322. NPV versus BCR part 1
There are two main criteria used for evaluating projects in Benefit: Cost Analysis (BCA): the Net Present Value (NPV = benefits minus costs) and the Benefit: Cost Ratio (BCR = benefits divided by costs). In what circumstances should you use one of the other or both or neither? It’s a question with quite a complex set of answers.
The advice on this question in BCA guidelines and textbooks is not always sufficiently helpful, or even correct. And there is at least one myth about the answer that is quite widely believed.
Let’s start with a simple case. If the budget available for funding projects is not limited, all projects with NPVs greater than zero or, equivalently, BCRs greater than one, should be funded. In this situation, there is no need to rank the projects, because all good projects can be funded. NPV and BCR give you the same information about whether a project is good enough to fund.
This unlimited-budget scenario is fine for cabinet or the treasury department because they can just generate more tax if it is needed. But for most organisations doing BCAs, their budget available to spend on projects is limited and it does matter whether you use BCR or NPV.
When there is a limited budget, the choice between using NPV and BCR depends on whether the projects are separate, unrelated projects. If projects A and B are separate, unrelated projects, it means that if you did project A, you could still also do project B, if you had enough money. The other possibility is that they could be mutually exclusive, meaning that if you do Project A1, you can’t do Project A2. This latter scenario would be the case where you are evaluating different versions of the same project, and you can only actually do one of them, even if you have unlimited money available.
If we have unrelated projects and a limited budget, what we want to do is rank the projects. We would fund the best-ranked projects up to the point where the available budget is exhausted. And, to generate the largest net benefits overall, the correct way to rank projects in this scenario is by BCR. (See the appendix for a minor caveat.) In that situation, ranking by NPV can give highly inferior results.
There is one more essential piece of information about this scenario: the costs that go into the denominator of the BCR are the costs that would be drawn from the limited pool of funds that are being allocated to projects. Other costs (e.g. compliance costs that will be borne by affected businesses) should be subtracted from the numerator because they are not constraining the selection of projects.
A failure to understand this last point has led to a pervasive myth about BCRs: that they are not reliable because you can manipulate them by moving costs between the denominator and the numerator. You can’t! It is absolutely clear which costs belong where, and only those costs drawn from the limited pool of funds go into the denominator. The myth even comes up in some official government guidelines on BCA (e.g. Department of Treasury and Finance, 2013; The Treasury, 2015). Even the Commonwealth of Australia (2006) specifies the use of NPV and not BCR. This advice is wrong more often than it is correct. One guideline that gets this issue right is New South Wales Government (2017).
To summarise, we’ve identified two simple rules that might be all you need.
NPV/BCR Rule 1. If you are assessing separate, unrelated projects, and the budget for funding the projects is not limited, you can use either NPV or BCR. They tell you the same thing.
NPV/BCR Rule 2. If you are assessing separate, unrelated projects, and the budget for funding the projects is limited, you rank the projects using BCR. Ranking with NPV is not correct.
In the next Pannell Discussion, we’ll look at a scenario where we are assessing different versions of the same project.
P.S. I got a question via email that made me realise that I need to clarify something. In all the examples I present, I’m assuming that the objective is to maximise the total NPV across all funded projects. The point is that to get the highest total NPV, you should not necessarily choose the projects with the highest individual NPVs. Sometimes that’s the case, but in other cases, it’s not. In certain cases (described above), prioritising the projects that have the highest individual NPVs will give a lower total NPV than prioritising the projects with the highest BCRs.
Further reading
Commonwealth of Australia (2006). Handbook of Cost-Benefit Analysis, Financial Management Reference Material No. 6, Department of Finance and Administration, Canberra.
Department of Treasury and Finance (2013). Economic Evaluation for Business Cases Technical guidelines, Department of Treasury and Finance, Melbourne.
New South Wales Government (2017). NSW Government Guide to Cost-Benefit Analysis, The Treasury, Sydney.
The Treasury (2015). Guide to Social Cost Benefit Analysis, New Zealand Government, Wellington.
Appendix
If projects have to be funded fully or not at all, and the ranking of projects implied by BCR results in some money being left over, then it may sometimes be optimal to deviate slightly from the project ranking implied by BCR in order spend the left-over money effectively. In practical terms, this is usually a minor issue and can be handled by an application of common sense when the selection of projects is being finalised. You could develop an integer programming model to solve it exactly (see PD324), but a bit of trial and error will probably get you to the same solution more easily.
Hi David,
I am somewhat doubtful that there can be right or wrong answers, or that BCR and NPV are the only options, though that is not to say that your article is not a stimulating introduction. One problem is evaluating benefits in monetary terms, often not a cut and dried business. Should one factor in dis-benefits? The example you give of ‘just raise taxes’ is pertinent – there can be many drawbacks to that, even if it is politically feasible. So too with raising borrowing to fund a project. Likewise, NPV has its weaknesses: one can never be certain about the effects of future inflation on the NPV. Who would have predicted the present long running climate of low inflation? Yet I am old enough to remember a mortgage rate set around 15% and rising. And what about the risk of cost over-runs?
Other ideas for deciding on projects arise if there is one issue takes priority over everything else because of public sentiment. Another is old fashioned democracy. Leave it to the uninformed public to decide. Brexit would be a good case in point for UK! None of these methods can be selected as perfect, only as worth considering. All the best, JohnC
Thanks John. Those are all pertinent and important issues, though I think they are a bit separate from the points I’m making here. Yes, it is hard to estimate benefits and costs, particularly into the distant future. I agree that there is a tendency for people to not fully appreciate the uncertainty going forward. We tend to assume too quickly that the future will be like the present. Yet, in evaluating project proposals, we still have to do our best to make those predicitions. The point of this post is to ask, once you have made those predictions, how should you weigh them up in a Benefit: Cost Analysis to make decisions. I’m assuming that we are doing a BCA, but of course, you are right that society often uses different mechanisms to make its decisions.
You should be able to get the right answer with NPV if you impose the correct shadow price on budget cost, derived from the Lagrange multiplier in constrained optimization. Note that this isn’t the same as (wrongly) increasing the discount rate.
Thanks John. I guess if you’ve solved the problem in a constrained optimization model, you don’t need to use NPV or BCR to guide your decision making.