formulas final i-sept09

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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Financial Accounting and Financial Statement Analysis

Copyright ACIIA

4.3.3 Central Bank and Monetary Policy............................................................... 29


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Copyright ACIIA page 1

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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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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Corporate Finance


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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Corporate Finance


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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Corporate Finance


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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Corporate Finance


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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Corporate Finance


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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Corporate Finance


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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Corporate Finance


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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Corporate Finance


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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Corporate Finance


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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Economics


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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Economics


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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Economics


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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Economics


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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Economics


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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Economics


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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Economics


( )( )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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Economics


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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Economics


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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Economics


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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Economics


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

formulas final i-sept09

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