the future quantity is positive.

For a value occurring at time t:

PVₜ = Vₜ ÷ (1 + r)ᵗ

where:

• PVₜ is the present value of the quantity occurring at time t.
• Vₜ is the undiscounted future cost or outcome.
• r is the annual discount rate expressed as a decimal.
• t is the time from the reference point, measured consistently with the rate.

For a stream of future values:

Total present value = Σ[Vₜ ÷ (1 + r)ᵗ]

The Discount Rate Present-Value Explorer allows readers to change the amount, timing and annual rate and compare the resulting present values.

A worked present-value example

The figures in this example are illustrative. A cost of £20,000 occurs five years after the reference point, and applying different annual discount rates changes its present value even though the future cost itself remains £20,000.

• 0% annual discount rate: The present value is £20,000.
• 1.5% annual discount rate: The present value is £18,565.
• 3.5% annual discount rate: The present value is £16,839.
• 5% annual discount rate: The present value is £15,671.

At an annual rate of 3.5%:

Present value = £20,000 ÷ (1.035)⁵ = £16,839

The calculation does not remove the future cost. It expresses that cost at the selected reference time so it can be combined with other values consistently.

How costs and health outcomes are discounted

Economic evaluations may apply discounting to both costs and health outcomes. Separate rates must be used when the governing reference case specifies different treatment for the two streams.

• Costs: PV of costs = Σ[Cₜ ÷ (1 + rC)ᵗ]
• Health outcomes: PV of outcomes = Σ[Eₜ ÷ (1 + rE)ᵗ]

In these calculations:

• Cₜ represents a cost occurring at time t.
• Eₜ represents a health outcome occurring at time t.
• rC represents the annual discount rate applied to costs.
• rE represents the annual discount rate applied to health outcomes.

Some institutions apply the same rate to both streams, while others use different rates. The analyst should report both rates explicitly even when they are equal.

Where the selected discount rate comes from

The discount rate is normally specified by the institution or reference case governing the evaluation. Analysts should not select a rate because it produces a preferred result.

The applicable rule may depend on the jurisdiction, type of evaluation, decision date and whether the quantity is a cost or health outcome. Current guidance must therefore be checked rather than assuming that a familiar rate remains valid.

• The analyst should identify the relevant decision-making institution and jurisdiction.
• The analyst should record the title, version and date of the governing guidance.
• The analyst should distinguish the reference-case rate from sensitivity-analysis rates.
• The analyst should record any permitted exceptions and the conditions attached to them.
• A rate used in one jurisdiction should not automatically be transferred to another.

Rates required by NICE, HM Treasury and the Dutch guideline

Three current sources show how far institutional rules differ. They were checked against the source text on 29 September 2026, and each may change, so the governing document should be rechecked at the time of analysis.

The NICE manual, "NICE technology appraisal and highly specialised technologies guidance: the manual" (PMG36, published 31 January 2022, last updated 31 March 2026), states in section 4.5.1 that costs and health effects should be discounted at the same rate of 3.5% a year in the reference case. Under section 4.5.3 the committee may consider a 1.5% rate for both costs and health effects only if the technology is for people who would otherwise die or have a very severely impaired life, it is likely to restore them to full or near-full health, and the benefits are likely to be sustained over a very long period. Sections 4.5.4 and 4.5.5 add that the committee must be confident of a highly plausible case for the long-term maintenance of benefit and satisfied that irrecoverable costs have been captured in the model or mitigated through commercial arrangements. The manual's update log for 2025 and 2026 records changes to the cost-effectiveness threshold, the budget impact test, HealthTech methods, health inequalities and surveillance, and none of these altered section 4.5.

The Green Book is HM Treasury guidance for appraisal across UK central government, while the NICE manual governs NICE's own technology evaluations, so the Green Book's declining schedule and separate 1.5% health rate sit alongside NICE's single 3.5% rate. The Dutch guideline derives its 1.5% health rate as the 3% cost rate minus an assumed 1.5% annual growth in the consumption value of health.

Why costs and health outcomes may use different rates

Differential discounting means applying one rate to costs and another rate to health outcomes. Whether differential discounting is required is an institutional and methodological question rather than a universal rule.

Keeler and Cretin showed in 1983 that if health benefits are left undiscounted while costs are discounted, a programme's cost-effectiveness ratio always improves by delay, as long as the ability to produce the health effect does not diminish too quickly over time. The result, often called the Keeler-Cretin paradox, led them to argue for equal rates and to warn that discounting benefits and costs at different rates can lead to anomalous results. The NICE reference case applies equal rates to costs and health effects.

Claxton, Paulden, Gravelle, Brouwer and Culyer re-examined the question in 2011 and showed that the answer depends on judgements of fact and value. These include whether the objective is to maximise discounted health or the present consumption value of health, whether the health care budget is fixed, and whether the cost-effectiveness threshold and the consumption value of health are expected to grow. With a fixed budget and decisions based on incremental cost-effectiveness ratios, discounting costs and health at the same rate is correct only if the threshold remains constant. They also showed that expected growth in the consumption value of health does not in itself justify differential rates but implies a lower rate for both streams.

Different rates can materially affect interventions that incur costs early but produce health gains much later. Separate cost and health rates should therefore be shown whenever the evaluation permits or requires them.

• Equal discounting applies the same annual rate to costs and health outcomes.
• Differential discounting applies different annual rates to the two streams.
• The governing reference case determines which approach belongs in the base case.
• Sensitivity analysis can show whether the conclusion depends on the difference between the rates.

How timing assumptions affect the calculation

A present-value calculation requires a clear reference time and a consistent assumption about when each cost or outcome occurs. Beginning-of-period, middle-of-period and end-of-period assumptions can produce different present values.

A value occurring at time zero is normally undiscounted because its discount factor is one. Fractional exponents or an explicitly stated timing correction may be used for events occurring partway through a year.

• A time-zero value normally uses t = 0 and a discount factor of 1.
• A value halfway through the first year may use t = 0.5 when that convention matches the model.
• Costs and outcomes should use timing assumptions that reflect when they are expected to occur.
• The same timing rules should be applied consistently across the alternatives being compared.
• Reports should identify the reference time and the timing convention.

How the discount rate differs from the time horizon

The time horizon determines which costs and outcomes enter the economic evaluation. The discount rate determines the present value assigned to included consequences according to when they occur.

These settings interact, but neither can replace the other. Discounting cannot recover important consequences excluded by an unjustifiably short time horizon.

• The time horizon controls the analytical endpoint.
• The discount rate controls present-value weighting within the selected horizon.
• A longer horizon generally exposes more costs and outcomes to discounting.
• Horizon and discount-rate scenarios may need to be examined together.
• Important long-term consequences should not be excluded merely because their discounted values are smaller.

How discounting changes economic-evaluation results

Discounting changes total and incremental costs and health outcomes when the alternatives have different timing patterns. It can therefore alter an incremental cost-effectiveness ratio, incremental net monetary benefit or net present value.

Interventions with early costs and delayed health benefits can be especially sensitive to the selected rates. The direction and size of the effect must be calculated from the actual streams rather than assumed.

• Discounting affects incremental cost when the alternatives incur costs at different times.
• Discounting affects incremental effectiveness when the alternatives produce health outcomes at different times.
• Differential discounting can change the balance between discounted incremental cost and discounted incremental effectiveness.
• A sufficiently influential rate assumption can change the preferred alternative at a stated threshold.
• Discount-rate effects should be interpreted alongside the time horizon and timing of the underlying events.

Keeping real and nominal values consistent

Real values remove general inflation, while nominal values include it. The price basis of the values must match the type of discount rate used in the calculation.

Mixing nominal values with a real rate, or real values with a nominal rate, can distort present values. Analysts should state the price year, inflation treatment and whether the discount rate is real or nominal.

• Real costs should be paired with a real discount rate.
• Nominal costs should be paired with a nominal discount rate.
• Inflation adjustment changes the price basis of a value.
• Discounting changes the value assigned to timing.
• Applying inflation and discounting requires separate, consistent calculations.

Testing alternative discount rates

Sensitivity analysis shows whether the result depends materially on the selected discount rate. The reference case should remain clearly identified, while alternative rates should be presented as scenarios rather than replacements selected after observing the results.

Alternative-rate analysis is particularly useful when consequences extend far into the future or when costs and health gains occur at substantially different times. The analyst should explain whether the resulting changes affect the size, interpretation or direction of the decision result.

• The reference-case cost and outcome rates are reported first.
• The alternative rates required by the governing guidance are tested.
• Additional justified scenarios are considered when long-term results are highly rate-sensitive.
• Incremental costs, incremental outcomes, ICERs and net benefit are recalculated for each scenario.
• The analysis states whether the preferred alternative changes.
• Sensitivity analysis is never a substitute for correcting a wrongly specified base case.

Using the downloadable discount-rate model

The Discount-Rate Incremental Results Model allows readers to enter separate cost and health discount rates and follow annual values through the present-value calculation. It then shows how discounting changes incremental cost, incremental QALYs, the ICER and incremental net monetary benefit.

The workbook uses synthetic teaching data and includes instructions, calculations, outputs, rate scenarios, sources and validation checks. Its narrated walkthrough demonstrates how the inputs flow through the model and how the resulting changes should be interpreted.

Applying discounting correctly in Excel

Excel formulas can calculate present values transparently when the timing convention is understood. Particular care is needed with the NPV function because the first value in the selected range is treated as occurring at the end of period one.

• Discount factor: =1/(1+DiscountRate)^Year
• Discounted value: =Value*DiscountFactor
• Direct present-value calculation: =Value/(1+DiscountRate)^Year
• Time-zero value plus later values: =TimeZeroValue+NPV(DiscountRate,Year1:YearN)
• Cost discounted separately: =Cost/(1+CostRate)^Year
• Outcome discounted separately: =Outcome/(1+OutcomeRate)^Year

A rate of 3.5% should normally be stored as 0.035 or entered as 3.5%. Entering 3.5 without percentage formatting represents 350%, not 3.5%.

Reporting discount rates, timing and price basis

Transparent reporting allows readers to reproduce the calculation and determine whether the chosen rates follow the relevant guidance. Reporting only a final discounted result is not enough because the result depends on the rate, timing and price basis used.

A complete report states:

• the discount rate applied to costs;
• the discount rate applied to health outcomes;
• the source, version and date of the governing guidance;
• the reference time and timing convention;
• the treatment of time-zero and partial-period values;
• the price year and whether monetary values and rates are real or nominal;
• the undiscounted and discounted results when useful for interpretation;
• the reference-case result and required alternative-rate scenarios;
• whether changing the rates alters the decision conclusion.

Common discounting errors in economic evaluation

Discounting errors often result from confusing the rate with another time-related model setting or applying the correct formula to incorrectly timed values. These errors can materially change both the numerical results and the preferred alternative.

• Discounting a time-zero value incorrectly reduces a quantity that occurs at the reference point.
• Entering 3.5 instead of 0.035 applies a rate of 350% rather than 3.5%.
• Treating Excel's first NPV value as time zero shifts the cash-flow timing by one period.
• Using an outdated or irrelevant jurisdictional rate makes the base case inconsistent with its stated reference case.
• Mixing real values with nominal rates creates an inconsistent price basis.
• Applying different rates to costs and outcomes without justification can bias the comparison.
• Confusing discounting with inflation adjustment combines two different analytical operations.
• Confusing the discount rate with the time horizon changes present-value weighting rather than the analytical endpoint.
• Using inconsistent timing conventions across alternatives undermines comparability.
• Using sensitivity analysis to conceal an incorrectly specified base case can misrepresent uncertainty.
• Choosing a discount rate because it produces a preferred conclusion introduces analytical bias.

Sources

• Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th edition. Oxford: Oxford University Press; 2015.
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 31 March 2026. Section 4.5, Discounting.
• HM Treasury. The Green Book (2026). London: HM Treasury; 2026. Chapter 6, Shortlist appraisal: Discounting.
• Zorginstituut Nederland. Richtlijn voor het uitvoeren van economische evaluaties in de gezondheidszorg (versie 2024). Zorginstituut Nederland; 16 January 2024. Section 4.2, Disconteren.
• Keeler EB, Cretin S. Discounting of life-saving and other nonmonetary effects. Management Science. 1983;29(3):300-306.
• Claxton K, Paulden M, Gravelle H, Brouwer W, Culyer AJ. Discounting and decision making in the economic evaluation of health-care technologies. Health Economics. 2011;20(1):2-15.
• Microsoft. NPV function. Microsoft Support; accessed 29 September 2026.