Professional Exam Review
Fundamental Equations for Sound Bytes
QUANTITATIVE METHODS: SOUND BYTE 2
三百字读后感>5色吧Effective Annual Rate:
EAR = (1 + r )m - 1.0 Future Value:
FV = PV (1 + r)n
Prent Value:
n r)(1FV
= FV/(1 + r)n = FV (1 + r)–n PV +=
Future Value of Ordinary Annuity:
PMT ⎥⎦⎤
⎢⎣⎡−+r r N 1)1( = PMT (FVIFA r,n )
Prent Value of Ordinary Annuity :
PMT ⎥⎥
⎥⎥
⎦
⎤
⎢⎢⎢⎢⎣⎡+−r r N )1(11= PMT(PVIFA r,n )
Future Value of Annuity Due:
FV annuity due = PMT(FVIFA r,n )(1+r)
Prent Value of an Annuity Due:
PV annuity due = PMT(PVIFA r,n )(1+r)
Prent Value of Perpetuities:
PV = PMT/i
Holding Period Return:
HPR = (P 1 – P 0 + D 1)/P 0
Bank Discount Yield:
r BD = t x F D 360
Holding Period Yield: HPY = 0
1
01P D P P +−
Effective Annual Yield:
EAY = (1 + HPY)365/t - 1
Money Market Yield:
R MM = HPY (360/t)
Arithmetic Mean:
μ = Σ X / N, X = Σ X / n
Weighted Mean:
X w = Σ w i × X i
Geometric Mean Return:
R G = [ Π (1 + r t ) ] - 1 = [ Π R t ) ]1/T - 1
Harmonic Mean:
X H = 1 / [ { Σ (1 / X ) } / n ] = n / Σ (1/X
Variance for a Population:
σ2 = ()N X 2∑μ−
Standard Deviation for a Population:
σ = √variance = (variance)1/2
Variance for a Sample:
s 2 = ()1n X X 2−−∑
Standard Deviation for a Sample:
二年级阅读记录卡s = √variance = (variance)1/2
Sharpe Ratio:
p
f
p s r r −
Joint Probability:
P(AB) = P(A ⏐B) × P(B)
Total Probability Rule:
P(A) = P(A ⏐S) P(S) + P(A ⏐S C ) P(S C )
Total Probability Rule for Expected Value:
E(X) = E(X ⏐S) P(S) + E(X ⏐S ) P(S )
渺无音讯Expected Value:
Expected value =
∑=n
1
i i i x p Covariance:
Cov (R i,R j ) = Σ [ (R i – E(R i )) (R j – E(R j )) P(S) ]
Correlation:
ρ(R i,R j ) = Corr(R i,R j ) = Cov(R i,R j ) / σ(R i ) σ(R j )
Calculating Covariances from Correlations:
Cov(R i,R j ) = Corr(R i,R j) σ(R i ) σ(R j )
Joint Probability Function:
Cov (R i,R j ) = Σ Σ P(R i,R j ) [R i - E(R i )] [(R j - E(R j )]
Bayes’ Formula: ()()
()P(A 1|B) = ()()()221111A B P A P A B P A P A B P A P ×+××
Combination Formula Notation:
n C r = !r *)!r n (!
n −
Permutation Formula Notation:
n P r = )!r n (!
n −
ECONOMICS: SOUND BYTE 3
Price Elasticity of Demand:
price in change %demanded
quantity in change %demand of elasticity price =食品供货合同
Cross Elasticity of Demand:
complement or substitute of price in change %demanded
quantity in change %demand of elasticity cross =
Income Elasticity of Demand:阿拉伯大写
income in change %demanded
quantity in demand of elasticity income =
Elasticity of Supply:
price in change %supplied
quantity in supply of elasticity =
Economic Profit:
= Total Revenues — (Opportunity costs)
= Total Revenues — Total Explicit Costs — Total Implicit Costs
CPI : CPI basket price at current prices × 100
CPI basket price at ba period prices
Inflation Rate :
蒜末(CPI ending - CPI beginning ) / CPI beginning
Money Multiplier:
(1 + c) / (r + c)
M:
[(1 + c) / (r + c)] × B
Inflation:
[(Ending price level - Beginning price level)] / Beginning price level
FINANCIAL STATEMENT ANALYSIS: SOUND BYTE 4 Basic Earnings Per Share:
dividends preferred - income net EPS Basic = Diluted Earnings Per Share with Convertible Preferred Stock:
婴儿红色胎记
⎟⎟⎠⎞⎜⎜⎝
⎛+=conversion at issued been have would that shares common new g outstandin shares of number average weighted income net EPS Diluted Diluted Earnings Per Share with convertible Debt:
⎟⎟⎠⎞⎜⎜⎝
⎛++=conversion at issued been have would that shares common new g outstandin shares of number average weighted dividends preferred -debt e convertibl on interest tax -after income net EPS Diluted Diluted Earnings Per Share with Stock Options:
⎟⎟⎟⎠
⎞⎜⎜⎜⎝⎛+=exerci from proceeds cash with purchad been have could the shares - exerci option at issued been have would that shares new g outstandin shares of number average weighted dividends preferred -income net EPS Diluted FCFF:
NI + NCC + interest (1 – Tax rate) – FCInv – WCInv
FCFF :
CFO + interest (1 – Tax rate) – FCInv
FCFE:
CFO – FCInv + Net borrowing – Net debt repayment
Formulas for Depreciation Expen (note n is the life of the ast):
• Straight-line:
() value salvage -cost original 1 i Year in expen on depreciati ×=n
• Sum-of-years’ digits:
()() value salvage -cost original 1 i Year in expen on depreciati ×+−=SYD i
n where SYD = 1 + 2 + … + n
