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CFA Lvl 1 > Formulas > Flashcards

Formulas Flashcards

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1
Q

Nominal interest rate=

A

Nominal interest rate= real risk-free rate + expected inflation rate

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2
Q

Required interest rate on security=

A

Required interest rate on security= nominal risk-free rate + default risk premium+ liquidity
premium + maturity risk premium

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3
Q

Effective Annual Return (EAR)=

A

Effective Annual Return (EAR)= EAR=(1+periodic rate)m -1

Periodic rate= stated annual rate/m
M= number of compounding periods per year

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4
Q

PV perpetuity =

A

PV perpetuity = PMT / (I/Y)

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5
Q

NPV =

A

NPV = ∑( CF / (1+r)^t)

CF= Expected cash flow
r =Discount rate

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6
Q

Holding period return (HPR) =

A

Holding period return (HPR) = (Ending Value - Beginning Value) / (Beginning Value)

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7
Q

Effective Annual Yield (EAY)=

A

Effective Annual Yield (EAY)= (1+HPY)^(365/t) -1

HPY= Holding period yield

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8
Q

Geometric Mean=

A

Geometric Mean= [(1+R1)(1+R2)…. (1+Rn)]^(1/n)-1
Geometric mean return is also known as compound annual rate of return

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9
Q

Harmonic Mean=

A

Harmonic Mean= N / ∑(1/x)

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10
Q

Position of observation at a given percentile

A

Ly=(n+1) (y / 100)

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11
Q

Mean Absolute Deviation (MAD)=

A

(∑Xi - X) / n

X = Arithmetic mean

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12
Q

Population Variance

A

σ^2 = (∑(Xi-μ)^2) / N

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13
Q

Standard Deviation

A

σ = square root of variance

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14
Q

Sample Variance

A

σ^2 = (∑(Xi-μ)^2) / (N - 1)

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15
Q

Chebyshev’s Inequality

A

Percentage of observations that lie within k standard deviations of the mean is at least= 1-1/k^2

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16
Q

Coefficient of Variation

A

CV = (standard deviation of x) / (average value of x)

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17
Q

Sharpe Ratio=

A

(Rp-RFR) / σp

Rp= Portfolio Return
RFR= Risk Free Rate
σp= standard deviation of portfolio return

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18
Q

Sample Skewness (Sk) =

A

(∑(Xi-x)^3) / (s^3)

s =sample standard deviation

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19
Q

Excess Kurtosis=

A

Excess Kurtosis= Sample Kurtosis - 3

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20
Q

Multiplication Rule Of Probability

A

P(AB)=P(A/B)*P(B)

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21
Q

Addition Rule Of Probability

A

P(A or B)= P(A)+P(B)-P(AB)

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22
Q

Total Probability Rule (Used to determine unconditional probability of an event)

A

P(A)=P(A/B1)P(B1)+P(A/B2)P(B2)+………+P(A/BN)P(BN)

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23
Q

Expected value of random variable=

A

weighted average of possible outcomes

Weights = probabilities that the outcome will occur

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24
Q

Bayes Formula

A

Updated Probability=( Probability of new information for a given event / unconditional
probability of new event )*(prior probability of event)

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25
Q

P/E =

A

P/E = (Dividend payout ratio) / (k - g)

dividend payout = 1 - retention rate

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26
Q

Weighted Average Cost of Capital =

A

WACC= (wd)[kd(1-t)]+(wps)(kps)+(wcc)(Kcc)
Wd= percentage of debt in capital structure.
Wps=percentage of preferred stock in the capital structure.
Wcc=percentage of common stock in the capital structure

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27
Q

Factorial

A

n! = n(n-1)(n-2)*(n-3)…… *1
0!=1

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28
Q

To standardize a normal variable

A

z=(Observation - Population Mean) / (Standard Deviation)

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29
Q

Roy’s safety first criteria

A

SFR= ([E(Rp)-Rl]) / (σ p)

**Choose the portfolio with largest SFR

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30
Q

Continuously compounded rate of return

A

Rcc=ln(1+HPR)

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31
Q

Standard Error of sample Mean

A

σx= σ / √n

σ= Standard deviation of population
n=Size of the sample

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32
Q

Price Elasticity of Demand =

A

%∆Quantity Demanded / %∆Price

33
Q

Cross Price Elasticity =

A

%∆Quantity Demanded / %∆Price of Related Goods

34
Q

Income Elasticity =

A

%∆Quantity Demanded / %∆ in Income

35
Q

Accounting profit=

A

Accounting profit=total revenue-total accounting costs

36
Q

Economic profit=

A

Economic profit=accounting profit-implicit opportunity costs
Or
Economic profit=total revenue-total economic costs

37
Q

Normal profit

A

Normal profit is the accounting profit that makes economic profit equal to zero

38
Q

Marginal Cost

A

MC=change in total cost / change in output

39
Q

Nominal GDP =

A

∑Pi, tQi, t
Pi,t= Price of good i in year t. Qi,t=Quantity of good I produced in year t

40
Q

GDP deflator=

A

GDP deflator= (nominal GDP / value of year t output at year t)*100

41
Q

Per Capita Real GDP=

A

Per Capita Real GDP = GDP / population

42
Q

GDP by expenditure approach

A

GDP = C + I + G + (X - M)

C = Consumption spending
I = Investments
G = Government purchases
X = Exports
M = Imports

43
Q

GDP by Income Approach

A

GDP=national income+ capital consumption allowance+ statistical discrepancy

44
Q

National Income=

A

National Income= compensation of employees (wages and benefits)
+ corporate and government enterprise profits before taxes
+Interest Income
+Unincorporated business net income (business owner’s income)
+rent
+indirect business taxes-subsidies

45
Q

Personal Income=

A

Personal Income= national Income
+transfer payments to households
-indirect business taxes
-corporate income taxes
-undistributed corporate profits

46
Q

Personal disposable income=

A

Personal disposable income = personal income - personal taxes

47
Q

CPI=

A

CPI= (Cost of basket at current prices / cost of basket at base period prices)*100

48
Q

Real Exchange Rate=

A

Real Exchange Rate= Nominal Exchange Rate(d/f) * ((CPI foreign) / (CPI domestic))

49
Q

Interest Rate Parity

A

foward / spot = (1+interest rate (domestic)) / (1+interest rate (foreign))

50
Q

Income statement equation

A

Net income = revenues - expenses

51
Q

Straight line depreciation expense=

A

(cost - residual value) / (useful life)

52
Q

Basic EPS=

A

(net income - preferred dividends) / (weighted average number of common shares outstanding)

53
Q

Diluted EPS=

A

(Adjusted income for common shareholders) / (weighted average common and potential common shares outstanding)

54
Q

Current Ratios=

A

(Current Assets) / (Current Liabilities)

55
Q

Quick Ratio=

A

(current assets – inventories) / current liabilities

56
Q

Cash Ratio=

A

(Cash + Marketable Securities) / (Current Liabilities)

57
Q

P/E =

A

dividend payout ratio / k - g

58
Q

Debt to equity ratio=

A

(Total debt) / (Total Shareholders Equity)

59
Q

Debt To Capital=

A

(Total debt) / (Total Debt + Total Shareholders Equity)

60
Q

Financial Leverage=

A

(Average Total Assets) / (Average Total Equity)

61
Q

Interest Coverage Ratio=

A

(Earnings Before Interest and taxes) / (Interest payments)

62
Q

Net profit margin=

A

(Net Income) / Revenue

Net income= earnings after taxes but before dividends

63
Q

Gross Profit Margin=

A

(Gross profit) / Revenue

Gross profit= Net Sales- COGS

64
Q

Operating profit margin=

A

(Operating Income (EBIT))
Revenue

65
Q

Return on assets (ROA)=

A

(Net Income) / (Average Total Assets)

66
Q

Return on Total Capital=

A

EBIT / (Average Total Capital)

67
Q

Return On Equity=

A

(Net Income) / (Average Total Equity)

or

(Net Income / Revenue) * (Revenue / Equity)

68
Q

Sustainable growth rate=

A

RR * ROE

RR= Retention rate
=1-dividend payout

69
Q

Coefficient of variation sales=

A

(Standard deviation of operating income) / (Mean sales)

70
Q

CV Operating Income=

A

(Standard deviation of operating income) / (mean operating income)

71
Q

CV Net Income=

A

(Standard deviation of net income) / (Mean net income)

72
Q

COGS=

A

beginning inventory + purchases - ending inventory

73
Q

Depreciation methods

A

i) straight line and ii) ddb covered earlier.
ii) units of production depreciation=

(Original cost-salvage value) / (life in output units) * Output units in the period

74
Q

Effective tax rate=

A

(Income tax expense) / (Pretax income)

75
Q

WACC=

A

(wd) (kd) (1 - t) + (wps) (kps) + (wcc) (Kcc)

Wd= percentage of debt in capital structure.
Wps=percentage of preferred stock in the capital structure.
Wcc=percentage of common stock in the capital structure
t = marginal tax rate
Kd = before tax cost of debt
Kcc = cost of common stock
Kps = cost of preferred stock

76
Q

After tax cost of debt=

A

kd (1 - t)

77
Q

Dividend discount model

A

D1 / (k-g)

D1= Next year dividend.
k = Required rate of return on common equity.
g = Firm’s expected constant growth rate.

78
Q

Required Return (RR) =

A

Rf + (RMarket – Rf) × Beta

RR = required return
Rf = risk-free rate
RMarket = market rate of return

CFA Lvl 1 (5 decks)

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