Concept Architecture
Concept
Theoretically, the Internal Rate of Return (IRR) is the discount rate at which the present value of the expected benefits of an investment equals the present value of its costs, resulting in a net present value of zero. It is based on discounted cash flow analysis and investment theory and represents the annualised rate of return generated by an investment over its lifetime. In health economics, IRR is primarily applied to investment appraisal for healthcare programmes, infrastructure and public health interventions where costs and monetary benefits occur over multiple time periods.
Mathematically, the Internal Rate of Return is the value of the discount rate that satisfies the net present value equation. Because the discount rate appears as an exponent, the solution cannot usually be obtained analytically and is instead estimated numerically using iterative algorithms such as Newton-Raphson or successive approximation.
In practice, IRR is estimated using projected streams of costs and monetary benefits over the investment horizon. Spreadsheet software and financial modelling packages solve the equation iteratively. The estimated IRR is then compared with a required rate of return, discount rate or cost of capital to determine whether an investment is economically worthwhile.
Purpose
Used to evaluate the financial attractiveness of healthcare investments by estimating the annual rate of return generated over the investment lifetime and comparing it with a required rate of return or decision threshold.
Mathematical Formulae
Primary Formula
0 = ????� CF? / (1 + r)?
where:
- CF? = net cash flow during period t
- r = Internal Rate of Return
- n = investment horizon
Supporting Formulae
Net Present Value:
NPV = ????� CF? / (1 + r)?
At the Internal Rate of Return:
NPV = 0
Related Mathematical Methods
- Discounted cash flow analysis
- Net Present Value analysis
- Present value analysis
- Investment appraisal
- Sensitivity analysis
- Scenario analysis
- Numerical root-finding methods
Example
A hospital invests �1,000,000 in a diagnostic imaging system.
Projected annual net cash flows are:
| Year | Net Cash Flow |
|---|---|
| 0 | ?�1,000,000 |
| 1 | �300,000 |
| 2 | �350,000 |
| 3 | �375,000 |
| 4 | �400,000 |
| 5 | �425,000 |
Using an iterative numerical solution, the Internal Rate of Return is approximately 16.3% per year.
If the organisation requires a minimum return of 10%, the investment would generally be considered financially acceptable because the IRR exceeds the required rate of return.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| IRR | =IRR(B2:B7) | Estimate the Internal Rate of Return for healthcare investment cash flows |
| XIRR | =XIRR(B2:B7,A2:A7) | Estimate IRR when cash flows occur on irregular dates |
| NPV | =NPV(0.035,B3:B7)+B2 | Compare IRR with Net Present Value calculations |
| IF | =IF(C2>0.10,""Accept"",""Reject"") | Compare the estimated IRR with the required rate of return |
VBA (Optional)
Automate Internal Rate of Return calculations for multiple healthcare investment scenarios and generate comparative investment appraisal reports.
Sources
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- Boardman AE, Greenberg DH, Vining AR, Weimer DL. Cost-Benefit Analysis: Concepts and Practice. Cambridge University Press.
- National Institute for Health and Care Excellence (NICE). Health Technology Evaluation Manual.
- Husereau D, Drummond M, Augustovski F, et al. CHEERS 2022 Statement: Updated Reporting Guidance for Health Economic Evaluations.
Related Concepts (2)
Library
Publications
1
Conjoint Analysis Applications in Health — A Checklist: A Report of the ISPOR Good Research Practices for Conjoint Analysis Task Force — Bridges, Hauber, Marshall, Lloyd, Prosser, Regier, Johnson & Mauskopf, Vol. 14, No. 4 ed., 2011 (Value in Health)
The ISPOR good-practice checklist for conjoint analysis and discrete-choice experiments in health — the stated-preference methods used to elicit patient and public preferences over treatment attributes for value assessment and priority-setting.
Journal ArticleView source →
Frequently Asked Questions (6)
What is the internal rate of return?
The discount rate at which the net present value of a stream of cash flows equals zero, used to summarise an investment's return.
Source: Brealey, Myers & Allen 2019
How is the internal rate of return calculated?
It is the discount rate at which the present value of a stream of cash flows equals zero, found by solving for the rate rather than assuming one. Because the equation is a polynomial in the rate, it is normally solved numerically. The resulting figure summarises the return an investment generates as a single percentage, which can be compared against the cost of capital or against a required rate. Where the flows are conventional, with an initial outlay followed by returns, a unique solution exists and the figure can be interpreted straightforwardly as the return the project generates.
Source: Brealey, Myers & Allen 2019
How does the internal rate of return compare with net present value?
Net present value applies a rate chosen by the decision maker and returns a monetary figure. The internal rate of return derives a rate from the cash flows and returns a percentage. For a straightforward investment the two agree on whether a project is worthwhile, but they can rank mutually exclusive projects differently, because a percentage says nothing about scale and a small project can show a higher return while generating far less value. The disagreement arises because the internal rate implicitly assumes reinvestment at itself, whereas net present value assumes reinvestment at the discount rate, and the second is the more realistic assumption.
Source: Brealey, Myers & Allen 2019
What are the technical problems with the internal rate of return?
A stream of cash flows changing sign more than once can produce multiple rates satisfying the equation, none of which is meaningful. A stream with no sign change produces none at all. The measure also implicitly assumes intermediate cash flows are reinvested at the internal rate itself, which is rarely realistic. These difficulties do not arise with net present value, which is why finance texts recommend it as the primary criterion. Modified formulations exist that impose an explicit reinvestment rate and resolve the multiple-solution problem, at the cost of requiring a further assumption that the simple version appeared to avoid.
Source: Brealey, Myers & Allen 2019
Where is the internal rate of return used in health?
In appraising capital schemes and in assessing investments where a return can be identified, including estate development, energy efficiency projects and revenue-generating activity. It is also used in social investment contexts where a rate of return on public spending is being communicated. Its appeal is that a percentage is easier to compare across proposals than a monetary figure, which is also the source of the ranking error it can produce. It is also commonly encountered in business cases prepared outside finance functions, where the percentage form is preferred for presentation without the accompanying net present value being calculated.
Source: Gapenski 2015
What should accompany an internal rate of return?
The net present value at the relevant discount rate, since that is the criterion on which the decision should rest and the two can disagree. The scale of the investment, because a percentage conveys nothing about how much value is created. The pattern of cash flows, so a reader can see whether the sign changes more than once. And the assumed reinvestment treatment, if the figure is being used for anything other than a simple accept or reject decision. Where the figure is being used to compare projects of different size or duration, that comparison should be made on net present value instead, with the internal rate reported as supporting information.
Source: Brealey, Myers & Allen 2019
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 1 Aug 2025
Content version: 1.0.0
Canonical Identity
- Term code
- HE-EE-CBA-028
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