Transcript ECONOMIC OPPORTUNITY COST OF CAPITAL (a)

Updated:08 March,2007
Lecture Notes
ECON 622: ECONOMIC COSTBENEFIT 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 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.
Determination of Market Interest Rates
Interest Rate and
Rate of Return
%
A
S(i) gross rate of return
received by savers before
personal income taxes

B
S(r) savings function net of
personal income taxes
I() return on investment
gross of all taxes
C
im
r
D
E
F
G
I(im) return on investment net
of corporate and property taxes
Q0
Quantity of Investment and Savings
The Economic Opportunity Cost of Capital
Interest Rate and
Rate of Return
% A
G
’
F
R

S(i)
C’
S(r)
C
i’m
J
H’
D’
H
K
im
D
r’
r
T
L
I()
I(im) + B
I(im)
N
M
QI
Q0 Qs
Quantity of Investment and Saving
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 ():
ie  f1   f 2  r
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.
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:
r   s    I  ( IT ST )
ie 
 s   I  ( IT ST )
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.
m
   ( S i ST )
s
i 1
s
i
n
   ( I j I T )
I
j 1
I
j
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;
jI 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.
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)
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:
EOCK  f1  f 2r  f3MC f
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.
MC
The Marginal Economic Cost of Foreign Borrowing
s
s
 i f  (1  t w )  ( i f  Q f )  (1  t w )    Q f
%
C
MC
L2MC’
L1MC0
i1f
Sif
B
D
E
i0f
D0f + B
A
D0f
Q0
Q1
Quantity of Foreign Borrowing
The Marginal Economic Cost of Foreign Borrowing
MC f  i f  (1  t w )  ( i f  Q sf )  (1  t w )    Q sf

MC f  i f  (1  t w )  (1  t w )    i f  (i f / Q sf ) * (Q sf / r f )

So equation becomes;
MC f  i f  (1  t w )(1   * (1 /  sf ))
NOTE:
where
i f (1  t w )  iiI
i If
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 iiI to fall.
Economic Cost of Foreign Borrowing
The economic cost of foreign borrowing can be measured by:


MC f  i f * 1  t w  * 1   *  1 s
 
f






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:
 i f * 1  t w   gP f  


1


MC f  
*
1


*


s
  
1  gP f

 
f 


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
EOCK  f1 *   f 2 * r  f3 * MC f
The weights can be expressed in terms of elasticities of demand
and supply:
EOCK 
 hs S h St  * r   sf S f St * MC f   I t St  * 
 hs S h St    sf S f St    I t St 
Where:
sh 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.
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 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%
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
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
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
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%
Calculations Have Been Undertaken to Determine the Cost of Foreign
Borrowing for South Africa:
[i f  (1  t w )  gp f ]  [1   
MC f 
1
 sf
(1  gp f )
[0.085  (1  0)  0.025 ]  [1  0.50 
MC f 
]
1
1 .5
(1  0.025 )
]
 7.80
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
It
)
St
 ( 1 0.73)
f1 

 0.692
S
0
.
5

0
.
20

1
.
5

0
.
15

(

1

0
.
73
)
S
I
f
 hs ( d )   sf (
)  ( t )
St
St
St
 (
Sd
)
St
0.5  0.20
f2 

 0.095
S
0.5  0.20  1.5  0.15  (1 0.73)
S
I
f
 hs ( d )   sf ( )   ( t )
St
St
St
 hs (
 sf (
Sf
)
St
1.5  0.15
f3 

 0.213
S
0
.
5

0
.
20

1
.
5

0
.
15

(

1

0
.
73
)
S
I
f
 hs ( d )   sf (
)  ( t )
St
St
St
Calculation of EOCK for South Africa
EOCK  f1  f 2 r  f 3 MC f
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%.