1 FINA623 ADVANCED CAPITAL BUDETING Lecture Nine Economic Opportunity Cost of Capital.
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1
FINA623
ADVANCED CAPITAL BUDETING
Lecture Nine
Economic Opportunity Cost of Capital
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 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.
5
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
6
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
7
• 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.
rffie 21
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 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.
)(
)(
TTIs
TTIse SI
SIri
9
)(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.
10
• To obtain the rate of return on private investment (i), 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 financial intermediation
11
Economic Opportunity Cost of CapitalIn 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. 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.
f321 MCfrffEOCK
13
Sif
MCC
i1f
Q0 Q1
D0f
D0f + B
B
A
%
L1MC0
i0f
ED
L2MC’
Quantity of Foreign Borrowing
The Marginal Economic Cost of Foreign Borrowing
Q)t1()Qi()t1(iMC wsffwf
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The Marginal Economic Cost of Foreign Borrowing
Iiwf iti )1(
))/1(*1)(1( sfwff tiMC
Q)t1()Qi()t1(iMC wsffwff
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 rQQrittiMC
Iii
15
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 Ф 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*
16
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
*SIMC*SSr*SSEOCK
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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%.
= 13.0%
18
Calculations of Gross of Tax Return to Domestic Investment for 2004
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
• 13 percent for is the average rate of returns for the period 1990 – 2004.
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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 in
forgone consumption.
• From our estimate, the rate of time preference (r) for forgone
consumption is approximately 0.045.
r = 4.5%
20
Calculations of Net of Tax Return to the Newly Stimulated Savings for 2004
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) = 129,029Percentage 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.
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
21
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%
22
)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 of the Cost of Foreign Borrowing
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 households, 65% 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
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
25
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%.
fMCfrffEOCK 321
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
Estimate of the EOCK for Canada
• Gross-of-tax return to domestic investment: 11 to 12%;
• Cost of newly stimulated domestic savings: 3.5 to 4.0%;
• Marginal economic cost of foreign financing: 6%;
• Other parameters and assumptions.
• EOCK for Canada: 8 percent real.
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