Chapter 8: The Economic Opportunity Cost of Capital PDF

COST-BENEFIT ANALYSIS FOR INVESTMENT DECISIONS, CHAPTER 8: THE ECONOMIC OPPORTUNITY COST OF CAPITAL Glenn P. Jenkins Queen’s University, Kingston, Canada and Eastern Medi...

COST-BENEFIT ANALYSIS FOR INVESTMENT DECISIONS, CHAPTER 8: THE ECONOMIC OPPORTUNITY COST OF CAPITAL Glenn P. Jenkins Queen’s University, Kingston, Canada and Eastern Mediterranean University, North Cyprus Chun-Yan Kuo Queen’s University, Kingston, Canada Arnold C. Harberger University of California, Los Angeles, USA Development Discussion Paper: 2011-8 ABSTRACT An investment project usually lasts for many years, hence its appraisal requires a comparison of the costs and benefits over its entire life. For acceptance, the present value of the project’s expected benefits should exceed the present value of its expected costs. Among a set of mutually exclusive projects, the one with the highest net present value (NPV) should be chosen. This criterion requires the use of a discount rate in order to be able to compare the benefits and costs that are distributed over the life of the investment. The discount rate recommended here for the calculation of the economic NPV of projects is the economic opportunity cost of capital for the country. If the economic NPV of a project is greater than zero, it is potentially worthwhile to implement the project. This implies that the project would generate more net economic benefits than the same resources would have generated if used elsewhere in the economy. On the other hand, if the NPV is less than zero, the project should be rejected on the grounds that the resources invested would have yielded a higher economic return if they had been left for the capital market to allocate them to other uses. This chapter explains how the economic opportunity cost of funds to an economy is derived and how it is used in the appraisal of an investment to calculate its economic present value. To Be Published As: Jenkins G. P, C. Y. K Kuo and A.C. Harberger,“The Economic Opportunity Cost Of Capital” Chapter 8, Cost-Benefit Analysis for Investment Decisions. (2011 manuscript) JEL code(s): H43 Keywords: discounting, discount rate, economic cost of capital, rate of time preference, gross of tax rate of return. CHAPTER 8: CHAPTER 8 THE ECONOMIC OPPORTUNITY COST OF CAPITAL 8.1 Why is the Economic Cost of Capital Important? An investment project usually lasts for many years, hence its appraisal requires a comparison of the costs and benefits over its entire life. For acceptance, the present value of the project’s expected benefits should exceed the present value of its expected costs. Among a set of mutually exclusive projects, the one with the highest net present value (NPV) should be chosen.1 This criterion requires the use of a discount rate in order to be able to compare the benefits and costs that are distributed over the life of the investment. The discount rate recommended here for the calculation of the economic NPV of projects is the economic opportunity cost of capital for the country. If the economic NPV of a project is greater than zero, it is potentially worthwhile to implement the project. This implies that the project would generate more net economic benefits than the same resources would have generated if used elsewhere in the economy. On the other hand, if the NPV is less than zero, the project should be rejected on the grounds that the resources invested would have yielded a higher economic return if they had been left for the capital market to allocate them to other uses. In the process of project design the economic cost of capital also plays an important role in the maximization of the potential economic NPV of a project. It is a critical parameter for decision making relating to the optimum size of the project and the appropriate timing for the implementation of an investment. Both are key factors affecting the project’s net benefits and its ultimate feasibility. In addition, the choice of technology for a project is influenced by the opportunity cost of capital. For example, a low cost of capital will 1 The benefit cost ratio is often used as a decision criterion in an economic evaluation. However, the NPV criterion is known to be more reliable than other criteria for both the financial and economic evaluation. For the financial appraisal, other criteria include the payback period, the debt service ratio, and the internal rate of return. Each of these criteria has its own shortcomings. Detailed discussions are presented in Chapter 4. 1 CHAPTER 8: encourage the use of capital-intensive technologies as opposed to labor- or fuel- intensive technologies. (a) Choosing the Scale of a Project An important decision in project appraisal concerns the size or scale at which a facility should be built. It is seldom that the scale of a project is constrained by technological factors, hence economic considerations should be paramount in selecting its appropriate scale. Even if the project is not built to its correct size, it may be a viable project because its NPV may still be positive, but less than its potential. The NPV is maximized only when the optimum scale is chosen. As was discussed in Chapter 5, the appropriate principle to use for determining the scale of a project is to treat (hypothetically, and on the drawing board, as it were) each incremental change in size as a project in itself. An increase in the scale of a project will require additional expenditures and will generate additional benefits. The present value of the costs and benefits of each incremental change should be calculated by using the economic discount rate. The NPV of each incremental project indicates by how much it increases or decreases the overall net present value of the project. This procedure is repeated (at the planning, drawing board stage) until a scale is reached where the net present value of incremental benefits and costs associated with an increment of scale changes from positive to negative. When this occurs, the previous scale (with the last upward step of NPV) is the optimum size of the plant. The effect that the economic opportunity cost of capital or economic discount rate has on determining the size of the net present value gives it a central role in the determination of the optimum scale of a project. (b) Timing of Investment Another important decision to be made in project analysis relates to the appropriate time for a project to start. A project that is built too soon could result in a large amount of idle capacity. In this case, the forgone return from the use of resources elsewhere might be 2 CHAPTER 8: larger than the benefits gained in the first few years of the project’s life. On the other hand, if the project is delayed too long, shortages may occur and the forgone benefits of the project will be greater than the alternative yields of the resources. Whenever the project is undertaken too early or too late, its net present value will be lower than what it could have been if developed at the right time. The net present value may still be positive, but it will not be at the project’s potential maximum. The key to making a decision on this issue is whether the costs of postponement of the project are greater or smaller than the benefits of postponement. In the easiest case, where investment costs K remain the same whether the project is started in either periods t or t+1, the costs of postponement from year t to year t+1 are simply the economic benefits Bt+1 forgone by delaying the project. On the other hand, the benefit of postponement is the economic return (re) that can be earned from the capital invested in the general economy. Thus the benefit from postponement is equal to the economic opportunity cost of capital multiplied by the capital costs (i.e., re × Kt).2 One can see again that the value for the economic opportunity cost of funds is an essential component for deciding the correct time for starting the project.3 (c) Choice of Technology In order to be worthwhile undertaking, any investment project must earn enough to cover the economic opportunity cost of capital. If this is not so, the capital would better be left to be allocated to other uses through the normal working of the capital market. Sometimes public sector projects face a financial cost of capital that is artificially low. This is true not only when they can raise funds at an artificially low rate of interest because of government subsidies or guarantees. It is even true (typically) when they raise 2 There are a number of cases where the benefits and capital costs are also a function of calendar time. They are discussed in Chapter 5. 3 This exercise applies when the benefits of the project in period t are the same, regardless of whether the investment was made in t, t+1, t+2, etc. and also that the stream of project benefits over time is increasing with time, i.e., Bt+2 >Bt+1 > Bt. 3 CHAPTER 8: funds at the market-determined rate of yield in government bonds. In either case, the cost of capital perceived by the project may be far below its economic opportunity cost. The use of a lower financial cost of capital instead of its economic opportunity cost would create an incentive for the project managers to use production techniques that are too capital intensive. The choice of an excessively capital-intensive technology would lead to economic inefficiency because the value of the marginal product of capital in this activity is below the economic cost of capital to the country. For example, in electricity generation, using a financial cost of capital that is lower than its economic cost will make capital-intensive options such as distant hydroelectric dams or nuclear power plants more attractive than oil- or coal-fired generation plants.4 A correct measure of the economic opportunity cost of capital is, therefore, necessary for making the right choice of technology. 8.2 Alternate Methods for Choosing Discount Rates for Public Sector Project Evaluation The choice of the discount rate to be used in economic cost benefit analysis has been one of the most contentious and controversial issues in this area of economics. The term “discount rate” refers to the time value of the costs and benefits from the viewpoint of society. It is similar to the concept of the private opportunity cost of capital used to discount a stream of net cash flows of an investment project, but the implications can be more complex. However, after much debate a consensus, or at least a reasonably good understanding of the issues, has emerged. There have been basically four alternative approaches put forth on this issue. First, some authors have suggested that all investment projects, both public and private, should be discounted by a rate equal to the marginal productivity of capital in the private sector.5 4 Jenkins, G.P., “Public Utility Finance and Economic Waste”, Canadian Journal of Economics, (August 1985). 5 Hirshleifer, J., DeHaven, J.C. and Milliman, J.W., Water Supply: Economics, Technology, and Policy, Chicago: University of Chicago Press, (1960). 4 CHAPTER 8: The rationale for this choice is that if the government wants to maximize the country’s output, then it should always invest in the projects which have the highest return. If private sector projects have a higher expected economic return than the available public sector projects, then the government should see to it that funds are invested in the private rather than public projects. Secondly, authors such as Little and Mirrlees, and Van der Tak and Squire have recommended the use of an accounting rate of interest.6 Their accounting rate of interest is the estimated marginal return from public sector projects given the fixed amount of investment funds available to the government. The accounting rate of interest is essentially a rationing device. If more projects look acceptable than available investible funds, the accounting rate of interest should be adjusted upwards; and if too few projects look promising, the adjustment should go the other way. Therefore, the accounting rate of interest does not serve to ensure that funds are optimally allocated between the public and private sectors but acts only to ensure that the best public sector projects are recommended within the constraint of the amount of funds available to the public sector. This approach does not recognize the fact that if the funds are not spent by the public sector, they can always be used to reduce the public sector’s debt. They will then be allocated by the capital market for the use by the private sector. Thirdly, it has been recommended that the benefits and costs of projects should be discounted by the social rate of time preference for consumption, but only after costs have been adjusted by the shadow price of investment to reflect the fact that forgone private investment has a higher social return than present consumption. This method has been proposed by such authors as Dasgupta, Sen, Marglin and Feldstein.7 6 Little, I.M.D. and Mirrlees, J.A., Project Appraisal and Planning for Developing Countries, London: Heinemann Educational Books Ltd., (1974); Squire, L. and van der Tak, H.G., Economic Analysis of Projects, Baltimore: The Johns Hopkins University Press, (1975). 7 Dasgupta, P., Sen, A. and Marglin, S., Guidelines for Project Evaluation, Vienna: United Nations Industrial Development Organization, (1972); Marglin, S., “The Social Rate of Discount and the Optimal Rate of Investment”, Quarterly Journal of Economics, (February 1963); Feldstein, M., “The Social Time Preference Discount Rate in Cost-Benefit Analysis”, Economic Journal, 74, (June 1964). 5 CHAPTER 8: Fourthly, Harberger and other authors have suggested that the discount rate for capital investments should be the economic opportunity cost of funds obtained from the capital market. This rate is a weighted average of the marginal productivity of capital in the private sector and the rate of time preference for consumption.8 This proposal has been reinforced by the theoretical work of Sandmo and Dreze9 and reconciled to a degree with the alternative approach of using a social rate of time preference in conjunction with a shadow price of investment by Sjaastad and Wisecarver.10 Many professionals have chosen to follow this weighted average opportunity cost of funds concept. Furthermore, Burgess has shown that under a wide range of circumstances the use of the economic opportunity cost of funds as the discount rate, leads to the correct investment choice, while other approaches lead to the selection of inferior projects.11 In its simplest form the economic opportunity cost of public funds (ie) is a weighted average of the rate of time preference for consumption (r) and the rate of return on private investment (ρ). It can be written as follows: i = W r + (1− W ) × ρ (8.1) e c c 8 Harberger, A.C., “On Measuring the Social Opportunity Cost of Public Funds”, in The Discount Rate in Public Investment Evaluation, Report No. 17, Conference Proceedings from the Committee on the Economics of Water Resources Development of the Western Agricultural Economics Research Council, Denver Colorado, (December 1968) and Harberger, A.C., “Reflections on Social Project Evaluation”, in Pioneers in Development, Vol. II, edited by G.M. Meier, Washington: The World Bank and Oxford: Oxford University Press, (1987). 9 Sandmo, A., and Dreze, J.H., “Discount Rates for Public Investment in Closed and Open Economies”, Economics 38, (November 1971); Dreze, J.H., “Discount Rates and Public Investment: A Post-Scriptum”, Economics 41, No. 161 (February 1974). 10 Sjaastad, L.A. and Wisecarver, D., “The Social Cost of Public Finance”, Journal of Political Economy 85 No. 3 (May 1977). 11 Burgess, D.F., “Removing Some Dissonance from the Social Discount Rate Debate”, University of Western Ontario, London, Ontario, Canada (June 2006). 6 CHAPTER 8: where Wc is the proportion of the incremental public sector funds obtained at the expense of current consumption and (l-Wc) is the proportion obtained at the expense of postponed investment.12 8.3 Derivation of the Economic Opportunity Cost of Capital The rates of interest observed in the capital markets are fundamentally determined by the willingness of people to save and the opportunities that are available for investment. In an economy characterized by perfect competition with full employment and no distortions, the real market interest rate would reflect the marginal valuation of capital over time and could be used as the economic discount rate. However, in reality there are distortions in the capital markets, such as business and personal taxes, and inflation, hence, market interest rates will neither reflect the saver’s time preferences for consumption nor the gross economic returns generated by private sector investment. Both savers and investors must take into consideration taxes and other distortions when entering the capital market to lend or borrow. The determination of the market interest rate can be illustrated in Figure 8.1 for the case where savers are required to pay personal income taxes on interest income and borrowers pay both business income taxes and property taxes from the investment. For the moment, the effects of inflation will be set aside so that all the rates of return are expressed in real terms. The curve GS(r) shows the relationship between the supply of savings and the rate of return (r) received from savings net of personal income taxes. This function tells us the minimum net return savers must receive before they are willing to postpone current consumption and save for future consumption. If there is a personal income tax, then savers will require a return sufficiently larger than r to allow them to pay income taxes on 12 For a more complete discussion of this derivation, see Harberger, A.C., “On Measuring the Social Opportunity Cost of Public Funds”, in The Discount Rate in Public Investment Evaluation, Report No. 17, Conference Proceedings from the Committee on the Economics of Water Resources Development of the Western Agricultural Economics Research Council, Denver Colorado, (December 1968) and Harberger, A.C., “Professor Arrow on the Social Discount Rate” in Project Evaluation, Chicago: University of Chicago Press, (1972). 7 CHAPTER 8: the interest income and still have a return of r left. The savings function which includes the taxes on interest income is shown as FS(i). Figure 8.1 Determination of Market Interest Rates Interest Rate and Rate of Return % A S(i) gross rate of return ρ received by savers before B personal income taxes S(r) savings function net of personal income taxes C I(ρ) return on investment gross of all taxes im D r E F I(i) return on investment net of G corporate and property taxes 0 Q0 Quantity of Investment and Savings At the same time, investors have a ranking of investment projects according to their expected gross of tax rates of return which is shown as the curve AI(ρ). If the owners of the capital have to pay property taxes and business income taxes, they will be willing to pay less for their investment funds than in a no-tax situation. CI(i) reflects the rate of return investors can expect to receive net of all business and property taxes. In this market situation the interest rate (im) will be determined by the gross-of-personal-income-tax savings function FS(i) and the net-of-tax demand for investment curve CI(i). 8 CHAPTER 8: The basic principle which must be followed to ensure that a project’s investment expenditures do not ultimately retard the level of the country’s economic output is that such investments must produce a rate of return at least equal to the economic return of other investment and consumption that is postponed, plus the true marginal cost of any additional funds borrowed from abroad as a direct or indirect consequence of this project. To form a general criterion for the economic opportunity cost of capital for a country, we must assess the sources from which that capital is extracted and attach an appropriate economic cost to each source. For most countries, it is realistic to assume that there exists a functioning capital market. That is not to say that it is free of distortions, for it is the existence of distortions such as taxes and subsidies which prevents us from using the real interest rate in the market as a measure of the economic opportunity cost of funds. In addition, most governments and private investors obtain marginal funds to finance their budgets from the capital market, and during periods of budgetary surplus typically reduce their debts. It is true that the financing for a government’s budget comes from many sources other than borrowing, such as sales and income taxes, tariffs, fees, and perhaps sales of goods and services. The average economic opportunity cost of all these sources of finance combined may well be lower than the economic opportunity cost of borrowing. This fact is irrelevant, however, for the purpose of estimating the marginal opportunity cost of the government’s expenditures. As in estimating the supply price of any other good or service, the marginal economic opportunity cost must reflect the ways in which an incremental demand will normally be met. Even in the very short run most governments are either borrowing or, when enjoying a budgetary surplus, paying off some of their debt.13 Therefore, if fewer public sector projects are undertaken in a given year, more funds will be available in the capital markets for private sector use. We do not wish to imply that every government uses each year the capital market as its source or repository of marginal funds. However, the overwhelming evidence from 9 CHAPTER 8: observing developing and developed countries indicates that this is a fair characterization of the behavior of most governments. As the economic discount rate is a parameter which should be generally applicable across projects and estimated consistently over time, it is prudent for a country to base its estimation of the economic opportunity cost on the cost of extracting the necessary funds from the capital market. The approach has a further advantage in that the capital market is clearly the marginal source of funds for most of the private sector. Hence, it follows that the economic opportunity cost of funds for both the public and private sectors are based on the costs derived from similar capital market operations. To estimate the economic opportunity cost of funds obtained via the capital market, we will first assume that the country’s capital market is closed to foreign borrowing or lending. It is also assumed that taxes such as property taxes and business income taxes are levied on the income generated by capital in at least some of the sectors. In addition, we assume that a personal income tax is applied to the investment income of savers. In Figure 8.2, we begin with a situation where the market rate of return is im, and the quantity of funds demanded and supplied in the capital market is Q0. At this point, the marginal economic rate of return on additional investment in the economy is ρ and the rate of time preference which measures the marginal value of current consumption is equal to r. We now borrow funds in the amount of B from the capital market to finance our project by the amount of (Qs - QI). This causes the total demand in the economy for loanable funds to shift from CI(i) to C’I(i)+B. However, the value of funds for investment elsewhere in the economy, and the net of tax returns to them, is measured by the curve CI(i). The gross of tax return on the investments is measured by the curve AI(ρ). The increase in the demand for funds by the project will cause the market cost of funds to increase from i to i’, thus inducing people to save more (postpone consumption) by an amount (Qs -Q0). At the same time, the higher cost of funds will cause people to postpone investments by an amount (Q0 - QI). 13 Some of this debt may reflect foreign as well as domestic borrowings. 10 CHAPTER 8: 11 CHAPTER 8: Figure 8.2 The Economic Opportunity Cost of Capital Interest Rate Rate of % A G ρ’ ρ R F S(i) C’ S(r) C J H’ I(ρ) i’ D’ H i D K r’ r T L I(i ) + B I(i ) N M 0 QI Q 0 Qs Quantity of Investment and Saving The economic cost of postponing consumption is equal to the area Q0TLQs, which is the net of tax return savers receive from their increased savings. This is measured by the area under the MS(r) curve between Q0 and Qs. With a linear supply function this area estimated by the average economic cost per unit, [(r + r’)/2], times the number of units, (Qs -Q0). Postponed investment has a gross of tax economic opportunity cost which is measured by the AI(ρ) curve. This includes both the net return given up by the private owners of the investment measured by the curve CI(i), plus the property and business taxes lost. This opportunity cost is shown by the shaded area QIGFQ0, of which QIJHQ0 is the net return forgone by the would-be owners of the investment, and JGFH represents the amount of taxes lost by the government. Again, this can be calculated by the economic opportunity cost per unit [(ρ + ρ’)/2] times the number of units (Q0 - QI). For marginal changes in government borrowing, we can safely disregard the triangles RGF and KLT which arise from the change in interest rates. The economic opportunity cost of capital ie can then be defined as: 12 CHAPTER 8: r × ( ∂ S ∂ i) − ρ × ( ∂ ∂ i) (8.2) ie = I ( ∂ S ∂ i ) − ( ∂ I∂ i) where (∂S/∂i) and (∂I/∂i) denote the reaction of savers and other investors, respectively, to a change in market interest rates brought about by the increase in government borrowing. Expressed in elasticity form, equation (8.2) becomes: r ×ε s−ρ ×η I×( I S T) (8.3) ie = T ) ε s − η I × ( I TS T where εs is the elasticity of supply of private-sector savings, ηI is the elasticity of demand for private-sector investment with respect to changes in the rate of interest, and IT/ST is the ratio of total private-sector investment to total savings. Let us suppose that ρ = 0.16 and r = 0.05. Also let us assume that εs = 0.3, ηI = -1.0 and IT/ST = 0.9. In this case the economic opportunity cost of capital can be calculated as: ie = [0.05 (0.3) - 0.16 (-1.0) (0.9)] / [0.3 - (-10)(0.9)] = (0.015 + 0.144) / (1.20) = 0.133 The economic opportunity cost of capital is 13.3%. Typically, it will be closer to the gross return from investment than the rate of time preference on consumption because the elasticity of private savings is generally much smaller than the absolute value of the elasticity of demand for private-sector investment. In equation (8.3), all the different groups of savers have been aggregated into one category, and all groups of investors have also been grouped into one sector. The 13 CHAPTER 8: aggregate elasticity of supply of savings and the aggregate elasticity of demand for investment can be disaggregated into their components as follows: m ε =∑εis(Si ST ) s (8.4) i=1 n η = ∑ηI (Ij IT ) I (8.5) j=1 where εis refers to the elasticity of supply of the ith group of savers, and (Si/ST) is the proportion of total savings supplied by this group; ηjI refers to the elasticity of demand for the jth group of investors, and (Ij/IT) is the proportion of the total investment demanded by this group. Substituting equations (8.4) and (8.5) into equation (8.3), we obtain an expression for the economic opportunity cost of capital which allows for consideration of different distortions within the classes of savers and investors: m s n ∑ i( I S T) ρ j (8.6) ε i / S T ) r i− ∑ η j ( I j / S j=1 i=1 ie = m s n I ∑ i( S i/ S T) −∑η j( I j/ S T) ε j=1 i=1 The classes of savers will usually be differentiated by income groups which face different marginal income tax rates. There is also saving done by domestic businesses. However, it is not clear if higher interest rates would affect the amount of business saving because the decisions businessmen make whether to pay or not dividends is based more on business investment opportunities. Thus the amount of business saving is assumed in this study to be independent of interest rates. We can also include in the broad class of savers the foreign savers which supply the funds to the country when it sources funds from abroad. As the international capital markets become more accessible to domestic investors, we 14 CHAPTER 8: would expect the elasticity of supply of this sector to increase relative to the other sources of savings. In some circumstances, we may even find that the cost of foreign borrowing and the elasticity of supply foreign savings might dominate the entire equation (8.6). It is therefore important to properly assess the economic cost of foreign borrowing which will be discussed in Section 8.5. On the demand side, investors are typically divided into the corporate sector, the noncorporate sector, housing, and agriculture, according to the different tax treatment provided to these sectors. 8.4 Determination of the Economic Cost of Alternative Sources of Funds Measuring the real rate of return to reproducible capital in a country is not an easy task. In most cases the most consistent approach is based on the country’s national income accounts. At the very least, the accounts presume to cover the full range of economic activities in the country (including such items, for example, the implicit income from owner-occupied houses, and the value added of many informal sector activities). Employing this method of calculation, one starts from a past base period, and the real amount of investment made during each period from the base year until the present. For these purposes, the amounts of real investment should be obtained by deflating nominal investment by the general GDP deflator (not the official investment deflator). The purpose of this is to express the capital stock of the country in the same units of account as are used to express the earnings of capital. Our methodology employs the GDP deflator as the general numeraire; it is used to convert all nominal values into real values. If investment is available by component, it is desirable to carry out the estimations component by component (buildings, machinery, vehicles, inventories), so as to allow for different depreciation rates on these categories. Once an initial capital stock Kj0 is estimated for each component, and its appropriate depreciation rate δj established, the 15 CHAPTER 8: time path of the capital stock is generated by the formula Kj,t+1 = Kjt(1 - δj) + Ijt where Ijt denotes the amount of new gross investment for each component. Obviously, one cannot speak of a separate rate of return to different pieces of the capital stock of the same entity, so we express the rate of return as Ykt/Kt, where Kt = ∑Kjt and Ykt is the income from capital at time t. It consists of the sum of interest, rent and profit income, as recorded in the national accounts. If these items do not appear explicitly, one usually can at least find a breakdown that includes wages and salaries as one category, corporate profits as a second, and the surplus of non-corporate enterprises as a third. Here the challenge is to separate the surplus of non-corporate enterprises into two components; one representing the value added due to time value of the owners and their family members, the other representing the gross return to capital in these enterprises. This does not complete the task, however. For certain, since we are building up a stock of Kt of reproducible capital, its value should necessarily exclude that of land (improvement to land, like fences, canals, even leveling, should, however, be treated as reproducible). So from the income stream accruing to capital we definitely want to exclude the portion that we estimate as accruing to land. Also we should exclude most elements of government capital from the capital base we use to calculate its rate of return. Likewise, we should exclude from the relevant “return to capital” any income from these items. In some countries, this would give us a rate of return straightforwardly based on the “real earnings of reproducible private-sector capital” (in the numerator) and the “real value of this private-sector capital stock” (in denominator). In most countries, however, these also exist in public sector productive entities like electricity companies, railroads, airlines, ports, and even manufacturing facilities that behave sufficiently like other business enterprises to warrant their being counted in the same calculation, alongside private business enterprises. To see clearly the motive for this treatment, readers should focus on the purpose for which we want to calculate the economic opportunity cost of capital in the first place. That purpose is best seen by visualizing the exercise of anybody -- a private company, 16 CHAPTER 8: one or more individuals, a non-profit institution, the government itself -- going into the country’s capital market to raise money. This puts added pressure on that market, and squeezes out other demanders for funds, while giving some additional stimulus to suppliers of funds in that market. We take the position that the actions of business firms and private savers are governed by natural economic motives, in the sense that we can take seriously in their case, the idea that they have reasonably well-defined supply and/or demand functions for funds as a function of interest rates and other variables in that country’s capital market. We feel that government (apart from those public enterprises that really behave like business firms) operates mainly with a different type of machinery -- legislative acts and authorizations, budgetary decisions, administrative edicts and the like. In short, we do not see previously authorized public investments being “naturally” squeezed out by a tightening capital market, in the same way as we see this same phenomenon for regular business investments. Our vision of the economic opportunity cost of capital is that as new demands for funds in a country’s capital market squeeze out alternative investments, the country loses (a perhaps better forgoes) the returns that would have been generated by these investments; at the same time, the country incurs the costs involved in covering the supply prices of the new amounts of saving that are stimulated by the new demand, plus whatever incremental costs are entailed in newly-generated capital inflows from abroad. We thus start with a weighted average of the marginal productivity (ρ) of displaced investments, the marginal supply price (r) of newly-stimulated savings and the marginal cost (MCf) associated with newly-stimulated inflows from abroad. This simple vision can be represented as: EOCK = ƒ1ρ + ƒ2 r + ƒ3 (MCf) (8.7) where ƒ1, ƒ2, and ƒ3 are the sourcing fractions linked, respectively, with sourcing from displaced investment, newly stimulated domestic savings, and newly stimulated capital inflows from abroad. Obviously ƒ1 + ƒ2 + ƒ3 should equal one. 17 CHAPTER 8: A key element in this story is ρ, since ƒ1 is typically the largest of the three sourcing fractions. As mentioned, we conceive of ρ as representing the typical marginal productivity of the class of investments it is meant to cover. We recommend its estimation, as indicated above, on the basis of the ratio of “returns to reproducible capital (net of depreciation but gross of taxes) in the productive sector of the economy” divided by “value of reproducible capital in the productive sector of the economy”. If the reproducible capital stock can be conveniently estimated only for the total economy, then we would advise reducing this stock by a fraction that one estimates would account for the bulk of public sector capital items -- government buildings, schools, roads, etc. that are not basically business-oriented. To get the rate of return that represents the supply price (r) of newly stimulated domestic savings, we must certainly exclude the taxes on income from capital that are paid directly by business entities, plus the property taxes paid by these entities as well as by homeowners. In addition, we would want to exclude the personal income taxes that are paid on the basis of the income from reproducible capital. If one works with aggregate national accounts data, we would recommend subtracting from the gross-of-tax return to reproducible capital the full amount of corporation income taxes paid and the full amount of property taxes paid, adjusted downward to exclude an estimated portion falling on land. In addition, one needs to subtract the full amount of personal income taxes paid on the income from capital, also adjusted downward to exclude the income taxes that are paid on the income derived from land. When this is done the remaining value covers not only the net-of-tax income received by individual owners of capital, but also the costs of intermediation -- easiest understood (in the case of bank loans) as the difference between the average rate of interest the banks receive on their loans and the average rate that they pay to their depositors. It is possible also to approach the estimation of the economic opportunity cost of capital in a more disaggregated way; distinguishing separate categories of displaced investment 18 CHAPTER 8: (e.g., corporate, non-corporate and housing) owing to different tax treatments they receive, and distinguishing different categories of savings on a similar basis (e.g., savers with marginal tax rates of 30, 20, 10, and zero percent). For example, in the latter case the higher is the individuals’ rate of personal income tax the lower will be the person’s equilibrium rate of time preference for consumption. In a situation where the market interest rate is equal to 0.08 and the marginal rate of personal income tax is assumed at 0.1, the value for r is 0.072. Now consider a high income individual who is faced with a marginal personal income tax rate of 0.4. In this case the rich will have low rates of time preference at 0.048 in their decisions of how to spend their consumption over time. Thus, high rates of time preference and high discount rates correspond more closely to the decisions of the poor concerning the distribution of their consumption over time. Furthermore, consumers who are borrowing in order to finance current consumption will typically have higher rates of time preference than people who only save. If the margin required by finance companies and money lenders over the normal market interest rate is M percentage points, then the rate of time preference for borrowers for consumer loans is the sum of the market interest rate and M percentage points. Suppose M is 0.11, then the rate of time preference for borrowers for consumer loans becomes 0.19, a rate which is often charged on credit cards, even in advanced countries. From these examples we can see that as we move from the poor borrowers to the rich groups in society which are net savers, the time preference rate can quite realistically fall from 0.19 to 0.048. However, we feel that this approach, which we ourselves have often used in the past,14 suffers from its de-linking to the aggregate national accounts framework. For example, our preferred framework deducts taxes actually paid, and thus incorporates all the effects of avoidance, evasion and corruption as they live and breathe in the country in question, 14 Jenkins, G.P., “The Measurement of Rates of return and Taxation from Private Capital in Canada”, in W.A. Niskanen et al., eds., Benefit-Cost and Policy Analysis, Chicago: Aldine, (1973) ; and Barreix, A., “Rate of Return, Taxation, and the Economic Cost of Capital in Uruguay”, a Ph. D. dissertation submitted to Harvard University, Cambridge, Cambridge, (2003). In the case by Barreix, the analysis is done using both aggregate and sector-disaggregated approaches and then shows that both estimates were completely reconcilable. 19 CHAPTER 8: while the disaggregated framework tends, perhaps naively, to make the assumption that the statutory marginal rates are rigorously applied. 8.5 Marginal Economic Cost of Foreign Financing In this section, we deal with the estimation of marginal economic cost of newly- stimulated capital inflows from abroad as a result of project funds raised in capital markets. Foreign capital inflows reflect an inflow of savings of foreigners which augments the resources available for investment. When the demand for investible funds is increased, this will not only induce domestic residents to consume less and save more, but it will also attract foreign saving. When the market interest rate is increased to attract funds, an additional cost is created in the case of foreign borrowing. This higher interest rate is paid not only on the incremental borrowing but will also be charged on all the variable interest rate debt both current and prior, which are made on a variable interest rate basis. Thus, it is the marginal cost of borrowing by the project that is material in this case.15 If the interest rate on foreign borrowing by the project is i’f, it only reflects the average cost of this financing. The marginal cost that is relevant is given by the sum of the cost of foreign financing of the additional unit and the extra financial burden on all other borrowings that are responsive to the market interest rate. This is shown in Figure 8.3. 15 Harberger, A., “Vignettes on the World Capital Market”, American Economic Review, Vol. 70, No. 2, (May 1980); Edwards, S., “Country Risk, Foreign Borrowing, and the Social Discount Rate in an Open Economy”, Journal of International Money and Finance, (1986). 20 CHAPTER 8: Figure 8.3 The Marginal Economic Cost of Foreign Borrowing % C MC f %MC’f %MCf B Sif i’f D E i0f D0f + B A D0f 0 Q0 Q1 Quantity of Foreign Borrowing If a country faces an upward sloping supply curve for foreign financing, the interest rate which borrowers have to pay will increase as the quantity of debt rises relative to the country’s capacity to service this foreign debt. With a demand curve for foreign borrowing shown as D0f the interest rate charged on such loans is shown at i0f and the quantity of foreign borrowings Q0. Now suppose the demand for loanable funds (B) increases such that its demand for foreign loans shifts to D0f + B. As a result of the additional funds (Q1 - Q0) demanded in the capital market, there will be a slightly higher market interest rate (i’f) paid to foreign savers. This higher interest rate i’f will be paid not only on the foreign borrowing of this year but on any variable interest rate loans in its stock of foreign financing which are affected by the increased market interest rate for foreign financing. The latter also includes the country risk for the country. With the greater stock of foreign financing that must be serviced using foreign exchange, the lender faces a greater exposure to the risk of default from macroeconomic instability. As a consequence, the marginal economic cost of foreign borrowing (MCf) is not given by the 21 CHAPTER 8: supply curve of foreign savings available to the country, but by the marginal economic cost curve which lies above the supply curve. Algebraically, the marginal economic cost of foreign borrowing is shown as: (8.8) MCf = if ×(1−tw) +(∂if ∂ L)×(1−tw)×φ×L where tw : the rate of withholding taxes charged on interest payments made abroad; L : total value of the stock of foreign financing; φ : the ratio of [the total foreign debt whose interest rate is flexible and will respond to additional foreign financing] to [the total stock of foreign financing for the country]; and ∂ if ∂ L : rate of change in the cost of foreign financing as the current foreign financing increases. Or alternatively, MC f = i f × ( 1 − t w { 1 + φ × ( 1 εf s )} (8.9) )× where εf is the supply elasticity of foreign funds to a country with respect to the cost of funds the country pays on its new foreign financing. Let us consider the case where if = 0.10, tw = 0.20, εf = 1.5, φ = 0.60. Using equation (8.9), MCf is equal to 0.112. In this case with a market interest rate of 10 percent for foreign loans, the marginal cost for foreign borrowing would be 11.2 percent. A final factor which needs to be considered when estimating the marginal economic cost of foreign borrowing is the effect of the expected rate of inflation. If gpf denotes the 22 CHAPTER 8: expected rate of foreign inflation, then the marginal economic cost of foreign borrowing (MC’f), after adjustment for inflation, can be derived as follows: 1 [ i f × ( 1 − t w ) − gp f ] ×[ 1 + φ × ] MC ′ f = ε sf (8.10) ( 1 + gp f ) To estimate the economic opportunity cost of capital in an open economy, we need to combine equation (8.7) with equation (8.10) and the estimate of gross-of-tax return from domestic investment (ρ) and the cost of newly stimulated domestic savings (r). It is these rates of opportunity cost along with their respective weights that generate the weighted average rate which should be used as the rate of discount for all government expenditures. 8.6 Inter-Generational and Risk-Adjusted Economic Discounting Questions have been raised whether a lower rate should be used for inter-generational discounting because many of the people affected by some project or policy may no longer alive over the distant future.16 However, there is little consensus in the economic literature on economic discounting for inter-generational projects or policies. There are several reasons for not favoring the use of different discount rates over the project impact period unless the opportunity cost of funds is abnormally high or low from one period to another. 16 E.g., United States Environmental Protection Agency, Guidelines for Preparing Economic Analyses, (September 2000). 23 CHAPTER 8: Second, for projects in which capital expenditures are incurred at the beginning of the project while benefits are spread over the life of the project applying one discount rate for the streams of costs and another for the streams of benefits can be tricky and empirically difficult for each project. The informational requirements are very demanding for converting all the streams of costs into consumption equivalents in a consistent manner. The problem becomes more complicated when the stream of costs and benefits occur simultaneously and are spread over all years. Using a weighted average of the economic rate of return on alternative sources of funds, the discount rate based on the opportunity cost of forgone investment and consumption can avoid the complicated adjustments. A risk-adjusted economic discount rate has also been suggested elsewhere to account for the systematic risk of future uncertainty.17 However, the discount rates derived above are associated with the average risk in the economy. Since the streams of uncertain future costs and benefits are mainly related to the input variables themselves, they are best dealt with in the Monte Carlo risk analysis as described in Chapter 6 rather than the adjusted economic discount rates. 17 E.g., Brean, D.J.S., Burgess, D.F., Hirshhorn, R. and Schulman, J., “Treatment of Private and Public Charges for Capital in a Full-Cost Accounting of Transportation”, Report Prepared for Transportation Canada, Government of Canada, (March 2005). 24 CHAPTER 8: 8.7 Country Study: Economic Cost of Capital for South Africa This section illustrates how the economic opportunity cost of capital for South Africa is estimated following the methodology outlined in the previous sections. South Africa is considered a small open developing economy. When funds are raised in the capital market to finance any investment projects those funds are likely to come from three alternative sources as described in Section 8.4. They are funds released from displaced or postponed investment, newly stimulated domestic savings, and newly stimulated foreign capital inflows. Following equation (8.7), the economic opportunity cost of capital can be estimated by the sum of multiplying the opportunity cost of each of the three alternative sources of funds by the shares of the funds diverted from each of these sources. 8.7.1 Estimation of the Economic Cost of the Three Diverted Funds (a) Gross-of-Tax Return to Domestic Investment Using the approach based on the national income and expenditure accounts, the return to domestic investment can be estimated from the GDP net of depreciation and the contributions made by labor, land, resource rents, and the associated sales and excise taxes. The total contribution of labor to the economy is the sum of wages and salaries paid by corporations and by unincorporated businesses. Since owners of unincorporated businesses are also workers but are often not paid with wages, the operating surplus of this sector thus includes the returns to both capital and labor. The labor content of this mixed income was estimated at 35% for South Africa during the period between 1995 and 1999.18 The 35 percent figure is used and assumed throughout the period from 1985 to 2004. Land is a fixed factor of production that makes a contribution to value added especially in the agriculture and housing sectors. The contribution of land in the agricultural sector is 18 This figure was obtained from officials of South African Reserve Bank in Pretoria. 25 CHAPTER 8: assumed to be one-third of the total value added in that sector.19 Regarding the housing sector, information is not available on the amount of value added produced by this sector nor is it available for the value added of the land component for the sector. Hence this component is not incorporated in the calculation. In South Africa resource rents arise due to the fact that in the past the mining of nonrenewable resources such as gold, coal, platinum and diamonds have made a substantial contribution to GDP. These specific resources are non-renewable; when exploited with the help of reproducible capital, they can yield substantial economic resource rents.20 These resource rents should be subtracted from the income to capital in order to derive the income to reproducible capital. Moreover, it should be noted that the value-added tax implemented in South Africa is a consumption-type tax and allows a full credit for the purchase of capital goods. Hence, the value-added tax is effectively borne by the value added of labor and not capital, hence it should be subtracted from GDP in order to derive the return to capital alone. To arrive at a rate of return, the value of the income attributed to the stock of reproducible capital is then divided by the total estimated value of the reproducible capital stock reduced by the value of the reproducible capital stock attributed to production of general government services. Over the past 15 years, the average real rate of return on investment 19 Data are not available for the agricultural sector alone, but available on a combined basis for agriculture, forestry and fishing. Because of the importance of agriculture in South Africa, it is assumed that the value added in the agricultural sector accounts for 95 percent of the total value added in the agricultural, forestry and fishing sector combined. Further, the assumption that the contribution of land set equal to one-third of the total value added of the agricultural is consistent with what has been estimated in countries of a similar level of development. 20 The resource rents were estimated by Blignaut, J.N. and Hassan, R.M., "A natural Resource Accounting Analysis of the Contribution of Mineral Resources to Sustainable Development in South Africa", South African Journal of Economic and Management Sciences, SS No. 3, (April 2001). However, the resource rents shown here are calculated based on the assumption that the real rate of return to the reproducible capital in mining is 10 percent real for the period from 1985 to 1993. From year 1994, the resource rents are assumed to increase with inflation rate due to absence of data for these years. 26 CHAPTER 8: in South Africa is estimated to be approximately 12.73% as shown in Appendix 8.1.21 The value of ρ is thus taken to be 13.0 percent for this exercise. (b) The Cost of Newly Stimulated Domestic Savings When project funds are raised in the capital markets, it will stimulate domestic savings in banks or other financial institutions. The net-of-tax return to the newly stimulated domestic savings can be measured by the gross-of-tax return to reproducible capital minus the amount of income and property taxes paid by corporations and the personal income taxes paid by individuals on their income from investments. It is further reduced by the cost of the financial intermediation services provided by banks and other financial institutions. These costs of financial intermediation are an economic resource cost that increases the spread between the time preference rate for consumption and the interest rate charged to borrowers. Due to lack of detailed data in this sector, it is estimated by assuming that the value added produced by financial institutions accounts for one half of the value added created by the total of all financial institutions and real estate combined. Furthermore the intermediation services are estimated as a further half of the value added in the financial institutions.22 The amount of return then divided by reproducible capital stock represents the net rate of return to households on newly stimulated savings. It also reflects the rate of time preference for forgone consumption. Using national accounts data over the past 20 years, the cost of newly stimulated domestic savings (r) for South Africa is estimated at about 4.50 percent as shown in Appendix 8.2. (c) Marginal Economic Cost of Foreign Financing 21 This estimate is lower than the one shown in Kuo, C.Y., Jenkins, G.P., and Mphahlele, M.B., “The economic Opportunity Cost of Capital in South Africa”, South African Journal of Economics, (September 2003) for the following reasons. First, the amount of return to capital in the Kuo-Jenkins-Mphahlele study was measured gross of depreciation and the reproducible capital stock was assumed the total stock in the economy including those of general government services. Second, the national accounts data appear to have been revised substantially in some areas especially since 1995. 22 See Statistics South Africa, Final Supply and Use Tables, 1998. The fraction of value added in the financial institutions was about 48 percent of those in the financial institutions, real estates, and business activities combined. The share of operating surplus in total value added in financial institutions was 53 percent. 27 CHAPTER 8: The real marginal cost of foreign financing (MCf) can be estimated by using equation (8.10). In South Africa, long-term debts currently account for more than 70 percent of total foreign debt. These long-term debts are mostly dominated in U.S. dollars. The coupon rate charged by the U.S. institutions ranges from 8.375 percent to 9.125 percent for U.S. dollar bonds.23 For this exercise, it is assumed that the average borrowing rate from abroad is about 8.5 percent per annum with the GDP deflator of 2.5 percent in the U.S. The fraction of long term loans outstanding with variable interest rates, φ, is about one- third.24 If we include both long and short term debts with variable interest rates they would amount to 53 percent of the total stock of South Africa’s foreign debt. For the purpose of this exercise, it is assumed to be about 50 percent. Thus the following information is given: if = 8.5%, tw = 0, gpf = 2.50%, and φ = 0.50. With the assumption of 1.5 for εf , one can obtain the value of MC’f that is approximately 7.80 percent. 8.7.2 Weights of the Three Diverted Funds The weights of the three diverted funds depend upon the initial shares of the sources of these funds and their price responsiveness to changes in the market interest rates. We estimate that the average ratio of the total private-sector investment to savings (IT/ST) for the past 20 year is about 73%. The average shares of total private-sector savings are assumed to be approximately 20% for households, 65% for businesses and 15% for foreigners.25 With the assumptions of the supply elasticity of household saving at 0.5, the supply elasticity of business saving at zero,26 the supply elasticity of foreign funds at 1.5 and the demand elasticity for private sector capital in response to changes in the cost of funds at -1.0, one can estimate the proportions of each of the diverted funds. They are 23 South African Reserve Bank, Quarterly Bulletin, (June 2006) 24 The percentage of long term debts with variable interest rate declined from 69.9 percent in 1994 to 33.8 percent in 1999. See the World Bank, Global Development Finance, (2001). 25 These shares fluctuate from year to year in South Africa. It is also a parameter for sensitivity analysis. 26 It is not clear if higher interest rates would affect the amount of business savings. This is because businesses are more concerned with investment opportunity. 28 CHAPTER 8: 9.48 percent from newly stimulated domestic savings, 21.33 percent from newly stimulated foreign capital, and 69.19 percent from displaced or postponed domestic investment. 8.7.3 Estimates of the Economic Cost of Capital The economic opportunity cost of capital can be estimated as a weighted average of the rate of return on displaced private-sector investment and the rate of return to domestic and foreign savings. Substituting the above data into equation (8.7), one can obtain an estimate of the economic cost of capital for South Africa of 11.08 percent. The empirical results depend on the values of several key parameters such as the supply elasticity of foreign capital, the initial share of each sector in total private-sector savings, the average rate of return on domestic investment, resource rents, the labor content of mixed capital-labor income for unincorporated businesses, foreign inflation rate, etc. A sensitivity analysis is performed to determine how robust the estimate of the economic cost of capital is. The results indicate that the value would range from 10.74 percent to 11.49 percent.27 Thus, a conservative estimate of the economic cost of capital in South Africa would be a real rate of 11 percent. 8.8 Conclusion The discount rate used in the economic analysis of investments is a key variable in applying the net present value or benefit-cost criteria for investment decision making. Such a discount rate is equally applicable to the economic evaluation, as distinct from a financial analysis, of both private as well as public investments. If the net present value of 27 For example, if the supply elasticity of foreign capital is 1.0 instead of 1.5, the share of financing from foreign funds becomes smaller but the marginal cost of foreign funds is increased. As a consequence, the economic opportunity cost of capital increases to 11.49 percent. On the other hand, if the supply elasticity of foreign capital is increased to 2.0, the economic cost of capital would be 10.74 percent. Perhaps the most important element in determining the economic cost of capital is the gross-of-tax return on domestic investment. If the average rate of return is 1.0 percentage point higher than 13.0% of the base case, then the economic opportunity cost of capital would become 11.77 percent. 29 CHAPTER 8: either type of project is negative when discounted by the economic cost of capital, the country would be better off if the project were not implemented. Estimates of the value of this variable for a country should be derived from the empirical realities of the country in question. Of course, the results of such a discounting effort are only as good as the underlying data and projection made of the benefits and costs for the project. This chapter began with the presentation of alternative approaches to choosing discount rates for investment projects and reviewed their strengths and weaknesses. An approach that captures the essential economic features uses a weighted average of the economic rate of return on private investment and the cost of newly stimulated domestic and foreign savings. Most practitioners have chosen to use a discount rate that follows this weighted average opportunity cost of funds concept. This chapter has described a practical framework for the estimation of the economic opportunity cost of capital in a small open economy. The model considers the economic cost of raising funds from the capital market. It takes into account not only the opportunity cost of funds diverted from private domestic investment and private consumption, but also the marginal cost of foreign borrowing. This methodology for illustrative purpose is applied to the case of South Africa. 30 CHAPTER 8: REFERENCES Barreix, A., “Rates of Return, Taxation, and the Economic Cost of Capital in Uruguay”, Ph.D. Dissertation, Harvard University, (August 2003). Blignaut, J. N. and Hassan, R.M., “A natural Resource Accounting Analysis of the Contribution of Mineral Resources to Sustainable Development in South Africa”, South African Journal of Economic and Management Sciences, SS No. 3, (April 2001). Brean, D.J.S., Burgess, D.F., Hirshhorn, R. and Schulman, J., “Treatment of Private and Public Charges for Capital in a Full-Cost Accounting of Transportation”, Report Prepared for Transportation Canada, Government of Canada, (March 2005). Burgess, D.F., “The Social discount Rate for Canada: Theory and Evidence”, Canadian Public Policy, Vol. 7, No. 3, (Summer 1981), pp. 383-394. Burgess, D.F., “Removing Some Dissonance from the Social Discount Rate Debate”, University of Western Ontario, London, Ontario, Canada, (June 2008). Burgess, D.F., “Toward a Reconciliation of Alternative Views on the Social Discount rate”, paper presented at the Conference on “Discount Rates for the Evaluation of Public Private Partnerships”, held at Queen’s University, Kingston, Ontario, Canada, October 3, 2008, (July 2009). Dasgupta, P., Sen, A. and Marglin, S., Guidelines for Project Evaluation, Vienna: United Nations Industrial Development Organization, (1972). Dreze, J.H., “Discount Rates and Public Investment: A Post-Scriptum’. Economics 41, No. 161 (February 1974), pp. 52-61. Edwards, S., “Country Risk, Foreign Borrowing, and the Social Discount Rate in an Open Economy”, Journal of International Money and Finance, Vol. 5, Sup. 1, (March 1986), S79-S96. Feldstein, M., "The Social Time Preference Discount Rate in Cost-Benefit Analysis", Economic Journal Vol. 74, No. 294, (June 1964), pp. 360-379. Harberger, A.C., “On Measuring the Social Opportunity Cost of Public Funds”, in The Discount Rate in Public Investment Evaluation, Report No. 17, Conference Proceedings from the Committee on the Economics of Water Resources 31 CHAPTER 8: Development of the Western Agricultural Economics Research Council, Denver Colorado, (December 1968), pp. 1-24. Harberger, A.C., “Professor Arrow on the Social Discount Rate” in Project Evaluation: Collected Papers, Chicago: the University of Chicago Press, (1972). Harberger, A.C., “Vignettes on the World Capital Market”, American Economic Review, Vol. 70, No. 2, (May 1980), pp. 331-337. Harberger, A.C. and Wisecarver, D.L., “Private and Social Rates of Return to Capital in Uruguay”, Economic Development and Cultural Change, Vol. 25, No. 3, (April 1977), pp. 411-445. Harberger, A.C., “Reflections on Social Project Evaluation”, in Pioneers in Development, Vol. II, edited by G.M. Meier, Washington: The World Bank and Oxford: Oxford University Press, (1987). Harberger, A.C., “New Frontiers in Project Evaluation: A Comment on Devarajan, Squire, and Suthiwart-Narueput”, The World Bank Research Observer, Vol.12, No. 1, (February 1997). Hirshleifer, J., DeHaven, J.C. and Milliman, J.W., Water Supply: Economics,Technology, and Policy, Chicago: University of Chicago Press, (1960). Jenkins, G.P., “The Measurement of Rates of return and Taxation from Private Capital in Canada”, in W.A. Niskanen et al., eds., Benefit-Cost and Policy Analysis, Chicago: Aldine, (1973). Jenkins, G.P., “The Public-sector Discount rate for Canada: Some Further Observations”, Canadian Public Policy, Vol. 17, No. 3, (Summer 1981), pp. 399-407. Jenkins, G. P., “Public Utility Finance and Economic Waste”, Canadian Journal of Economics, Vol. 18, No. 3, (August 1985), pp. 484-498. Kuo, C.Y., Jenkins, G.P., and Mphahlele, M.B., “The Economic Opportunity Cost of Capital in South Africa”, South African Journal of Economics, Vol. 71:3, (September 2003), pp. 525-543. Lind, Robert C., et al., Discounting for Time and Risk in Energy Policy, Washington D.C.: Resources for the Future, Inc., (1982). 32 CHAPTER 8: Little, I.M.D. and J.A. Mirrlees, Project Appraisal and Planning for Developing Countries, London: Heinemann Educational Books Ltd., (1974). Marglin, S., “The Social Rate of Discount and the Optimal Rate of Investment”, Quarterly Journal of Economics, Vol. 77, No. 1, (February 1963), pp. 95-11. Poterba, J.M., “The Rate of Return to Corporate Capital and Factor Shares: New Estimates Using Revised National Income Accounts and Capital”, National Bureau of Economic Research, Inc., (November 1997). Sandmo, A., and Dreze, J.H., “Discount Rates for Public Investment in Closed and Open Economies”, Economica 38, (November 1971), pp. 395-412. Sjaastad, L.A. and Wisecarver, D.L., “The Social Cost of Public Finance”, Journal of Political Economy, Vol. 85, No. 3 (May 1977), pp. 513-547. Squire, L. and van der Tak, H.G., Economic Analysis of Projects, Baltimore: The Johns Hopkins University Press, (1975). United States Environmental Protection Agency, Guidelines for Preparing Economic Analyses, (September 2000). World Bank, Global Development Finance, (2001 and 2006). 33 CHAPTER 8: Appendix 8.1 Return to Domestic Investment in South Africa, 1985-2004 (millions of Rands) Expressed in Current Prices Expressed at 2000 Prices Percentage Year GDP Total Taxes on Value Subsidies GVA in Resource Depre- Return to GDP Real Capital Rate Labor Products Added Tax Agriculture Rents ciation Capital Deflator Return to Stock of Return Income Index Capital (Mid- Year) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) 1985 127,598 69,115 11,791 - 1,536 6,091 6,323 21,003 22,283 18.00 123,801 1,358,877 9.11 1986 149,395 80,969 13,946 - 1,814 6,831 8,994 26,348 22,725 21.07 107,850 1,377,945 7.83 1987 174,647 95,102 16,141 - 2,146 8,994 11,605 29,823 25,713 24.13 106,583 1,383,741 7.70 1988 111,556 20,936 - 2,241 12,269 34,521 35,504 27.79 127,766 1,391,734 9.18 209,613 11,149 1989 134,204 26,505 - 2,375 12,933 40,978 44,023 32.58 135,107 1,407,786 9.60 251,676 12,332 1990 158,557 29,153 - 2,488 13,596 45,990 50,249 37.64 133,494 1,425,970 9.36 289,816 12,184 1991 182,514 31,096 18,792 2,523 12,411 50,251 56,232 43.56 129,088 1,440,425 8.96 331,980 13,825 1992 209,129 33,190 17,506 4,519 11,227 54,227 66,457 49.91 133,156 1,448,246 9.19 372,227 13,056 1993 234,347 41,611 25,449 6,320 10,042 58,575 82,873 56.44 146,833 1,452,144 10.11 426,133 16,284 1994 260,776 48,373 29,288 6,400 11,005 64,500 98,830 61.86 159,775 1,458,980 10.95 482,120 20,252 1995 295,467 53,644 32,768 5,898 12,134 71,827 117,460 68.20 172,239 1,472,298 11.70 548,100 19,317 1996 332,191 58,119 35,903 5,635 13,115 78,817 137,366 73.71 186,353 1,492,361 12.49 617,954 23,720 1997 366,463 63,419 40,096 4,856 14,178 87,188 156,216 79.69 196,034 1,517,125 12.92 685,730 25,140 1998 401,632 74,473 43,677 6,923 15,271 96,615 158,848 85.83 185,067 1,544,460 11.98 742,424 25,434 1999 436,124 80,528 48,330 5,718 16,350 107,966 177,618 91.89 193,288 1,565,853 12.34 813,683 26,179 2000 478,812 87,816 48,377 3,886 17,792 119,237 226,708 100.00 226,708 1,580,321 14.35 922,148 27,451 2001 514,603 96,363 54,455 4,571 19,156 130,848 267,391 107.67 248,350 1,595,909 15.56 1,020,007 32,588 2002 564,357 109,820 61,057 4,664 21,126 149,329 329,119 118.74 277,180 1,612,489 17.19 1,164,945 44,179 33  2003 618,498 120,219 70,150 3,336 22,075 161,635 338,513 124.07 272,833 1,630,963 16.73 1,251,468 42,007 2004 676,231 146,738 80,682 2,671 23,377 172,394 372,402 131.39 283,428 1,656,231 17.11 1,374,476 41,323 Sources: For the period from 1985 to 2000, South African Reserve Bank, South Africa's National Income Accounts 1946-2004, (June 2005). Notes: Column (2) is obtained from the sum of wages and salaries paid by corporations and 35% of net operating surplus generated by unincorporated businesses. Column (9) = (1) - (2) - (4) - 0.95*(1/3)*(6) - {(2)/[(1)-(3)+(5)]}*[(3)-(4)]-(7)-(8). Column (12) is obtained from the total capital stock net of those of general government services. 34 CHAPTER 8: Appendix 8.2 The Cost of Newly Stimulated Domestic Savings, 1985-2004 (millions of Rands) Expressed in Current Prices Expressed Percentage at 2000 Prices Year GDP Total Taxes on GVA in Resource Depre- Income and Income and Wages and Property Value Return to Real Rate of Labor Products Agriculture Rents ciation Wealth Wealth Salaries Income Added Domestic Return to Return to Income Taxes paid Taxes paid Received Received in FIs, Savings Domestic Domestic by by by by Real Savings savings Corporations Household Household Household Estates s s s (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) 1985 127,598 69,115 11,791 6,091 6,323 21,003 7,434 9,038 65,078 16,861 15,849 4,181 23,230 1.71 1986 149,395 80,969 13,946 6,831 8,994 26,348 8,486 10,513 75,444 18,772 17,312 2,096 9,949 0.72 1987 174,647 95,102 16,141 8,994 11,605 29,823 8,736 12,354 88,577 25,107 20,688 2,491 10,326 0.75 1988 111,556 20,936 12,269 34,521 10,194 14,468 103,565 34,228 25,069 6,746 24,276 1.74 209,613 11,149 1989 134,204 26,505 12,933 40,978 11,249 19,723 124,050 42,485 30,265 9,304 28,553 2.03 251,676 12,332 1990 158,557 29,153 13,596 45,990 15,284 23,831 146,240 49,541 36,039 8,338 22,151 1.55 289,816 12,184 1991 182,514 31,096 12,411 50,251 13,547 28,961 169,516 59,380 44,945 19,033 43,694 3.03 331,980 13,825 1992 209,129 33,190 11,227 54,227 10,963 35,050 193,250 73,942 53,265 26,341 52,778 3.64 372,227 13,056 1993 234,347 41,611 10,042 58,575 12,579 37,599 216,368 82,383 62,861 37,739 66,866 4.60 426,133 16,284 1994 260,776 48,373 11,005 64,500 14,565 45,280 240,416 94,052 76,491 46,132 74,580 5.11 482,120 20,252 1995 295,467 53,644 12,134 71,827 14,115 51,623 272,916 110,378 82,162 59,390 87,087 5.92 548,100 19,317 1996 332,191 58,119 13,115 78,817 21,408 59,496 306,225 121,807 94,122 66,332 89,987 6.03 617,954 23,720 1997 366,463 63,419 14,178 87,188 24,134 68,048 338,204 142,844 110,488 74,558 93,562 6.17 685,730 25,140 1998 401,632 74,473 15,271 96,615 29,935 75,422 370,589 155,866 122,227 63,557 74,048 4.79 742,424 25,434 1999 436,124 80,528 16,350 107,966 30,220 84,335 402,375 176,116 140,673 73,362 79,834 5.10 813,683 26,179 2000 478,812 87,816 17,792 119,237 33,248 87,848 440,299 206,496 156,252 109,440 109,440 6.93 922,148 27,451 33 2001 514,603 96,363 19,156 130,848 58,701 89,700 471,816 231,010 177,531 116,150 107,879 6.76 1,020,007 32,588 2002 564,357 109,820 21,126 149,329 68,807 95,801 515,053 271,925 204,590 153,266 129,079 8.00 1,164,945 44,179 2003 618,498 120,219 22,075 161,635 70,356 99,451 567,024 280,899 228,075 155,418 125,263 7.68 1,251,468 42,007 2004 676,231 146,738 23,377 172,394 75,343 108,628 618,215 305,088 247,514 169,534 129,029 7.79 1,374,476 41,323 Sources: For the period from 1985 to 2000, South African Reserve Bank, South Africa's National Income Accounts 1946-2004, (June 2005). Statistics South Africa, Final Supply and Use Tables 1998. Notes: Column (12) = (1) - (2) - (3) - 0.95*(1/3)*(4) - (5) - (6) - (7) - (8)*{(10)/[(9) + (10)]} - (11)*0.5*0.5. Column (14) is obtained by dividing Column (13) by Column (12) of Appendix 8.1. 34