Transcript ECONOMIC OPPORTUNITY COST OF CAPITAL (a)

Lecture Notes
ECON 437/837: ECONOMIC COSTBENEFIT ANALYSIS
Lecture Four
1
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.
2
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.
3
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.
4
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
5
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
6
•
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
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.
7
•
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.
8
•
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
   ( Si ST )
s
i 1
s
i
n
   ( I j IT )
I
j 1
I
j
Where:
is is 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.
9
•
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
10
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.
11
•
The weighted average of these three costs can be expressed as:
EOCK  f1  f 2 r  f3MCf
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.
12
The Marginal Economic Cost of Foreign Borrowing
MC  rf  (1  tw )  (rf  Qsf )  (1  tw )   Qf
%
C
MC
L2MC’
L1MC0
i1f
Sif
B
D
E
i0f
D0f + B
A
D0f
Q0
Q1
Quantity of Foreign Borrowing
13
The Marginal Economic Cost of Foreign Borrowing

MC f  rf  (1 tw )  (1 tw )   rf  (rf / Qsf ) * (Qsf / rf )

So equation becomes:
MC f  rf  (1 tw )[1  * (1/  sf )]
NOTE:
where
rf (1  tw )  ri I
ri I
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 ri I to fall.
14
The Marginal Economic Cost of Foreign Borrowing
• The economic cost of foreign borrowing can be measured by:



MC f  r 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 Ф is 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:
 i f * 1  t w   gP f
MC f  
1  gP f

 

 * 1   *  1 s
 
 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.
15
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:
sh Sh St * r  sf Sf St * MCf  I t St * 
EOCK 
sh Sh St   sf Sf St   I t St 
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.
16
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%
17
Calculations of Gross of Tax Return to Domestic Investment for 2004
Parameters for Estimating Return to Domestic Investment in South Africa (2001 prices)
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
Subsidies
GVA in Agriculture
2,671
41,323
GDP Deflator for 2004 (base GDP Def.2000=100)
Real Return to Capital
Capital Stock (Mid-Year)
Percentage Rate of Return (2004)
131.39
283,428
1,656,231
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%
• 13 percent for  is the average rate of returns for the period 1990 – 2004.
18
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%
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Calculations of Net of Tax Return to the Newly Stimulated Savings for 2004
Parameters for Estimating Return to Domestic Savings in South Africa (2001 prices)
GDP
1,374,476
Property Income Received by Housholds
305,088
247,514
Total Labor Income
676,231
Value Added in Fin.Institutions, Real Estates
Taxes on Products
146,738
Resource Rents
Value Added Tax
80,682
Subsidies
2,671
23,377
Depreciation
172,394
Return to Domestic Savings
169,534
GVA in Agriculture
41,323
GDP Deflator for 2004 (base GDP Def.2000=100)
Income & Wealth Taxes (Corp.)
75,343
Real Return to Domestic Savings
Income & Wealth Taxes (Households)
108,628
Capital Stock (Mid-Year)
Wages & Salaries Received by Housholds
618,215
Percentage Rate of Return to Dom. Sav. (2004)
131.39
129,029
1,656,231
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%
• 4.5 percent for r is the average rate of return over period 1990 -2004.
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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%
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Calculations of the Cost of Foreign Borrowing
[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  0.025 )
1
]
1.5
 7.80%
22
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.
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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
24
Calculation of EOCK for South Africa
EOCK  f1  f 2 r  f 3MC f
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%.
25
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
26
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.
27