Lecture Notes

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Lecture Notes FINA623 ADVANCED CAPITAL
BUDETING Lecture Seven Economic Opportunity
Cost of Capital Cost of Foreign Exchange
(EOCFX) and Shadow Price of Non-Tradable Outlays
(SPNTO)
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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.

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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.

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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.

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Determination of Market Interest Rates
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The Economic Opportunity Cost of Capital
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• 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.

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• 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 gt 0 is the elasticity of supply of
  private-sector savings,
• ?I lt 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.

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• 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 ?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.
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• 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 financial intermediation

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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.

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• 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.

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The Marginal Economic Cost of Foreign Borrowing
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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 if to increase not to fall.
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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 ? 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.

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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, ?
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.
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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

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• Calculations of Gross of Tax Return to Domestic
  Investment for 2004

Parameters for Estimating Return to Domestic
Investment in South Africa
Return to Capital GDP Total Labor Income
VAT (0.951/3GVA 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

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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
Return to Domestic Savings GDP Total Labor
Income Taxes on Products (0.951/3GVA 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
Estates0.50.5)


Return to Domestic Savings 1,374,476 676,231
146,738 (0.951/341,323) 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 (?) 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
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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.

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Calculations of Weights
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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.

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Cost of Foreign Exchange (EOCFX) and Shadow Price
of Non-Tradable Outlays (SPNTO)
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Definition of EOCFX and SPNTO

• These variables (EOCFX and SPNTO) are estimated
  to measure the value of the distortions created
  when funds are sourced in the capital market and
  used to purchase either tradable goods, or
  non-traded goods.
• These actions are repeated many times for each
  project and are identical for such actions across
  projects.
• It is efficient to estimate these variables once
  for a country and use the same values repeatedly
  as needed.
• To make the estimates we do not include the
  specific distortions on the particular tradable
  or non-tradable good. These effects are included
  when we estimate the economic cost of the
  specific item.

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Estimation of Economic Exchange Rate and Premium
of Foreign Exchange under two situations

• Partial Model. Project already has raised funds,
  which it now will use to purchase foreign
  exchange to purchase tradable goods. (Premium on
  Foreign Exchange)
• Project raises funds in capital markets and
  spends funds on
• Tradable goods (Premium of Foreign Exchange)
• Non-tradable goods (Premium of non-traded
  outlays)

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Economic Cost of Foreign Exchange

• When the numeraire is the domestic currency at
  the domestic price level, the foreign exchange
  effect of the change in the demand (or supply) of
  tradable commodities must be converted into
  domestic currency.
• Conversion should take place at the shadow
  exchange rate, or economic price of foreign
  exchange (Ee).
• If there are no distortions on the demand or
  supply of tradable goods, and if the exchange
  rate is determined by market forces, then the
  economic price of foreign exchange is equal to
  the market exchange rate (Em).

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Economic Cost of Foreign Exchange (Contd)

• 1. Partial Model. Only distortions that affect
  international trade are considered. No
  consideration of how financing of Foreign
  Exchange affects estimation.
• Trade Distortions
• Trade distortions will change the demand and/or
  supply of foreign exchange such that the market
  exchange rate no longer measures the economic
  price of foreign exchange. For example,
• Tariffs - lower the market demand for foreign
  exchange and cause Em to be less than Ee
• Export Taxes - Decrease the market supply of
  foreign exchange and cause the Em to be greater
  than Ee
• Export Subsidies - Increase the market supply of
  foreign exchange and cause the Em to be less than
  Ee

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• All goods are divided into three types
• 1. Importable
• 2. Exportable
• 3. Non-traded goods
• Importable and Exportable goods are referred to
  as TRADABLE GOODS.
• Prices of TRADABLE GOODS are determined by
  international markets and expressed in units of a
  foreign exchange currency.
• Domestic prices of such goods are determined by
  multiplying the internationally given import
  price PIw or the export price PEw by the market
  exchange rate EM, i.e. PDI EMPIw, PDEEMPEw

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• As the world prices of these tradable goods are
  fixed, their domestic prices relative to
  Non-traded goods and the quantity domestically
  demanded or domestically supplied of these goods
  will depend on the real exchange rate.
• Because world prices are fixed, their quantities
  can be expressed in units of foreign exchange.
• Importable and Exportable goods can be aggregated
  as the market for tradable goods.
• This market is also the market for Foreign
  Exchange.
• This market will determine the countrys real
  exchange rate.

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Demand for Foreign Exchange An equivalent way to
see how the exchange rate is determined as to
draw the demand for imports and supply of exports

• Importable Market
  Demand for
  Imports
• P
  SImportable EM
• EM0
  EM0
• EM1
  DImportable E1
  
  DM
• 
  
  
  
  
  
  
• QIS Import
  QID Q Importable(QFx)
  QFXD
• The demand for imports Demand for importable
  goods - Supply of importable goods

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• Supply of Foreign Exchange
• Exportable Market
  Imports and Exports
• P
  SExportable
  
• 
  
  
  SX
• EM0
• EM1
  
  E1
• 
  
  
  
  DM
• 
  DExportable
• QED Export
  QES Q Exportable(QFx)
  QFXD/S

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Market for Foreign Exchange

• Importable Exportable
  Market for Foreign Exchange
• EM
  
  
• 
  
• 
  
• 
  
  
  
• QSI QDI
  
• Equilibrium in tradable goods market also means
  that there is equilibrium in foreign exchange
  market.
• QDI QDE QDT
  where QDT demand for tradable
• 
  
  
• QSI QSE QST
  QST supply of tradable
• In equilibrium QDT QST
• Hence QDIQDE QSIQSE QDI-QSI QSE-QDE
  ImportsExports

SI
DI
SX
SE
DE
E0
DX
QSE
QDE
QFX0
Export
Import

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Determination of Market Exchange RateNo
Distortions
Exchange Rate of units of domestic currency
per unit of Foreign Exchange
S0fex
EeEm
D0fex
Q0
Quantity of foreign exchange US
EeEm
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Determination of Exchange Rate with Distortions

• Case One Funds Available to purchase foreign
  exchange
• Import Tariff Tm

Exchange Rate
S0
E0m(1Tm)
D0
Dt project
Dt (net of tax)
Quantity of Foreign exchange Traded
d1
s1
Q0
Q
Q
Ee Ws Em Wd Em(1Tm)
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Determination of Exchange Rate with Distortions
Exchange Rate

• Case Two
• Export Subsidy kx

S0
S0export subsidy
E1m(1kx)
E0m(1kx)
D0 Project
D0
Quantity of Foreign exchange Traded
s1
d1
Q0
Q
Q
Ee WsEm(1kx) WdEm
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Determination of Exchange Rate with Distortions
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Determination of Exchange Rate with Distortions
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Determination of Exchange Rate with Distortions
and Capital Flows
Exchange Rate

• Case Five
• Market determined Exchange Rate
• Balance of Payments Deficit Sustained through
  Capital Inflows
• Import Tariff Tm
• Export Tax tx

St
S
A
B
J
L
K
N
D
H
M
G
DP
F
Dt
Quantity of Foreign Exchange Traded
s1
s0
d1
d0
Q
Q
Q
Q
Ee WsEm(1-tx) WdEm(1Tm)
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Conclusion No change in basic estimation
procedure.
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Economic Price of Foreign Exchange

• Trade Distortions
• An increase in demand for imported inputs will
  cause a (slight) depreciation in the domestic
  currency, which in turn will cause a reduction in
  imports and an increase in exports.
• The economic value of the foreign exchange
  required by a project is determined by the
  economic values of the forgone imports and
  increased exports.
• Example The main trade distortions are tariffs
  on imported goods and taxes on exports. The
  economic price per unit of foreign exchange is
• Ee WsEm(1-tx) WdEm(1 Tm)
• Where Ws The proportion of an extra unit of
  foreign exchange that is met by an increased
  supply of exports
• Wd The proportion of an extra unit of foreign
  exchange that is met by a reduction in other
  imports

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Example for Indonesia (1991)

• The Economic Cost of Foreign Exchange is
  calculated as follows
• Where
• Ee Economic exchange rate
• Em Market exchange rate 1,950.3 Rp/1.0
• Ws Weight on supply 0.33
• Wd Weight on demand 0.67
• t xadj Weighted average rate of tax on
  price-responsive exports
• 0.00157
• Tadj Weighted average rate of tariff on
  price-responsive imports
• 0.0919
• Therefore,
• Ee 0.331,950.3(1-0.00157)
  0.671,950.3(10.0919) 2,069.38
• Foreign Exchange Premium (FEP) Ee/Em - 1
  0.061
• Note The market exchange rate is obtained from
  International Financial Statistics, October 1992.
  Data for oil and non-oil imports and exports,
  and for imports, are from the Central Bureau of
  Statistics. Data for government imports are from
  the Quarterly Report of Balance of Payment, April
  1992, Central Bank of Indonesia. Data for import
  duty and export tax are obtained from Ministry
  of Finance, Nota Keuangan 1992/93.

Ee WsEm(1 - t xadj) WdEm(1 Tadj)
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Calculation of Foreign Exchange Premium
If the elasticity of foreign exchange supply (?s)
is equal to the elasticity of foreign exchange
demand (?d) ?s - ?d Then, a simple way
to calculate the foreign exchange premium is
Tariff Revenues Export Subsidies - Export
Taxes Value of Imports Value of Exports
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Calculation of Foreign Exchange Premium
If the elasticity of foreign exchange supply (?s)
is equal to the elasticity of foreign exchange
demand (?d) ?s - ?d Then, a simple way to
calculate the foreign exchange premium is
Tariff Revenues Export Subsidies - Export
Taxes FEP -------------------------------
---------------------------------------
Value of Imports Value of Exports Data for
Uganda (2002) Tariff Revenues 385,700 million
Shillings Export Subsidies 0 Export Taxes
0 Value of Imports 1,998,152 million
Shillings Value of Exports 795,511 million
Shillings 385,700 0 0
385,700 FEP for Uganda -------------------------
-- ------------------- 13.8 1,998,152
795,511 2,793,663 Source Government Finance
Statistics, IMF, 2004, p. 456
International Financial Statistics, IMF, 2004,
p. 644
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Application of Foreign Exchange Premium

• To value tradable goods at economic prices, the
  CIF prices of importable goods, or the FOB prices
  of exportable goods should be converted into
  domestic prices using the economic exchange rate
  (Ee).

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• Alternatively, this valuation at economic prices
  can be achieved by adding a foreign exchange
  premium (Ee/Em) - 1 per unit of foreign
  exchange demanded (or supplied) by a project.
• Economic Analysis
• In the case of Imports In the case of Exports

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A Case of South Africa

• A General Equilibrium Analysis
• Take into account
• - project funds sourced from the capital
  market (62.5 from displaced investment, 11.5
  from household saving and 26.0 from foreign
  savings).
• - all distortions in import tariff, subsidy,
  value-added tax, and other indirect taxes.

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