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Lecture Notes ECON 437/837: ECONOMIC COST-BENEFIT ANALYSIS Lecture Four

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Economic Opportunity Cost of Capital

- The economic opportunity cost of capital (EOCK) reflects the real rate of return forgone in the economy when resources are shifted out of the capital market.
- The EOCK or the social discount rate is considered 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 EOCK is also used to determine the optimal scale and timing of a project and make adjustment for different project life.
- The EOCK is the most important parameter and its magnitude is one of the most contentious issues in the cost benefit analysis.

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.
- Very important in making correct choice of technology.

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 forgone due to the stimulation of domestic savings.
- The EOCK can be measured as a weighted average of the rate of return on displaced investment and the rate of time preference for consumption to savers.

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 ():

- Where:
- f1 is the proportion obtained at the expense of postponed investment, and f2 is the proportion of the incremental public 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.

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 ie 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
- IT/ST is the ratio of total private-sector investment to total savings.

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.

Where:

isis the supply elasticity of the ith group of savers, and (Si/ST) is the proportion of total savings supplied by this group;

jI is the demand elasticity for the jth group of investors, and (Ij/IT) is the proportion of the total investment demanded by this group.

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.

- To obtain the rate of time preference for consumption (r), estimate the real net-of-tax rate of return on savings:
- r = – corporation income taxes – property taxes
- – personal income taxes on capital
- – cost of financial intermediation

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 forgone 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.

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. f1, f2, and f3 are the proportions of the public sector funds obtained at the expense of other domestic investment, at the expense of current consumption, and at the cost of additional foreign capital inflow to the economy.
- The cost of foreign borrowing (MCf) is valued at its marginal cost.

The Marginal Economic Cost of Foreign Borrowing

So equation becomes:

NOTE:

where

is the required real net of withholding tax that foreign (international) investors require for investing in country i.

If tw increases, this will cause rf to increase not to fall.

The Marginal Economic Cost of Foreign Borrowing

- The economic cost of foreign borrowing can be measured by:
- Where rf is the real interest rate charged on the foreign loan prevailing in the markets, tw is the withholding tax rate on foreign borrowing, and Фis the share of total stock foreign borrowing whose interest rate is floating to the total stock of foreign capital inflows. With nominal interest rates, MCf can be calculated as:
- Where if is the nominal interest rate and gPf is the GDP deflator in the U.S., if foreign borrowing is denominated in U.S. dollars.

Derivation of EOCK for Country

The weights can be expressed in terms of elasticities of demand and supply:

Where:

sh is the supply elasticity of household savings, sf is the supply elasticity of foreign funds,

St is the total savings available in the economy, of which Sh is the contribution to the total savings by households, and Sf is the total contribution of net foreign capital inflows,

is the elasticity of demand for capital relative to changes in the interest rate.

Economic Return from Domestic Investment

in South Africa

- The return to capital is calculated as a residual by subtracting from GDP depreciation and 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%.
- = 13.0%

Parameters for Estimating Return to Domestic Investment in South Africa (2001 prices)

Calculations of Gross of Tax Return to Domestic Investment for 2004

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%

- 13 percent for is the average rate of returns for the period 1990 – 2004.

Time Preference for Forgone Consumption

- 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 for forgone consumption.
- From our estimate, the rate of time preference (r) for forgone consumption is approximately 0.045.
- r = 4.5%

Parameters for Estimating Return to Domestic Savings in South Africa (2001 prices)

Calculations of Net of Tax Return to the Newly Stimulated Savings for 2004

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%

- 4.5 percent for r is the average rate of return over period 1990 -2004.

Marginal Cost of Foreign Financing

- 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, MCf, is estimated to be about 7.8%.
- MCf = 7.8%

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 households, 65% for businesses, and 15% for foreigners.
- With the assumptions that 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; and the demand elasticity for private sector capital in response to changes in the cost of funds at -1.0.
- Based on 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.

Calculation of EOCK for South Africa

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

EOCK for Canada

- Background

- Treasury Board, Benefit Cost Analysis Guide,1976

- Debates, Burgess vs Jenkins, Canadian Public Policy, 1981

- Treasury Board, Benefit Cost Analysis Guide,1998

- PCO, Social Discount Rates, 2007

- Queen’s University, JDI, 2010

Estimate of the EOCK for Canada

- Gross-of-tax return to domestic investment: 9.0%;
- Cost of newly stimulated domestic savings (time preference for consumption): 4.5%;
- Marginal economic cost of foreign financing: 6.0%;
- Other parameters and assumptions.
- EOCK for Canada: 7 percent real.

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