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Public Sector Discount Rates: A Comparison of Alternative Approaches

4 The social opportunity cost of capital

The social opportunity cost of capital (SOC) approach takes the view that public projects should be discounted by reference to the rate of return that could be earned from the next best alternative use of public funds.

This next best alternative is usually taken to be a private sector project with similar risk characteristics to the public project under consideration. In other words, private sector rates of return are usually considered to be the relevant measure of opportunity cost. This is the approach that the New Zealand Treasury currently uses to recommend discount rates.

4.1  The rationale for a SOC approach

The rationale for the SOC approach is based on the idea that the return on public projects must at least meet the ‘hurdle' of the next best rate of return available to the public. Otherwise in principle an improvement could be made by investing public funds at the higher rate of return available in the private sector (or letting individuals do this themselves), and then distributing the proceeds from that investment to society. In New Zealand, one way of achieving this, for example, would be to increase the government's investment in the Superannuation Fund. As a result, the SOC plays an important role in disciplining public sector investment.

Another important property of the SOC is that market rates of return reflect not only the return that can be earned on market investments, but also the return that is demanded by individuals for such investments.[9] That is, as mentioned above, in large well-functioning markets, the SOC reflects how the market as a whole balances individuals' preferences for trading-off the future with the productive potential of investment.

However, this also means that taking a market-based SOC as the basis for public sector discount rates takes the view that the government should trade-off the future for public sector investments in the same way that individuals and businesses do when making decisions about their own personal consumption and investment. This might be appropriate for investments that are expected to earn a return for present generations, but some people might argue that it is not appropriate for projects which have inter- and intra-generational impacts. The benefits arising from public projects may also be, by their nature, very difficult to value in money terms compared with private investments. The assumption that they can all easily be incorporated in the calculation of a project's benefits is a strong one.

In addition, the next best use of the funds might, in the absence of a public project, be to take on less risk and a lower return than a comparable private sector investment. Therefore, taking the traditional SOC view that the next best use of the funds would be to invest in a private project with a given risk profile imposes a key assumption about individuals' preferences for taking on risk in the absence of a government investment.

A SOC-based view also assumes that the government is concerned about the same types of risk, and prices risk in the same way as markets. These assumptions may not be appropriate for all government projects. For example, the risks associated with public projects may not be strongly correlated with those in the market.

As a result, a SOC-based approach is not, as is often assumed, a completely objective way of determining public sector discount rates. Rather, the decision to use a market-based SOC involves several implicit assumptions that need to be explicitly recognised. These issues are explored in further detail in section 6.

4.2  Determination of SOC rate

At a high level, SOC-based approaches use asset-pricing models to estimate the expected rate of return from a public sector project. This is carried out by benchmarking or comparing the public project against private sector projects or companies considered to have similar risk characteristics.

Given the choice to use a SOC-based approach, determining discount rates is then largely a technical exercise using well-established methods in the finance literature. A choice can be made between several different asset pricing models. These include the capital asset pricing model, arbitrage pricing theory, and multi-factor models.

This is essentially the approach that private companies use to estimate their discount rates and cost of capital. This is also the basis for the NZ Treasury's current approach to recommending public sector discount rates, using the Capital Asset Pricing Model (CAPM). The central insight of the CAPM is that, in a competitive market, the expected rate of return on any asset is equal to the risk-free rate of return, plus an equity premium that varies in direct proportion to the riskiness of that asset. This insight is captured by the basic CAPM formula:

Where:

  • r is the rate of return required, that is, the opportunity cost of investing in a public project. In other words, it is the required discount rate.
  • rf is the risk-free rate of return. This is estimated by reference to the yields on long-term (10 year) government bonds.
  • rm - rf is the equity-risk premium. This is the difference between the average rate of return available in the stock market (rm) and the risk-free rate (rf).
  • β is a measure of the riskiness of the private sector asset/company against which the government project is being benchmarked. It measures how sensitive the returns on the asset are (on average) to overall market returns.

Therefore the CAPM formula can be used to estimate the discount rate as follows:

1. Select a set of private sector projects/companies that are considered to have similar risk characteristics to the public sector project under consideration

2. Estimate the average beta of these companies/projects (discussed further below)

3. Input this estimated beta, along with estimates of the risk-free rate and the equity premium, into the CAPM formula.[10]

The result can be interpreted as the expected rate of return on a market-based portfolio with similar risk characteristics to the public project under consideration. In other words, it is the ‘next best alternative' rate of return available to the public for a given risk appetite.

4.3  The definition of risk

It is important to stress that β measures risk in a precise sense. Usually, risk is understood to mean the variability of asset returns. However, if an investor chooses assets carefully, the portfolio can be balanced so as to offset at least some of the variability of individual assets while still yielding a positive expected rate of return on the portfolio overall. In other words, investors can diversify.

If diversification is approximately costless, all investors seek to balance their portfolios so as to eliminate all diversifiable risk. In other words, investors hold well-diversified portfolios in equilibrium.

This means that the only risk that investors bear is that part of an asset's variability that cannot be diversified away by adding it to a well-balanced portfolio. This is referred to as ‘non-diversifiable' risk. This is what is measured by β, and it is estimated by regressing the returns of an individual asset on market returns. It can be interpreted as the sensitivity of the returns of an individual asset to overall market movements.[11]

The key insight of the CAPM is that beta is the only notion of risk that is relevant to determining an asset's risk premium. In particular, the CAPM predicts that this risk premium takes a particularly simple form: it is proportional to beta.

However, this measure of risk does not automatically carry over well to public sector portfolios. It may not even be meaningful in a public sector context. A further issue is the way in which risks of public projects are correlated with the private market. This type of question is considered further in section 6.

4.4  Current public sector discount rates in New Zealand

In New Zealand, the Treasury is responsible for advising central and local government agencies on the discount rate to be used for appraising public spending initiatives financed by general taxation. In addition to the default public sector discount rate (which is used to discount most government initiatives as well as for calculating departmental capital charge) Treasury also currently recommends specific discount rates for buildings, infrastructure and technology. These discount rates are set out in Table 1, and are specified in real pre-tax terms.

Table 1 Recommended Public Sector Discount Rates in New Zealand[12]
Category Annual rate
Default rate 7.0
General purpose office and accommodation buildings 4.0

Infrastructure and special purpose (single-use) buildings:

  • Water and energy
  • Prisons
  • Hospitals
  • Hospital energy plants
  • Road and other transport projects

7.0

 

Telecommunications, media and technology , IT and equipment, Knowledge economy (R&D) 8.0

They are set by reference to the rates of return that the government could hypothetically earn by investing public funds in a private sector project with similar risk characteristics to public investments. Treasury also allows for agencies to use project-specific discount rates, if these can be determined on clearly rationalised grounds for the case in hand.

The 7 per cent default rate is the rate used to appraise initiatives in CBAx - Treasury's cost-benefit analysis tool. However, agencies can also conduct sensitivity testing using a 3 per cent discount rate, which reflects a risk-free rate of return set by reference to government bond yields.[13]

Notes

  • [9]These two concepts are equated in equilibrium, as discussed in section 3.
  • [10]In reality, some technical adjustments are made to the basic CAPM formula to account for the effects of taxation, inflation and the capital structure of the companies/projects being used for benchmarking. Further detail on the precise formula currently used to estimate public sector discount rates is available at: http://www.treasury.govt.nz/publications/guidance/planning/costbenefitanalysis/discountrates
  • [11]For example, an asset with beta of 1.3 means that when the market rises or falls by an extra 1 per cent, on average the asset price will change by 1.3 per cent.
  • [12]New Zealand Treasury (2017).
  • [13]For further details of how Treasury determines public sector discount rates, see NZ Treasury (2008) and NZ Treasury (2016).
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