Handbook for
Formulas
List of formulas for
Level 1
CFA
####### ®
Program
TIME VALUE OF MONEY
1 Nominal interest rate= real risk-free rate + expected inflation rate
2 Required interest rate on security= nominal risk-free rate + default risk premium+ liquidity premium + maturity risk premium
3 Effective Annual Return (EAR)= EAR=(1+periodic rate)m – Periodic rate= stated annual rate/m M= number of compounding periods per year
FV= future value PV= Present value I/Y=Rate of return per compounding period N=Number of compounding periods
CF= Expected cash flow r =Discount rate
IRR= Internal rate of return.
HPR= Holding period return
RBD= D/F*360/t RBD= Annualised yield on a bank discount basis D=Dollar discount= purchase price – face value F=Face value t=Number of days until maturity 360=Bank convention of number of days in a year
4 FV= PV(1+ I/Y)N
5 PV perpetuity = PMT (I/Y)
6
PV= N Y 1+I
FV
PMT= Fixed periodic cash flow
DISCOUNTED CASH FLOW APPLICATION
CF (1+r)t
7 IRR
8
9
Effective Annual Yield (EAY)= (1+HPY)365/t – HPY= Holding period yield
10
HPR=
CF (1+IRR)
CF (1+IRR) 2
(Ending Value-Beginning Value) (Beginning Value)
CF (1+IRR) 3 0=CF+ + +
PROBABILITY CONCEPTS
COMMON PROBABILITY DISTRIBUTIONS
27 Multiplication Rule Of Probability, P(AB)=P(A/B)*P(B)
28 Addition Rule Of Probability, P(A or B)= P(A)+P(B)-P(AB)
29 Total Probability Rule (Used to determine unconditional probability of an event) P(A)=P(A/B1)P(B1)+P(A/B2)P(B2)+&&&+P(A/BN)P(BN)
30 Expected value of random variable= weighted average of possible outcomes, Weights = probabilities that the outcome will occur
31 Covariance Cov(Ri, Rj)= E{[Ri-E(Ri)][(Rj-E(Rj)]} Cov(Ri, Rj)= Corr(Ri, Rj) σ(Ri)σ(Rj)
32 Correlation Cofficient
33 Weight of asset in portfolio, w= market value of investment in asset i/market value of the portfolio
34 Portfolio Expected Value E(Rp)=w1E(R1) + w2E(R2)+&& wnE(Rn)
35 Variance of 2 Asset Portfolio
36 Variance of 3 asset Portfolio
37 Bayes Formula, Updated Probability=( Probability of new information for a given event / unconditional probability of new event )*(prior probability of event)
38 Factorial n! = n*(n-1)(n-2)(n-3)&& * 0!=
39 Labelling, n! / (n1!)(n2!)&. ( nn!)
40 Combination, n Cr=n! /(n-r)!r!
41 Permutation, n! /(n-r)!
42 To standardize a normal variable,
Corr(Ri,Rj)= (Cov(Ri,Rj)) (σ(Ri)σ(Rj))
z=
(Observation – Population Mean) (Standard Deviation)
43 Roy9s safety first criteria,
44 Continuously compounded rate of return, Rcc=ln(1+HPR)
45 Standard Error of sample Mean, σx= σ σ= Standard deviation of population n=Size of the sample
46 t-distribution to construct a confidence interval, When variance is unknown, x=tα/2
When variance is known, x=tα/2*σ x= Point estimate of population mean tα/2=The t-reliability factor
48 t-statistic When population variance is unknown,
49
When population variance is known,
47
**Choose the portfolio with largest SFR
SFR=
([E(Rp)-Rl]) (σ p)
Test Statistic=
(Sample Mean – Hypothesized Mean) (Standard Error of Sample Mean)
TRIN=
(Number of advancing Issues / Number of declining issues) (Volume of advancing issues / Volume of declining issues)
SAMPLING AND ESTIMATION
SAMPLING AND ESTIMATION
TECHNICAL ANALYSIS
(x-μ) (s/√n)
Tn-1=
(x-μ) (σ/√n)
Tn-1=
(n-1)s σ
Chi-square test: X2=
50 F-distribution test, F=s12/s
51 Arms Index or Short Term Trading Index,
66 Personal Income= national Income +transfer payments to households -indirect business taxes -corporate income taxes -undistributed corporate profits
67 Personal disposable income=personal income-personal taxes
68 Quantity Theory Of Money, MV=PY M=Money Supply, V=Velocity of money in transactions, P=Price level Y=Real GDP
69 Recessionary Gap or Output Gap=Real GDP-Full Employment GDP
70 Potential GDP=aggregate hours worked*labour productivity In terms of economic growth, Growth in potential GDP=growth in labour force+ growth in labour productivity
71 Production Function, Y=A*f(L,K) Y=Aggregate economic output, L=Size of labour force, K=Amount of capital available, A=Total factor productivity
72 CPI= (Cost of basket at current prices/cost of basket at base period prices)*
73 Total amount of money that can be created, Money created= new deposit/reserve requirement
74 Money Multiplier=1/Reserve Requirement
75 Fisher Effect, Rnom=Rreal+E(I)+RP Rnom=Nominal interest rate, Rreal=Real Interest rate RP=Risk premium for uncertainty
76 Neutral Interest Rate= Real trend rate of economic growth + inflation target
77 Fiscal Multiplier= 1/[1-MPC(1-t)]
78 Relation between trade deficit, saving and domestic investment, Exports-imports= private savings+ government savings+ domestic investment
79 Real Exchange Rate= Nominal Exchange Rate(d/f)*
UNDERSTANDING BUSINESS CYCLES
CURRENCY EXCHANGE RATES
(CPI foreign) (CPI domestic)
80 Interest Rate Parity,
81 Accounting Equation, (Balance Sheet) Assets= liabilities + equity Assets=liabilities+ contributed capital+ ending retained earnings Assets=liabilities+ contributed capital+ beginning retained earnings+ revenue-expens- es-dividends
87 Free Cash flow to firm, FCFF= NI+ NCC+ Interest(1-Tax Rate) 3FC Inv-WC Inv FCFF=CFO+ Interest(1-Tax Rate)-FC Inv NI= Net income NCC= Non cash charges FC Inv= Fixed capital investment WC Inv= Working Capital Investment
88 Free cash flow to equity, FCFE=CFO-FC Inv + net borrowing Net borrowing= debt issued- debt repaid
82 Income statement equation, Net income=revenues-expenses
84 Accelerated depreciation- double declining balance method
DDB depreciation= 2 (cost-accumulated depreciation) useful life
85
83 Straight line depreciation expense=
foward spot
(1+interest rate (domestic) (1+interest rate (foreign)
(cost-residual value) (useful life)
(net income-preferred dividends) (weighted average number of common shares outstanding)
=
FINANCIAL STATEMENT ANALYSIS: AN INTRODUCTION
Basic EPS=
86 (Adjusted income for common shareholders) (weighted average commom and potential common shares outstanding)
([Net income-preferred dividends]+[convertible preferred dividends] +[convertible debt interest](1-tax rate)) ([Weighted average shares]+[shares from conversion of converted preferred shares] +[shares from conversion of debt]+[shares issuable from stock options])
Diluted EPS=
Diluted EPS=
UNDERSTANDING CASHFLOW STATEMENTS
104 Payables turnover= Purchases (Average trade payables)
105 Number of days of payables= 365 (Payable turnover)
106 Total asset turnover= (Revenue ) (Average total assets)
107 Fixed asset turnover= Revenue (Average net fixed assets)
108 Working capital turnover= Revenue (Average working capital)
109 Current Ratios= (Current Assets) (Current Liabilities)
110 Quick Ratio= (Cash+Marketable Securities+Receivables) (Current Liabilities)
111 Cash Ratio=(Cash+Marketable Securities) (Current Liabilities)
112 Defensive Interval= (Cash+Marketable Securities+Receivables) (Average Daily Expenditures)
114 Debt to equity ratio= (Total debt) (Total Shareholders Equity)
115 Debt To Capital= (Total debt) (Total Debt+Total Shareholders Equity)
116 Debt To Assets= (Total Debt) (Total Assets)
117 Financial Leverage= (Average Total Assets) (Average Total Equity)
118 Interest Coverage Ratio= (Earnings Before Interest and taxes) (Interest payments)
119 Fixed Charge Coverage= (Earnings Before Interest & Taxes+Lease Payments) (Interest payments+Lease payments)
113
LIQUIDITY RATIOS
SOLVENCY RATIOS
Cash Conversion Cycle= (Days sales outstanding)+(days on inventory on hand)-(number of days of payables)
PROFITABILITY RATIOS
120
Net income= earnings after taxes but before dividends
Net profit margin=
(Net Income) Revenue
121
Gross profit= Net Sales- COGS
Gross Profit Margin=
(Gross profit) Revenue
122 Operating profit margin= (Operating Income (EBIT)) Revenue
123 Pretax margin=
EBT Revenue
124 Return on assets (ROA)= (Net Income) (Average Total Assets)
125 Operating return on assets=
(Operating Income) (Average Total Assets)
128 Return on common equity=
129 Sustainable growth rate= RR*ROE RR= Retention rate =1-dividend payout
(Net Income-Preferred Dividends) (Average Common Equity)
126 Return on Total Capital= EBIT (Average Total Capital)
127 Return On Equity=
= Net Profit Margin * Equity Turnover
=Net Profit MarginAsset TurnoverLeverage Ratio
=Tax Burden Interest BurdenEBIT MarginAsset turnoverfinancial leverage
Return On Equity By Du Pont Equation,
ROE By Extended Dupont Equation,
Or
(Net Income) (Average Total Equity)
Return On Equity=
Return On Equity=
(Net Income) Revenue
(Net Income) Sales
ROE= (Net Income) EBT
EBIT Revenue
Revenue (Total Assets)
EBT EBIT
(Sales ) Assets
Revenue Equity
*
* * *
(Total Assets )
* (Total Equity)
(Assets)
* Equity
*
141 Capital asset pricing model (CAPM) Kce=RFR+β[E(Rm)-RFR] Kce=Cost of equity capital RFR= Risk free rate E(Rm)= Expected return on market.
142 Dividend discount model,
143 Bond yield plus risk premium approach, Kce=bond yield + risk premium
D/E= Comparable company9s debt to equity ratio
144 Asset Beta,
145 Project Beta,
146
147
Revised CAPM using country risk premium, Kce=Rf+β[E(Rm)-RFR+CRP CRP= Country risk premium
Sovereign yield spread= difference between the yields of government bonds in in the developing country and treasury bonds of similar maturities
D1= Next year dividend. K=Required rate of return on common equity. g = Firm9s expected constant growth rate.
D Po= (k-g)
ΒAsset=βEquity
(1+(1-t) D E
ΒProject=βAsset
1 (1-t)D 1+ E
CRP=
Break Points=
(Annualised standard deviation of equity index of developing country) (Annualised standard deviation of sovereign bond Market in terms of the developed market currency)
148 Break Point (any time the cost of one of the components of the company9s WACC changes.)
(Amount Of Capital at which the components cost of capital changes) (weight of the he component in the capital structure)
)
MEASURES OF LEVERAGE
DIVIDENDS AND SHARE REPURCHASE BASICS
WORKING CAPITAL MANAGEMENT
149
150
Degree of operating leverage,
Q= Quantity of units sold P=Price per unit V= Variable cost per unit F= Fixed costs S= Sales TVC=Total variable costs
DOL=(Percentage change in EBIT) (Percentage change in sales)
Degree of financial leverage,
151 Degree Of Total Leverage
152 Breakeven Quantity Of Sales,
153
DFL for particular level of operating units,
DFL= (Percentage change in EPS) (Percentage change in EBIT)
DFL= EBIT (EBIT-Interest)
QBE= (Fixed perating costs+Fixed financing costs) (Price-Variable cost per unit)
Eps after buyback= (Total earnings-After tax cost of funds) (Shares outstanding after buyback)
154 Cost of trade credit=(1+ (%discount) 365/days past discount – (1-%discount)
DTL= Q(P-V) (Q(P-V)-F-I)
(S-TVC) (S-TVC-F-I)
DTL= (% change in EBIT) (% change in Sales)
(% change in EPS) (% change in EBIT)
(% change in EPS) (% Change in Sales)
DOL for a particular level of units,
DOL= Q(P-V) = (Q(P-V)-F)
(S-TVC) (S-TVC-F)
DTL=DOL+DFL
- =
=
EQUITY VALUATION: CONCEPTS AND BASIC TOOLS
168 Dividend discount model, One year holding period:
169 Free cash to equity,
FCFE= net income+ depreciation-increase in working capital-fixed capital investment-debt principal repayments+ new debt issues
FCFE=CFO-FC investment + net borrowing CFO= Cash flow from operations.
171 Enterprise Value (EV) EV= market value of common and preferred stock + market value of debt 3cash and short term investment
Book value of equity= common shareholders equity = (total assets- total liabilities)-pre- ferred stock
Vo= Current stock value Dt=Dividend at time t Ke=Required rate of return
Two year holding period DDM,
Vo=
Dt ((1+ke) )
Value=
D ((1+ke) )
Value=
D1/ (1+ke) )
Pn=
(Dn+1) (Ke-gc)
Preferred stock value= Dp= Fixed dividend Kp=Required rate of return
Dp kp
D (1+ke)
D (1+ke)
P ((1+ke)2)
(Year End Price) ((1+ke)) +
Dn ((1+ke)n )
Pn ((1+ke)n)
Multi-stage dividend discount model:
170
Trailing P/E=
(Market price per share) (EPS over previous 12 months)
172
Leading P/E= (Market price per share) (Forecast EPS over next 12 months)
173
P/B Ratio=
(Market value of equity) (Book value of equity)
(Market price per share) (Book value per share)
174 =
175
INTRODUCTION TO FIXED INCOME VALUATION
UNDERSTANDING FIXED INCOME RISK AND RETURN
Modified duration, For annual pay bond: Modified duration= Macualay duration/ (1+YTM) For semi-annual bond, ModDursemi=MacDur/(1+ YTM/2 ) V¬_ = price increase V+=price decrease V0=current price
P/S Ratio=
177 Price of annual coupon bond,
179 Current Yield=
178 Full Price= Flat price + Accrued interest
181
182
Option Value= z spread 3OAS
183
180 Relation between forward rates and spot rates,
(1+s 2 )=(1+S 1 )(1+1y1y)
YTM= Yield to maturity
Price of semi-annual coupon bond,
(Market value of equity) (Total sales)
(Annual cash coupon payment) (Bond price)
184 Effective duration= (V_ -V+)
176 P/CF Ratio
(Market value of equity) (Cash flow)
Price=
Coupon ((1+YTM))
YTM 2
Approximate modified duration =
(V¬_ -V+)
Price= 1+
Coupon YTM 2
Principal+ Coupon YTM 2 1+ 1+
Coupon
Coupon ((1+YTM)2)
(Principal+ Coupon)
- +&&& + ((1+YTM)n)
+&&& + n*
196 Option value= intrinsic value+ time value
197 Put-call parity: C= Call P=Put S=Stock
198 Put call parity with assets cashflows,
199 Plain vanilla interest rate swap,
(Net fixed rate payment)t = (Swap rate- LIBORt-1)((Number of days) 360)*
notional principal
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