1. Updated:08 March,2007 Lecture Notes ECON 622: ECONOMIC COST- BENEFIT ANALYSIS Lecture Three

2. ECONOMIC OPPORTUNITY COST OF CAPITAL The economic opportunity cost of capital or the social discount rate is defined as the minimum economic rate of return that either a private or public sector investment must earn if it is to contribute to the growth of the economy. The economic cost of capital reflects the real rate of return forgone in the economy when resources are shifted out of the capital market.

3. ECONOMIC OPPORTUNITY COST OF CAPITAL Economic net benefits and costs and economic externalities of the investment over the life of the project should be discounted by the economic cost of capital. If the NPV of these economic benefits and costs is equal to or greater than zero, then the project is feasible from an economic point of view. If the NPV is less than zero, the project should be rejected on the grounds that the investment resources of the country could be put to better use elsewhere.

4. ECONOMIC OPPORTUNITY COST OF CAPITAL IN A CLOSED ECONOMY In a closed economy in terms of foreign borrowing or lending, there are two principal sources of diverted funds which include: (1) those invested in other investment activities either displaced or postponed; and (2) those spent on private consumption foregone due to the stimulation of domestic savings. The economic cost of capital (EOCK) can be measured as a weighted average of the rate of return on displaced investment, and the rate of time preference to savers.

5. Determination of Market Interest Rates

6. The Economic Opportunity Cost of Capital The economic opportunity cost of capital (ie) is a weighted average of the rate of time preference for consumption (r) and the gross of tax rate of return on private investment (  ):

7. Where, f 1 is the proportion obtained at the expense of postponed investment, and f 2 is the proportion of the incremental public or private sector funds obtained at the expense of current consumption.  is the foregone gross-of-tax return to the domestic investment, and the rate of time preference (r) is the cost of postponed consumption resulting from additional savings to households.

8. When the weights are expressed in terms of elasticities of demand and supply of funds with respect to changes in interest rates, the economic opportunity cost of capital i e can then be defined: Where  s > 0 is the elasticity of supply of private-sector savings,  I < 0 is the elasticity of demand for private-sector investment with respect to changes in the rate of interest, and I T /S T is the ratio of total private-sector investment to total savings.

9. Where:  i s is the elasticity of supply of the i th group of savers, and (S i /S T ) is the proportion of total savings supplied by this group;  j I is the elasticity of demand for the j th group of investors, and (I j /I T ) is the proportion of the total investment demanded by this group. The above supply and demand elasticities can be considered as an aggregate elasticity that may be decomposed by the types of savers and by the groups of investors.

10. To obtain the rate of return on private investment (  ), estimate the gross-of-tax return to the domestic investment from the national accounts or firm-level data. i =  - corporation income taxes – property taxes To obtain the rate of time preference for consumption (r), estimate the real net-of-tax rate of return on savings: r = i – personal income taxes on capital – cost of intermediation If consumers are borrowing through consumer loans: i=market interest rate (0.08) r B =rate on consumer loan M=cost of intermediation(0.11) r B = i+M=0.08+0.11=0.19

11. ECONOMIC OPPORTUNITY COST OF CAPITAL IN AN OPEN ECONOMY There are three principal sources of diverted funds which include: (1) those invested in other investment activities either displaced or postponed; (2) those spent on private consumption foregone due to the stimulation of domestic savings; and (3) the attraction of additional foreign capital inflows. The economic cost of capital (EOCK) can be measured as a weighted average of the rate of return on displaced investment, the rate of time preference to savers, and the cost of additional foreign capital inflows.

12. The weighted average of these three costs can be expressed as: Where the weights are equal to the proportion of funds diverted or sourced from each sector. f 1, f 2, and f 3 are the proportions of the public sector funds obtained at the expense of current consumption, at the expense of other domestic investment, and at the cost of additional foreign capital inflow to the economy. The cost of foreign borrowing (MC f ) is valued at its marginal cost.

13. The Marginal Economic Cost of Foreign Borrowing

14. So equation becomes; NOTE: whereis the required real net of withholding tax that foreign (international) investors require for investing in country i. If t w increases this will cause i f to increase not to fall.

15. Economic Cost of Foreign Borrowing The economic cost of foreign borrowing can be measured by: Where r f is the real interest rate charged on the foreign loan prevailing in the markets, t w is the withholding tax rate on foreign borrowing, and k is the share of total stock foreign borrowing whose interest rate is floating to the total stock of foreign capital inflows. With the adjustment for inflation, it can be written below: Where i f is the nominal interest rate and gP f is the GDP deflator in the U.S., if foreign borrowing is denominated in U.S. dollars.

16. Derivation of EOCK for Country The weights can be expressed in terms of elasticities of demand and supply: Where:  s h is the supply elasticity of household savings,  s f is the supply elasticity of foreign funds,  is the elasticity of demand for capital relative to changes in the interest rate, S t is the total savings available in the economy, of which S h is the contribution to the total savings by households, and S f is the total contribution of net foreign capital inflows.

17. Economic Return from Domestic Investment in South Africa The return to capital is calculated as a residual by subtracting from GDP the contributions to the value added by labor, land, resource rents, and the associated sales and excise taxes. The amount of return to capital is then divided by the total capital stock to arrive at its rate of return. Since 1990, the real rate of return to capital (  ) has been about 13%.  = 0.13

18. Calculations Have Been Undertaken to Determine Gross of Tax Return to Domestic Investment for 2004 in South Africa: Parameters for Estimating Return to Domestic Investment in South Africa GDP1,374,476Resource Rents23,377 Total Labor Income676,231Depreciation172,394 Taxes on Products146,738Return to Capital372,402 Value Added Tax80,682GDP Deflator for 2004 (base GDP Def. 2000 =100)131.39 Subsidies2,671Real Return to Capital283,428 GVA in Agriculture41,323Capital Stock (Mid-Year)1,656,231 Percentage Rate of Return (2004)17.11 Return to Capital = GDP – Total Labor Income – VAT – (0.95*1/3*GVA in Agriculture) – ((Total Labor Income / (GDP – Taxes on Products + Subsidies)) * ((Taxes on Products – VAT) – Resource Rents – Depreciation) Return to Capital = 1,374,476 – 676,231 – 80,682 – (0.95 * 1/3 * 41,323) – ((676,231 / (1,374,476 – 146,738 + 2,671) )* ((146,738 – 80,682) – 23,377 – 172,394) = 372,402 Real Return to Capital = Return to Capital * (GDP Def2000 / GDP Def2004) = 372,402 * (100 / 131.39) = 283,428 Percentage Rate of Return = Real Return to Capital / Capital Stock = 283, 428 / 1,656,231 = 17.11 Average real rate of return on investment in South Africa (  = 13 percent) has been obtained by calculating arithmetic average of percentage rate of returns for the period 1990 – 2004.

19. Time Preference for Forgone Consumption for South Africa All corporation income tax, property taxes and personal income taxes are deducted from the income accruing to capital. In addition the value added of financial institutions arising from financial intermediation is also deducted to obtain the net return to savers. This is the estimate of rate of time preference in forgone consumption. From our estimate, the rate of time preference (r) for forgone consumption is approximately 0.045. r = 4.5%

20. Calculations Have Been Undertaken to Determine Net of Tax Return to the Newly Stimulated Domestic Savings for 2004 in South Africa: Parameters for Estimating Return to Domestic Savings in South Africa Return to Domestic Savings = GDP – Total Labor Income – Taxes on Products – (0.95*1/3*GVA in Agriculture) – Resource Rents – Depreciations – Income & Wealth Taxes paid by Corp. – (Income & Wealth Taxes paid by Housholds * ((Property Income Received by Housholds / (Wages & Salaries Received by Housholds + Property Income Received by Housholds))) – (Value Added in FIs, Real Estates*0.5*0.5) Return to Domestic Savings = 1,374,476 – 676,231 – 146,738 – (0.95*1/3*41,323) – 23,377 – 172,394 – 75,343 – (108,628 * ((305,088 / (618,215 + 305,088))) – 247,514 * 0.5 *0.5 = 169,534 Real Return to Domestic Savings = Return to Domestic savings * (GDP Def2000 / GDP Def2004) = 169,534 * (100 / 131.39) = 129,029 Percentage Rate of Return to Domestic Savings = Real Return to Domestic Savings / Capital Stock = 129,029 / 1,656,231 = 7.79 On average (1990 -2004) the cost of newly stimulated savings (r) for South Africa is about 4.50 percent GDP1,374,476Property Income Received by Housholds305,088 Total Labor Income676,231Value Added in Fin.Institutions, Real Estates247,514 Taxes on Products146,738Resource Rents23,377 Value Added Tax80,682Depreciation172,394 Subsidies2,671Return to Domestic Savings169,534 GVA in Agriculture41,323GDP Deflator for 2004 (base GDP Def. 2000 =100)131.39 Income & Wealth Taxes (Corp.)75,343Real Return to Domestic Savings129,029 Income & Wealth Taxes (Households)108,628Capital Stock (Mid-Year)1,656,231 Wages & Salaries Received by Housholds618,215Percentage Rate of Return to Dom. Sav. (2004)7.79

21. Marginal Cost of Foreign Financing for South Africa The nominal-borrowing rate by South Africa in the U.S. market is about 8.5%. With a 2.5% U.S. GDP deflator and no withholding tax, the real borrowing rate should be 5.85%. The share of total foreign borrowing with floating interest rate (Ф) has been estimated at approximately 50%. The supply elasticity of foreign funds (in terms of the stock of foreign investment) is assumed at 1.5. The marginal cost of foreign financing, MC f, is estimated to be about 7.8%. MC f = 7.8%

22. Calculations Have Been Undertaken to Determine the Cost of Foreign Borrowing for South Africa:

23. Weights of the Three Diverted Funds 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 approximately 20% for households65% for businesses and 15% for foreigners. The supply elasticity of household saving at 0.5, the supply elasticity of business saving at zero, the supply elasticity of foreign funds at 1.5. The demand elasticity for private sector capital in response to changes in the cost of funds at -1.0. According to values described above, the proportions of funds used to finance the investment project are then estimated at 9.5% from household savings, 21.3% from foreign capital, and 69.2% from displaced or postponed domestic investment.

24. Calculations of Weights

25. Calculation of EOCK for South Africa EOCK= 0.692 (0.13) + 0.095 (0.045) + 0.213 (0.078)=0.1108 The estimate of for the EOCK would therefore be a real rate of 11%.