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
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 ?
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?
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% ???
CAPITAL ASSET PRICING MODEL
(which derives from portfolio theory)
E(ri) = Rf + bi (E(rm) – Rf)
E(ri) = return required on financial asset i
Rf = risk-free rate of return
bI = beta value for financial asset i
E(rm) = average return on the capital market
E(rm) – Rf 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.
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.
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.
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.
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.
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
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.
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.
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”.