Signature
PV_total = sum_(t=0)^T [V_t/(1+r)^t]
| Inputs | Definition | Unit |
|---|---|---|
V_t | Undiscounted cost or health outcome occurring at time t | currency or the relevant health-outcome unit |
r | Annual discount rate expressed as a decimal | proportion per year |
t | Time from the reference point for each value | years |
PV_total | Sum of the discounted values across all included times | same as V_t |
|---|
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.
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Implementations
Excel
Time-zero value plus later values
Excel NPV treats the first value in its range as occurring at the end of period 1, so a time-zero value is added separately.
=TimeZeroValue+NPV(DiscountRate,Year1:YearN)
Assumptions
Consistent timing convention
Every value is assigned to a time point using the same beginning-, middle- or end-of-period convention across alternatives.
Complete included stream
The stream contains all relevant values within the justified time horizon; discounting does not correct omitted consequences.
Worked examples
Three-year cost stream
Costs of £10,000 at time zero and £5,000 at the end of years 1 and 2 have a total present value of approximately £19,498 at 3.5%.
T = 2; r = 0.035; t = [0,1,2]; V_t = [10000,5000,5000]; PV_total = 19498.47
Common errors
Treating Excel NPV as beginning at time zero
Including a time-zero value inside the NPV range discounts it by one period and shifts every cash flow's timing.
Sources
Second Panel recommendations
Sanders GD, Neumann PJ, Basu A, Brock DW, Feeny D, Krahn M, et al. Recommendations for conduct, methodological practices, and reporting of cost-effectiveness analyses: Second Panel on Cost-Effectiveness in Health and Medicine. JAMA. 2016;316(10):1093-1103.
Canonical Identity
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