Yearly Archives: 2019

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.



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.

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.


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.

321 – Communicating economics to policy makers

When it comes to communicating research results to policy makers, economists have some advantages over other disciplines. But economists commonly make a range of mistakes when trying to communicate to policy makers.

Included amongst the advantages that economists have are that economics can be used to clarify the pro’s and cons of different decision options, and this is exactly what policy makers need in many cases.

Secondly, a good economic analysis is holistic, bringing together all, or at least most, of the relevant elements, including social, biological, physical, financial, behavioural elements, accounting for risk and uncertainty.

Thirdly, economics tries to assess outcomes from the perspective of society as a whole, rather than a particular interest group, so it can be seen as more balanced and independent than some other disciplines.

On the other hand, economists often squander these advantages by making basic communication mistakes. Too often they fail to cut out the technical jargon that is meaningless and perhaps annoying to their audience. They focus too much on abstruse technical details of their analysis, rather than focusing on why it is important and what the results mean. They explain things in abstract, conceptual terms, rather than giving examples and telling stories to make things tangible and real. In short, they are often not tuned into, or don’t understand, the perceptions and needs of their policy-maker audience.

In July I attended the annual meeting of the Agricultural and Applied Economics Association, in Atlanta, Georgia. One of the highlights for me was the presidential address by new president Keith Coble from Mississippi State University. His address was on “Relevant and/or Elegant Economics”, but mainly on making sure economics is relevant. I got a nice surprise when, about half way through the talk, he started talking positively about an old paper of mine on communicating economics to policy makers (Pannell 2004).

In that paper, I reported results from a small survey, including responses from economists who work in the policy world, senior bureaucrats, past or present politicians and a former ministerial adviser.

The most strongly emphasised advice provided by these people was to understand the policy maker’s situation and perspective.

Other messages included to be practical and pragmatic, to be persistent, to understand the importance of timing, to establish networks in order to build support, to not tell your target audience that they are wrong, and to keep your communication brief and clear.

There are many other useful pieces of advice in the Pannell (2004) paper, so have a read.

Further reading

Pannell, D.J. (2004). Effectively communicating economics to policy makers. Australian Journal of Agricultural and Resource Economics 48(3), 535-555. AgEcon SearchJournal web page * IDEAS page

Gibson, F.L., Rogers, A.A., Smith, A.D.M., Roberts, A., Possingham, H., McCarthy, M. and Pannell, D.J., (2017). Factors influencing the use of decision support tools in the development and design of conservation policy, Environmental Science and Policy 70(1): 1-8. Journal web page * Pre-publication version * IDEAS page

320 – Fixed costs and input rates

Optimal input rates (e.g. of fertilizer to a crop) are not affected by fixed costs. I had an interesting discussion with a Canadian poultry farmer last month, who needed to be convinced of this fact.

In Canada last month I gave a seminar at the Ontario Ministry of Agriculture, Food and Rural Affairs on water pollution from agricultural fertilizers, and how an understanding of the economics of fertilizer application can help identify cost-effective policy strategies for reducing pollution.

One thing I talked about was the economics of applying too much fertilizer (more than would be in the farmer’s own financial interests).

One attendee at the seminar was a poultry farmer (who was also a scientist) who later wanted to talk to me about a reason for increasing input rates that I had not mentioned. The reason he suggested was that, by increasing input rates a farmer can increase his or her production, and even if the resulting increase in revenue is not enough to cover the additional input costs, it helps to dilute the fixed costs of production over a larger value of outputs, making the farmer better off overall.

He said that this is an idea that is common amongst poultry farmers, at least in Ontario. The problem is that it’s completely wrong. There is no way that increasing input rates above the level that maximises the difference between revenue and input costs can make a farmer better off, even if it does mean that the average fixed costs per unit of output is lower.

A simple numerical example will make this clear.

Fixed costs ($/ha)Fertilizer cost ($/ha)Yield (tonne/ha)Revenue ($/ha)Net revenue ($/ha)Average fixed cost ($/tonne)

In this example, there is a production cost of $50/ha which is not affected by the rate of fertilizer used. In this sense it is “fixed”.

As the rate of fertilizer applied increases, the input cost goes up, and so does the crop yield, although it increases at a decreasing rate.

The net revenue is the difference between the revenue and the total costs (fixed costs plus fertilizer costs). Given this pattern of revenue and costs, the fertilizer rate that maximises net revenue is the rate corresponding to a cost of $60/ha (the fourth row of numbers in the table), giving a net revenue of $290/ha. This is the fertilizer rate that maximises profit to the farmer.

The last column shows the fixed cost per unit of production. Because the yield keeps increasing at fertilizer rates above the economic optimum, the fixed cost per unit of production keeps falling. The lowest fixed cost per unit of production is in the last row of the table, but this clearly doesn’t have the highest profit.

When you are considering the optimal level of an input, the only costs that matter are the costs that vary as you vary the level of the input. Fixed costs cannot possibly affect the optimal rate of an input because they are fixed. They stay the same at all input rates. The fact that average fixed costs per unit of output might fall at higher input rates is completely irrelevant.

I think I convinced the Canadian poultry farmer. He said he was going to talk to his other farmer friends about it.

Although boosting an input rate loses a farmer money, in many cases the amount lost will be quite small unless the input rate is especially high (due to “flat payoff functions” – see Pannell 2006). That may be why the error has not been detected by the farmer or his friends. The loss may be too small to be noticeable.

To the extent that farmers think that diluting fixed costs is a good idea, explaining to them that it is pointless may help to reduce some farmers’ tendency to apply too much fertilizer. If successful, this may contribute to reducing water pollution.

Further reading

Pannell, D.J. (2006). Flat-earth economics: The far-reaching consequences of flat payoff functions in economic decision making, Review of Agricultural Economics 28(4), 553-566. Journal web page * Prepublication version here (44K). * IDEAS page

Pannell, D.J. (2017). Economic perspectives on nitrogen in farming systems: managing trade-offs between production, risk and the environment, Soil Research 55, 473-478. Journal web page

319 – Reducing water pollution from agricultural fertilizers

I gave a talk to the Ontario Ministry of Agriculture, Food and Rural Affairs (OMAFRA) on July 16, 2019, exploring ways to reduce water pollution from agricultural fertilizers.

Many methods have been proposed to reduce water pollution from agricultural fertilizers. The list includes use of nitrification inhibitors, land retirement, vegetation buffer strips along waterways, flood-plain restoration, constructed wetlands, bioreactors, cover crops, zero till and getting farmers to reduce their fertilizer application rates.

Last year, while I was at the University of Minnesota for several months, I reviewed the literature on these options and came to the conclusion that the option with the best prospects for success is reducing fertilizer application rates. It’s the only one of these options that is likely to be both effective and cheap.

In my talk, I made the case for agencies who are trying to reduce pollution to focus on reducing fertilizer rates.

In brief, I identified three key reasons why there are untapped opportunities to reduce fertilizer rates.

1. Some farmers apply more fertilizer than is in their own best interests. Surveys in the US suggest that something like 20 to 30% of American farmers could make more profit if they reduced their rates. If it was possible to identify these farmers and convince them of this, it would be a rare win-win for farmers and the environment.

2. Even those farmers who currently apply fertilizer close to the rates that would maximize their profits could cut their rates without sacrificing much profit. Within the region of the economically optimal rate, the relationship between fertilizer rate and profit is remarkably flat. New estimates by Yaun Chai (University of Minnesota) of this relationship for corn after corn in Iowa indicate that farmers could cut their rates by 30% below the profit-maximizing rate and only lose 5% of their profits from that crop. For corn after soybeans, the equivalent opportunity is for a 45% cut!

3. Some farmers believe that applying an extra-high rate of fertilizer provides them with a level of insurance. They think it reduces their risk of getting a low yield. However, the empirical evidence indicates exactly the opposite. When you weigh up the chances of an above-average yield and a below-average yield, higher fertilizer rates are actually more risky than lower rates. In addition, price risk interacts with yield risk to further increase the riskiness of high rates.

I think there is a real opportunity to explore these three factors in more depth and try to come up with policy approaches that could deliver reduced fertilizer usage in a highly cost-effective way. Some of it would just be about effective communication (e.g. the design of “nudges”, as popularised in behavioural economics) while some might require a modest financial commitment from government or industry. One idea is to offer something like a money-back guarantee to those farmers who agree to reduce their rates by a specified amount. If they lose money as a result, they get compensation. Because of the flatness of the fertilizer-profit relationship, the payments required would usually be very small.

I recorded the presentation to OMAFRA, and it’s available here.

Further reading

Pannell, D.J. (2006). Flat-earth economics: The far-reaching consequences of flat payoff functions in economic decision making, Review of Agricultural Economics 28(4), 553-566. Journal web page * Prepublication version here (44K). * IDEAS page

Pannell, D.J. (2017). Economic perspectives on nitrogen in farming systems: managing trade-offs between production, risk and the environment, Soil Research 55, 473-478. Journal web page