IRR versus NPV versus BCR, Which Metric Tells the Truth
Any serious project appraisal reports at least one of net present value, internal rate of return, or benefit-cost ratio. Many report all three. Each answers a distinct question. Confusing them, or presenting one as if it answered another, is one of the most common failures in bankability analysis submitted to funders in emerging and developed markets alike.
This piece sits under the m2 pillar on bankability and viability. It explains what each metric actually measures, when each is the right choice, and the traps that produce answers that are technically correct but decision-misleading.
Net present value (NPV)
NPV is the sum of a project's cash flows over its life, discounted to today at a chosen rate, minus the initial investment.
Mathematically: NPV equals the sum, across all periods, of the period's net cash flow divided by the quantity of one plus the discount rate, raised to the power of the period number.
A positive NPV means the project creates value at the chosen discount rate; a negative NPV means it destroys value. The convention in corporate finance is to invest in projects with positive NPV and reject projects with negative NPV, ranked where possible by NPV size.
The elegance of NPV is that it produces a single answer in units of currency: this project creates R X million of value at Y percent discount. The trap is that most of the answer is buried in the discount rate. Change the rate by two percentage points and the NPV can flip sign. A project with a positive NPV at eight percent and a negative NPV at ten percent is a project whose approval depends on how the analyst chose the discount rate (Brealey, Myers, and Allen, 2020).
Sponsors who use a single point-estimate discount rate and do not show the sensitivity around it are hiding the underlying uncertainty from themselves and from the funder. Any credible NPV presentation shows the base-case discount rate, plus a sensitivity across a range of plausible rates.
Internal rate of return (IRR)
IRR is the discount rate at which the NPV of a project equals zero. It is the "break-even" discount rate: below IRR, the project has positive NPV; above IRR, negative.
The attraction of IRR is that it does not require the analyst to pre-select a discount rate. The IRR falls out of the cash flows themselves, and can be compared directly with the borrower's cost of capital or the funder's hurdle rate. A project with an IRR of 15 percent compares favourably with a 10 percent hurdle rate; a project with an IRR of 8 percent does not.
Three traps recur with IRR.
Multiple IRRs on non-conventional cash flows. Where the project's cash flows change sign more than once (a construction phase with negative cash flow, an operating phase with positive cash flow, and a decommissioning phase with negative cash flow), the polynomial that produces the IRR can have multiple solutions. Most software returns only one, and the returned value may or may not be the economically meaningful one. Analysts encountering non-conventional cash flows should use modified IRR (MIRR) or return to NPV with explicit assumptions about reinvestment rates.
Comparing IRRs across project sizes. A ten percent IRR on a one-million-rand project and a nine percent IRR on a one-billion-rand project are not comparable in any decision-useful way. IRR is a rate; it does not tell you the size of the value created. Ranking projects by IRR alone favours small projects over large ones and can lead to portfolio decisions that leave capital deployed sub-optimally.
Assumed reinvestment at the IRR. The IRR calculation implicitly assumes that intermediate cash flows are reinvested at the IRR itself. Where the IRR is materially above the reinvestment rate actually available (the borrower's cost of capital, or the market's yield on comparable investments), the IRR overstates the effective return. MIRR corrects for this by using an explicit reinvestment rate.
The safe posture is to report both IRR and NPV together, using the funder's hurdle rate as the NPV discount rate, so the two metrics answer complementary questions and the analyst is not tempted to lean on the wrong one.
Benefit-cost ratio (BCR)
BCR is the ratio of the present value of a project's benefits to the present value of its costs. Standard in socio-economic evaluation and in most public-sector infrastructure appraisal frameworks, including National Treasury's Budget Facility for Infrastructure methodology in South Africa (National Treasury, 2019) and the World Bank's public investment appraisal guidance (World Bank, 2017).
A BCR above one means benefits exceed costs; a BCR of one means they exactly balance; a BCR below one means costs exceed benefits.
BCR answers a different question from NPV or IRR. NPV and IRR are financial metrics: they measure returns to the sponsor or the equity holder. BCR is a welfare metric: it measures returns to society at large. A project can have a strong financial IRR and a weak BCR if the private returns come at a large socio-economic cost; conversely, a project with a modest financial IRR can have a strong BCR if it generates substantial socio-economic benefits (health outcomes, time saved, environmental damage avoided).
The trap with BCR is that it depends heavily on how benefits are defined and quantified. Two analysts can look at the same project and produce BCRs one full number apart depending on the shadow prices they choose for non-market benefits (a statistical life saved, an hour of travel time avoided, a ton of carbon dioxide not emitted).
The National Treasury BFI framework in South Africa is prescriptive about the shadow prices to be used in submissions (National Treasury, 2010), which reduces the variance across submissions and makes BCRs from different projects at least loosely comparable. Analysts working outside prescribed frameworks should be explicit about the shadow prices used and the source for each, so the reader can understand which parts of the BCR are robust and which are contested.
When to use which
The three metrics are not interchangeable, and the right one depends on the question being asked.
Use NPV when: the discount rate is well-established (from the borrower's cost of capital or the funder's hurdle rate); the question is "how much value does this project create at that rate"; you want a single-currency answer that can be aggregated across a portfolio of projects.
Use IRR when: the discount rate is uncertain or contested; the question is "what return does this project generate"; you want a rate-based comparison with other investment opportunities. Always supplement with NPV and check for the traps above.
Use BCR when: the project has material socio-economic dimensions (public infrastructure, health, education, environmental); the funder requires socio-economic evaluation; the framework you are submitting under prescribes it.
Serious project appraisals often report all three: NPV as the aggregate value measure, IRR as the return measure, and BCR as the welfare measure. The combination gives the reader multiple angles on the same underlying project.
Cross-border considerations
Cross-border infrastructure and investment projects add complications to each metric. The discount rate for NPV needs to reflect the country risk of the project's location, not just the sponsor's own cost of capital. IRR comparisons across jurisdictions need to be currency-adjusted and inflation-adjusted. BCR shadow prices vary by country because willingness-to-pay estimates and cost-of-life-saved values differ across societies.
The World Bank's public-private partnerships reference guide (World Bank, 2017) provides one framework for handling these adjustments consistently across cross-border projects. Analysts working on cross-border transactions should choose an evaluation framework and apply it consistently, rather than mixing conventions from multiple sources.
What to do
Before reporting NPV, IRR, or BCR to a funder or a credit committee, four questions should be answered honestly:
- Are the cash flows behind the metric a defensible representation of what the project will actually generate, or are they aspirational?
- Is the discount rate (for NPV) or the reinvestment rate (for MIRR) sourced from a defensible benchmark, or picked to produce the desired answer?
- If BCR, are the shadow prices sourced from a recognised framework, or invented for this submission?
- Do the metrics tell a consistent story, or does one look strong while the others look weak?
Consistent metrics tell a story. Inconsistent metrics tell a different story, which is that one of them was massaged. Credit committees and evaluation panels have seen enough of both to distinguish them at a glance.
The CentraSolve Bankability and Viability module builds each metric from the underlying cash flows in a way that ties them together and enforces internal consistency. What the summary page shows for NPV, IRR, and BCR reproduces from the raw inputs to the cent, and the sensitivity analysis around each metric is built into the workbook rather than bolted on as an afterthought.
References
Textbook and framework sources
Brealey, R. A., Myers, S. C., and Allen, F. (2020). Principles of corporate finance (13th ed.). New York: McGraw-Hill Education.
National Treasury, Republic of South Africa. (2010). A guide to socio-economic cost-benefit analysis for public investments. Pretoria: National Treasury.
National Treasury, Republic of South Africa. (2019). Budget Facility for Infrastructure: guidelines and templates. Pretoria: National Treasury.
World Bank Group. (2017). Public-private partnerships reference guide (Version 3.0). Washington, DC: World Bank.
Yescombe, E. R., and Farquharson, E. (2018). Public-private partnerships for infrastructure: principles of policy and finance (2nd ed.). Oxford: Butterworth-Heinemann.