CFA level 1 june 2015 formula sheet

Formula Sheet Volume 1: Quantitative Methods Reading 6: Discounted Cash Flow Applications 3... Formula Sheet Volume 1: Quantitative Methods Reading 12: Technical Analysis 1.. Formula S

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Formula Sheet Volume 1: Quantitative Methods

• Interest Rate = Real Risk Free Interest Rate + Inflation Premium + Default Risk

Premium + Liquidity Premium + Maturity Premium

• Nominal Risk Free Interest rate = Real Risk Free Interest Rate + Inflation Premium

• Interest rate as a growth rate = g = -1

2 PV and FV of Cash Flow =

• FV (for more than one Compounding per year) = FVN = 1 + ×

• FV (for Continuous Compounding) = FVN = &' ×(

• Solving for Number of periods = N = )( *+,+

)( (where LN = natural log)

4 Stated & Effective Rates

• Periodic Interest Rate = -./.01 2334/5 63.0 0 7/.0

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Reading 6: Discounted Cash Flow Applications

3 Net Present Value = ∑ ; G

G

3 H − BVW

4 IRR (when project’s CFs are perpetuity) = NPV = - Initial Investment + ;XXXX

677 = 0

5 Holding Period Yield (HPR) = Y Z Y [ \ Z

Y [

6 Money Weighted Rate of Return (MWR) = ∑=HW ;677G = 0 (IRR represents the MWR)

7 Time Weighted Rate of Return (TWR):

• TWR (when no external cash flows) = rTWR = HPR = rt = ^

^

• TWR (for more than one periods) = rTWR = [(1+rt,1)× (1+rt,2)×… (1+rt,n)] -1

• Annualized TWR (when investment is for more than one year)

= _ 1 + D O1 + D`… + 1 + D3 Pbc_1

• TWR (for the year) = rTWR = [(1+R1)× (1+R2)×… (1+R365)] -1 where R1 = ^

^

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8 Bank Discount Yield = BDY = rBD = efW

3 / / =T0 therefore Price = Par 1 −3 × gh

efW

9 Holding Period Yield = HPY = Y Z Y [ \ Z

Y [

10.Effective Annual Yield = EAY = 1 + i&j efk/.− 1 (Rule: EAY > BDY)

11.Money Market Yield (or CD equivalent Yield) r MM :

12.Bond Equivalent Yield = BDY = Semiannual Yield × 2

Reading 7: Statistical Concepts and Market Returns

1 Range = Maximum Value – Minimum Value

2 Class Interval = i ≥ o )

p where

• i = class interval, H = highest observed value, L = lowest observed value, k = number of

classes

3 Absolute Frequency = Actual number of observations in a given class interval

4 Relative Frequency = qrstuvwx yzx{vx|}~

•tw€u v rxz t• ‚rsxzƒ€w„t|s

5 Cumulative Absolute Frequency = Add up the Absolute Frequencies

6 Cumulative Relative Frequency = Add up the Relative Frequencies

7 Arithmetic Mean = …v t• trsxzƒ€w„t|s „| w†x ‡€w€r€sx

t.t• trsxzƒ€w„t|s „| w†x ‡€w€r€sx

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8 Median = Middle number (when observations are arranged in ascending/descending order)

• For Even number of observations locate median at 3

11.Geometric Mean = GM = c‹‰ ‰`… ‰3 with Xi≥0 for i = 1,2,…n

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22.Semi-deviation (Semi Standard Deviation) = √ œ%• % "B = š∑ ‘„ ‘X —

3 ytz €uu ‘ „ ›‘X

3 ytz €uu ‘ „ ›ž where B = Target Value

3 ytz €uu ‘ „ ›ž

25.Coefficient of Variation = CV =

-‘X where s= sample S.D and ‰X = sample mean

26.Sharpe Ratio = x€| Ytzw•tu„t ¡xwvz| x€| ¡„s¢ •zxx ¡xwvz|

….\ t• Ytzw•tu„t ¡xwvz|

27.Excess Kurtosis = Kurtosis – 3

28.Geometric Mean return ≈ £ % ℎœ %B I " D # " − / =/3T0 9: 70.4 3`

Reading 8: Probability Concepts

1 Empirical Probability of an event E = P(E) = Yztr€r„u„w~ t• xƒx|w ¤

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5 Multiplication Rule (Joint probability that both events will happen):

P(A and B) = P(AB) = P(A\B) × P(B)

P(B and A) = P(BA) = P(B\A) × P(A)

6 Addition Rule (Probability that event A or B will occur):

P(A or B) = P(A) + P(B) – P(AB)

P(A or B) = P(A) + P(B) (when events are mutually exclusive because P(AB) = 0)

7 Independent Events:

• Two events are independent if: P(B\A) = P(B) or if P(A\B) = P(A)

• Multiplication Rule for two independent events = P(A & B) = P(AB) = P(A)× P(B)

• Multiplication Rule for three independent events = P(A and B and C) = P(ABC) =

P(A) × P(B) × P(C)

8 Complement Rule (for an event S) = P(S) + P(SC) = 1 (where SC is the event not S)

9 Total Probability Rule:

P(A) = P(AS) + P(ASC) = P(A\S)×P(S) + P(A\SC)×P(SC)

P(A) = P(AS1) + P(AS2) +….+ P(ASn) = P(A\S1)×P(S1) + P(A\S2)×P(S2)… P(A\Sn)×P(Sn)

(where S1, S2, …,Sn are mutually exclusive and exhaustive scenarios)

10.Expected Return = E(wiRi) = wiE(Ri)

where (wi is weight of variable i and Ri is random variable i)

11.Covariance (between two random variables Ri and Rj):

Cov (Ri Rj) = ∑ O¥ D3 =− ¦D= POD§− ¦D§P

=H

Cov (Ri Rj) = Cov (Rj Ri)

Cov (R, R) = σ2

(R)

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15.Bayes’ Formula = & ¦• " \¯ C"VA œ %A" = (0° 63:9(0° 63:9/.=93\±«03./.=93 ×

& & %A ¥ A² AV ¦• "

16.Multiplication Rule of Counting = n factorial = "! = n (n-1)(n-2)(n-3)…1

17.Multinomial Formula (General formula for labeling problem) = 3 !33!—!…3´!

18.Combination Formula (Binomial Formula) = 3 ¨ = O3P = 33!! !

where n = total number of objects and r = number of objects selected

19.Permutation = 3 &= 3!

3 !

Reading 9: Common Probability Distributions

1 Probability Function (for a binomial random variable) p(x) = p(X=x) = O3µP¥µ 1 − & 3 µ =

= 3 µ !µ!<3!¶ < c·¶ (for x = 0,1,2….n) where x = success out of n trials, n-x = failures out of

n trials, p = probability of success, 1-p = probability of failure, n= number of trials

2 Probability Density Function (pdf) = f(x) = ¸8 /

0 VA ≤ º ≤ ² =

F(x) = µ /

8 / VA < º < ²

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3 Normal Density Function = V º =-√`¼ º¥ µ –`-— — for − ∞ < º < + ∞

4 Estimations by using Normal Distribution:

• Approximately 50% of all observations fall in the interval Á ±`e™

• Approximately 68% of all observations fall in the interval Á ± ™

• Approximately 68% of all observations fall in the interval Á ± 2™

• Approximately 68% of all observations fall in the interval Á ± 3™

• More precise intervals for 95% of the observations are Á ± 1.96™ and for 99% of the

observations are Á ± 2.58™

5 Z-Score (how many S.Ds away from the mean the point x lies)

É = "! ! "A œ $ "!Aœ • % ²$ = ‘ –- (when X is normally distributed)

6 Roy’s Safety-Frist Criterion = SF Ratio = Ê± 7 , 7 Ë Ì

- ,

7 Sharpe Ratio = = _± 7 , 7 Í b

- ,

8 Value at Risk = VAR = Minimum loss (in money terms e.g $) expected over a specified

period at a specified probability level

9 Mean (µ L ) of a lognormal random variable = exp (µ + 0.50σ2)

10.Variance (σ L 2 ) of a lognormal random variable = exp (2µ+ σ2) × [exp (σ2) – 1]

11.Log Normal Price = ST = S0exp (r0,T)

Where, exp = e and r0,t = Continuously compounded return from 0 to T

12.Price relative = Ending price / Beginning price = St+1/ St=1 + Rt, t+1

where,

R t, t+1 = holding period return on the stock from t to t + 1

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13.Continuously compounded return associated with a holding period from t to t + 1:

rt, t+1= ln(1 + holding period return) or

rt, t+1 = ln(price relative) = ln (St+1 / St) = ln (1 + Rt,t+1)

(The continuously compounded return < associated holding period return)

14.Continuously compounded return associated with a holding period from 0 to T:

R0,T= ln (ST / S0) or W, = , + `, + ⋯ + W,

Where,

15.When one-period continuously compounded returns (i.e r 0,1 ) are IID random variables

with mean µ and variance σ 2 , then

¦O W, P = ¦O , P + ¦O `, P + ⋯ + ¦O W, P = ÁJ And

' % "B = ™`O W, P = ™`J

S.D = σ (r0,T) = σ√J

16.Annualized volatility

= sample S.D of one period continuously compounded returns × √J

where, T = Number of trading days in a year = 250

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Reading 10: Sampling and Estimation

1 Variance of the distribution of the sample mean = -—

3

2 Standard deviation of the distribution of the sample mean = š-3—

3 Standard Error of the sample mean:

• When the population S.D (σ) is known = ™‘ Ï = √3-

• When the population S.D (σ) is not known = ‘ Ï = √3 where s = sample S.D estimate of

s = ‹ œ¥$ • % "B = √ ` ℎ ` = ∑c ‘Ž ‘X —

Ž•

4 Finite Population Correction Factor = fpc = šQ( 3( R where N= population

5 New Adjusted Estimate of Standard Error = (Old estimated standard error × fpc)

6 Construction of Confidence Interval = Point estimate ± (Reliability factor × Standard

(where t = critical value of t-distribution with df = n-1 and area of /2 in each tail)

(used when population variance is not known for both small and large sample sizes)

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Reading 11: Hypothesis Testing

1 Test Statistic = …€ Ñux …w€w„sw„} Ò~Ñtw†xs„Óx‡ Ô€uvx t• ÑtÑvu€w„t| Ñ€z€ xwxz

sw€|‡€z‡ xzztz t• s€ Ñux sw€w„sw„} ∗

*

when population S.D is unknown, the standard error of sample statistic is give by Ö‘ Ï = √3-

*

when population S.D is unknown, the standard error of sample statistic is give by ™‘ Ï = √3-

2 Power of Test = 1-Probability of Type II Error

(when sample size is large or small and population S.D is unknown and

population sampled is normally or approximately normally distributed)

6 Test Statistic for a test of the difference between two population means (normally

distributed populations, populations variances unknown but assumed equal)

7 Test Statistic for a test of the difference between two population means (normally

distributed populations, unequal and unknown populations variances unknown)

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Ú Û——

c—Ý

— c—

8 Test Statistic for a test of mean differences (normally distributed populations, unknown

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Ö` = œ¥$ • % "B AV V% œ¥$ % ℎ " A² • %A"

Ö` = œ¥$ • % "B AV BA"! œ¥$ % ℎ "` A² • %A"

!V = " − 1 "#œ A ! Ÿ AV V !Aœ

!V` = "`− 1 ! "Aœ%" A ! Ÿ AV V !Aœ

11 Relation between Chi Square and F-distribution = à = ‘‘—á

—á3

where:

• ‰` is one chi square random variable with one m degrees of freedom

• ‰`` is another chi square random variable with one n degrees of freedom

12 Spearman Rank Correlation = = 1 −f ∑cŽ• 1—

3 3 —

• For small samples rejection points for the test based on are found using table

• For large sample size (e.g n>30) t-test can be used to test the hypothesis i.e

= " − 21 − ` /`/`

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Reading 12: Technical Analysis

1 Ratio (Relative Strength Analysis) = Yz„}x t• €| €ssxw w†€w „s rx„|â €|€u~Óx‡

Yz„}x t• w†x žx|}† €z¢ qssxw

2 Price Target for the

• Head and Shoulders = Neckline – (Head – Neckline)

• Inverse Head and Shoulders = Neckline + (Neckline– Head)

3 For the Double Tops Pattern:

• Height = Highest high – Lowest Low

• Price target = Lowest Low – Height of the pattern

4 For the Double Tops Pattern:

• Height = Highest high – Lowest Low

• Price target = Highest High + Height of the pattern

5 Height of a Triangle = Price at the start of the downward slopping trend line – Price at the

start of the upward sloping trend line

6 Flags and Pennants Pattern

• Flag Price Target = Price level at which the flag ends – (Price level at which the trend

starts – Price level at which the flag starts to form)

• Pennant Price Target = Price level at which the pennant ends – (Price level at which the

trend starts – Price level at which the pennant starts to form)

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7 Simple Moving Average = Y Z Y ã Y ä … Y |

8 Momentum Oscillator (or Rate of Change Oscillator ROC):

• ROC = 91/Så ;m/3>0 –;m/3>0 3 <0 =91 />9

;m/3>0 3 <0 =91 />9 × 100

• Momentum Oscillator Value M = (V-Vx) × 100

(where V = most recent closing price and Vx = closing price x days ago)

• Alternate Method to calculate M =

• %D = Average of the last three %K values calculated daily

11. Put/Call Ratio (Type of Sentiment Indicators) = Ôtuv x t• Yvw ‚Ñw„t|s •z€‡x‡

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Formula Sheet

Level I 2015

F i n Q u i z

Volume 2: Economics

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Formula Sheet Volume 2: Economics

Reading 13: Demand and Supply Analysis: Introduction

• Area (for calculating Consumer Surplus) = ½ (Base × Height) = ½ (Q0 × P0)

4 Producer Surplus = Total revenue received from selling a given amount of a good – Total

variable cost of producing that amount

• Total revenue = Total quantity sold × Price per unit

• Area (for calculating Producer Surplus) = ½ (Base × Height) = ½ {(Q0) × (P0 – intercept

point on y-axis**)}

**where supply curve intersects y-axis

5 Total Surplus = Consumer surplus + Producer surplus

6 Total Surplus = Total value – Total variable cost

7 Society Welfare = Consumer surplus + Producer surplus

)(

2 1 2 1

1 2

P P

Q Q

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)(

2 1 2 1

1 2

I I

Q Q

2 Equation of Budget Constraint Line = (Price of Good X × Quantity of Good X) + (Price

of Good Y × Quantity of Good Y)

=

Reading 15: Demand and Supply Analysis: The Firm

1 Profit = Total revenue – Total cost

2 Accounting Profit = Total Revenue – Explicit Costs(or Accounting costs)

3 Economic Profit

• = Total Revenue – Explicit Costs – Implicit Costs or

• = Accounting Profit – Implicit Costs or

• = Total Revenue – Total Economic Costs

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4 Economic costs = Explicit costs + Implicit costs

5 Normal Profit = Accounting Profit – Economic Profit

6 Accounting profit = Economic Profit + Normal Profit

7 Economic rent = (New “Higher” Price after increase in Demand – Previous Price before

increase in Demand) × Quantity supplied before increase in Demand

8 Total Revenue (TR):

• = Price × Quantity or

• = Sum of individual units sold × Respective prices of individual Units sold = Σ (Pi × Qi)

11.Total Variable Cost = Variable Cost per unit × Quantity Produced

12.Total Cost = Total Fixed + Total Variable

16.Marginal revenue (When there is perfect competition) = Avg Revenue = Price = Demand

17.Profit can be increased by increasing output when MR> MC

18.Profit can be increased by decreasing output when MR< MC

19.Break-even price: P = ATC Output level where Price = Average Revenue = Marginal

Revenue = Average Total Cost where, Total Revenue = Total Cost

20.Firms earn Economic Profits when Price > Average Total Cost

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21.Profits occur when Total Revenue (TR) ≥ Total Cost (TC) AND when Price = Marginal

Cost firm will continue operating

22.Losses are incurred when there are Operating profits (Total Revenue ≥ Variable Cost) but

Total Revenue < Total Fixed Cost + Total Variable Cost AND when Price = Marginal Cost

while losses are < fixed costs firm will continue operating

23.Losses are incurred when there are Operating losses (Total Revenue ≤ Variable Cost) AND

when losses ≥ fixed costs firm will shut down

26.Least-cost optimization Rule:

$ # $ # =

27.Profit is maximized when: MRP = Price or cost of the input for each type of resource that is

used in the production process

28.Marginal Revenue product = Marginal Product of an input unit × Price of the Product =

29.Surplus value or contribution of an input to firm’s profit = MRP – Cost of an input

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Reading 16: The Firm and Market Structures

1 When there is perfect competition, Marginal revenue = Avg Revenue = Price = Demand

(

4 Herfindahl-Hirshman Index = Sum of the squares of the market shares of the top N

companies in an industry

Reading 17: Aggregate Output, Prices, and Economic Growth

1 Nominal GDP t = Prices in year t × Quantity produced in year t

2 Real GDP t = Prices in the base year × Quantity produced in year t

3 Implicit price deflator for GDP or GDP deflator =

6 GDP = Consumer spending on final goods and services + Gross private domestic investment

+ Government spending on final goods and services + Government gross fixed investment +

Exports – Imports + Statistical discrepancy

7 Net Taxes = Taxes – Transfer payments

8 GDP = National income + Capital consumption allowance + Statistical discrepancy

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9 National Income = Compensation of employees (i.e wages) + Corporate and government

enterprise profits before taxes + Interest income + unincorporated business net income

(proprietor’s income) + rent + indirect business taxes les subsidies

10.Total Amount Earned by Capital = Profit + Capital Consumption Allowance

11.PI = National income – Indirect business taxes – Corporate income taxes – Undistributed

corporate profits + Transfer payments

12.Personal disposable income (PDI) = Personal income – Personal taxes OR GDP (Y) +

Transfer payments (F) – (R/E + Depreciation) – direct and indirect taxes (R)

13.Business Saving = R/E + Depreciation

14.Household saving = PDI - Consumption expenditures - Interest paid by consumers to

business - Personal transfer payments to foreigners

15.Business sector saving = Undistributed corporate profits + Capital consumption allowance

16.Total Expenditure = Household consumption (C) + Investments (I) + Government spending

(G) + Net exports (X-M)

17.Private Sector Saving = Household Saving + Undistributed Corporate Profits + Capital

Consumption Allowance

18.GDP = Household consumption + Private Sector Saving + Net Taxes

19.Domestic saving = Investment + Fiscal balance + Trade balance

20.Trade Balance = Exports - Imports

21.Fiscal balance = Government Expenditure – Taxes = (Savings – Investment) – Trade

Balance

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23.Quantity theory of money equation: Nominal Money Supply × Velocity of Money = Price

Level × Real Income or Expenditure

24.Percentage change in unit labor cost = % change in nominal wages - % change in

productivity

25.Economic growth = Annual % change in real GDP

26.Total Factor Productivity growth = Growth in potential GDP – [Relative share of labor in

National Income × (Growth in labor) + [Relative share

of capital in National Income × (Growth in capital)]

27.Growth in potential GDP = Growth in technology + (Relative share of labor in National

Income × Growth in Labor) + (Relative share of capital in National Income × Growth in capital]

28.Capital share =Corporate profits + net interest income + net rental income + (depreciation/

GDP)

Reading 18: Understanding Business Cycle

1 Price index at time t 2 = 9:;<= >? @A= B>CD<CE@F>G H:DI=@ :@ @FC= @ J

9:;<= >? @A= B>GD<CE@F>G H:DI=@ :@ @FC= @ K × 100

Inflation Rate = 0LMNOP QRSPT UV VNWP VJ KXX 5 − 1

2 Fisher Index = YZ[ × Z\ (where, IL = Laspeyres index and Ip = Paasche Index)

3 ]GF@ ;:^>_ `>D@ (]bB) FGdF`:@>_ = # % e ( e (

4 fPghONVi hj WhRPi = &

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Reading 19: Monetary and Fiscal Policy

1 Total amount of money created = New deposit/ Reserve requirement

3 Narrow money = M1= currency held outside banks + checking accounts + traveller’s check

4 Broad money = M2 = M1 + time deposits + saving deposits

5 M3 = M2 + deposits with non-bank financial institution

6 Quantity Theory of Money = M × V = P × Y where,

M = Quantity of money

V = Velocity of circulation of money

P = Average price level

Y = Real output

7 Neutral Rate = Trend Growth + Inflation Target

8 Impact of Taxes and Government Spending: The Fiscal Multiplier

The net impact of the government sector on AD:

• G – T + B = Budget surplus or Budget deficit

where, G = government spending , T =taxes, B =transfer benefits

• Disposable income = Income – Net taxes = (1 – t) Income

where, Net taxes = taxes – transfer payments, t = net tax rate

9 Fiscal Multiplier (in the absence of taxes) = 1/(1 - MPC)

where, MPC = Marginal propensity to consume

MPS = Marginal propensity to save and is estimated as MPS = 1 – MPC

• Total increase in income and spending = Fiscal multiplier × G

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• Total increase in income and spending = Fiscal multiplier × G

• Initial increase in consumption due to reduction in taxes = MPC × tax cut amount

• Total or cumulative effect of tax cut = multiplier × initial change in consumption

3 Net exports = Value of a country's exports - Value of country's imports

4 Net welfare effect = consumer’s surplus loss + producer’s surplus gain + Govt revenue

5 Closed Economy’s output = Y = C+I+G

6 Open Economy’s output = Y = C+I+G+(X-M)

• Current Account Balance = X-M = Y- C+I+G

7 Consumption = Income + transfers – taxes – saving

C=Yd - Sp =Y+R-T-Sp And,

CA = Sp- I+ Government surplus (or government saving) = Sp- I+ (T- G- R)Sp + Sg = I + CA

where, Sg = government savings

S p = I + CA – Sg

• Current Account Imbaance CA = Sp + Sg – I

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Sd/f =Spot exchange rate (quoted in terms of the number of units of domestic currency per

one unit of foreign currency)

Pf = Foreign price level quoted in terms of the foreign currency

Pd = Domestic price level in terms of the domestic currency

6 Points on a forward rate quote = Forward exchange rate quote –Spot exchange rate quote

7 Forward rate = Spot exchange rate + vhMšUMSxhNRVz

KX,XXX

8 œ>_•:_d E_=CF<C/dFD`><G@ (FG %) = zxhV PTOžURwP MUVP•(jhMšUMS xhNRVz/KX,XXX)zxhV PTOžURwP MUVP − 1

9 To convert spot rate into a forward quote (when points are represented as %) = Spot

exchange rate × (1 + % premium or discount)

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3•“ ‰ ª5 « (where « is quoted interest rate period)

13.Relationship between the trade balance and expenditure/ saving decisions:

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ԐM =price elasticity of domestic country demand for imports

17.Trade balance = Income (GDP) – Domestic expenditure = Absorption

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Formula Sheet Volume 3: Financial Reporting and Analysis

Reading 22 – Financial Statement Analysis: An Introduction

1 Gross Profit = Revenue – Cost of sales

2 Operating Profit or EBIT = Gross profit – Operating costs + Other operating income

3 Profit before tax = EBIT – Interest expense

4 Profit after tax = Profit before tax – Income tax expense

Reading 23: Financial Reporting Mechanics

1 Owner’s Equity = Contributed Capital + Retained Earnings

2 Ending retained earnings = Beginning retained earnings + Net income – Dividends

3 Assets = Liabilities + Contributed Capital + Beginning retained earnings + Revenue –

Expenses – Dividends

Reading 24: Financial Reporting Standards

- - -

Reading 25: Understanding Income Statements

2 Revenue recognized under Percentage-of-Completion Method = % of Total cost spent by

the firm × Total Contract Revenue

3 Revenue recognized when outcome cannot be reliably measured = Contract costs

incurred

4 Revenue recognized under installment method = × Cash receipt

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7 COGS using LIFO = Total cost – Value of ending inventory

14 Net Profit Margin = ( )

15 Gross Profit Margin =

16 Comprehensive EPS = EPS + Other Comprehensive Income per share

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Reading 26 – Understanding Balance Sheets

1 Percentage of Accounts Receivable estimated to be uncollectible =

2 Net Identifiable Assets = Fair value of identifiable assets – Fair value of liabilities &

contingent liabilities

3 Amortized cost of PPE = Historical cost – Accumulated depreciation – Impairment losses

4 Carrying value for PPE under revaluation model

= Fair value at date of revaluation – Accumulated depreciation (if any)

5 Net Identifiable Assets = Fair value of identifiable assets – Fair value of liabilities &

contingent liabilities

6 Amortized cost of PPE = Historical cost – Accumulated depreciation – Impairment losses

7 Carrying value for PPE under revaluation model

= Fair value at date of revaluation – Accumulated depreciation (if any)

8 Deferred tax liability = Taxable income < Reported Financial Statement Income before

taxes

9 Deferred tax liability = Actual income tax payable in a period < Income tax expense

10.Vertical common-size balance-sheet = 4

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Reading 27: Understanding Cash Flow Statements

1 Ending Cash = Beginning cash + Cash receipts (from operating, investing, and financing

activities) – Cash payments (for operating, investing, and financing activities)

2 Ending Accounts Receivable = Beginning Accounts Receivable + Revenues – Cash

collected from customers

3 Cash received from customers = Revenue – Increase in accounts receivable

4 Purchases from suppliers = Cost of goods sold + Increase in inventory

5 Cash paid to suppliers = Cost of goods sold + Increase in inventory – Increase in accounts

payable

6 Ending Inventory = Beginning inventory + Purchases – Cost of goods sold

7 Ending accounts payable = Beginning accounts payable + Purchases – Cash paid to

suppliers

8 Cash paid to employees = Salary and wages expense – Increase in salary and wages payable

9 Ending salary and wages payable = Beginning salary and wages payable + Salary and wages

expense – cash paid to employees

10.Cash paid for other operating expenses = Other operating expenses – Decrease in prepaid

expenses – Increase in other accrued liabilities

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11.Cash paid for interest = Interest expense + Decrease in interest payable

12.Ending Interest Payable = Beginning interest payable + Interest expense – Cash paid for

interest

13.Cash paid for income taxes = Income tax expense – Increase in income tax payable

14.Historical cost of equipment sold = Beginning balance equipment + Equipment purchased

– Ending balance equipment

15.Accumulated depreciation on equipment sold = Beginning balance accumulated

depreciation + Depreciation expense – Ending balance accumulated depreciation

16.Cash received from sale of equipment = Historical cost of equipment sold – Accumulated

depreciation on equipment sold + gain on sale of equipment

17.Dividends paid = Beginning balance of retained earnings + Net income – Ending balance of

retained earnings

18.Free cash flow to the Firm (FCFF) = Net income + Non-cash charges + Interest expense (1

– tax rate) – Capital expenditures – Working capital expenditures

19.FCFF = CFO + Interest expense (1 – Tax rate) – Capital expenditures

20.Free cash flow to Equity (FCFE) = CFO – Capital expenditures + Net borrowing

21.Cash flow to revenue = 89

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Reading 28: Financial Analysis Techniques

1 Compound Growth Rate = ; 4 ," , !, !

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12.Average Accounts Receivable Balance = Average Days’ Credit Sales × DSO or

• ROE = ROA × Leverage

• ROE = Tax Burden × Interest Burden × EBIT Margin × Total Asset Turnover ×

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Reading 30: Long-Lived Assets

4 Carrying amount under revaluation model = Fair value at the date of revaluation – Any

subsequent Accumulated Depreciation or Amortization

5 Impairment Loss (IFRS) = Recoverable Amount – Net Carrying Amount

Where, Recoverable amount = Max [(Fair value – Costs to sell); Value in Use)] and Value

in use = PV of Expected Future Cash Flows

6 Impairment Loss (US GAAP) = Asset’s Fair Value – Carrying Amount …….If Carrying

amount > Undiscounted Expected Future Cash Flows

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