BLUFFERS’ GUIDE TO COST OF CAPITAL.

Shortly before lockdown in 2020 I was asked to provide an introduction to this subject - discounting, net present value, and cost of capital - for an Oxford Martin School seminar. It’s a vitally important subject for policy making on the major infrastructure investments that will be needed in our climate mitigation strategies, and that was a primary interest for that particular audience.

Unfortunately it’s also a subject that enjoys a very limited degree of consensus among economists, especially in relation to questions of social time preference, which bring in major ethical issues. 

Equally unfortunate is the disconnect between most people’s intuitive understanding of risk and the concept of risk that underpins the dominant CAPM model in modern finance theory.

I don’t pretend to have definitive answers on many of these questions, but many colleagues have found this brief description or “bluffer’s guide” quite helpful, and I finally decided to make it a blog post

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A tourist’s guide to the landscape of finance theory, investment choices, NPV and IRR, and other cost of capital issues

 

Why it matters ?

Summary of the CAPM model.

Multiple fallacies and pitfalls.

Context is vital.

And the time value of CO₂ ?

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WHY DO WE WORRY ABOUT RISK, RATES OF RETURN AND COST OF CAPITAL?

Multiple contexts for RoR and CoC. And do we expect consistency?

 

Financial sector – fund management. Portfolio theory. Selecting portfolio of investments (balancing risk and return).

 

Basis for valuing an asset/ business. Future revenue and cost stream discounted at an appropriate cost of capital [usually defined by the “(market correlated) risk” attached to type and sector of business, eg consumer goods/capital/utility].

 

Valuing future liabilities (eg pensions and life insurance) to determine how much to hold in financial assets– [vide pensions crisis]. Analogous to funds required to be set aside as provision for decommissioning costs.

 

Investment appraisal. Decisions by a company on (selection of or between) investment projects.  Analysis of revenue stream discounted at the company’s cost of capital to a net present value (NPV). Can dramatically impact choice between technologies.

 

Regulation of utility prices. The “allowed rate of return” on a regulated asset base (RAB). Beta value of about 0.5 for utility businesses with low market-correlated risk. 

 

Public policy choices. What is the social “time preference rate”? [presumes applicability of cost benefit analysis in order to generate stream of costs/ benefits over time.] Can this reconcile with markets?

 

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BASIC MATHEMATICAL/ARITHMETICAL TOOLS

 

Compound interest calculations and actuarial annuity tables.

 

Calculation of net present value (NPV) for a given cost of capital/ discount rate.

 

Calculation of internal rate of return (IRR) for a given stream of costs and revenues. [NB there is not necessarily a unique solution for IRR**.]

 

The Capital Asset Pricing Model, “CAPM”, for risk adjustment of the cost of capital.

 

** eg the net revenue stream: -50, +10 for 20 years, then -150. IRR is either 0 or 14.8% ???

 

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CAPITAL ASSET PRICING MODEL
(which derives from portfolio theory)

 

E(r_i) = R_f + b_i (E(r_m) – R_f)

 

where

 

E(r_i) = return required on financial asset i

 

R_f = risk-free rate of return

 

b_I = beta value for financial asset i

 

E(r_m) = average return on the capital market

E(r_m) – R_f is usually known as the equity premium. The beta value is the sensitivity/ correlation of the individual stock i with the overall market. The risk-free rate is usually taken as the rate on government bonds.

 

 

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WEIGHTED AVERAGE COST OF CAPITAL

 

Modigliani-Miller Theorem. The overall WACC should be independent of the ratio of debt to equity financing.

 

The higher the debt ratio, the more financial (market correlated) risk attaches to the residual equity component and hence the cost of equity capital.

 

Tax interferes with this simple message, since debt interest is tax deductible. This tends to favour debt financing.

 

The main implication is that when businesses talk about cost of capital or expected return it is important to be crystal clear about what this means, WACC or equity component.

 

Also we always need to be clear as to whether we are analysing any problem in real or nominal terms.

 

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ASSUMPTIONS THAT LIE BEHIND THE CAPM MODEL

 

We should ignore project-specific risk. This is because investors can in principle diversify away from specific risks. Of course individual managers may have very different perspectives (both directions). (For most people this is a counter-intuitive concept of what we mean by risk, and accounts for a great deal of misunderstanding in relation to how “risk” should affect cost of capital.)

 

We can measure or assume a “risk-free” rate – typically the return on government bonds. This is a non-trivial exercise but is relatively uncontroversial.

 

We can measure the overall “equity premium”. This is more controversial, and depends (mainly) on interpretation of long term historical data.

 

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QUALIFICATIONS TO CAPM IN CONTEXT OF RISK

 

CAPM is focused entirely on “market correlated” risk – an investor perspective.

 

Managers and other stakeholders may have very different attitudes to project specific risk – eg either excessive aversion or complete indifference.

 

[Managers may avoid high return projects with some project specific risk if employment is at risk. Or they may promote dubious projects if the risks are long term and past their event horizon – eg retirement.] 

 

For most people their intuitive concept of risk is mostly project –specific or competitive, on which subjects CAPM says nothing per se.

 

The market correlation of a particular investment opportunity may have a very different  “profile” from that of the company and the sector as a whole.

 

For a big project, the risks and cost of capital may differ markedly for different parts of the project, eg construction versus long term operation as utility asset.

 

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WHEN SPECIFIC RISK IMPACTS COST OF CAPITAL

 

CAPM was largely about the market correlation of “equity” earnings in financial markets.

 

But financial markets also need to deal with debt, about future payments that are denominated as fixed and not market related; in this instance lenders need to discount the possibility that the debt will not be honoured. This can have market and non-market components.

 

So a promised payment of £100, with a 5% probability of default, is only worth £95 (or less because of risk aversion); conversely the borrower has to promise to pay £100 rather than £95. For a twelve month loan this would be equivalent to a 5% increase in cost of capital.

 

Hence the importance of credit ratings, eg wrt sovereign debt. They affect both ability to borrow and its cost. If risk of default is high, projects/ borrowing becomes non-financeable at any cost of capital. [cf basket case economies].

 

The corresponding core issue in the context of infrastructure investment is regulatory and policy certainty. For high capital cost projects, this will have a massive impact on affordability.

 

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INVESTMENT APPRAISAL PROBLEMS AND FALLACIES

 

Widespread appraisal optimism. Promoters of projects will often tend to overstate benefits/ revenues and underestimate costs.

 

The sensible solution in this context is not to impose a high “hurdle rate”. This confuses risk with the time value of money. The answer is to address directly the validity of the revenue stream estimates.

 

High hurdle rates or “payback time” approaches produce “short-termism” outcomes.

 

Comparing IRR for choice between different projects will normally give very similar answers to NPV, but can go badly wrong if there is back-end loading of significant costs, eg decommissioning.

 

Theoretically the right approach is NPV, using realistic estimates and assuming the right values for cost of capital

 

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SO WHERE ARE WE IN THE REAL WORLD?

 

It used to be assumed risk free cost of capital was c.1.0-3.0% real, based on observed return on government bonds inflation adjusted, … and the equity premium was about 3% real (very long term analysis).

 

Utility returns (on regulated asset base), with a company beta of c 0.5, typically around 5%, but

 

… currently the risk-free cost of capital is close to zero, or even negative. (What does this mean? And will it hold?)

 

Global glut of capital, so real cost of capital ought to be assumed to be extremely low, especially for infrastructure projects with little or no market correlated risk, or “essential” low carbon “must do” projects.

 

Some evidence that projects really can be financeable with very low real terms cost of capital, of order of 1-2 % pa. This depends on clever financial structures to meet actual financial market preferences, segmenting risks, and contractual or other guarantees against regulatory/project specific risk.

 

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IMPLICATIONS TO TAKE FROM THIS BRIEF TOUR

 

We should use very low CoC for policy choice purposes (essentially the Stern position), and this is broadly consistent with a Stern/ social time preference approach to climate policies.

 

It is possible to reconcile this with financial market measures of cost of capital, at least in broad terms and on favourable assumptions.

 

But achieving a low cost of capital also requires taking out project specific risks that are outside control of investor. Hence need for some combination of regulatory/ policy certainty and contractual commitment.

 

Real world factors make it hard for many of the agents to achieve low CoC. eg domestic consumers, market distortions, poor legal/regulatory framework, countries with sovereign debt risk, financial market issues etc.

 

Always be aware of context eg market situation, political framework etc. And define terms: real or nominal, equity or WACC, pre/post tax.

 

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WHAT ABOUT THE TIME VALUE OF CO₂ EMISSIONS?

 

This has all been about the time value of money. What about the time value of CO₂? Emissions also have a time value. 

 

Because CO₂ is cumulative, emissions now do more harm than emissions in 10 years time. (ie 10 years extra harm).  [ ≈ c 2% pa.]

 

Confirmed by some IA models but rarely reported.

 

An issue quite separate from cost of capital.

 

Ought to have an equivalent impact on policy.

 

Favours early emissions payoff projects, eg known technology rather than “wait and see”.

 

 

 

 

COSTING AN ELECTRIC VEHICLE FUTURE. IGNORE THE ALARMISTS.

 

Contrary to recent claims from a group of our MPs, EV demands on our power system infrastructure do not lead to national bankruptcy.

The All Party Parliamentary Group opposing government policy on electric vehicles claim in a new report that the required investment in electricity generation will “bankrupt UK plc”. Unfortunately for this claim, it is based on some major errors of fact and understanding. These exaggerate investment costs by a factor of 25 or more, even on the basis of a rather pessimistic cost assumption that is the authors’ starting point.

Thirteen MPs and Lord Lilley have endorsed a new report[1] from the All Party Parliamentary Group[2] for Fair Fuel for UK motorists and UK hauliers. The press release describes it as ground-breaking. However the report consists largely of a stitching together of questionable “facts”, opinions and arguments from multiple sources and special interest groups, and contains major and consequential errors, of both fact and understanding, for electricity in particular.

Inevitably a central focus of the analysis, and for press headlines, is the additional investment cost required to service the additional electric vehicles implied by government targets. It is this estimate of required investment cost that has provoked the “bankruptcy” claim and headline, so it is worth examining its credibility. The  calculations are set out quite unambiguously in the report.

“FairFuel UK and the ABD have also analysed the economic consequences of dumping ICEs and concur with ... [the] prodigious cost conclusions shown here, to all our lives. The Government’s unilateral decision to commit UK to 75% reduction in carbon by 2030-2035 will increase our national debt by £2.17 trillion.[3]

2020 Consumption of petrol, diesel, bio diesel, bioethanol was 30 million metric tonnes per year. … A 75% reduction target by 2030 -2035 or whatever target date is chosen, means finding enough energy to replace 22.5 million tonnes of fuel per year.

The average energy density of the fuels: petrol, diesel, bio diesel, bioethanol is 12.5 kWh per kilo. That [equates to] 281.25 TWh pa.

Considering one nuclear power station generates about 4 TWh/year, [this] means 70 nuclear power stations are required to offset the 75% reduction in petrol and diesel.

A nuclear power station costs £22 billion, so 70 nuclear power stations =  £1.54 trillion.”

Order of Magnitude Error 1. The calculation ignores efficiency in use.

What matters to the consumer, and hence for aggregate energy consumption, is the efficiency with which different fuels can provide useful energy to deliver the service required.  Internal combustion engines (ICE) have very low efficiencies in the delivery of useful energy compared to electric vehicles (EVs), but the report assumes they are the same.

A typical claim made for EVs by charging networks is that EVs are 85-90% efficient while internal combustion engine cars 17-21%. If accurate, this implies we should divide the APPG estimate of 281.25 TWh by a factor of 4 or 5.

Calculating an equivalent electricity requirement is not just a matter of comparing technical parameters. The reality will depend on many factors including speed, driver behaviour and driving conditions, so there is no single universal answer. Hence it is worth comparing alternative sources and informed assessments. The following quote is from the Australian Energy Council[4]. 

“EVs convert over 77 per cent of the electrical energy from the grid to power at the wheels. Conventional gasoline vehicles only convert about 12 per cent – 30 per cent of the energy stored in gasoline to power at the wheels,” according to the US Department of Energy. …. Particularly in city driving, IC engines waste fuel while idling or operating at very low outputs compared to their design capacity, and engines at low output achieve very low efficiencies. … And, unlike EVs, most conventional vehicles do not recover the energy wasted to heat by braking for traffic lights.

The well-researched Committee on Climate Change (in its Sixth Carbon Budget[5]) uses an efficiency multiple of about 3, less than the above, but recognises that the nature of EV load also implies a less than proportionate requirement for additional capacity, a view shared by the National Grid.

Carbon Commentary also provide a first approximation estimate[6] of total requirements, for cars, based on an intuitively reasonable calculation from official transport statistics.

A 2017 electric car will typically get 4 miles from a kilowatt hour of energy.[NB 40 mpg for a typical petrol driven car would be equivalent to about one mile per kWh] The average car in the UK travels about 8,000 miles a year. That means that a typical electric car will use about 2,000 kWh a year.  In 2016 there were 36.7 million cars on the road in the UK. The total amount of energy required to power these cars if they were all electric would be about 75 TWh a year.  The total consumption of electricity in the UK last year was about 300 TWh. So if all car and taxi transport was by electric vehicles, the total amount of electricity needed would rise by approximately 20%.

This of course is an estimate that covers only cars and taxis, but assumes 100% rather than 75% replacement. The National Grid[7] likewise does not seem to be unduly concerned with the issue and suggests that “even if the impossible happened and we all switched to EVs overnight”, peak demand[8] (measured in GW not TWh) would only increase by around 10 per cent, or about 6 GW. One reason for this rather low number for peak capacity requirement is that vehicle charging load can be managed so that incremental TWh can potentially be met by much less incremental capacity than would be required for other consumer loads.

Order of Magnitude Error 2.

The report is also at odds with reality in its depiction of the scale of output expected from a 3.2 GW nuclear plant. It takes as its cost benchmark the reported numbers projected for the construction cost of EdF’s 3.2 GW Hinkly Point C nuclear plant (over £ 20 billion), but assumes an electrical output of 4 TWh for that plant. Hence it deduces the need for 70 Hinkly Point C equivalents, or 224 GW of additional capacity. However EdF have quoted an annual output (assuming 90% load factor) of 25 TWh, a scale confirmed by the government in its evidence to the Public Accounts Committee.[9] A more accurate statement of the expected output from this benchmark 3.2 GW plant therefore reduces the scale of investment by a factor of 6.

The error factors are multiplicative, and the result is that the implied 224 GW of capacity calculated in the report, for a 75% switch to EVs, exceeds the more realistic 6 GW suggested by National Grid, for a 100% changeover, by a factor of 37.

Is the Hinkly Point nuclear plant a reliable cost benchmark anyway?

There are several reasons to suppose it is not. The Public Accounts Committee was critical of government procurement performance, and clearly feels the cost of this contract was excessive. It is also generally assumed that subsequent nuclear power plant of similar design would be cheaper. Not least, not everyone will agree with the assumption that all-nuclear is the least cost route to expanding power generation, the implicit assumption that underpins the report’s cost estimates.

Dieter Helm[10] and others have also argued that about 50% of the estimated very high cost of Hinkly C is entirely attributable to the very high return to be earned by EdF over the life of the project. If this were indeed to be financed through addition to the national debt, one might surely expect to apply a much lower rate of return, closer to government borrowing rates. Helm argues for rates as low as 2 or 3%, halving the cost of a station such as Hinkly C. By implication Helm’s arguments alone would imply a further cost reduction by a factor of 2.

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The misunderstandings in the report, at least on relative efficiency and likely cost, and an overall error factor of perhaps between 25 and 50, even on the basis of its own assumptions and methodology, are all the more surprising given that the House of Commons Library has just published (June 2021) an analysis, Electric Vehicles and Infrastructure[11], on the same subject. This is a brief but well-researched source of basic information on the subject under discussion. One might assume it was available to MPs.

In reality, if we do proceed successfully with low carbon generation, electric vehicles have a major positive role to play in helping to balance power systems associated with less flexible generation from nuclear or renewable plant. This makes them an economically net positive option in any low carbon future. But that is a bigger subject to which we can return, and which I have addressed elsewhere[12].

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Updated on 3 September 2021 to include additional sources and references

[1] APPG 2030 Ban (fairfueluk.com)

[2] Readers should note that these informal groups of MPs do not have the official standing of parliamentary Select Committees.

[3] This number seems to be the national debt in April 2021, as referenced later. It is intended, one assumes, to be the £1.54 trillion calculated by the APPG researcher.

[4]  EVs: Are they really more efficient? (energycouncil.com.au)

 [5] Sixth Carbon Budget - Climate Change Committee (theccc.org.uk). Sector summary, surface transport.

[6] 100% EVs can be easily accommodated on the UK grid. | Carbon Commentary

[7] 6 myths about electric vehicles busted | National Grid Group

[8] In large power systems, it is important to distinguish between the additional energy requirement, kWh or TWh, and the amount of additional generation capacity required. The relationship between the two, for different types of consumption, is a crucial element of system economics.

[9] Hinkley Point C - Committee of Public Accounts - House of Commons (parliament.uk). The Department (BEIS) is recorded as stating that Hinkly Point C is expected to supply about 7% of UK requirements, ie about 20-25 TWh.

[10] Energy Policy: What happens next? - Dieter Helm

[11] CBP-7480.pdf (parliament.uk). Electric vehicles and infrastructure June 2021

 [12] Enabling Efficient Networks For Low Carbon Futures | The ETI

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ADDENDUM. 19 October 2021

This APPG report has been modified since the above was posted, but the fundamental errors remain.

The relevant paragraphs have been revised to suggest that the output of a nuclear plant of the same scale as Hinkly C could be between 8 (not 4) and 25 TWh, and therefore that the EV requirement is for “between 12 and 35 new nuclear power stations” (not the more realistic 3 that use of more conventional arithmetic would imply).

CHANGES	previous	current
Estimated energy requirement (c 4x factor error)	281 TWh	281 TWh
Output of “a Hinkly C” – a 3.2 GW station	4TWh	8 -25 TWh
Number of such stations required	70	12-35
Cost of a station (presumably a 3.2 GW station)	£ 22 bn	£ 10-50 bn

  

So what has happened.

·       The author has continued to ignore the ICE/EV efficiency issue, which creates an error factor of about 4,

·       and has also taken the point that EdF are claiming an expected 25 TWh for Hinkly C, but simply made this one end of a wide range. As far as I can judge from correspondence, the 8 TWh figure seems to have been constructed in rather an odd way, by looking at the maximum output of any current UK nuclear power station, ie about 1.0 GW, and multiplying by 8000 as the approximate number of hours in a year. But of course Hinkly C is a planned 3.2 GW, and Sizewell B, which is the most recent of existing nuclear plant has a nameplate of 1.2 GW, ie about a third of the size. This has all the hallmarks of someone who does’nt understand the basic units of measurement, or indeed what they are doing at all.

·       The author has also invented a new figure of £ 50 billion as the upper end of the cost range for “a nuclear plant” – implicitly another Hinkly C. This implicitly acknowledges my comment that a £ 22 bn cost of Hinkly might be over the top anyway (and not just because of cost of capital issues), but only by putting in a lower end of £10 bn. The £ 50 bn is sufficiently large, when combined with top end of the range on stations required, to give a high final number that even exceeds the previous estimate of total cost. But both bits are absurd numbers which remain unexplained.

John Rhys. 

COST OF CAPITAL ARGUMENTS AND CLIMATE POLICY. PART ONE.

Debates on policies to combat climate change often include a collection of long running arguments around the cost of capital, or the time discount rate for comparing costs and benefits. These were prominent in arguments over the recommendations of the Stern Review, mainly in attempts at a cost benefit analysis (CBA) of the public policy case for action to mitigate climate change. But assumptions on cost of capital do also matter a lot in what are now the very real questions of comparing alternative investments to reduce emissions. And of course the actual cost of capital employed will have a major impact on the affordability of future energy use, and prices to consumers. Sadly this is one of the areas where the disciplines of economics and finance have been at their weakest, in failing to provide a rigorous and consistent approach to the subject, at least in relation to the public discourse.

Let us start with the public policy arguments around climate policies, and the claim sometime made that the case for action depends on the assumed discount rate, the rate at which we discount the significance of future benefits or costs. One version of this argued that the costs calculated by Stern[1] could only justify action to mitigate climate change if the time discount rate could be assumed to be 1% or lower. Given that even a modest probability of human extinction (or more realistically of the massive forced reductions in population of the kind against which some environmentalists warn us) might be considered to have a near infinite cost, the approach was always intrinsically unlikely to convince anyone. At times, much of the debate on this subject resembled nothing so much as the supposed[2] discussions of mediaeval scholars as to how many angels could stand on the head of a pin.

The real problem in these arguments was the weakness of a cost benefit approach in dealing with systemic risks and possible catastrophes on a long term and global basis. CBA is usually targeted on situations where the alternatives can in some sense all be considered “at the margin”, Inter alia it became increasingly clear that the real problem lay less in evaluating notional GDP projections in alternative climate scenarios, and much more in the climate induced consequences, including migration and conflict. These considerations were compounded by the problem CBA has in dealing with uncertainty and with risks that are not amenable to simple probability quantification. Add to that the nature of the potential risks, which are on an unimaginable scale, and it ought to be clear why the calculation of the costs of a dystopian future, for comparison against an almost equally impossible set of counterfactuals as a baseline, is a rather futile exercise.

Economic models designed for fairly simplistic macro-economic analysis (and they often prove to be not very good even for this relatively straightforward task) were applied to timescales and hypothetical events well beyond their design capability, and it was quickly recognised that they did not come remotely close to capturing the true nature of climate risk. What is now accepted, and is implicit in the international acceptance of the Paris agreement, is that the risk of climate catastrophe is simply too big to be borne, and that mitigatory or remedial action is therefore a necessity.

Fortunately this part of the argument over climate policy is now settled in the public domain, with almost all[3] nations united in their recognition of the need for actions of the kind indicated in Paris[4].  Cost of capital arguments were ultimately of little importance in determining the fundamental imperative for policy action in relation to climate. Even so the arguments were revealing in the differing attitudes they uncovered. Nigel Lawson’s polemic[5] against science driven climate policies argued strongly that we should care increasingly less for the futures of our grandchildren or more remote generations, arguing for much higher discount rates, of the order of 10% or more, largely on the grounds that these were closer to the target rates applied in business decision making.

The impact of discounting at such high rates makes damages a 100 years hence worth a very small fraction in terms of today’s values. Unfortunately for this argument, and as we suggest above, the scale of the perceived risk – sometimes stated in worst case scenarios as a forced population reduction of many billions - can also be described as almost infinitely large, and this is clearly the position implicit in what we might describe as the “Paris consensus”.

The Lawson position was, I suspect, based on a profound misunderstanding of how business works, especially in extrapolation of the most superficial approaches to investment appraisal. It may reflect multiple confusions over the way businesses treat investment appraisal, the debt and equity balance, use of real or nominal rates, and the appropriate assumptions about market correlation, which are a major feature of the standard CAPM model of finance. Another interesting corollary of using a high discount rate would, of course, be that it would not be necessary to set aside any significant sums today for nuclear or other decommissioning in 100 years time. Needless to say this is not an approach that is argued very often.

Lawson’s hypothetical rates are so far from the actual rates of return achieved in most business, most of the time, that we must assume one of two things. Either business is incompetent in investment appraisal, or Lawson just does not understand the subject. As he was perhaps one of the less able Chancellors of modern times, and remains someone who clearly fails to get to grips with climate science or the interpretation of statistics, the latter seems more likely.

The reality seems to be that, under the right conditions, major projects can be financed at very low real rates of interest. But that is an important issue to which I hope to return.  The subject remains important in practical terms, both for choosing investments and making them affordable.

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[1] To give credit to Stern he never proposed CBA as a main driver of policy, and his post-Review thinking on the subject gave much more weight to the catastrophe avoidance arguments.

[2] In fact this may be an early modern fabrication, or simply an illustration of a category error in a more substantial metaphysical discussion.

[3] The exceptions being Trump’s USA, and Nicaragua, but the latter on the grounds that the proposals did not go far enough.

[4] The reality of actions is of course far less clear, but there is progresss.

[5] An Appeal to Reason.  Nigel Lawson. Duckworth Overlook, 2008.