Updated:08 March,2007

Lecture Notes

ECON 622: ECONOMIC COST-BENEFIT ANALYSIS

Lecture Three

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.

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.

ECONOMIC OPPORTUNITY COST OF CAPITALIN 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.

A

B

C

D

E

FG

im

r

S(i) gross rate of return received by savers before personal income taxes

S(r) savings function net of personal income taxes

I() return on investment gross of all taxes

I(im) return on investment net of corporate and property taxes

Q0 Quantity of Investment and Savings

Interest Rate and Rate of Return

%

Determination of Market Interest Rates

The Economic Opportunity Cost of Capital

A

D

NM

i

r

Q0Quantity of Investment and Saving

%

Interest Rate and Rate of Return

r’

i’

G

F

D’

QsQI

C’

R

J H’

H

LTK

C

’

m

m

S(i)

S(r)

I()

I(im) I(im) + B

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 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.

rffie 21

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:

Wheres > 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.

)(

)(

TTIs

TTIse SI

SIri

)(1

Ti

m

i

si

s SS

n

jTj

Ij

I II1

)(

Where:

is is the elasticity of supply of the ith group of savers, and (Si/ST)

is the proportion of total savings supplied by this group; j

I is the elasticity of demand for the jth group of investors, and

(Ij/IT) 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.

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 intermediationIf consumers are borrowing through consumer loans: i=market interest rate (0.08)rB=rate on consumer loan

M=cost of intermediation(0.11)rB= i+M=0.08+0.11=0.19

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.

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 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 (MCf) is valued at its marginal

cost.

fMCfrffEOCK 321

Sif

MCC

i1f

Q0 Q1

D0f

D0f + B

B

A

%

L1MC0

i0f

ED

L2MC’

Quantity of Foreign Borrowing

The Marginal Economic Cost of Foreign Borrowingsfw

sffwf QtQitiMC )1()()1(

The Marginal Economic Cost of Foreign Borrowing

Iiwf iti )1(

))/1(*1)(1( sfwff tiMC

sfw

sffwff QtQitiMC )1()()1(

So equation becomes;

NOTE:

where Ifi is the required real net of withholding tax that foreign

(international) investors require for investing in country i. If tw increases this will cause if to increase not to fall.

)/(*)/()1()1( fsf

sfffwwff rQQiittiMC

Iii

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 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 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.

s

ff

fwf

fgP

gPtiMC

1*1*

1

1*

s

fwff tiMC

1*1*1*

fMCfrffEOCK *** 321 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, sf is the supply

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

tttf

sfth

sh

ttftfsfth

sh

SISSSS

SIMCSSrSSEOCK

***

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

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

GDP 1,374,476 Resource Rents 23,377

Total Labor Income 676,231 Depreciation 172,394

Taxes on Products 146,738 Return to Capital 372,402

Value Added Tax 80,682 GDP Deflator for 2004 (base GDP Def.2000=100) 131.39

Subsidies 2,671 Real Return to Capital 283,428

GVA in Agriculture 41,323 Capital 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.

Time Preference for Forgone Consumptionfor 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%

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

GDP 1,374,476 Property Income Received by Housholds 305,088

Total Labor Income 676,231 Value Added in Fin.Institutions, Real Estates 247,514

Taxes on Products 146,738 Resource Rents 23,377

Value Added Tax 80,682 Depreciation 172,394

Subsidies 2,671 Return to Domestic Savings 169,534

GVA in Agriculture 41,323 GDP Deflator for 2004 (base GDP Def.2000=100) 131.39

Income & Wealth Taxes (Corp.) 75,343 Real Return to Domestic Savings 129,029

Income & Wealth Taxes (Households) 108,628 Capital Stock (Mid-Year) 1,656,231

Wages & Salaries Received by Housholds 618,215 Percentage Rate of Return to Dom. Sav. (2004) 7.79

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, MCf, is estimated to be

about 7.8%.

MCf = 7.8%

)1(

]1

1[])1([

f

fs

fwf

fgp

gpti

CM

80.7)025.01(

]5.1

150.01[]025.0)01(085.0[

fCM

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

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.

Calculations of Weights

692.0)73.01(15.05.120.05.0

)73.01(

)()()(

)(

1

t

t

t

fsf

t

dsh

t

t

S

I

S

S

S

S

S

I

f

095.0)73.01(15.05.120.05.0

20.05.0

)()()(

)(

2

t

t

t

fsf

t

dsh

t

dsh

S

I

S

S

S

S

S

S

f

213.0)73.01(15.05.120.05.0

15.05.1

)()()(

)(

3

t

t

t

fsf

t

dsh

t

fsf

S

I

S

S

S

S

S

S

f

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%.

fMCfrffEOCK 321