2  Approaches to determining discount rates

There are two main approaches to thinking about discount rates and how they are determined. A key feature of both approaches is that they have an element of opportunity cost underlying them. The first approach thinks of a discount rate as the rate of return an investor would expect from different opportunities that have equal risk. The second approach is to think of a discount rate as the change in the value of consumption in different periods.

This section examines why the choice of approach to the discount rate is important, and considers the options for choosing the discount rate.

It is important to understand why the choice of approach to the discount rate issue is not simple. The simplest situation is when all markets clear, there is one market interest rate, perfect information and there are no aspects that are not covered by markets. Under these assumptions the market clears at a rate where the time preference for consumption equates to the opportunity cost of capital. The time preference for consumption reflects the rate at which people are prepared to trade consumption today for consumption tomorrow. The opportunity cost of capital is the rate of return the capital must return to investors in order for them to invest. In this case the market-clearing rate would be the discount rate. This situation is shown in Diagram 1.

Diagram 1: The impact of a market imperfection

The savings line, S, indicates the value people put on savings when considering whether or not to consume now or in the future. This is the supply of capital because the amount saved out of current production is available for investment. People save more if the rate of return is higher. The savings line can be used to determine the social rate of time preference.

The investment line, I, shows the relationship between how much investors receive for different levels of investment in production. As the rate of return falls, firms find it economic to employ more capital. Therefore this line it the demand for capital and can be used to determine the social opportunity cost of capital.

If all markets were to clear, then there would be a rate of return of r_o where the private rate of substitution between consumption and savings (return to savers) is equal to the rate of transformation for investment (return to investors). At this point savings would be S_o and Investment would be I_o. The economically efficient rate of discount in this situation would be r_o.

Due to market imperfections the perspective of the individual as an investor and as a consumer do not equate so there is a question about which approach to use. The imperfection can arise because there are monopoly suppliers, there is imperfect information in the market, or there is no market for certain commodities. It may be due to taxation, unemployment or externalities. Diagram 1 shows what can happen with the introduction of a market imperfection, for example a taxation distortion.

In this situation there is a market imperfection of some kind that introduces a gap between the social opportunity cost (SOC), which relates to the return to investors, and the social rate of time preference (SRTP), which relates to the returns to savers. It is unclear which one, if either, should be used (in the first instance) as the discount rate.

The following subsections detail the various alternatives for selecting the appropriate discount rate and what they mean. A range of approaches can be used including social opportunity cost, social rate of time preference, weighted average of the two approaches, and shadow price of capital. The following subsections discuss each of these approaches in turn.

2.1  Social Opportunity Cost

The social opportunity cost rate of discount is the rate that reduces the net present value of the best alternative private use of the funds to zero. This means that the social opportunity cost largely reflects the cost in financial market terms. This leads to an approach where the government takes into account what “similar” projects would provide in returns if undertaken in the private sector.

New Zealand is a small open economy where capital is allocated in a global market. This means that there might not be a best alternative use of funds in New Zealand because of the access to overseas capital markets. However, there is also a need to think about the potential impact of projects on financial markets, and the availability of capital more generally. This approach also needs to be in the context of the Government operating with a budget constraint with decisions impacting on debts level and tax rates.

If the public sector uses this discount rate and only invests in positive NPV projects, then public projects would not displace higher value private sector projects. The social opportunity cost rate determines the “efficient” allocation of resources between the public and private sectors. This is similar to a required rate of return approach except that it relates to the particular investments that would be displaced.

If the government is making decisions on the efficient level of public investment (for example a power station or a new road), on financial grounds then the social opportunity cost approach can be used to provide the appropriate discount rate. This means that valuable public sector projects will be undertaken that may not have been undertaken by the private sector for any number of reasons. The social opportunity cost approach is the most appropriate approach if the government is thinking about investments that could also be undertaken by the private sector, for example if the government is investing in state owned enterprises and service delivery crown entities. Two examples of a service delivery crown entity are Learning Media Limited and Quotable Value New Zealand Limited.

In a large number of circumstances, the government is trying to decide the best way to produce its outputs. This often involves decisions around leasing and buying or whether or not to invest in a new system to produce existing outputs - for example the production of birth, death and marriage certificates. In these cases, the decision is about whether the investment represents value for money, so the social opportunity cost is the appropriate discount rate to use.

The social opportunity cost approach to the discount rate is also the most appropriate approach to consider when undertaking cost recovery of an existing activity or one that could be undertaken in the private sector. This is because it relates to the investment decision being made rather than the service being provided.

2.2  Social Rate of Time Preference

The social rate of time preference is equal to the marginal rate of substitution between consumption in one period and the next period. In other words it is the rate of return needed to make society indifferent between consuming x today and x(1+r) in the next period. In an efficient allocation (with no distortions or other market imperfections) all individuals have the same marginal rate of time preference.[1]

Marglin (1963) has suggested that individuals would be better off by undertaking more public investment collectively than is optimal for them as individuals. This would lead to a lower social discount rate relative to the social discount rate when individuals do not take into account the actions of others. This position is supported when individuals are altruistic towards future generations. However, Tullock (1964) has argued against this by raising the question why one generation should be altruistic towards future generations when the future generations are likely to be richer. This would lead to a higher discount rate. If the arguments of both Marglin (1963) and Tullock (1964) were taken into consideration, the starting discount rate would be adjusted upwards and then downwards, potentially ending up at a rate similar to the starting rate.

Arrow and Lind (1970) argue that there is reduced risk with public investments due to the ability to spread risks amongst all members of the public. This means that the impact of risk is reduced leading to a lower social rate of time preference. This view takes an implicit view that the cost of raising capital from taxes is less than the transaction costs for the private sector to make the same investment. Given that taxation is not costless at the margin, it is not clear that this view would hold in all circumstances.

This assumes that the risks faced in public investment are uncorrelated with individuals’ outside investments in the market or other resources; see Bazelon and Smetters (1999). This may or may not hold depending on the circumstances. This means that any social discount rate must reflect the relevant risks and will not necessarily be lower than an individual’s own social rate of time preference.

Another reason why the social rate of time preference is different from individuals’ marginal rate of substitution between consumption and savings within a period is due to the fact that individuals have a finite lifespan, whereas society is ongoing. The discount rate for public projects may be higher or lower than individual rates of time preference for private projects.

The social rate of time preference reflects social preferences and not just financial sector considerations. The benefits or costs to society would be included in the costs and benefits to be discounted by the rate used. Even without using a social discount rate, the net present value calculation can take into account social considerations by discounting society’s costs and benefits.

In addition, when the government is deciding whether or not to undertake a new government service or activity, the social rate of time preference is an appropriate discount rate. For example the social rate of time preference is appropriate if deciding whether or not to introduce a new social service or environmental regulation. This will take into account social preferences for whether investments are undertaken by government for public consumption. This is the appropriate rate for deciding whether or not the government should be involved in various social activities.

In a number of circumstances, whichever social discount rate used (social opportunity cost or social rate of time preference) the resulting decision will be the same (see the diagram below). However, this is not always true and the choice at the margin is important.

Diagram 2: A situation of mixed results

This point is demonstrated in Diagram 2, which is a stylised version of the situation shown in Stiglitz (1994). In Diagram 2 “r” stands for the social opportunity cost discount rate and “i” stands for the social rate of time preference discount rate. In areas I and III, the use of either approach for the discount rate leads to the same result. This means that either rate could be a proxy for the other rate depending on which can be estimated. In areas II and IV, the conclusions of an NPV analysis would differ depending on the approach taken to determining the discount rate, so these are the areas of interest in this discussion.

2.3  Weighted Average

Several Economists, including Broadman et al (1996), and Sadmo and Dreze (1971), have suggested that the social discount rate should be calculated in terms of the source of the resources used in a particular project. This would be a weighted average cost of the above two approaches. The social rate of time preference would be used to reflect the cost of forgone consumption, while the social opportunity cost would be used to represent the loss in private investment. In the extreme cases, the result would be the same as either the social rate of time preference or the social opportunity cost. This is represented as:

Social discount rate = (α)SOC + (1- α)SRTP (1)

where α is the proportion of resources or costs displacing private investment and (1- α) equals the proportion of resources or costs displacing current consumption. There is an issue about setting α, which is project dependent. It may not be clear what the impact will be on private investment and consumption levels.