323 – NPV versus BCR part 2

In PD322 we looked at whether to use Net Present Value (NPV) or Benefit: Cost Ratio (BCR) in Benefit: Cost Analysis (BCA) when assessing and comparing separate, unrelated projects. What if they are not separate, unrelated projects?

The most common scenario where you have to go beyond the simple rules presented in PD322 is where you are comparing different versions of the same project (e.g. different scales or different actions, but addressing the same broad goal in the same region). They are not separate, unrelated projects – they are mutually exclusive. If you do one of them, it rules out doing any of the others.

It is good practice to assess multiple versions of the same project before settling on a particular version. Versions of a project with more ambitious targets can deliver greater benefits, but also incur greater costs, so it is usually not readily apparent how ambitious the project should be. (Project versions also vary on dimensions other than ambitiousness, such as their spatial targeting, or the specific actions they will include.) The first project version to be specified may or may not end up being the best version when several versions are compared.

However, if you are ranking projects, and the projects you are ranking consist of multiple versions of the same project, using BCR for the ranking process will probably not give you the correct result.

The following example should give you a feel for why BCR does not give you the correct project ranking in this situation.

Suppose that projects X1 and X2 are two versions of project X. If you did project version X2, you would have to bear the cost of doing X2, and in addition, you would bear the opportunity cost of not doing project X1 (i.e., you would miss out on the net benefits of doing X1). Similarly, the full cost of doing X1 should include the opportunity cost of not doing X2. That’s why the traditional BCRs of projects X1 and X2 do not provide a reliable ranking — there are additional costs that a BCR doesn’t capture.

The obvious solution is to include the opportunity cost of not doing the best alternative project when calculating the BCR. However, this is an inconvenient approach because the identity of the best alternative project depends on the available budget. Each time you generated results for a different budget level, you would have to recalculate all the BCRs based on different opportunity costs.

A much simpler approach (that gives the same answer) is to choose the project with the largest NPV that you can afford within the funds allocated for this project. For example, if you were faced with choosing from amongst the five project versions in the table below, and the available budget was $600, you could afford any of the projects and you would choose project 4, which provides the largest NPV of $490. If the budget was only $200, you would choose project 3, which provides an NPV of $440. (You could no longer afford project 4 because it costs $310.)

Note that projects 3 and 4 don’t offer the highest traditional BCRs, which is provided by project 1 (BCR = 20), but we don’t want project 1 because it has the lowest NPV (only $190), and the lowest adjusted BCR.

ProjectPV(Benefits)PV(Costs)NPVBCR
1$200$10$19020.0
2$400$60$3406.7
3$600$160$4403.8
4$800$310$4902.6
5$1000$560$4401.8

 

NPV/BCR Rule 3: If selecting from different versions of the same project, choose the project with the largest NPV that you can afford within the funds allocated for this project.

The above NPV rule is based on the assumption that you must choose one project version from a set of mutually exclusive project versions, and that the funding is committed to be used for one of these project versions and won’t be used for other projects.

The next Pannell Discussion looks at a more complex scenario where the decision-maker is faced with choosing from multiple separate projects, and there are multiple mutually-exclusive versions of at least one of the projects.

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