Formulas Final I-sept09
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Formulae Final Examination
Financial Accounting and Financial Statement Analysis Equity Valuation and Analysis Corporate Finance Economics
Table of Contents
1.
Financial Accounting and Financial Statement Analysis
1
1.1 Generally Accepted Accounting Principles: Assets, Liabilities and 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 1.3.2 1.3.3
2.
Profitability Analysis.......................................................................................... 2 Risk Analysis ....................................................................................................... 5 Break-Even Analysis.......................................................................................... 6
Equity Valuation and Analysis
7
2.1 Valuation Model of Common Stock .............................................................7 2.1.1 2.1.2 2.1.3
3.
Dividend Discount Model ................................................................................. 7 Free Cash Flow Model....................................................................................... 8 Measures of Relative Value.............................................................................. 8
Corporate Finance
9
3.1 Fundamentals of Corporate Finance ...........................................................9 3.1.1 3.1.2
Discounted Cash Flow ...................................................................................... 9 Capital Budgeting............................................................................................... 9
3.2 Short-Term Finance Decisions....................................................................14 3.2.1 3.2.2
Short-Term Financing...................................................................................... 14 Cash Management............................................................................................ 14
3.3 Capital Structure and Dividend Policy ......................................................16 3.3.1
4.
Leverage and the Value of the Firm............................................................. 16
Economics
18
4.1 Macroeconomics.............................................................................................18 4.1.1 4.1.2 4.1.3 4.1.4
Measuring National Income and Prices...................................................... 18 Equilibrium in the Real Market...................................................................... 19 Equilibrium in the Money Market.................................................................. 21 Aggregate Supply and Determination of Price of Goods/Services ..... 22
4.2 Macro Dynamics..............................................................................................23 4.2.1 4.2.2 4.2.3
Inflation ............................................................................................................... 23 Economic Growth............................................................................................. 23 Business Cycles ............................................................................................... 24
4.3 International Economy and Foreign Exchange Market ........................24 4.3.1 4.3.2
Open Macro Economics.................................................................................. 24 Foreign Exchange Rate................................................................................... 27
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Financial Accounting and Financial Statement Analysis
4.3.3
Central Bank and Monetary Policy............................................................... 29
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Financial Accounting and Financial Statement Analysis
1.
Financial Accounting and Financial Statement Analysis
1.1 Generally Accepted Accounting Principles: Assets, Liabilities and Shareholders’ 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 = 2·Straight 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
SYD =
n ⋅ (n + 1) 2
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
EPS =
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Earnings available to the common stockholders Number of shares of common stock outstanding
page 1
Financial Accounting and Financial Statement Analysis
With a change in the number of shares outstanding during the year, the formula is modified as follows:
EPS =
Earnings available to the common stockholders Weighted average number of common shares outstanding
1.2.1.2 Using EPS to Value Firms - Constant Dividend Growth Model (Gordon-Shapiro)
P0 =
π ⋅ EPS 0 ⋅ (1 + g) (k e − g)
where: P0 g ke π EPS0
initial market price growth rate cost of equity payout ratio 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 Annual Re turn =
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Annual profit Invested capital
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Financial Accounting and Financial Statement Analysis
Return on Assets
Earnings before interests and tax (EBIT) Assets
ROA = return on assets =
ROA =
EBIT Sales · = EMR · ATR Sales Assets
where: EMR = economic margin ratio = ATR = asset turnover ratio =
EBIT Sales
Sales Assets
Return on Total Assets
ROTA =
EBIT Total assets
Return on Operating Assets ROOA =
OEBIT Operating assets
Return on Non-Operating Assets RONOA =
EBIT − OEBIT Assets − Operating assets
where: OEBIT ROOA RONOA
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operating earnings before interests and tax return on operating assets return on non-operating assets
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Financial Accounting and Financial Statement Analysis
Let ROTA be an average return of the two parts:
ROTA = ROOA · x1 + RONOA · x2 where: x1 x2 1.3.1.2
weight of the operating assets (Operating assets/Total assets) weight of the non-operating assets (x2 = 1 – x1) ROCE
Return on Equity (ROE) or Return on Common Equity (ROCE) ROE =
Net Profit (1 - t)(EBIT - Interest) = Equity Equity
which can be written: EBIT − Interest ROE = ( 1 − t ) ⋅ Equity ROA ⋅ Assets − i ⋅ Debt = (1 − t )⋅ Equity Equity + Debt Debt = ( 1 − t ) ⋅ ROA ⋅ −i⋅ Equity Equity Debt = ( 1 − t ) ⋅ ROA + ( ROA − i ) ⋅ Equtiy = ( 1 − t ) ⋅ ROEbT ROE can be decomposed as follows: ROE =
Net profit Earning before tax EBIT Sales Assets · · · · Earning before tax EBIT Sales Assets Equity
where: i
average interest rate on total debts =
EBIT t
earnings before interests and tax corporate tax rate
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Interest expenses Total debts
Financial Accounting and Financial Statement Analysis
Return on Equity before Tax ROEbT =
EBT Debt = ROA + (ROA – i) · Equity Equity
where: i
average interest rate on total debts =
EBT
earnings before income tax
Interest expenses Total debts
1.3.2 Risk Analysis 1.3.2.1
Short-Term Liquidity Risk
Current Ratio
Current assets Current liabilities
Quick Ratio
Current assets - Inventory Current liabilities
or
Cash + Marketable securities + Receivables Current liabilities
Working Capital Activity Ratio Sales revenue Average Working Capital
1.3.2.2
Long-Term Solvency Risk
Debt Ratio Debt Equity
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Financial Accounting and Financial Statement Analysis
Interest Coverage Ratio EBIT Interest Expenses
1.3.3 Break-Even Analysis Break-even volume = where: s v F s-v=m
unit sales price unit variable costs fixed cost during a period unit contribution margin
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F m
Equity Valuation and Analysis
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
P0 =
Div kE
where
P0 Div kE
2.1.1.2
price of share dividend (assumed constant) cost of equity capital
Constant Growth Model
Constant Dividend Growth Model P0 =
Div1 kE − g
where P0 Div1 kE g
price of share Div0 ⋅ (1 + g ) = expected dividend in period 1 cost of equity capital growth rate of dividend (assumed constant)
Gordon Shapiro Model P0 =
EPS1 ⋅ π k E − (1 − π ) ⋅ r
where P0 EPS1
π
kE 1–π r
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price of share earnings per share in t = 1 payout ratio cost of equity capital earnings retention rate return on equity (ROE)
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Equity Valuation and Analysis
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
P0 = EPS ⋅ where P0 EPS P/E
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price of the share earnings per share price-earnings ratio
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P E
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
CF CF = t k t =1 ( 1 + k )
Present value = ∑
1 ⋅ 1 − n (1+ k )
where CF k n
constant cash flow discount rate, assumed to be constant over time number of cash flows
The future value of an annuity is given by ( 1 + k )n − 1 Future value = CF ⋅ k
where CF k n
constant cash flow discount rate, assumed to be constant over time number of cash flows
3.1.2 Capital Budgeting 3.1.2.1
Investment Decision Criteria
Net Present Value N
NPV = − I 0 + ∑ t =1
E (FCFt ) (1 + WACCt ) t
where I0 initial investment E( FCFt ) expected free cash flows in period t WACCt weighted average cost of capital in period t N number of cash flows NPV Net Present Value
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Corporate Finance
3.1.2.2
Cost of Capital
Cost of Equity Capital CAPM
k E = R f + (RM − R f ) ⋅ β E where kE Rf RM – RF
βE
cost of equity capital risk-free return expected return on the market portfolio – risk-free return, expected Risk premium beta equity = systematic or market risk of equity
The beta equity (βE) can be calculated using the following formula:
βA = βD
D( 1 − t c ) E + βE D( 1 − t c ) + E D( 1 − t c ) + E
where
βA βD βE tc D E
beta asset beta debt beta equity marginal corporate tax rate for the firm being valued market value of interest-bearing debt market value of equity
If we assume that the debt is riskless ( β D = 0) the beta of the firm’s asset can be written as:
βA = βE
E D( 1 − t c ) + E
In this case, the beta equity ( β E ) can be written as:
β E = β A 1 + (1 − t c ) ⋅ with beta asset = β A = β Unlevered beta equity = β E = β Levered
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D E
Corporate Finance
Modigliani-Miller
k E = k u + (k u − k d )(1 − T) ⋅
D E
where kE ku kd T D E
cost of equity (required return on equity) equity rate of return were the company 100% equity cost of debt (required return on debt) statutory marginal tax rate debt (market value) equity (market value)
Zero Growth Model
kE =
Div P0
where
kE Div P0
cost of equity capital dividend (assumed constant) price of share
Constant Growth Model kE =
Div1 +g P0
where
kE g Div1 P0
cost of equity capital growth rate of dividend Div0 ⋅ (1 + g ) = expected dividend in period 1 market price of share
Earnings-Price Ratio Approach
kE =
EPS1 P
where kE EPS1 P
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cost of equity capital expected earnings per share in t=1 current market price of share
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Corporate Finance
Gordon Shapiro Model kE =
EPS1 ⋅ π + (1 − π ) ⋅ ROE P0
where kE EPS1
π
P0 ROE
cost of equity capital earnings per share in t=1 payout ratio price of share return on equity
Cost of Debt Capital Cost of Debt Capital before Taxes - CAPM
(
)
k D = R f + RM − R f ⋅ β D
where kD Rf RM – Rf
βD
cost of debt capital (expected return on debt) risk-free return expected excess return on the market portfolio beta debt = systematic or market risk of debt
- Yield to Maturity N
k D = ∑ wi ⋅ YTM i i =1
where kD wi YTMi
cost of debt capital weight of debt i yield to maturity of debt i
Cost of Debt Capital after Taxes k DA = k D ⋅ ( 1 − t c )
where kDA kD tc
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cost of debt capital after taxes cost of debt capital before taxes marginal corporate tax rate
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Corporate Finance
Weighted Average Cost of Capital (WACC) WACC = k D (1 − t c )
D E + kE V V
where kD kE tc D E V
pre (corporate) tax cost of debt cost of equity marginal corporate tax rate for the entity being valued market value of interest-bearing debt market value of equity =E + D
If the firm has preferred stock, WACC becomes: WACC = k D (1 − t c )
D E P + kE + kP V V V
where kP P V
after tax cost of preferred stock market value of preferred stock = E + D + P (here)
Corporate Taxes, Interest Subsidy and Cost of Capital Average Tax Rate Taxes t = average tax rate = Earnings before taxes Average Interest Rate i = average interest rate =
Interest payments Debt
Value of Tax Shield Value of tax shield =
k D ⋅ D ⋅ tc = D ⋅ tc kD
where D kD tc
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market value of debt cost of debt 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
Accounts Receivable ⋅ 365 Sales
Optimal Cash Balance (Baumol Model) 2FC I
where F C I
fixed cost incurred when selling securities to raise cash annual cash disbursement annual interest earned on the marketable securities portfolio
Target Cash Balance (Miller-Orr model)
3F σ Target Cash Balance = Z = 4 I daily
2
1 3
+L
where F
σ
2
L Idaily
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fixed cost of buying and selling securities variance of the net daily cash flows lower control limit, determined by the firm 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 N
V = − I0 + ∑
E(FCFt )
t =1(1 + WACC t )
t
where V value of the firm E( FCFt ) expected free cash flows in period t WACCt weighted average cost of capital in period t With the continuing value (terminal value) of the firm at time T equal to: Continuing value at time T =
FCFT +1 WACC − g
where T FCFT+1 WACC g
point in time where the explicit free cash flow forecasting horizon ends level of expected free cash flow in the first year after the explicit forecast period; then assumed to grow at rate g weighted average cost of capital (assumed constant) expected growth rate of free cash flows after T (assumed constant)
Firm Value V = D+E
where V D E
value of the firm debt (market values) equity (market values)
MM Proposition I (assuming no taxes)
V = VL = VU = D + E =
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EBIT kA
Corporate Finance
where VL VU D E EBIT kA
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value of levered firm value of unlevered firm debt (market values) equity (market values) earning before interest and taxes (assumed permanent) 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 Y = C + I + G + ( X − M ) + NIRA
where:
Y GNP C private consumption I investment G government expenditure X exports M imports NIRA net income received from abroad X − M + NIRA current account balance National Saving and Current Account Balance CA = S P + S G − I = S P − BD − I
where CA SP SG SP + SG BD I
current account balance private saving government saving national saving (S) budget deficit investment
Price Index: GDP (implicit price) Deflator and Consumer Price Index (CPI)
GDP deflatort =
CPI t
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∑p = ∑p
Nominal GDPt ⋅ 100 = Real GDPt
i
it
⋅ q*i
i
* i
⋅ qi*
⋅ 100
page 18
∑ p ∑p it
it
⋅ qit
i
* i
⋅ qit
⋅ 100
Economics
where p it
price of final good or service i in year t
qit
quantity of final good or service i in year t
pi*
price of final good or service i in the base year
qi*
quantity of final good or service i in the representative basket
Inflation Rate
πt =
Pt − Pt -1 Pt -1
where Pt −1
(index) price level at time t (index) price level at time t-1
πt
inflation rate over period t-1 to t
Pt
Ex-post Fisher Parity rt ≈ it − π t
where rt
real interest rate for the period (t-1, t)
it
nominal interest rate for the period (t-1, t)
πt
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 c0 c1 Y-T
desired consumption constant intercept term marginal propensity to consume (MPC) disposable income
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Economics
Investment Function I(r,Y) = d 0 − d1 ⋅ r + d 2 ⋅ Y where: I d0 d1, d2 r Y
demand for investment autonomous investment positive parameters real interest rate output
Budget Surplus BS = T − (G + TR + NINT )
where: BS T TR NINT G
budget surplus taxation transfer payments net interest payments on public debt government expenditure
Government-Purchases Multiplier Y =
1 ⋅ (c 0 + d 0 + G - c1 ⋅ T - d 1 ⋅ r ) 1 - (c1 + d 2 )
where: Y c0 c1 d0 d1, d2 G T r 1 1 - (c1 + d 2 )
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output constant intercept term (from the consumption function) marginal propensity to consume autonomous investment positive parameters (from the investment function) government expenditure taxation real interest rate government-purchases multiplier
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Economics
Equilibrium Condition for the Market for Goods and Services (Closed economy) I + G = SP +T
where: investment government expenditure private sector savings taxation
I G SP T
IS Relation (Closed economy) Y = Z= C(Y-T) + I(r,Y) + G
where: Y Z C(.) Y −T I(.) r G
output demand for goods and services private consumption function disposable income investment function real interest rate government expenditure
4.1.3 Equilibrium in the Money Market Demand for Money
MD = L(Y , i ) = b0 + b1 ⋅ Y − b2 ⋅ i, P where:
MD P L(.) Y i b0 b1 ,b2
nominal money demand general price level demand function real income (output) nominal interest rate constant parameter positive parameters
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Economics
Equilibrium Relationship in the Monetary Market: LM Curve
MS MD = ≡ L(Y , i ), P P where: MS MD P L(.) Y i
nominal money supply (exogenous) nominal money demand general price level demand function real income (output) nominal interest rate
Quantity Theory of Money (Absolute Form) M ⋅V = P ⋅ Y ,
⇒P=
M ⋅V , Y
where:
M V P Y
quantity of money velocity, a measure of turnover of money stock in a year general price level real income (output)
4.1.4 Aggregate Supply and Determination of Price of Goods/Services Aggregate Supply Relation (short-run) P = E(P)⋅(1+µ)⋅F( 1 −
where: P E(P)
µ
F(.) Y L z
price level expected price level markup variable function output labor force catchall variable
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Y ,z), L
Economics
4.2 Macro Dynamics 4.2.1 Inflation Expectations-Augmented Phillips Curve
π t = π te + α − β (u t − u t* ), where:
πt
inflation rate
π α β
expected inflation rate for time t constant parameter constant positive parameter cyclical unemployment (or “Keynesian” unemployment) at time t
e t
u t − u t*
4.2.2 Economic Growth Aggregate Production Function Y = A ⋅ F (K , L ),
where:
Y A F(.) L K
aggregate output total factor productivity aggregate production function aggregate labour supply aggregate capital stock
Growth Accounting Equation
∆Y ∆A ∆K ∆L = + ξK ⋅ + ξL ⋅ , Y A K L where:
∆Y Y ∆A A ∆K K ∆L L
ξK =
growth of the output growth in productivity growth of the capital stock growth of the labour supply K ∂F (K , L ) ⋅ F (K , L ) ∂K
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elasticity of output with respect to capital
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Economics
ξL =
L ∂F (K , L ) ⋅ F (K , L ) ∂L
elasticity of output with respect to labour
4.2.3 Business Cycles Random Productivity Shocks Yt = F (K t , Lt ) ⋅ At ε t ,
where: Yt F(.) Kt , Lt
εt
At ε t
aggregate output at time t aggregate function production aggregate capital and labour supply at time t random productivity shock at time t 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 BP = CA + KA − ∆RA,
where:
BP CA KA ∆RA
balance of payments current account capital account official reserve account
Government-Purchases Multiplier in an Open Economy ∆Y =
1 ⋅ ∆G 1 - (c1 + d 2 − S real ⋅ m1 )
where:
∆Y m1 c1 d2 Sreal ∆G
variation of the output positive constant parameter (marginal propensity to import) marginal propensity to consume positive parameters (from the investment function) real exchange rate variation of the government expenditure
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Economics
IS Relation in an Open Economy
Y = C + I + G − Sreal ⋅ M + X , where:
Y C I G Sreal X M
output private consumption investment government expenditure real exchange rate exports imports in foreign currency
Equilibrium Condition for the Goods and Services Market in an Open Economy in terms of GDP: NX = S + (T − G ) − I ,
in terms of GNP:
CA = S + (T − G ) − I ,
where: NX CA S T−G I
net exports current account balance private saving public saving investment
Real Exchange Rate Sreal =
Sn ⋅ P F , P
where:
Sn PF P
nominal spot exchange rate (in American terms) foreign general price level in foreign currency domestic general price level in domestic currency
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Economics
Trade Balance and Depreciation: the Marshall-Lerner Condition ∆X − ∆M − ∆Sreal > 0. X M Sreal
where:
∆X X ∆M M ∆Sreal Sreal
proportional change in exports proportional change in imports proportional change in the real exchange rate
Equilibrium Model of an Open Economy, the Mundell-Fleming Model Y = C(Y − T) + I(r,Y) + G + NX(Y,YF ,
E(Sn ) ), 1 + i − iF
MS MD = = L(Y , i ). P P where: Y C(.) T I(.) i,r G NX(.) YF iF E(Sn) MS MD P L(.)
output consumption taxation investment function (domestic) nominal and real interest rate government expenditure net exports function output in the rest of the world foreign nominal interest rate expected nominal spot exchange rate (in American terms) nominal money supply nominal money demand general price level demand function
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Economics
Aggregate Demand in an Open Economy (for the Mundell-Fleming Model with Fixed Exchange Rate)
AD = C(Y − T) + I(i − E( π )) + G + NX(Y,YF ,
Sn ⋅ P F ) P
where: C(.) Y T I(.) i E(π) G NX(.) YF Sn P, PF
consumption function domestic output (income) taxation investment function domestic nominal interest rate expected inflation government expenditure net exports function foreign output (income) nominal fixed exchange rate domestic and foreign prices level
4.3.2 Foreign Exchange Rate Absolute Purchasing Power Parity St =
Pt , Pt F
where: nominal spot exchange rate at t
St
Pt Pt
F
foreign general price level in foreign currency at t domestic general price level in domestic currency at t
Relative Purchasing Power Parity st =
S t − S t −1 S t −1
=
(1 + π t )
(1 + π ) F t
− 1 ≈ π t − π tF ,
where: st St
π tF πt
relative spot exchange rate over period t-1 to t nominal spot exchange rate at t foreign inflation rate over period t-1 to t domestic inflation rate over period t-1 to t
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Economics
Covered Interest Rate Parity (CIP) Ft −1,t S t −1
−1 =
1 + it − 1 ≈ it − itF , F 1 + it
where: Ft −1,t − 1 relative forward foreign exchange rate premium S t −1 Ft −1,t forward foreign exchange rate over period t-1 to t
St −1 itF it
nominal spot exchange rate at t-1 foreign nominal interest rate over period t-1 to t domestic nominal interest rate over period t-1 to t
Uncovered Interest Rate Parity (UIP) E (S t ) 1 + it −1 = − 1 ≈ it − itF , F S t −1 1 + it
where:
E(St ) −1 expected relative depreciation of the domestic currency St −1 itF foreign nominal interest rate over period t-1 to t it domestic nominal interest rate over period t-1 to t
Monetary Approach s = (p – pF) = (ms – msF) – ϕ⋅(y – yF) + λ⋅(li – liF) where: s logarithm of the spot exchange rate, F p, p the logarithm of the domestic and foreign price levels ms,msF logarithm of the domestic and foreign money supplies y, yF logarithm of the domestic and foreign real incomes li, liF logarithm of the domestic and foreign interest rates ϕ, λ 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 + F*, Sn
where B + B* = B , F + F* = F , and where: w , w* the nominal portfolio wealths of the home and foreign private sectors MS, 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 bearing claims on the home and foreign governments, referred to as bonds or securities * * B,F foreign residents privately-held stocks of interest bearing claims on the home and foreign governments B, F home residents privately-held stocks of interest bearing claims on the home and foreign governments Sn nominal exchange rate
The Risk Premium
φt = it − it* − Et −1(St )−St −1 , St −1 where: i, i* Et-1(.)
the domestic and foreign interest rates expectation at time t-1 represents a premium for bearing a composite of exchange rate risk and the difference in credit risks nominal exchange rate at time t
φ
St
4.3.3 Central Bank and Monetary Policy Money Multiplier M1 = m ⋅ M0 ,
with m = 1+c , c+θ
where: M1 m M0 c
θ
money stock M1 money multiplier monetary base the ratio of the demand for currency to the demand for sight deposit the ratio of reserves to sight deposits
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Financial Accounting and Financial Statement Analysis Equity Valuation and Analysis Corporate Finance Economics
Table of Contents
1.
Financial Accounting and Financial Statement Analysis
1
1.1 Generally Accepted Accounting Principles: Assets, Liabilities and 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 1.3.2 1.3.3
2.
Profitability Analysis.......................................................................................... 2 Risk Analysis ....................................................................................................... 5 Break-Even Analysis.......................................................................................... 6
Equity Valuation and Analysis
7
2.1 Valuation Model of Common Stock .............................................................7 2.1.1 2.1.2 2.1.3
3.
Dividend Discount Model ................................................................................. 7 Free Cash Flow Model....................................................................................... 8 Measures of Relative Value.............................................................................. 8
Corporate Finance
9
3.1 Fundamentals of Corporate Finance ...........................................................9 3.1.1 3.1.2
Discounted Cash Flow ...................................................................................... 9 Capital Budgeting............................................................................................... 9
3.2 Short-Term Finance Decisions....................................................................14 3.2.1 3.2.2
Short-Term Financing...................................................................................... 14 Cash Management............................................................................................ 14
3.3 Capital Structure and Dividend Policy ......................................................16 3.3.1
4.
Leverage and the Value of the Firm............................................................. 16
Economics
18
4.1 Macroeconomics.............................................................................................18 4.1.1 4.1.2 4.1.3 4.1.4
Measuring National Income and Prices...................................................... 18 Equilibrium in the Real Market...................................................................... 19 Equilibrium in the Money Market.................................................................. 21 Aggregate Supply and Determination of Price of Goods/Services ..... 22
4.2 Macro Dynamics..............................................................................................23 4.2.1 4.2.2 4.2.3
Inflation ............................................................................................................... 23 Economic Growth............................................................................................. 23 Business Cycles ............................................................................................... 24
4.3 International Economy and Foreign Exchange Market ........................24 4.3.1 4.3.2
Open Macro Economics.................................................................................. 24 Foreign Exchange Rate................................................................................... 27
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Financial Accounting and Financial Statement Analysis
4.3.3
Central Bank and Monetary Policy............................................................... 29
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Financial Accounting and Financial Statement Analysis
1.
Financial Accounting and Financial Statement Analysis
1.1 Generally Accepted Accounting Principles: Assets, Liabilities and Shareholders’ 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 = 2·Straight 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
SYD =
n ⋅ (n + 1) 2
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
EPS =
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Earnings available to the common stockholders Number of shares of common stock outstanding
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Financial Accounting and Financial Statement Analysis
With a change in the number of shares outstanding during the year, the formula is modified as follows:
EPS =
Earnings available to the common stockholders Weighted average number of common shares outstanding
1.2.1.2 Using EPS to Value Firms - Constant Dividend Growth Model (Gordon-Shapiro)
P0 =
π ⋅ EPS 0 ⋅ (1 + g) (k e − g)
where: P0 g ke π EPS0
initial market price growth rate cost of equity payout ratio 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 Annual Re turn =
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Annual profit Invested capital
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Financial Accounting and Financial Statement Analysis
Return on Assets
Earnings before interests and tax (EBIT) Assets
ROA = return on assets =
ROA =
EBIT Sales · = EMR · ATR Sales Assets
where: EMR = economic margin ratio = ATR = asset turnover ratio =
EBIT Sales
Sales Assets
Return on Total Assets
ROTA =
EBIT Total assets
Return on Operating Assets ROOA =
OEBIT Operating assets
Return on Non-Operating Assets RONOA =
EBIT − OEBIT Assets − Operating assets
where: OEBIT ROOA RONOA
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operating earnings before interests and tax return on operating assets return on non-operating assets
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Financial Accounting and Financial Statement Analysis
Let ROTA be an average return of the two parts:
ROTA = ROOA · x1 + RONOA · x2 where: x1 x2 1.3.1.2
weight of the operating assets (Operating assets/Total assets) weight of the non-operating assets (x2 = 1 – x1) ROCE
Return on Equity (ROE) or Return on Common Equity (ROCE) ROE =
Net Profit (1 - t)(EBIT - Interest) = Equity Equity
which can be written: EBIT − Interest ROE = ( 1 − t ) ⋅ Equity ROA ⋅ Assets − i ⋅ Debt = (1 − t )⋅ Equity Equity + Debt Debt = ( 1 − t ) ⋅ ROA ⋅ −i⋅ Equity Equity Debt = ( 1 − t ) ⋅ ROA + ( ROA − i ) ⋅ Equtiy = ( 1 − t ) ⋅ ROEbT ROE can be decomposed as follows: ROE =
Net profit Earning before tax EBIT Sales Assets · · · · Earning before tax EBIT Sales Assets Equity
where: i
average interest rate on total debts =
EBIT t
earnings before interests and tax corporate tax rate
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Interest expenses Total debts
Financial Accounting and Financial Statement Analysis
Return on Equity before Tax ROEbT =
EBT Debt = ROA + (ROA – i) · Equity Equity
where: i
average interest rate on total debts =
EBT
earnings before income tax
Interest expenses Total debts
1.3.2 Risk Analysis 1.3.2.1
Short-Term Liquidity Risk
Current Ratio
Current assets Current liabilities
Quick Ratio
Current assets - Inventory Current liabilities
or
Cash + Marketable securities + Receivables Current liabilities
Working Capital Activity Ratio Sales revenue Average Working Capital
1.3.2.2
Long-Term Solvency Risk
Debt Ratio Debt Equity
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Financial Accounting and Financial Statement Analysis
Interest Coverage Ratio EBIT Interest Expenses
1.3.3 Break-Even Analysis Break-even volume = where: s v F s-v=m
unit sales price unit variable costs fixed cost during a period unit contribution margin
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F m
Equity Valuation and Analysis
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
P0 =
Div kE
where
P0 Div kE
2.1.1.2
price of share dividend (assumed constant) cost of equity capital
Constant Growth Model
Constant Dividend Growth Model P0 =
Div1 kE − g
where P0 Div1 kE g
price of share Div0 ⋅ (1 + g ) = expected dividend in period 1 cost of equity capital growth rate of dividend (assumed constant)
Gordon Shapiro Model P0 =
EPS1 ⋅ π k E − (1 − π ) ⋅ r
where P0 EPS1
π
kE 1–π r
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price of share earnings per share in t = 1 payout ratio cost of equity capital earnings retention rate return on equity (ROE)
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Equity Valuation and Analysis
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
P0 = EPS ⋅ where P0 EPS P/E
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price of the share earnings per share price-earnings ratio
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P E
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
CF CF = t k t =1 ( 1 + k )
Present value = ∑
1 ⋅ 1 − n (1+ k )
where CF k n
constant cash flow discount rate, assumed to be constant over time number of cash flows
The future value of an annuity is given by ( 1 + k )n − 1 Future value = CF ⋅ k
where CF k n
constant cash flow discount rate, assumed to be constant over time number of cash flows
3.1.2 Capital Budgeting 3.1.2.1
Investment Decision Criteria
Net Present Value N
NPV = − I 0 + ∑ t =1
E (FCFt ) (1 + WACCt ) t
where I0 initial investment E( FCFt ) expected free cash flows in period t WACCt weighted average cost of capital in period t N number of cash flows NPV Net Present Value
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Corporate Finance
3.1.2.2
Cost of Capital
Cost of Equity Capital CAPM
k E = R f + (RM − R f ) ⋅ β E where kE Rf RM – RF
βE
cost of equity capital risk-free return expected return on the market portfolio – risk-free return, expected Risk premium beta equity = systematic or market risk of equity
The beta equity (βE) can be calculated using the following formula:
βA = βD
D( 1 − t c ) E + βE D( 1 − t c ) + E D( 1 − t c ) + E
where
βA βD βE tc D E
beta asset beta debt beta equity marginal corporate tax rate for the firm being valued market value of interest-bearing debt market value of equity
If we assume that the debt is riskless ( β D = 0) the beta of the firm’s asset can be written as:
βA = βE
E D( 1 − t c ) + E
In this case, the beta equity ( β E ) can be written as:
β E = β A 1 + (1 − t c ) ⋅ with beta asset = β A = β Unlevered beta equity = β E = β Levered
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D E
Corporate Finance
Modigliani-Miller
k E = k u + (k u − k d )(1 − T) ⋅
D E
where kE ku kd T D E
cost of equity (required return on equity) equity rate of return were the company 100% equity cost of debt (required return on debt) statutory marginal tax rate debt (market value) equity (market value)
Zero Growth Model
kE =
Div P0
where
kE Div P0
cost of equity capital dividend (assumed constant) price of share
Constant Growth Model kE =
Div1 +g P0
where
kE g Div1 P0
cost of equity capital growth rate of dividend Div0 ⋅ (1 + g ) = expected dividend in period 1 market price of share
Earnings-Price Ratio Approach
kE =
EPS1 P
where kE EPS1 P
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cost of equity capital expected earnings per share in t=1 current market price of share
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Corporate Finance
Gordon Shapiro Model kE =
EPS1 ⋅ π + (1 − π ) ⋅ ROE P0
where kE EPS1
π
P0 ROE
cost of equity capital earnings per share in t=1 payout ratio price of share return on equity
Cost of Debt Capital Cost of Debt Capital before Taxes - CAPM
(
)
k D = R f + RM − R f ⋅ β D
where kD Rf RM – Rf
βD
cost of debt capital (expected return on debt) risk-free return expected excess return on the market portfolio beta debt = systematic or market risk of debt
- Yield to Maturity N
k D = ∑ wi ⋅ YTM i i =1
where kD wi YTMi
cost of debt capital weight of debt i yield to maturity of debt i
Cost of Debt Capital after Taxes k DA = k D ⋅ ( 1 − t c )
where kDA kD tc
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cost of debt capital after taxes cost of debt capital before taxes marginal corporate tax rate
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Corporate Finance
Weighted Average Cost of Capital (WACC) WACC = k D (1 − t c )
D E + kE V V
where kD kE tc D E V
pre (corporate) tax cost of debt cost of equity marginal corporate tax rate for the entity being valued market value of interest-bearing debt market value of equity =E + D
If the firm has preferred stock, WACC becomes: WACC = k D (1 − t c )
D E P + kE + kP V V V
where kP P V
after tax cost of preferred stock market value of preferred stock = E + D + P (here)
Corporate Taxes, Interest Subsidy and Cost of Capital Average Tax Rate Taxes t = average tax rate = Earnings before taxes Average Interest Rate i = average interest rate =
Interest payments Debt
Value of Tax Shield Value of tax shield =
k D ⋅ D ⋅ tc = D ⋅ tc kD
where D kD tc
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market value of debt cost of debt 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
Accounts Receivable ⋅ 365 Sales
Optimal Cash Balance (Baumol Model) 2FC I
where F C I
fixed cost incurred when selling securities to raise cash annual cash disbursement annual interest earned on the marketable securities portfolio
Target Cash Balance (Miller-Orr model)
3F σ Target Cash Balance = Z = 4 I daily
2
1 3
+L
where F
σ
2
L Idaily
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fixed cost of buying and selling securities variance of the net daily cash flows lower control limit, determined by the firm 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 N
V = − I0 + ∑
E(FCFt )
t =1(1 + WACC t )
t
where V value of the firm E( FCFt ) expected free cash flows in period t WACCt weighted average cost of capital in period t With the continuing value (terminal value) of the firm at time T equal to: Continuing value at time T =
FCFT +1 WACC − g
where T FCFT+1 WACC g
point in time where the explicit free cash flow forecasting horizon ends level of expected free cash flow in the first year after the explicit forecast period; then assumed to grow at rate g weighted average cost of capital (assumed constant) expected growth rate of free cash flows after T (assumed constant)
Firm Value V = D+E
where V D E
value of the firm debt (market values) equity (market values)
MM Proposition I (assuming no taxes)
V = VL = VU = D + E =
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EBIT kA
Corporate Finance
where VL VU D E EBIT kA
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value of levered firm value of unlevered firm debt (market values) equity (market values) earning before interest and taxes (assumed permanent) 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 Y = C + I + G + ( X − M ) + NIRA
where:
Y GNP C private consumption I investment G government expenditure X exports M imports NIRA net income received from abroad X − M + NIRA current account balance National Saving and Current Account Balance CA = S P + S G − I = S P − BD − I
where CA SP SG SP + SG BD I
current account balance private saving government saving national saving (S) budget deficit investment
Price Index: GDP (implicit price) Deflator and Consumer Price Index (CPI)
GDP deflatort =
CPI t
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∑p = ∑p
Nominal GDPt ⋅ 100 = Real GDPt
i
it
⋅ q*i
i
* i
⋅ qi*
⋅ 100
page 18
∑ p ∑p it
it
⋅ qit
i
* i
⋅ qit
⋅ 100
Economics
where p it
price of final good or service i in year t
qit
quantity of final good or service i in year t
pi*
price of final good or service i in the base year
qi*
quantity of final good or service i in the representative basket
Inflation Rate
πt =
Pt − Pt -1 Pt -1
where Pt −1
(index) price level at time t (index) price level at time t-1
πt
inflation rate over period t-1 to t
Pt
Ex-post Fisher Parity rt ≈ it − π t
where rt
real interest rate for the period (t-1, t)
it
nominal interest rate for the period (t-1, t)
πt
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 c0 c1 Y-T
desired consumption constant intercept term marginal propensity to consume (MPC) disposable income
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Economics
Investment Function I(r,Y) = d 0 − d1 ⋅ r + d 2 ⋅ Y where: I d0 d1, d2 r Y
demand for investment autonomous investment positive parameters real interest rate output
Budget Surplus BS = T − (G + TR + NINT )
where: BS T TR NINT G
budget surplus taxation transfer payments net interest payments on public debt government expenditure
Government-Purchases Multiplier Y =
1 ⋅ (c 0 + d 0 + G - c1 ⋅ T - d 1 ⋅ r ) 1 - (c1 + d 2 )
where: Y c0 c1 d0 d1, d2 G T r 1 1 - (c1 + d 2 )
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output constant intercept term (from the consumption function) marginal propensity to consume autonomous investment positive parameters (from the investment function) government expenditure taxation real interest rate government-purchases multiplier
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Economics
Equilibrium Condition for the Market for Goods and Services (Closed economy) I + G = SP +T
where: investment government expenditure private sector savings taxation
I G SP T
IS Relation (Closed economy) Y = Z= C(Y-T) + I(r,Y) + G
where: Y Z C(.) Y −T I(.) r G
output demand for goods and services private consumption function disposable income investment function real interest rate government expenditure
4.1.3 Equilibrium in the Money Market Demand for Money
MD = L(Y , i ) = b0 + b1 ⋅ Y − b2 ⋅ i, P where:
MD P L(.) Y i b0 b1 ,b2
nominal money demand general price level demand function real income (output) nominal interest rate constant parameter positive parameters
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Economics
Equilibrium Relationship in the Monetary Market: LM Curve
MS MD = ≡ L(Y , i ), P P where: MS MD P L(.) Y i
nominal money supply (exogenous) nominal money demand general price level demand function real income (output) nominal interest rate
Quantity Theory of Money (Absolute Form) M ⋅V = P ⋅ Y ,
⇒P=
M ⋅V , Y
where:
M V P Y
quantity of money velocity, a measure of turnover of money stock in a year general price level real income (output)
4.1.4 Aggregate Supply and Determination of Price of Goods/Services Aggregate Supply Relation (short-run) P = E(P)⋅(1+µ)⋅F( 1 −
where: P E(P)
µ
F(.) Y L z
price level expected price level markup variable function output labor force catchall variable
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Y ,z), L
Economics
4.2 Macro Dynamics 4.2.1 Inflation Expectations-Augmented Phillips Curve
π t = π te + α − β (u t − u t* ), where:
πt
inflation rate
π α β
expected inflation rate for time t constant parameter constant positive parameter cyclical unemployment (or “Keynesian” unemployment) at time t
e t
u t − u t*
4.2.2 Economic Growth Aggregate Production Function Y = A ⋅ F (K , L ),
where:
Y A F(.) L K
aggregate output total factor productivity aggregate production function aggregate labour supply aggregate capital stock
Growth Accounting Equation
∆Y ∆A ∆K ∆L = + ξK ⋅ + ξL ⋅ , Y A K L where:
∆Y Y ∆A A ∆K K ∆L L
ξK =
growth of the output growth in productivity growth of the capital stock growth of the labour supply K ∂F (K , L ) ⋅ F (K , L ) ∂K
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elasticity of output with respect to capital
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Economics
ξL =
L ∂F (K , L ) ⋅ F (K , L ) ∂L
elasticity of output with respect to labour
4.2.3 Business Cycles Random Productivity Shocks Yt = F (K t , Lt ) ⋅ At ε t ,
where: Yt F(.) Kt , Lt
εt
At ε t
aggregate output at time t aggregate function production aggregate capital and labour supply at time t random productivity shock at time t 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 BP = CA + KA − ∆RA,
where:
BP CA KA ∆RA
balance of payments current account capital account official reserve account
Government-Purchases Multiplier in an Open Economy ∆Y =
1 ⋅ ∆G 1 - (c1 + d 2 − S real ⋅ m1 )
where:
∆Y m1 c1 d2 Sreal ∆G
variation of the output positive constant parameter (marginal propensity to import) marginal propensity to consume positive parameters (from the investment function) real exchange rate variation of the government expenditure
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Economics
IS Relation in an Open Economy
Y = C + I + G − Sreal ⋅ M + X , where:
Y C I G Sreal X M
output private consumption investment government expenditure real exchange rate exports imports in foreign currency
Equilibrium Condition for the Goods and Services Market in an Open Economy in terms of GDP: NX = S + (T − G ) − I ,
in terms of GNP:
CA = S + (T − G ) − I ,
where: NX CA S T−G I
net exports current account balance private saving public saving investment
Real Exchange Rate Sreal =
Sn ⋅ P F , P
where:
Sn PF P
nominal spot exchange rate (in American terms) foreign general price level in foreign currency domestic general price level in domestic currency
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Economics
Trade Balance and Depreciation: the Marshall-Lerner Condition ∆X − ∆M − ∆Sreal > 0. X M Sreal
where:
∆X X ∆M M ∆Sreal Sreal
proportional change in exports proportional change in imports proportional change in the real exchange rate
Equilibrium Model of an Open Economy, the Mundell-Fleming Model Y = C(Y − T) + I(r,Y) + G + NX(Y,YF ,
E(Sn ) ), 1 + i − iF
MS MD = = L(Y , i ). P P where: Y C(.) T I(.) i,r G NX(.) YF iF E(Sn) MS MD P L(.)
output consumption taxation investment function (domestic) nominal and real interest rate government expenditure net exports function output in the rest of the world foreign nominal interest rate expected nominal spot exchange rate (in American terms) nominal money supply nominal money demand general price level demand function
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Economics
Aggregate Demand in an Open Economy (for the Mundell-Fleming Model with Fixed Exchange Rate)
AD = C(Y − T) + I(i − E( π )) + G + NX(Y,YF ,
Sn ⋅ P F ) P
where: C(.) Y T I(.) i E(π) G NX(.) YF Sn P, PF
consumption function domestic output (income) taxation investment function domestic nominal interest rate expected inflation government expenditure net exports function foreign output (income) nominal fixed exchange rate domestic and foreign prices level
4.3.2 Foreign Exchange Rate Absolute Purchasing Power Parity St =
Pt , Pt F
where: nominal spot exchange rate at t
St
Pt Pt
F
foreign general price level in foreign currency at t domestic general price level in domestic currency at t
Relative Purchasing Power Parity st =
S t − S t −1 S t −1
=
(1 + π t )
(1 + π ) F t
− 1 ≈ π t − π tF ,
where: st St
π tF πt
relative spot exchange rate over period t-1 to t nominal spot exchange rate at t foreign inflation rate over period t-1 to t domestic inflation rate over period t-1 to t
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Economics
Covered Interest Rate Parity (CIP) Ft −1,t S t −1
−1 =
1 + it − 1 ≈ it − itF , F 1 + it
where: Ft −1,t − 1 relative forward foreign exchange rate premium S t −1 Ft −1,t forward foreign exchange rate over period t-1 to t
St −1 itF it
nominal spot exchange rate at t-1 foreign nominal interest rate over period t-1 to t domestic nominal interest rate over period t-1 to t
Uncovered Interest Rate Parity (UIP) E (S t ) 1 + it −1 = − 1 ≈ it − itF , F S t −1 1 + it
where:
E(St ) −1 expected relative depreciation of the domestic currency St −1 itF foreign nominal interest rate over period t-1 to t it domestic nominal interest rate over period t-1 to t
Monetary Approach s = (p – pF) = (ms – msF) – ϕ⋅(y – yF) + λ⋅(li – liF) where: s logarithm of the spot exchange rate, F p, p the logarithm of the domestic and foreign price levels ms,msF logarithm of the domestic and foreign money supplies y, yF logarithm of the domestic and foreign real incomes li, liF logarithm of the domestic and foreign interest rates ϕ, λ 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 + F*, Sn
where B + B* = B , F + F* = F , and where: w , w* the nominal portfolio wealths of the home and foreign private sectors MS, 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 bearing claims on the home and foreign governments, referred to as bonds or securities * * B,F foreign residents privately-held stocks of interest bearing claims on the home and foreign governments B, F home residents privately-held stocks of interest bearing claims on the home and foreign governments Sn nominal exchange rate
The Risk Premium
φt = it − it* − Et −1(St )−St −1 , St −1 where: i, i* Et-1(.)
the domestic and foreign interest rates expectation at time t-1 represents a premium for bearing a composite of exchange rate risk and the difference in credit risks nominal exchange rate at time t
φ
St
4.3.3 Central Bank and Monetary Policy Money Multiplier M1 = m ⋅ M0 ,
with m = 1+c , c+θ
where: M1 m M0 c
θ
money stock M1 money multiplier monetary base the ratio of the demand for currency to the demand for sight deposit the ratio of reserves to sight deposits
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