Category Archives: Economics

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.

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)
5001.122017045.45
50201.530023033.33
50401.836027027.77
50602.040029025.00
50802.0541028024.39
501002.0841626624.04
501202.142025023.81

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

318 – Measuring impacts from environmental research

There have been some studies considering the relationship between research and environmental policy but studies capturing the impact of research on environmental management, environmental policy, and environmental outcomes are relatively rare. Here is one attempt.

Environmental research may generate benefits in a variety of ways including by providing: information or technology that allows improved management of an environmental issue; information that fosters improved decision-making about priorities for environmental management or policy; or information about an environmental issue that is of intrinsic interest to the community. There are several reasons why it can be worth measuring the impacts of environmental research, including making a case for the funding of environmental research, informing decisions about research priorities, and helping researchers to make decisions about their research that increase its ultimate benefits.

Earlier this year we released the results of an assessment of the engagement and impacts of a particular environmental research centre, the ARC Centre of Excellence for Environmental Decisions (CEED). The assessment includes impacts on policy, management and the community, as well as measures of academic performance, including publications, citations and collaborations. Data were collected in several ways: a survey of all project leaders for the Centre’s 87 projects, the preparation of detailed case studies for selected projects, and collection of statistics on publications, citations and collaborations.

The approach taken was informed by a recent paper of ours called “Policy-oriented environmental research: What is it worth?” (Pannell et al. 2018). The full report is available here.

The Centre’s engagement with end users and stakeholders was strong in Australia and around the world. Researchers reported many examples of engagement with research users involved in policy and management. Results were highly heterogeneous and somewhat skewed, with the majority of observed impact occurring in a minority of the projects.

For almost half of the projects, the potential future increase in impact was assessed as being moderate or high. To some extent, this reflects the time lags involved in research attempting to influence policy and management, but the information was also used to identify projects for which additional engagement effort could be beneficial. The correlation between impact and academic performance was positive but low.

To obtain richer detail about impacts, detailed case studies were prepared for nine research projects. The projects were selected to be diverse, rather than representative. These case studies highlight the unique circumstances faced by each project in endeavouring to have an impact. Each project must be framed within a strong understanding its domain and be deeply engaged with research users if impact is to occur. Substantial benefits for policy or management are apparent in a number of the case studies.

A factor contributing greatly to the impact of CEED was the research communication magazine Decision Point. This publication was widely accepted as a valued communication resource for academic findings in the field of environmental decision sciences, and was rated by people in government and academic institutions as relevant and informative.

Some valuable lessons and implications of the impact analysis are identified in the report. Research impact does not depend only on good relationships, engagement and communication, but also importantly on what research is done. Therefore, embedding a research culture that values impact and considers how it may be achieved before the selection of research projects is potentially important. The role of the Centre leadership team in this is critical. Embedding impact into the culture of a centre likely occurs more effectively if expertise in project evaluation is available internally, either through training or appointments.

A challenge in conducting this analysis was obtaining information related to engagement and impact. There may be merit in institutionalising the collection of impact-related data from early in the life of a new research centre.

Interestingly, we found little relationship between (a) impact from translation and engagement and (b) measures of academic merit. It should not be presumed that the most impactful projects will be those of greatest academic performance.

At the time of the assessment, CEED had generated 848 publications which had been cited 14,996 times according to the Web of Science. CEED publications are disproportionately among the most cited papers in their disciplines. More than a quarter of CEED publications are in the top 10% of the literature, based on their citations. For 39 CEED publications (one in 22), their citations place them in the top 1% of their academic fields in the past 10 years.

There are often long lags between the start of research and delivering the impact — decades in many cases. Therefore, there is a need to allow the longest possible time lag when assessing research impact. On shorter timescales, it may be possible to detect engagement, but not the full impact that will eventually result.

Further reading

Pannell, D.J., Alston, J.M., Jeffrey, S., Buckley, Y.M., Vesk, P., Rhode, J.R., McDonald-Madden, E., Nally, S., Gouche, G. and Thamo, T. (2018). Policy-oriented environmental research: What is it worth? Environmental Science and Policy 86, 64-71. Journal web page

Thamo, T., Harold, T., Polyakov, M. and Pannell, D. (2018). Assessment of Engagement and Impact for the ARC Centre of Excellence for Environmental Decisions, CEED, University of Queensland. http://ceed.edu.au/resources/impact-report.html

317 – The worth of wildlife

What is a threatened species worth? It may seem like a strange question, but it’s one that environmental economists have done a fair bit of research on.

If you measured their worth in commercial terms, the answer would be, probably nothing in most cases. But most of us care about threatened species and would be willing to pay something to prevent them from going extinct. There have been many studies conducted by environmental economists to estimate just how much people are willing to pay to protect particular threatened species. PhD student Vandana Subroy is lead author on a new study in the journal Ecological Economics where we conducted a “meta-analysis” – a review of 109 willingness-to-pay estimates from 47 studies around the world.

We found that the average willingness to pay to protect a species was US$414 per household (once off, not per year). Over a large population, this adds up to very large budgets being justified – vastly larger than the current budget for threatened species recovery in Australia.

Of course, the range across different species in different studies in different countries was enormous: as low as US$1 per household and as high as US$4,400.

Photo: J.J. Harrison (CC BY-SA 3.0)

Not surprisingly, people’s willingness to pay was much higher for “charismatic” species. Determining which species are “charismatic” is clearly subjective, but it’s safe to say they are typically large vertebrates that instinctively appeal to humans (e.g., elephants, pandas, and whales). In our study, species were treated as charismatic if they had been characterized as such in the original study, or elsewhere. The average willingness to pay was US$572 for charismatic species compared with US$106 for non-charismatic species.

Surprisingly the difference in willingness to pay between developed and developing countries was small, and not statistically significant.

One of the most surprising things we learned from doing the study was just how poorly done many of the studies were. In many cases, it was not at all clear in the question that was asked of survey respondents what was being valued. An amazing number of surveys were not clear about the base case – e.g. if there was no new intervention, what would be the probability of extinction of the species? Without that, you can’t give a meaningful willingness-to-pay response. Many surveys asked vaguely about “protecting” the species, but without saying what it was being protected from, or how protected it would be. Because of these and other weaknesses, we had to leave a lot of studies out of the meta-analysis. I commented to my colleagues that I wanted to cancel the economics degrees of the people who did these studies (assuming they had economics degrees).

If you’re interested, the paper can be downloaded for free even without a subscription, until August 30, 2019: here.

Further reading

Subroy, V., Gunawardena, A., Polyakov, M., Pandit, R. and Pannell, D.J. (2019). The worth of wildlife: A meta-analysis of global non-market values of threatened species, Ecological Economics (forthcoming). Journal web page