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8/14/2019 Formulas Final I-sept09
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FormulaeFinal Examination
Financial Accounting and FinancialStatement Analysis
Equity Valuation and Analysis
Corporate Finance
Economics
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Copyright ACIIA
Table of Contents
1. Financial Accounting and Financial Statement Analysis 1
1.1 Generally Accepted Accounting Principles: Assets, Liabilitiesand Shareholders Equities............................................................................1
1.1.1 Assets: Recognition, Valuation and Classification ................................... 1
1.2 Financial Reporting and Financial Statement Analysis .........................1
1.2.1 Earning per Share............................................................................................... 1
1.3 Analytical tools for Assessing Profitability and Risk .............................2
1.3.1 Profitability Analysis.......................................................................................... 2
1.3.2 Risk Analysis ....................................................................................................... 5
1.3.3 Break-Even Analysis.......................................................................................... 6
2. Equity Valuation and Analysis 72.1 Valuation Model of Common Stock .............................................................7
2.1.1 Dividend Discount Model ................................................................................. 7
2.1.2 Free Cash Flow Model ....................................................................................... 8
2.1.3 Measures of Relative Value.............................................................................. 8
3. Corporate Finance 9
3.1 Fundamentals of Corporate Finance ...........................................................9
3.1.1 Discounted Cash Flow ...................................................................................... 9
3.1.2 Capital Budgeting............................................................................................... 9
3.2 Short-Term Finance Decisions....................................................................14
3.2.1 Short-Term Financing...................................................................................... 14
3.2.2 Cash Management............................................................................................ 14
3.3 Capital Structure and Dividend Policy ......................................................16
3.3.1 Leverage and the Value of the Firm ............................................................. 16
4. Economics 18
4.1 Macroeconomics.............................................................................................18
4.1.1 Measuring National Income and Prices ...................................................... 18
4.1.2 Equilibrium in the Real Market ...................................................................... 19
4.1.3 Equilibrium in the Money Market.................................................................. 21
4.1.4 Aggregate Supply and Determination of Price of Goods/Services..... 22
4.2 Macro Dynamics..............................................................................................23
4.2.1 Inflation ............................................................................................................... 23
4.2.2 Economic Growth............................................................................................. 23
4.2.3 Business Cycles ............................................................................................... 24
4.3 International Economy and Foreign Exchange Market ........................24
4.3.1 Open Macro Economics.................................................................................. 244.3.2 Foreign Exchange Rate................................................................................... 27
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4.3.3 Central Bank and Monetary Policy............................................................... 29
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Financial Accounting and Financial Statement Analysis
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1. Financial Accounting and Financial Statement Analysis
1.1 Generally Accepted Accounting Principles: Assets, Liabilities andShareholders Equities
1.1.1 Assets: Recognition, Valuation and Classification
1.1.1.1 Property, Plant, Equipment and Intangible Assets
Depreciation Methods
Straight Line Method
Depreciation per Year = (Original Cost Salvage Value) / Useful Life
Accelerated Method
- Double-Declining-Balance-Depreciation
Depreciation = 2Straight Line Rate Book Value at the Beginning of the Year
where:
straight line rate = 1 / Estimated Useful Life
- Sum-of-the-Years Method (SYD)
Depreciation = (Original Cost Salvage Value) Applicable Fraction
where:
Applicable Fraction = number of years of estimated useful life remaining / SYD,where
2
1)(nnSYD
+=
and n= estimated useful life
1.2 Financial Reporting and Financial Statement Analysis
1.2.1 Earning per Share
1.2.1.1 Calculation of EPS
goutstandinstockcommonofsharesofNumber
ersstockholdcommonthetoavailableEarningsEPS =
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With a change in the number of shares outstanding during the year, the formula ismodified as follows:
goutstandinsharescommonofnumberaverageWeighted
ersstockholdcommonthetoavailableEarningsEPS =
1.2.1.2 Using EPS to Value Firms
- Constant Dividend Growth Model (Gordon-Shapiro)
g)(k
g)(1EPSP
e
00
+=
where:
P0 initial market priceg growth rateke cost of equity payout ratioEPS0 earning per share in t = 0
1.3 Analytical tools for Assessing Profitability and Risk
1.3.1 Profitability Analysis
1.3.1.1 Return on Assets
Annual Return
capitalInvested
profitAnnualturnReAnnual =
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Return on Assets
ROA = return on assets =Assets
(EBIT)taxandinterestsbeforeEarnings
ROA =Sales
EBIT
Assets
Sales= EMR ATR
where:
EMR = economic margin ratio =Sales
EBIT
ATR = asset turnover ratio =Assets
Sales
Return on Total Assets
assetsTotal
EBITROTA =
Return on Operating Assets
ROOA = assetsOperating
OEBIT
Return on Non-Operating Assets
RONOA =assetsOperatingAssets
OEBITEBIT
where:
OEBIT operating earnings before interests and taxROOA return on operating assetsRONOA return on non-operating assets
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Let ROTA be an average return of the two parts:
ROTA = ROOA x1 + RONOA x2
where:
x1 weight of the operating assets (Operating assets/Total assets)x2 weight of the non-operating assets (x2= 1 x1)
1.3.1.2 ROCE
Return on Equity (ROE) or Return on Common Equity (ROCE)
ROE =Equity
ProfitNet=
Equity
Interest)-t)(EBIT-(1
which can be written:
ROEbT)t1(
Equtiy
Debt)iROA(ROA)t1(
Equity
Debti
Equity
DebtEquityROA)t1(
Equity
DebtiAssetsROA)t1(
Equity
InterestEBIT)t1(ROE
=
+=
+=
=
=
ROEcan be decomposed as follows:
ROE =
taxbeforeEarning
profitNet
EBIT
taxbeforeEarning
Sales
EBIT
Assets
Sales
Equity
Assets
where:
i average interest rate on total debts =Interest expenses
Total debts
EBIT earnings before interests and taxt corporate tax rate
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Return on Equity before Tax
ROEbT =Equity
EBT= ROA + (ROA i)
Equity
Debt
where:
i average interest rate on total debts =Interest expenses
Total debts
EBT earnings before income tax
1.3.2 Risk Analysis
1.3.2.1 Short-Term Liquidity Risk
Current Ratio
sliabilitieCurrent
assetsCurrent
Quick Ratio
sliabilitieCurrent
Inventory-assetsCurrent or
sliabilitieCurrentsReceivable+ssecuritieMarketable+Cash
Working Capital Activity Ratio
CapitalWorkingAverage
revenueSales
1.3.2.2 Long-Term Solvency Risk
Debt Ratio
Equity
Debt
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Interest Coverage Ratio
ExpensesInterest
EBIT
1.3.3 Break-Even Analysis
Break-even volume =m
F
where:
s unit sales pricev unit variable costsF fixed cost during a periods - v = m unit contribution margin
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Equity Valuation and Analysis
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2. Equity Valuation and Analysis
2.1 Valuation Model of Common Stock
2.1.1 Dividend Discount Model
2.1.1.1 Zero Growth Model
Ek
DivP =0
where
P0 price of shareDiv dividend (assumed constant)kE cost of equity capital
2.1.1.2 Constant Growth Model
Constant Dividend Growth Model
gk
DivP
E
1
0
=
where
P0
price of share
Div1 )1(0 gDiv + = expected dividend in period 1
kE cost of equity capitalg growth rate of dividend (assumed constant)
Gordon Shapiro Model
rk
EPSP
E
=
)1(
10
where
P0 price of shareEPS1 earnings per share in t= 1
payout ratiokE cost of equity capital
1 earnings retention rater return on equity (ROE)
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2.1.2 Free Cash Flow Model
Net Income (Net Profit)
Net Sales
Cost of goods sold
Selling, general + administrative expenses
Depreciation
= EBIT = Earnings before interest and taxes
Interest
= EBT = Earnings before taxes
Taxes
= Net Income
Free Cash Flows (FCF)
Earnings from operations before interest and taxes (EBIT)
Taxes (calculated as EBIT tax rate)
+ non cash relevant expenses (depreciation, provisions for doubtful debt,etc.)
non cash relevant revenues (adjustments for currency changes, etc.)
= Gross cash flow
Increase in net working capital
+ Reduction in net working capital
Capital expenditure (buildings, equipment, )
+ Liquidation of fixed assets
= Free cash flow from operations
2.1.3 Measures of Relative Value
2.1.3.1 Price Earnings Ratio
E
PEPSP =0
where
P0 price of the shareEPS earnings per share
P/E price-earnings ratio
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3. Corporate Finance
3.1 Fundamentals of Corporate Finance
3.1.1 Discounted Cash Flow
The present value of an annuity is given by
+=
+=
=n
1tt
)k1(
11
k
CF
)k1(
CFnluePresent va
where
CF constant cash flowk discount rate, assumed to be constant over timen number of cash flows
The future value of an annuity is given by
+=
k
1)k1(CF
n
valueFuture
where
CF constant cash flow
k discount rate, assumed to be constant over timen number of cash flows
3.1.2 Capital Budgeting
3.1.2.1 Investment Decision Criteria
Net Present Value
NPV = ( )( )= +
+N
1tt
t
t
0WACC1
FCFEI
where
I0 initial investment
)FCF(E t expected free cash flows in period t
tWACC weighted average cost of capital in period t
N number of cash flowsNPV Net Present Value
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3.1.2.2 Cost of Capital
Cost of Equity Capital
CAPM
)EfMfE RRRk +=
where
kE cost of equity capitalRf risk-free returnRM RF expected return on the market portfolio risk-free return,
expected Risk premium
E beta equity = systematic or market risk of equity
The beta equity (E) can be calculated using the following formula:
E)t1(D
E
E)t1(D
)t1(D
c
E
c
c
DA+
++
=
where
A beta assetD beta debtE beta equity
tc marginal corporate tax rate for the firm being valuedD market value of interest-bearing debtE market value of equity
If we assume that the debt is riskless ( D = 0) the beta of the firms asset can be
written as:
E)t1(D
E
c
EA+
=
In this case, the beta equity ( E ) can be written as:
( )
+=E
Dt11 cAE
with
beta asset = UnleveredA =
beta equity = LeveredE =
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Modigliani-Miller
E
DT))(1k(kkk duuE +=
wherekE cost of equity (required return on equity)ku equity rate of return were the company 100% equitykd cost of debt (required return on debt)T statutory marginal tax rateD debt (market value)E equity (market value)
Zero Growth Model
0
EP
Divk =
where
kE cost of equity capitalDiv dividend (assumed constant)P0 price of share
Constant Growth Model
gP
Divk
0
1
E +=
where
kE cost of equity capitalg growth rate of dividend
Div1 )1(0 gDiv + = expected dividend in period 1
P0 market price of share
Earnings-Price Ratio Approach
P
EPSk 1E =
where
kE cost of equity capitalEPS1 expected earnings per share in t=1P current market price of share
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Gordon Shapiro Model
ROEP
EPSkE +
= )1(
0
1
where
kE cost of equity capitalEPS1 earnings per share in t=1
payout ratioP0 price of shareROE return on equity
Cost of Debt Capital
Cost of Debt Capital before Taxes
- CAPM
DfMfD RRRk +=
where
kD cost of debt capital (expected return on debt)Rf risk-free returnRM Rf expected excess return on the market portfolio
D beta debt = systematic or market risk of debt
- Yield to Maturity
=
=N
iiiD YTMwk
1
where
kD cost of debt capitalwi weight of debt iYTMi yield to maturity of debt i
Cost of Debt Capital after Taxes
)t1(kk cDDA =
where
kDA cost of debt capital after taxeskD cost of debt capital before taxestc marginal corporate tax rate
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Weighted Average Cost of Capital (WACC)
WACC= ( )V
Ek
V
Dt1k EcD +
wherekD pre (corporate) tax cost of debtkE cost of equity
ct marginal corporate tax rate for the entity being valued
D market value of interest-bearing debtE market value of equityV =E + D
If the firm has preferred stock, WACCbecomes:
WACC= ( )VPk
VEk
VDtk PEcD ++1
where
kP after tax cost of preferred stock
P market value of preferred stockV = E + D + P(here)
Corporate Taxes, Interest Subsidy and Cost of Capital
Average Tax Rate
t = average tax rate =Taxes
Earnings before taxes
Average Interest Rate
i= average interest rate =Debt
paymentsInterest
Value of Tax Shield
Value of tax shield= cD
cD tDk
tDk=
where
D market value of debtkD cost of debttc marginal average corporate tax rate
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3.2 Short-Term Finance Decisions
3.2.1 Short-Term Financing
3.2.1.1 Current Asset Financing
Net Working Capital
Net Working Capital = Current assets Current liabilities
where
Current assets= cash + receivable + inventories
3.2.2 Cash Management
Inventory Turnover
Cost of goods sold
Inventory
Accounts Receivable Turnover
Sales
Accounts receivable
Accounts Payable Turnover
Material purchases
Accounts payable
Inventory Period
365 (or 360) days
Inventory turnover
Accounts Receivable Period
365 (or 360) days
Accounts receivable turnover
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Accounts Payable Period
365 (or 360) days
Accounts payable turnover
Operating Cycle
Inventory period + Accounts receivable period
Cash Conversion Cycle
Operating Cycle - Accounts payable period
Average Collection Period
Sales
365ReceivableAccounts
Optimal Cash Balance (Baumol Model)
I
2FC
whereF fixed cost incurred when selling securities to raise cashC annual cash disbursementI annual interest earned on the marketable securities portfolio
Target Cash Balance (Miller-Orr model)
LI4
F3ZBalanceCashTarget
3
1
daily
2
+
==
where
F fixed cost of buying and selling securities
2 variance of the net daily cash flowsL lower control limit, determined by the firmIdaily opportunity cost of holding cash
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3.3 Capital Structure and Dividend Policy
3.3.1 Leverage and the Value of the Firm
Free Cash Flow Approach
V =( )
( )= +
+N
tt
t
t
WACC
FCFI
10
1
E
where
V value of the firm
)( tFCFE expected free cash flows in period t
tWACC weighted average cost of capital in period t
With the continuing value (terminal value) of the firm at time Tequal to:
Continuing value at timegWACC
FCFT 1T
= +
where
T point in time where the explicit free cash flow forecasting horizonends
FCFT+1 level of expected free cash flow in the first year after the explicitforecast period; then assumed to grow at rate g
WACC weighted average cost of capital (assumed constant)g expected growth rate of free cash flows after T (assumed
constant)
Firm Value
EDV +=
whereV value of the firmD debt (market values)E equity (market values)
MM Proposition I (assuming no taxes)
A
ULk
EBITE =DVVV +===
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where
VL value of levered firmVU value of unlevered firmD debt (market values)E equity (market values)EBIT earning before interest and taxes (assumed permanent)kA constant overall cost of capital (return on assets)
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4. Economics
4.1 Macroeconomics
4.1.1 Measuring National Income and Prices
GNP
( ) NIRAMXGICY ++++=
where:
Y GNPC private consumptionI investmentG government expenditureX exports
M importsNIRA net income received from abroad
MX +NIRA current account balance
National Saving and Current Account Balance
IBDS
ISSCA
P
GP
=
+=
where
CA current account balanceP
S private savingG
S government savingGP
SS + national saving (S)BD budget deficitI investment
Price Index: GDP (implicit price) Deflator and Consumer Price Index (CPI)
100qp
qp100
GDPReal
GDPNominaldeflatorGDP
i it
*
i
it itit
t
tt
==
100qp
qpCPI
i
*
i
*
i
i
*
iit
t
=
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where
itp price of final good or service iin year t
itq quantity of final good or service iin year t*
ip price of final good or service iin the base year*
iq quantity of final good or service iin the representative basket
Inflation Rate
-1t
-1ttt
P
PP =
where
tP (index) price level at time t
1tP (index) price level at time t-1
t inflation rate over period t-1 to t
Ex-post Fisher Parity
ttt ir
where
tr real interest rate for the period (t-1, t)
ti nominal interest rate for the period (t-1, t)
t inflation rate for the period (t-1, t)
4.1.2 Equilibrium in the Real Market
Consumption Function
C = c0+ c1(Y-T)
where:
C desired consumption
0c constant intercept term
c1 marginal propensity to consume (MPC)Y-T disposable income
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Investment Function
YdrddY)I(r, 210 +=
where:
I demand for investmentd0 autonomous investmentd1, d2 positive parametersr real interest rateY output
Budget Surplus
( )NINTTRGTBS ++=
where:
BS budget surplusT taxationTR transfer paymentsNINT net interest payments on public debtG government expenditure
Government-Purchases Multiplier
)()
rd-Tc-Gdcd(c-1
1Y
110021
+++
=
where:
Y output
0c constant intercept term (from the consumption function)
c1 marginal propensity to consumed0 autonomous investmentd1, d2 positive parameters (from the investment function)G government expenditureT taxation
r real interest rate
)21 d(c-1
1
+government-purchases multiplier
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Equilibrium Condition for the Market for Goods and Services (Closedeconomy)
I + G = SP+T
where:
I investmentG government expenditureSP private sector savingsT taxation
IS Relation (Closed economy)
Y = Z= C(Y-T) + I(r,Y) + G
where:
Y outputZ demand for goods and servicesC(.) private consumption function
YT disposable incomeI(.) investment functionr realinterest rateG government expenditure
4.1.3 Equilibrium in the Money Market
Demand for Money
,),( 210 ibYbbiYLP
MD+==
where:
MD nominal money demandP general price levelL(.) demand functionY real income (output)i nominal interest rate
0b constant parameter
21 ,bb positive parameters
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Equilibrium Relationship in the Monetary Market: LM Curve
MS
P
MD
PL Y i= ( , ),
where:
MS nominal money supply (exogenous)MD nominal money demandP general price levelL(.) demand functionY real income (output)i nominal interest rate
Quantity Theory of Money (Absolute Form)
M V P Y
PM V
Y
=
=
,
,
where:
M quantity of moneyV velocity, a measure of turnover of money stock in a yearP general price levelY real income (output)
4.1.4 Aggregate Supply and Determination of Price of Goods/Services
Aggregate Supply Relation (short-run)
P =E(P)(1+)F(1Y
L,z),
where:
P price levelE(P) expected price level
markup variableF(.) functionY outputL labor forcez catchall variable
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4.2 Macro Dynamics
4.2.1 Inflation
Expectations-Augmented Phillips Curve
,*tte
tt uu +=
where:
t inflation ratee
t expected inflation rate for time t
constant parameter constant positive parameter
*
tt uu cyclical unemployment (or Keynesian unemployment) at time t
4.2.2 Economic Growth
Aggregate Production Function
( ),,LKFAY =
where:
Y aggregate outputA total factor productivity
F(.) aggregate production functionL aggregate labour supplyK aggregate capital stock
Growth Accounting Equation
Y
Y
A
A
K
K
L
LK L= + + ,
where:
YY growth of the output
A
Agrowth in productivity
K
Kgrowth of the capital stock
L
Lgrowth of the labour supply
( )( )K
LKF
LKF
KK
=
,
, elasticity of output with respect to capital
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( )( )L
LKF
LKF
LL
=
,
, elasticity of output with respect to labour
4.2.3 Business Cycles
Random Productivity Shocks
( ) ,, ttttt ALKFY =
where:
Yt aggregate output at time tF(.) aggregate function productionKt, Lt aggregate capital and labour supply at time t
t random productivity shock at time t
tt
A total factor productivity at time t
4.3 International Economy and Foreign Exchange Market
4.3.1 Open Macro Economics
4.3.1.1 International Balance of Payment and Capital Flows
Balance of Payments Accounting
,RAKACABP +=
where:
BP balance of paymentsCA current accountKA capital accountRA official reserve account
Government-Purchases Multiplier in an Open Economy
GmSd(c-1
1Y
1real21
+
=)
where:
Y variation of the outputm1 positive constant parameter (marginal propensity to import)c1 marginal propensity to consumed2 positive parameters (from the investment function)Sreal real exchange rateG variation of the government expenditure
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IS Relation in an Open Economy
Y C I G S M X real= + + + ,
where:
Y outputC private consumptionI investmentG government expenditureSreal real exchange rateX exportsM imports in foreign currency
Equilibrium Condition for the Goods and Services Market in an OpenEconomy
in terms of GDP:
NX S T G I = + ( ) ,
in terms of GNP:CA S T G I = + ( ) ,
where:
NX net exportsCA current account balanceS private saving
TG public savingI investment
Real Exchange Rate
SS P
Preal
n
F
=
,
where:
Sn nominal spot exchange rate (in American terms)FP foreign general price level in foreign currency
P domestic general price level in domestic currency
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Trade Balance and Depreciation: the Marshall-Lerner Condition
.0>real
real
SS
MM
XX
where:
X
Xproportional change in exports
M
Mproportional change in imports
S
S
real
real
proportional change in the real exchange rate
Equilibrium Model of an Open Economy, the Mundell-Fleming Model
)ii1
)E(S,YNX(Y,GY)I(r,T)C(YY
F
nF
++++= ,
MS
P
MD
PL Y i= = ( , ).
where:
Y outputC(.) consumptionT taxation
I(.) investment functioni,r (domestic) nominal and real interest rateG government expenditureNX(.) net exports functionYF output in the rest of the world
iF foreign nominal interest rate
E(Sn) expected nominal spot exchange rate (in American terms)MS nominalmoney supplyMD nominalmoney demandP general price level
L(.) demand function
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Aggregate Demand in an Open Economy (for the Mundell-Fleming Modelwith Fixed Exchange Rate)
)P
PS,YNX(Y,G))E(I(iT)C(YAD
Fn
F
+++=
where:
C(.) consumption functionY domestic output (income)T taxationI(.) investment functioni domestic nominal interest rate
E() expected inflationG government expenditureNX(.) net exports functionYF foreign output (income)
Sn nominal fixed exchange rateP, PF domestic and foreign prices level
4.3.2 Foreign Exchange Rate
Absolute Purchasing Power Parity
,F
t
t
tP
PS =
where:
tS nominal spot exchange rate at tF
tP foreign general price level in foreign currency at t
tP domestic general price level in domestic currency at t
Relative Purchasing Power Parity
( )
( ),1
1
1
S
SSs
F
ttF
t
t
1t
1tt
t
+
+=
=
where:
ts relative spot exchange rate over period t-1 to t
St nominal spot exchange rate at tF
t foreign inflation rate over period t-1 to t
t domestic inflation rate over period t-1 to t
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Covered Interest Rate Parity (CIP)
,ii1i1
i11
S
FF
ttF
t
t
1t
t,1t +
+=
where:
11
,1
t
tt
S
Frelative forward foreign exchange rate premium
ttF ,1 forward foreign exchange rate over period t-1 to t
St1 nominal spot exchange rate at t-1F
ti foreign nominal interest rate over period t-1 to t
ti domestic nominal interest rate over period t-1 to t
Uncovered Interest Rate Parity (UIP)
( ),ii1
i1
i11
S
SE FttF
t
t
1t
t +
+=
where:
( )1
1
t
t
SSE
expected relative depreciation of the domestic currency
F
ti foreign nominal interest rate over period t-1 to t
ti domestic nominal interest rate over period t-1 to t
Monetary Approach
s = (p pF) = (ms msF) (y yF) + (li liF)
where:s logarithm of the spot exchange rate,p, pF the logarithm of the domestic and foreign price levelsms,msF logarithm of the domestic and foreign money suppliesy, yF logarithm of the domestic and foreign real incomesli, liF logarithm of the domestic and foreign interest rates
, are income and interest rate elasticities.
Portfolio Balance Approach
The nominal portfolio wealths of the home and foreign private sectors:
w= MS + B + Sn F,
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Economics
w*= MS* + B*1
Sn+ F*,
where B + B*= B , F + F*= F, and where:
w, w* the nominal portfolio wealths of the home and foreign private sectorsMS, MS*home and foreign money supply, which is assumed to consist only of
monetary base
B , F respectively denote the privately-held stocks of interest bearingclaims on the home and foreign governments, referred to as bonds orsecurities
B*, F* foreign residents privately-held stocks of interest bearing claims onthe home and foreign governments
B, F home residents privately-held stocks of interest bearing claims on thehome and foreign governments
Sn nominal exchange rate
The Risk Premium
t = it *ti ( )
1
11
t
ttt
SSSE
,
where:
i, i* the domestic and foreign interest ratesEt-1(.) expectation at time t-1
represents a premium for bearing a composite of exchange rate riskand the difference in credit risks
St nominal exchange rate at time t
4.3.3 Central Bank and Monetary Policy
Money Multiplier
M1 = mM0, with m= ++
cc1 ,
where:
M1 money stock M1
m money multiplierM0 monetary basec the ratio of the demand for currency to the demand for sight deposit
the ratio of reserves to sight deposits