Signature
PV_C = sum_(t=0)^T [C_t/(1+r_C)^t]; PV_E = sum_(t=0)^T [E_t/(1+r_E)^t]
| Inputs | Definition | Unit |
|---|---|---|
C_t | Cost occurring at time t | currency |
r_C | Annual discount rate applied to costs | proportion per year |
t | Time from the reference point for each cost or outcome | years |
E_t | Health outcome occurring at time t | the relevant health-outcome measure |
r_E | Annual discount rate applied to health outcomes | proportion per year |
PV_C | Total discounted cost across the included time horizon | currency |
|---|---|---|
PV_E | Total discounted health outcomes across the included time horizon | the relevant health-outcome measure |
TLast included time point under the model time horizon (years)
Function
Present-value discounting function
Maps future costs or health outcomes to values at a common reference time using the applicable discount rate and timing convention.
Try this function
Implementations
Excel
Discount costs and outcomes separately
Use separate named rate cells so the model remains valid when cost and outcome rates differ.
=Cost/(1+CostRate)^Year; =Outcome/(1+OutcomeRate)^Year
Assumptions
Rates follow the governing reference case
The selected cost and outcome rates, whether equal or different, come from the applicable current institutional guidance.
Comparable timing
Cost and outcome streams use explicit timing conventions applied consistently across the alternatives being compared.
Worked examples
Differential discounting in year 10
A £10,000 cost and 1 QALY in year 10 have present values of £7,440.94 and 0.8617 QALYs when costs are discounted at an illustrative 3% and outcomes at 1.5%.
T = 10; t = 10; C_t = 10000; E_t = 1; r_C = 0.03; r_E = 0.015; PV_C = 7440.94; PV_E = 0.8617
Common errors
Applying one rate when differential discounting is required
Using the same rate for costs and outcomes despite a reference case requiring different rates can materially change incremental results.
Sources
NICE manual for the equal-rate reference case
National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 13 October 2026. Section 4.5, Discounting: 3.5% a year for both costs and health effects (4.5.1); 1.5% for both only when all the criteria in 4.5.3 are met.
Dutch guideline with differential rates
Zorginstituut Nederland. Richtlijn voor het uitvoeren van economische evaluaties in de gezondheidszorg (versie 2024). Zorginstituut Nederland; 16 January 2024. Section 4.2, Disconteren: costs 3% and effects 1.5% a year.
Equal versus differential discounting
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.
Canonical Identity
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