cfa level 1, june, 2016 - formula sheet
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8/16/2019 CFA Level 1, June, 2016 - Formula Sheet
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FinQuiz Formula Sheet CFA Level I 2016
• r MM = opf ( qr
opf/ G ( qr (Rule: r MM>
r BD)10. Bond Equivalent Yield = BDY =
Semiannual Yield ! 2
Reading 7: Statistical Concepts & MarketReturns
1. Range = Max Value – Min Value
2. Class Interval = i " z/B
{ where
• i = class interval• H = highest value• L = lowest value, k = No. of classes.
3. Absolute Frequency = Actual No ofObservations (obvs) in a given classinterval
4. Relative Frequency = K|7OwSGI !(I}SILa`
*OGHw 1O OP U|~7
5. Cumulative Absolute Frequency = Add upthe Absolute Frequencies
6. Cumulative Relative Frequency = Add upthe Relative Frequencies
7. Arithmetic Mean = FS. OP O|~7 ML JHGH|H7I
1O•OP O|~7 ML GxI JHGH|H7I
8. Median = Middle No (when observationsare arranged in ascending/descendingorder)
• For Even no of obvs locatemedian at L
k
• For Odd no. of obvs locate
median at L'&
k
9. Mode = obvs that occurs most frequentlyin the distribution
10. Weighted Mean = € 8 2 M € MLM[& =
(w1X1+ w 2X2+….+ w nXn)
11. Geometric Mean = GM = €& € k l € Lm
with X i" 0 for i = 1,2,…n.
12. Harmonic Mean = H.M = € z 8 L%
‚ ƒmƒ„%
13. Population Mean = µ =…ƒ
mƒ
1 with € M † j
for i = 1,2,.,.,n.
14. Sample Mean = € 8…ƒ
mƒ
L where n =
number of observation in the sample
15.
Measures of Location:• Quartiles = iM7G(M|SGMOL
‡
• Quintiles = iM7G(M|SGMOL
u
• Deciles = iM7G(M|SGMOL
&f,
• Percentiles = L y = = , + `
&ff
16. Mean Absolute Deviation = MAD =…Z/…m
ƒ„%
L
17. Population Var = !2 = …ƒ/ˆ ‰#
ƒ„%
1
18. Population S.D = Š k =…ƒ/ˆ ‰#
ƒ„%
1
19. Sample Var = s 2 = …ƒ/… ‰mƒ„%
L/&
20. Sample S.D = s =…ƒ/… ‰m
ƒ„%
L/&
21. Semi-var = …ƒ/… ‰
L/&!O( Hww …ƒ‹…
22. Semi-deviation (Semi S.D) =
94Œ> ;5>;=X4 = …ƒ/… ‰
L/&!O( Hww …ƒ‹…
23. Target Semi-var = …ƒ/y ‰
L/&!O( Hww …ƒ‹y
where B = Target Value
24. Target Semi-Deviation =:;5Ž4: 94Œ> ;5>;=X4 =
…ƒ/y ‰
L/&!O( Hww …ƒ‹y
25. Coefficient of Variation = CV = F…
where s= sample S.D and € = samplemean
26. Sharpe Ratio = )IHL $O(GPOwMO N/)IHL NP N
F•i OP $O(GPOwMO N
27. Excess Kurtosis = Kurtosis – 3
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FinQuiz Formula Sheet CFA Level I 2016
• x = success out of n trials• n-x = failures out of n trials• p = probability of success• 1-p = probability of failure
•
n = no of trials.
2. Probability Density Function (pdf) = f(x)
=&
|/Hj
eW5 ; ¢ £ ¢ œ =
F(x) = Ÿ/H
|/H eW5 ; ¤ £ ¤ œ
3. Normal Density Funct = e £ 8&
™ k¥4£’ /cŸ/ˆd ‰
k™‰ ¦§¨ ? © ¤ £ ¤ , ©
4. Estimations by using Normal Distribution:
• Approximately 50% of all obsv fall in
the interval ª « k
oŠ
• Approx 68% of all obvs fall in theinterval ª « Š
• Approx 95% of all obvs fall in theinterval ª «¬Š
• Approx 99% of all obvs fall in theinterval ª « Š
• More precise intervals for 95% of theobvs are ª « +•®¯Š and for 99% of theobservations are ª « ¬•°±Š•
5. Z-Score (how many S.Ds away from themean the point x lies) ² 89:;=<;5< =W5Œ;³ 5;=<WŒ ;5>;œ³4 8
…/ˆ
™ (when X is normally distributed)
6. Roy’s Safety-Frist Criterion = SF Ratio = NE /N ´
™E
7. Sharpe Ratio = = NE /N µ
™E
8. Value at Risk = VAR = Minimum $ lossexpected over a specified period at aspecified prob level.
9. Mean (µ L) of a lognormal random variable= exp (µ + 0.50 %2)
10. Variance ( %L2) of a lognormal random
variable = exp (2µ+ %2) ! [exp ( %2) – 1].
11. Log Normal Price = S T = S 0exp (r 0,T)Where, exp = e and r 0,t = Continuouslycompounded return from 0 to T
12. Price relative = End price / Beg price =St+1/ S t=1 + R t, t+1
where,
Rt, t+1 = holding period return on the stock from t to t + 1 .
13. Continuously compounded returnassociated with a holding period from t to t+ 1:
r t, t+1= ln(1 + holding period return) orr t, t+1 = ln(price relative) = ln (S t+1 / S t) = ln(1 + R t,t+1)
14. Continuously compounded returnassociated with a holding period from 0 toT:
R 0,T= ln (S T / S 0) or 5f–* 8 5 */&–* ,5*/k–*/& , ¶ , 5 f–&
Where,r T-I, T = One-period continuouslycompounded returns
15. When one-period continuouslycompounded returns (i.e. r 0,1) are IIDrandom variables.
“ 5f–* 8 “ 5 */&–* , “ 5 */k–*/& ,
¶ , “ 5 f–& 8 ª] And
A;5>;=X4 8 Š k 5f–* 8 Š k ]
S.D. = % (r 0,T) = % ]
16. Annualized volatility = sample S.D. ofone period continuously compoundedreturns ! ]
Reading 10: Sampling and Estimation
1. Var of the distribution of the sample mean
= ™‰
L
2. S.D of the distribution of the sample mean
= ™‰
L
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FinQuiz Formula Sheet CFA Level I 2016
3. Standard Error of the sample mean:• When the population S.D ( ! ) is known
= Š… 8 ™
L
• When the population S.D ( ! ) is notknown = 9… 8 7
L where s = sample
S.D estimate of s =
9;Œ’³4 ;5>;=X4 8
9k 23454 9 k =…ƒ/… ‰m
ƒ„%
L/&
4. Finite Population Correction Factor = fpc
= 1/L
1/& where N= population
5. New Adjusted Estimate of Standard Error= (Old estimated standard error ! fpc)
6. Construction of Confidence Interval (CI) =Point estimate ± (Reliability factor ! Standard error)
• CI for normally distributed populationwith known variance = £ « ² Hvk
™
L
•
CI for normally distributed populationwith unknown variance = £ « ² Hvk
F
L
where S = sample S.D.
7. Student’s t distribution
µ = € « : HvkF
L
8. Z-ratio = Z =
x ! µ
! / n
9. t-ratio = t =
x ! µ
s / n
Reading 11: Hypothesis Testing
1. Test Statistic =·¸¹º»¼ ·½¸½¾¿½¾À Áºýļ¿¾Å¼Æ Ǹ»È¼ ÃÉ ºÃº º¸Ê¸¹¼½¼Ê
¿½¸ËƸÊÆ ¼ÊÊÃÊ ÃÉ ¿¸¹º»¼ ¿½¸½¾¿½¾ÀÌ
*when Pop S.D is unknown, the standarderror of sample statistic is give by Í … 8
F
L
*when Pop S.D is unknown, the standarderror of sample statistic is give by Š… 8 ™
L
2. Power of Test = 1-Prob of Type II Error
3. ² 8 …/ˆ hÎm
(when sample size is large or
small but pop S.D is known)
4. ² 8 …/ˆ h-m
(when sample size is large but
pop S.D is unknown where s is sampleS.D)
5. : L/& 8 …/ˆ h-m
(when sample size is large or
small and pop S.D is unknown and pop
sampled is normally or approximatelynormally distributed)
6. Test Statistic for a test of diff b/w two popmeans (normally distributed, pop varunknown but assumed equal)
t = …%/… ‰ / ˆ %/ˆ ‰
Ï Ð‰
m%'
Ï Ð‰
m‰
%v‰ where Í Rk = pooled
estimator of common variance =L%/& F %
‰' L ‰/& F ‰‰
L%' L ‰/k where <e 8 = & , = k ?
¬.
7. Test Statistic for a test of diff b/wn two pop means (normally distribu ted, unequaland unknown pop var unknown)
t = …%/… ‰ / ˆ %/ˆ ‰
Ï %‰
m%'
Ï ‰‰
m‰
%v‰ In this df calculated as
<e 8
Ï %‰
m% '
Ï ‰‰
m‰
‰
Ï %‰
m%
‰
m%'
Ï ‰‰
m‰
‰
m‰
8. Test Statistic for a test of mean differences(normally distributed populations,unknown population variances)
• : 8 J/ˆ Ñh
FJ
• sample mean difference = < 8
&L
<MLM[&
• sample variance = Í Jk 8
J %/J ‰mƒ„h
L/&
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FinQuiz Formula Sheet CFA Level I 2016
• sample S.D = Í Jk
• sample error of the sample mean
difference = 9 < 8 FÑ
L
8. Chi Square Test Statistic (for testconcerning the value of a normal
population variance) € k 8 L/& F ‰
™h‰ where
= ?+ 8 <e ;=< Í k 8
9;Œ’³4 ;5>;=X4 8…ƒ/… ‰m
ƒ„h
L/&
9. Chi Square Confidence Interval forvariance
Lower limit = L = L/& F ‰
…Òv‰‰ and Upper limit
= U = = L/& F ‰
…%¡Òv‰‰
10. F-test (test concerning differences betweenvariances of two normally distributed
populations) F = F%‰
F‰‰
Í &k 8 +9: 9;Œ’³4 ;5 2>:3 = & Wœ9 Í&k 8
¬=< 9;Œ’³4 ;5 2>:3 = k Wœ9
<e& 8 = & ? + =ÓŒ45;:W5 <e<ek 8 = k ? + <4=WŒ>=;:W5 <e
11. Relation between Chi Square and F-
distribution = Ô 8…%
‰.
…‰‰
L where:
• €&k is one chi square random variable
with one m degrees of freedom
• € kk is another chi square random
variable with one n degrees offreedom
12. Spearman Rank Correlation = 57
8 + ?¯ <&
kLM[&
= =k ? +
• For small samples rejection points forthe test based on 57are found usingtable.
• For large sample size (e.g. n>30) t-testcan be used to test the hypothesis i.e.
: 8= ? ¬ &vk57
+ ? 5 7k &vk
Reading 12: Technical Analysis
1. Relative Strength Analysis =ÕʾÀ¼ ÃÉ ̧ ¿¿¼½
ÕʾÀ¼ ÃÉ ½Ä¼ Ö¼ËÀŸÊ× Ø¿¿¼½
2. Price Target for the• Head and Shoulders = Neckline –
(Head – Neckline)• Inverse Head and Shoulders =
Neckline + (Neckline– Head)
3. Simple Moving Average = ÕÙ'Õ Ú'Õ Ûl•'Õ Ë
Ü
4. Momentum Oscillator (or Rate of ChangeOscillator ROC):
• Momentum Oscillator Value M = (V-Vx) 0+jj
(where V = most recent closing priceand V x = closing price x days ago)
• Alternate Method to calculate M ="
"0+jj
5. Relative Strength Index = RSI = +jj ?
&ff
&'NF where
RS = ÝR axHLTI7
iO L axHLTI7
6. Stochastic Oscillator (composed of twolines %K and %D):
• Þß 8 +jj Q/B&‡
z&‡/B&‡ where:
C = latest closing price, L14 = lowest price in last 14 days, H14 is highest price in last 14 days
• % D = Average of the last three % K values calculated daily.
7. Put/Call Ratio (Type of Sentiment
Indicators) = Çûȹ¼ ÃÉ ÕȽ ຽ¾ÃË¿ áʸƼÆ
Çûȹ¼ ÃÉ â¸»» ຽ¾ÃË¿ áʸƼÆ
8. Short Interest Ratio (Type of Sentiment
Indicators) = ·ÄÃʽ ã˽¼Ê¼¿½ Øä¼Ê¸å¼ 渾»Â áʸƾËå Çûȹ¼
9. Arms Index TRIN i.e. Trading Index (Typeof Flow of funds Indicator) = 5Œ ›=<4£ W5 ]Y›š 8
1O•OP KJ~HL g77SI7 ç1O•OP iIawML g77SI7
"OwS.I OP KJ~HL g77SI7ç"OwS.I OP iIawML g77SI7
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FinQuiz Formula Sheet CFA Level I 2016
Reading 13: Demand & Supply Analysis:Introduction
1. Slope of the demand curve =è éê ëìéíî
è éê ïðñêòéòó ôîõñêöîö
2. Slope of the supply curve =è éê ëìéíî
è éê ïðñêòéòó ÷ðøøùéîö
3. Consumer Surplus = Value that aconsumer places on units consumed –Price paid to buy those units• Area (for calculating Consumer
Surplus) = & (Base ! Height) = & (Q0
! P0)
4. Producer Surplus = Total revenue receivedfrom selling a given amount of a good –Total variable cost of producing thatamount
• Total revenue = Total quantity sold ! Price per unit
• Area (for calculating Producer
Surplus) = & (Base ! Height) = & {(Q 0) ! (P0 – intercept point on y-axis**)}
**where supply curve intersects y-axis
5. Total Surplus = Consumer surplus +Producer surplus
6. Total Surplus = Total value – Totalvariable cost
7. Society Welfare = Consumer surplus +Producer surplus
8. Price Elasticity of Demand =Þ è éê ïðñêòéòó ôîõñêöîö
Þ è éê ëìéíî
)(
)(P%Q%
2121
12
2121
12
P P P P QQQQ
+
!
+
!
="
"
9. Income Elasticity of Demand =Þ è éê ïðñêòéòó ôîõñêöîö
Þ è éê úêíûõî=
)(
)(I%Q%
2121
12
2121
12
I I I I QQQQ
+
!
+
!
="
"
10. Cross Elasticity =Þ èéê ïðñêòéòó ôîõñêöîö ûü ýûûö þ
Þ è éê ëìéíî ûü ýûûö ÿ
Reading 14: Demand & Supply Analysis:Consumer Demand
1. Marginal Utility = è éê ! ûòñù " òéùéòó
è éê ïðñêòéòó # ûê $ðõîö
2. Equation of Budget Constraint Line = (P X ! QX ) + (P Y ! QY)
3. Slope of Budget Constraint Line = è éê ï %
è éê ï ‚ =
ë ‚
ë %
4. Marginal Rate of Substitution = è éê ï %
è éê ï ‚ =
& ñì ' éêñù " òéùéòó ûü ýûûö þ
& ñì ' éêñù " òéùéòó ûü ýûûö ÿ
Reading 15: Demand & Supply Analysis: TheFirm
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
4.
Economic costs = Explicit costs + Implicitcosts5. Normal Profit = Accounting Profit –
Economic Profit
6. Accounting profit = Economic Profit + Normal Profit
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FinQuiz Formula Sheet CFA Level I 2016
7. Economic rent = (New “Higher” Priceafter ( in Demand – Previous Price before( in Demand) ! QS before ( in Demand
8. Total Revenue (TR):• = Price ! Quantity or• = Sum of individual units sold !
Respective prices of individual Unitssold = ' (Pi ! Qi)
9. Average Revenue (AR) = ! ûòñù ) î * îêðî
ïðñêòéòó
10. Marginal Revenue (MR) = è éê ! ûòñù ) î * îêðî
è éê ïðñêòéòó
11. Total Variable Cost = Variable Cost perunit ! Quantity Produced
12. Total Cost = Total Fixed + Total Variable
13. Average total cost (ATC) =! ûòñù # û $ò
ïðñêòéòó ëìûöðíîö = Avg. Fixed Cost + Avg.
Variable Cost
14. Marginal cost (MC) = è éê ! ûòñù # û$ò
è éê ïðñêòéòó ëìûöðíîö
15. Marginal Variable Cost =è éê ! ûòñù + ñìéñ , ùî # û $ò
è éê ïðñêòéòó ëìûöðíîö
16. Marginal revenue (in perfect competition)= Avg. Revenue = Price = Demand
17. Profit can be increased by increasingoutput when MR> MC
18. Profit can be increased by decreasingoutput when MR< MC
19. Break-even price: P = ATC ! Outputlevel where Price = Average Revenue =Marginal Revenue = Average Total Cost! where, Total Revenue = Total Cost.
20. Firms earn Economic Profits when Price >Average Total Cost
21. Profits occur when Total Revenue (TR) "
Total Cost (TC) & when Price = MarginalCost ! firm will continue operating.
22. Losses are incurred when there areOperating profits (Total Revenue " Variable Cost) but Total Revenue < TotalFixed Cost + Total Variable Cost ANDwhen Price = Marginal Cost while lossesare < fixed costs ! firm will continueoperating.
23. Losses are incurred when there areOperating losses (Total Revenue ( Variable Cost) AND when losses " fixedcosts ! firm will shut down.
24. Average Product = ! ûòñù ëìûöðíò
ïðñêòéòó ûü - ñ , ûì
25. Marginal Product = è éê ! ûòñù ëìûöðíò
è éê ïðñêéòó ûü - ñ , ûì =
è éê ! ûòñù . ðòøðò
è éê / û ûü 0 ûì 1 îì $
26. Least-cost optimization Rule:& ñì ' éêñù ëìûöðíò ûü - ñ , ûì
ëìéíî ûü - ñ , ûì8
& ñì ' éêñù ëìûöðíò ûü ë 2ó$éíñù # ñøéòñù
ëìéíî ûü ë 2 óéíñù # ñøéòñù
27. Profit is maximized when: MRP = Price orcost of the input for each type of resourcethat is used in the production process
28. Marginal Revenue product = MarginalProduct of an input unit ! Price of the
Product = Price of the input =è éê ! ûòñù ) î * îêðî
è éê ïðñêòéòó ûü úêøðò îõøùûóîö
29. Surplus value or contribution of an input tofirm’s profit = MRP – Cost of an input
Reading 16: The firm & Market Structures
1. In perfect competition, Marginal revenue =Avg. Revenue = Price = Demand
2. Marginal Revenue = 3 ¨456 0 + ?
&
ëìéíî 7 ùñ$òéíéòó ûü ôîõñêö
3. Concentration Ratio =÷ðõ ûü $ñùî $ *ñùðî $ ûü ò2 î ùñì ' î $ò &f üéìõ $
! ûòñù & ñì 1 îò ÷ñùî $
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FinQuiz Formula Sheet CFA Level I 2016
4. Herfindahl-Hirshman Index = Sum of thesquares of the market shares of the top Ncompanies in an industry
Reading 17: Aggregate Output, Prices &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 =*ñùðî ûü íðììîêò óì ûðòøðò ñò íðììîêò óì øìéíî $
*ñùðî ûü íðììîêò óì ûðòøðò ñò , ñ$î óì øìéíî $ !
100
4. Real GDP = [(Nominal GDP / GDPdeflator) ÷ 100]
5. GDP deflator = / ûõéêñù ýôë
) îñù ýôë0+jj
6. GDP = Consumer spending on final good& services + Gross private domestic invst+ Govt. spending on final goods & services+ Govt. gross fixed invst + Exp – Imp +Statistical discrepancy
7. Net Taxes = Taxes – Transfer payments8. GDP = National income + Capital
consumption allowance + Statisticaldiscrepancy
9. National Income = Compensation ofemployees + Corp & Govt enterprise
profits before taxes + Interest income +unincorporated business net income + rent+ indirect business taxes less subsidies
10. Total Amount Earned by Capital = Profit +Capital Consumption Allowance
11. PI = National income – Indirect businesstaxes – Corp income taxes – UndistributedCorp 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 - Consumptionexpenditures - Interest paid by consumersto business - Personal transfer payments toforeigners
15. Business sector saving = Undistributedcorporate profits + Capital consumptionallowance
16. Total Expenditure = Householdconsumption (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 + PrivateSector Saving + Net Taxes
19. Domestic saving = Investment + Fiscal balance + Trade balance
20. Trade Balance = Exports – Imports
21. Fiscal balance = Government Expenditure – Taxes = (Savings – Inves tment) – TradeBalance
22. Average propensity to consume (APC) =8'' ìî ' ñòî # ûê $ðõøòéûê
) îñù úêíûõî
23. Quantity theory of money equation: Nominal Money Supply ! Velocity ofMoney = Price Level ! Real Income orExpenditure
24. % è in unit labor cost = % è in nominalwages - % è in productivity
25. Economic growth = Annual % è in realGDP
26. Total Factor Productivity growth = Growthin potential GDP – [Relative share of laborin National Income ! (Growth in labor) +[Relative share of capital in NationalIncome ! (Growth in capital)]
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FinQuiz Formula Sheet CFA Level I 2016
27. Growth in potential GDP = Growth intechnology + (Relative share of labor in
National Income ! Growth in Labor) +(Relative share of capital in NationalIncome ! Growth in capital]
28. Capital share =Corporate profits + netinterest income + net rental income +(depreciation/ GDP)
29. Labor share = 7 õøùûóîî # ûõøîê $ñòéûê
ýôë
Reading 18: Understanding Business Cycles
1. Price index at time t 2 ="HwSI OP GxI QO.7S.RGMOL yH7{IG HG G ‰
"HwSI OP GxI QOL7S.RGMOL yH7{IG HG G %0+jj
Inflation Rate = ëìéíî úêöî 9 ñò òéõî òk
&ff? +
2. Fisher Index = ›’ 0› : (where, I L =Laspeyres index and I p = Paasche Index)
3. ; =>: ³;œW5 XW9: c;: d >=<>X;:W5 8! ûòñù ùñ, ûì íûõøîê $ñòéûê øîì 2ûðì øîì < ûì 1 îì
. ðòøðò øîì 2 ûðì øîì < ûì 1 îì
4. =6>§54?@ §¦ A §B6@ 8 / ûõéêñù ýôë
& ûêîó ÷ðøøùó
Reading 19: Monetary & Fiscal Policy
1. Total Money created = New deposit/Reserve Req
2. Money Multiplier =&
) î $îì * î ) î C ûì ìî $îì * î ìñòéû
3. Narrow money = M1= currency held
outside banks + checking accounts +traveller’s check
4. Broad money = M2 = M1 + time deposits+ saving deposits
5. M3 = M2 + deposits with non-bank financial institution
6. Quantity Theory of Money = M ! V = P ! Y where,
M = Quantity of moneyV = Velocity of circulation of moneyP = Average price levelY = Real output
7. Neutral Rate = Trend Growth + InflationTarget
8. Impact of Taxes and GovernmentSpending: The Fiscal Multiplier
The net impact of the government sectoron AD:
• G – T + B = Budget surplus or Budgetdeficitwhere, G = government spending , T=taxes, B =transfer benefits
• Disposable income = Income – Nettaxes = (1 – t) Income
where, Net taxes = taxes – transfer payments, t = net tax rate
9. Fiscal Multiplier (in the absence of taxes)= 1/(1 - MPC)• MPS = 1 – MPC.• Total increase in income and spending
= Fiscal multiplier ! G
10. Fiscal Multiplier (in the presence of taxes)
• MPC (with taxes) = MPC ! (1 - t)
• Fiscal multiplier = &
&/)$Q &/G
• Total ( in income and spending =
Fiscal multiplier ! G• Initial ( in consumption due to
reduction in taxes = MPC ! tax cutamount
• Total or cumulative effect of tax cut =multiplier ! initial change inconsumption
11. Cumulative multiplier =íðõðùñòé * î îüüîíò ûê ìîñù ýôë û * îì ò 2 î ò < û óîñì $
Þ OP Di$
Reading 20: International Trade & CapitalFlows
1. Terms of trade = ëìéíî ûü î 9øûìò $ëìéíî ûü éõøûìò $
2. Terms of Trade (as an index number) =8*' øìéíî ûü î 9øûìò $8*' øìéíî ûü éõøûìò $
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FinQuiz Formula Sheet CFA Level I 2016
3. Net exports = Value of a country's (exports –imports)
4. Net welfare effect = consumer’s surplusloss + 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 = Y d - S p =Y+R-T-S p And,CA = S p- I+ Govt surplus (or Govt saving)= S p- I+ (T- G- R)S p + S g = I + CA
where, S g = Govt savingsS p = I + CA – S g
• Current Account Imbalance CA = Sp+ Sg – I
Reading 21: Currency Exchange Rates
1. E§¨ 64FB G̈ 456 >6H6> 4B I §A6J?45 5K̈ ¨ 6B5@ 8Lövü 0 3ü
2. M6N> 6O5PNBF6 ¨N?6côvüd 8 c Lö ü 0 3ü dv3ö 8
Lö ü 0c 3ü v3ö d
3. M6N> QO5PNBF6 MN?6 öûõî $òéívüûìîé ' ê 8
Lövü 0 #ëúR
# ëúS
4. TPNBF6 4B M6N> QO5PNBF6 ¨N?6 8
+ ,è÷ S vR
÷SvR 0
&'è UR UR
&'è USUS
? +
5. Direct Quote = &
úêöéìîíò ïðûòî
6. Points on a forward rate quote = Fwd X-rate quote –Spot X-rate quote
7. Forward rate = Spot X-rate + Vûì < ñìö øûéêò $
&f–fff
8. E§¨ WN̈I G̈ 6A4KAvI4J5§KB? c4B Þd 8
$øûò þ/ìñòî'cüûì < ñìö øûéêò $v&f–fffd
$øûò þ/ìñòî? +
9. To convert spot rate into a forward quote(when points are represented as %) = Spotexchange rate ! (1 + % premium ordiscount)
10. Arbitrage relationship is stated as follows:
• + , > J 8 Í µÑ
+ , > P&
! µÑ
• In case of indirect quote, Arbitragerelationship is: + , > J 8+vÍ PvJ + , > P ÔPvJ
• ÔµÑ
8 Í µÑ
&'Mµ
&'MÑ
• Forward rate as a % of spot rate =! µvÑ
FµvÑ8
&'Mµ
&'MÑ
11. Return on hedged foreign investment(with a quoted forward rate) = Í PvJ + ,
>P&
! µvÑ
12. Expected % change in the spot rate =FZ^%
FZ? + 8 ÞèÍ G'& 8
Mµ /MÑ
&'MÑ
• Forward points: ÔPvJ ? Í PvJ 8
Í PvJMµ /MÑ
&'MÑX Y (where Y is quoted
interest rate period)
13. Relationship between the trade balance andexpenditure/ saving decisions:= Ex – Im = (Sav – Inv) + (T – G)
where T= taxes net of transfersG= government expenditures)
14. Price elasticity of demand = ) =Þ í 2 ñê ' î éê Cðñêòéòó
Þ í 2 ñê ' î éê øìéíî = – Þ è ï
Þ è ë
15. Expenditure (R) = Price ! Quantity = P ! Q• % * in expenditure = % * R = % * P
+ % * Q = (1- ) ) % * P
16. Basic idea of Marshall-Lerner condition =ZŸ[ Ÿ , Z ) [ ) ? + † j where,
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FinQuiz Formula Sheet CFA Level I 2016
+ x=share of exports) X=price elasticity of foreign demand fordomestic country exports+ M=share of imports) M =price elasticity of domestic countrydemand for imports
17. Trade balance = Income (GDP) –Domestic expenditure = Absorption
Reading 22: Financial Statement Analysis: AnIntroduction
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 +R.E
2. End R.E = Beg R.E + Net income –Dividends
3. Assets = Liabilities + Contributed Capital+ Beg R.E + Revenue – Expenses –Dividends
Reading 24: Financial Reporting Standards
Reading 25: Understanding Income Statements
1. Revenue recognized on Prorated basis =! ûòñù 8 õûðêò ûü # û $ò
! éõî ûü ò 2 î íûêòìñíò
2. Revenue recognized under Percentage-of-Completion Method = % of Total costspent by the firm ! Total ContractRevenue
3. Revenue recognized when outcome cannot be reliably measured = Contract costsincurred
4. Revenue recognized under installment
method = ëìûüéò
÷ñùî $ 0 Cash receipt
5. Wgtd Avg cost per unit =! ûòñù # û $ò ûü ýûûö $ ñ*ñéùñ, ùî üûì ÷ñùî
! ûòñù ðêéò $ ñ*ñéùñ, ùî üûì ÷ñùî
6. COGS using Wghtd Avg Cost = No of
units sold ! Wghtd Avg cost per unit
7. COGS using LIFO = Total cost – Value ofending inventory
8. Annual Depreciation Expense (using
Straight-Line Method) = # û $ò/ ) î $éöðñù + ñùðî7$ òéõñòîö "$ îüðù - éüî
9. Annual Depreciation Expense (Declining
balance method) = &ffÞ
"$ îüðù ùéüî ! Acceleration
factor (say 200% or 2) ! Net Book Value
10. Basic EPS =/ îò úêíûõî/ëìîüîììîö ôé *éöîêö $
0'2 ò 8*' / û ûü $2 ñìî $ ûðò $òñêöéê '
11. Diluted EPS for preferred stock =/ îò úêíûõî
0'2 ò 8*' / û ûü $2 ñìî $ ûv$' / î < íûõõûê $2 ñìî $ ò2 ñò< ûðùö 2 ñ* î , îîê é $$ðîö ñò íûê * îì $éûê
12. Diluted EPS for convertible debt =/ îò éêíûõî ' 8! M ûê
íûê * îìòé , ùî öî , ò/ëìîüîììîö ôé *0'2 ò 8*' ûü $2 ñìî $ ûv$' 8 öö
ò2 ñò < ûðùö 2ñ* î , îîê é $$ðîö ñò íûê * îì $éûê
13. Diluted EPS using Treasury Stock Method=
c/ îò úêíûõî/ëìîüîììîö öé *éöîêö $d\0'2 ò 8*' ûü $2 ñìî $'c
÷2ñìî $ øðìí 2 ñ$îö < éò2 # ñ$2 ìîíîé * îö ðøûê î 9îìíé $î d 0cëìûøûìòéûê ûü ÿìd ]
14. Net Profit Margin = / îò úêíûõî) î * îêðî
15. Gross Profit Margin =ýìû $$ ëìûüéò
) î * îêðî
16. Comprehensive EPS = EPS + OtherComprehensive Income per share
Reading 26: Understanding Balance Sheets
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FinQuiz Formula Sheet CFA Level I 2016
1. Percentage of A/C Receivable estimated to be uncollectible =
8 ùùû< ñêíî üûì ôûð , òüðù8 v#ýìû $$ ñõûðêò ûü 8 v# ) îíîé *ñ , ùî
2. Net Identifiable Assets = Fair value ofidentifiable assets – Fair value of liabilities& contingent liabilities
3. Amortized cost of PPE = Historical cost –Accumulated depreciation – Impairmentlosses
4. Carrying value for PPE under revaluationmodel= Fair value at date of revaluation –Accumulated depreciation (if any)
5. Amortized cost of PPE = Historical cost –Accumulated depreciation – Impairmentlosses
6. Carrying value for PPE under revaluationmodel= Fair value at date of revaluation –Accumulated depreciation (if any)
7. Deferred tax liability = Taxable income <Reported Financial Statement Income
before taxes
8. Deferred tax liability = Actual income tax payable in a period < Income tax expense
9. Vertical common-size balance-sheet =^ ñùñêíî $2 îîò 8 õûðêò
! ûòñù 8$$ îò $
10. Current ratio = # ðììîêò 8$$ îò $# ðììîêò - éñ, éùéòéî$
11. Quick (acid test) =# ñ$2 ' & ñì 1 îòñ , ùî $îíðìéòéî $' ) îíîé *ñ , ùî $
# ðììîêò - éñ, éùéòéî$
12. Cash ratio = # ñ$2 ' & ñì 1 îòñ , ùî $îíðìéòéî $ # ðììîêò - éñ, éùéòéî$
13. Long-term debt-to-equity =! ûòñù ùûê ' /òîìõ öî , ò
! ûòñù 7Cðéòó
14. Debt-to-Equity = ! ûòñù ôî , ò
! ûòñù 7C ðéòó
15. Total Debt = ! ûòñù ôî , ò! ûòñù 8$$ îò $
16. Financial Leverage = ! ûòñù 8$$ îò $! ûòñù 7Cðéòó
Reading 27: Understanding Cash FlowStatements
1. End Cash = Beg cash + Cash receipts(from operating, investing, and financing
activities) – Cash payments (for operating,investing, and financing activities)
2. End A/c Receivable = Beg A/c Receivable+ Revenues – Cash collected fromcustomers
3. Cash received from customers = Revenue – Increase in a/c receivab le
4. Purchases from suppliers = COGS +Increase in inventory
5. Cash paid to suppliers = Cogs + Increasein inventory – Increase in a/c payable
6. End Inventory = Beg inventory +Purchases – COGS
7. End a/c payable = Beg a/c payable +Purchases – Cash paid to suppliers
8. Cash paid to employees = Salary andwages expense – Increase in salary and
wages payable
9. End salary and wages payable = Beg salaryand wages payable + Salary and wagesexpense – cash paid to employees
10. Cash paid for other operating expenses =Other operating expenses – Decrease in
prepaid expenses – Increase in otheraccrued liabilities
11. Cash paid for interest = Interest expense +Decrease in interest payable
12. End Interest Payable = Beg interest payable + Interest expense – Cash paid forinterest
13. Cash paid for income taxes = Income taxexpense – Increase in income tax payable
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FinQuiz Formula Sheet CFA Level I 2016
14. Historical cost of equipment sold = Beg balance equipment + Equipment purchased – End balance equipment
15. Accumulated Dep on equipment sold =Beg balance accumulated dep + Depexpense – End balance accumulated dep
16. Cash received from sale of equipment =Historical cost of equipment sold –Accumulated dep on equipment sold +gain on sale of equipment
17. Dividends paid = Beg balance of R.E +
Net income – End balance of R.E
18. FCFF = Net income + Non-cash charges +Interest expense (1 – tax rate) – Cap exp –WC expenditures
19. FCFF = CFO + Interest expense (1 – Taxrate) – Cap exp
20. FCFE = CFO – Cap exp + Net borrowing
21. CF to revenue = #V.
/ îò ) î * îêðî
22. Cash ROA = #V.8* îìñ ' î ! ûòñù 8$$ îò $
23. Cash ROE = #V.8* îìñ ' î $2 ñìî 2 ûùöîì $_î Cðéòó
24. Cash to income = #V.. øîìñòéê ' éêíûõî
25. Cash flow per share =#V. /ëìîüîììîö ôé *éöîêö $/ û ûü íûõõûê $2 ñìî $ ûv$
26. Debt Coverage = #V.! ûòñù ôî , ò
27. Interest Coverage =#V. 'úêòîìî $ò øñéö' ! ñ9î $ øñéö
úêòîìî $ò øñéö
28. Reinvestment = #V.# ñ$2 øñéö üûì ùûê ' /òîìõ ñ $$îò $
29. Debt payment =#V.
# ñ$2 øñéö üûì -! öî , ò ìîøñóõîêò
30. Dividend payment = #V.ôé *éöîêö $ øñéö
31. Investing and Financing =#V.
# ñ$2 ûðòüùû<$ üûì éê * î $òéê' ñêö üéêñêíéê ' ñíòé *éòéî$
Reading 28: Financial Analysis Techniques
1. Compound Growth Rate =
7 êö + ñùðî^ î ' + ñùðî
%`a aR bcdeaSf ? +
2. Combined ratio = - û$$î $ ñêö 79 øîê $î $/ îò ëìîõéðõö 7 ñìêîö
3. Operating ROA = . øîìñòéê ' úêíûõî
8*' ! ûòñù 8$$ îò $
4. ROA = / îò úêíûõî
8*' ! ûòñù 8$$ îò $ or
ROA =/ îò úêíûõî'úêòîìî $ò 79 øîê $î &/ ! ñ9 ìñòî
8*' ! ûòñù 8$$ îò $
5. Effective Tax Rate = úêíûõî ! ñ97 ñìêéê '$ , îüûìî ! ñ9
6. Vertical common size income statement =úêíûõî $òñòîõîêò úòîõ
) î * îêðî
7. Horizontal common size balance sheet =^ ñùñêíî $2 îîò éòîõ éê ÿîñì k
^ ñùñêíî $2 îîò éòîõ éê ÿîñì &
8. Inventory turnover =# û $ò ûü $ñùî $ ûì íû $ò ûü ' ûûö $ $ûùö
8*' úê* îêòûìó
9. Days of Inventory on Hand (DOH) =/ û ûü ôñó $ éê øîìéûö
úê*îêòûìó ! ðìêû * îì
10. Receivables Turnover = ) î * îêðî
8*' ) îíîé *ñ , ùî $
11. Days of Sales Outstanding (DSO)
= / û ûü ôñó $ éê ëîìéûö
) îíîé *ñ , ùî$ òðìêû * îì
12. Avg A/c Receivable Balance = Avg Days’Credit Sales ! DSO or
Avg A/c Receivable Balance = ÷ñùî $! ðìêû * îì
=÷ñùî $
ghijkl
13. Payables turnover = ëðìí 2 ñî $
8*' òìñöî øñóñ , ùî $
14. No of Days of Payables = / û ûü ôñó $ éê øîìéûö
ëñóñ , ùî $ ! ðìêû * îì
15. WC Turnover = ) î *îêðî
8*' 0#
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FinQuiz Formula Sheet CFA Level I 2016
16. Fixed Asset Turnover = ) î * îêðî
8*' / îò Vé9îö 8$$ îò $
17. Total Asset Turnover = ) î * îêðî
8*' ! ûòñù 8$$ îò $
18. Pretax margin =7 ñìêéê '$ , îüûìî òñ 9 , ðò ñüòîì éêòîìî $ò
) î * îêðî
19. Return on Total Capital =7^ ú!
÷2 ûìò ñêö ùûê ' òîìõ öî , ò ñêö î Cðéòó
20. ROE = / îò úêíûõî
8*' ! ûòñù 7Cðéòó
• ROE = ROA ! Leverage• ROE = Tax Burden ! Interest Burden
! EBIT Margin ! Total AssetTurnover ! Leverage
21. Return on Common Equity =/ îò úêíûõî/ëìîüîììîö ôé *éöîêö $
8*' # ûõõûê 7Cðéòó
22. Coefficient of Variation of Operating
Income = ÷•ô ûü . øîìñòéê ' úêíûõî
8*' . øîìñòéê ' úêíûõî
23. Coefficient of Variation of Net Income =÷•ô ûü / îò úêíûõî
8*' / îò úêíûõî
24. Coefficient of Variation of Revenues =÷•ô ûü ) î * îêðî
8*' ) î * îêðî
25. Monetary Reserve Requirement (Cash
Reserve Ratio) = ) î $îì * î $ 2 îùö ñ $ # îêòìñù ^ ñê 1÷øîíéüéîö ôîøû $éò- éñ, éùéòéî$
26. Liquid Asset Requirement =
) îñöéùó & ñì 1 îòñ , ùî ÷îíðìéòéî $÷øîíéüéîö ôîøû $éò- éñ, éùéòéî$
27. Net Interest Margin =/ îò úêòîìî $ò úêíûõî
! ûòñù úêòîìî $ò 7 ñìêéê ' 8$$ îò $
28. Sales per Square Meter =) î * îêðî
! ûòñù ) îòñéù ÷øñíî éê ÷ Cðñìî & îòîì $
29. Average Daily Rate = ) ûûõ ) î * îêðî/ û ûü ) ûûõ $ $ûùö
30. Occupancy Rate = / û ûü ) ûûõ $ ÷ûùö
/ û ûü ) ûûõ $ ñ*ñéùñ, ùî
31. EBIT Interest Coverage = 7^ ú!ýìû $$ úêòîìî $ò
32. EBITDA Interest Coverage = 7^ ú! ô 8ýìû $$ úêòîìî $ò
33. FFO Interest Coverage =VV. 'úêòîìî $ò ëñéö/ . øîìñòéê ' - îñ $î 8 ö mð $òõîêò $
ýìû $$ úêòîìî $ò
34. Return on Capital = 7^ ú!8*' # ñøéòñù
=7^ ú!
8*' c7Cðéòó' / ûê íðììîêò öîüîììîö òñ 9î $'öî , òd
35. FFO to Debt = VV.! ûòñù ôî , ò
36. Free Operating CF to Debt = #V. / # ñø 79 ø
! ûòñù ôî , ò
37. Discretionary CF to Debt =#V. / # ñø î 9ø/ôé *éöîêö $ øñéö
! ûòñù öî , ò
38. Net CF to Capital expenditures =VV. /ôé *éöîêö $
# ñø î 9ø
39. Debt to EBITDA = ! ûòñù öî , ò
7^ ú! ô 8
40. Total Debt to total debt plus Equity =! ûòñù öî , ò
! ûòñù öî , ò' 7Cðéòó
41. Z-Score = 1.2 ! #8 / #-!8
+ 1.4 ! ) •7!8
+
3.3 ! 7^ ú!!8
+ 0.6 ! &+ ûü $òûí 1^+ ûü ùéñ, éùéòéî$
+ 1.0
! ÷ñùî $!8
42. Segment margin = ÷î ' õîêò ëìûüéò c - û$$d
÷î ' õîêò ) î * îêðî
43. Segment turnover = ÷î ' õîêò ) î * îêðî
÷î ' õîêò 8$$ îò $
44. Segment ROA = ÷î ' õîêò ëìûüéò c - û $$d÷î ' õîêò 8$$ îò $
45. Segment Debt Ratio = ÷î ' õîêò - éñ, éùéòéî$÷î ' õîêò 8$$ îò $
Reading 29: Inventories
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FinQuiz Formula Sheet CFA Level I 2016
1. NRA = Estimated Selling Price –Estimated Costs of completion anddisposal
2. Inventory amount net of valuationallowance = Carrying amount of Inventory
– Write downs
3. (NRA – Normal Profit Margin) ( MV ( NRA
Reading 30: Long-Lived Assets
1. Dep Exp under Straight-line Method =ôîøìîíéñ , ùî # û $ò
7$ òéõñòîö "$ îüðù - éüî =
n é$òûìéíñù # û $ò/ 7$ òéõñòîö ) î $éöðñù $ñù*ñ ' î + ñùðî7$ òéõñòîö "$ îüðù - éüî
2. Dep Exp under Units-of-ProductionMethod = Depreciable Cost !
ëìûöðíòéûê éê ò 2 î ëîìéûö
7$ òéõñòîö ëìûöðíòé * î # ñøñíéòó
3. Carrying amount under cost model =Historical Cost – Accumulated Dep orAmortization
4.
Carrying amount under revaluation model= Fair value at the date of revaluation –Any subsequent Accumulated Dep orAmortization
5. Impairment Loss (IFRS) = RecoverableAmount – Net Carrying Amount
Where, Recoverable amount = Max [(Fairvalue – Costs to sell); Value in Use)] andValue in use = PV of Expected Future CFs
6. Impairment Loss (US GAAP) = Asset’sFair Value – Carrying Amount …….IfCarrying amount > Undiscounted ExpectedFuture Cash Flows
Reading 31: Income Taxes
1. Deferred tax asset = Company’s taxableincome > Accounting profit
2. Tax base of revenue received in advance =
Carrying amount – Any amount of revenuethat will not be taxed at a future date
3. Reported Effective Tax Rate =úêíûõî ! ñ9 î 9øîê $î
ëìî òñ 9 éêíûõî ûì 8 ííûðêòéê ' ëìûüéò
4. Deferred tax liability = Carrying amountof asset > Tax base of asset
5. Deferred tax asset = Carrying amount ofasset < Tax base of asset
6. Deferred tax asset = Carrying amount ofliability > Tax base of asset
7. Deferred tax liability = Carrying amount ofliability < Tax base of asset
8. Company’s tax expense (or credit)reported on its income statement = Income
tax liability currently payable + è indeferred tax asset / liabilityWhere,
• Income Tax liability currently payable = Taxable income ! Taxrate
• è in deferred tax asset / liability =Diff b/w the balance of thedeferred tax asset / liability for thecurrent period and the balance ofthe previous period.
9. The company’s tax expense (or credit)reported on its income statement = Taxes
payable + ( * Deferred tax liability - *
Deferred tax asset)Where,
• Income Tax liability currently payable = Taxable income ! Taxrate
• Deferred tax liability = (carryingamount – tax base) ! tax rate
• Deferred tax asset = (tax base –carrying amount) ! tax rate
10. Tax base of a liability = Carrying amountof the liability – Amounts that will bedeductible for tax purposes in the future
Reading 32: Non-current (Long-term)Liabilities
1. Annual Interest Payment = Face Value ! Coupon Rate
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FinQuiz Formula Sheet CFA Level I 2016
2. Sale proceeds of bond = Sum of PV ofInterest Payments + PV of Face value ofBond
3. When Face value - Sale proceed is > zero,discount
4. When Face value – Sale proceed is < zero, premium
5. Bond payable = Face value – (+) Discount(Premium)
6. Total Interest Expense (in case of discount)= Periodic interest payments +
Amortization of Discount7. Total Interest Expense (in case of
premium) = Periodic interest payments -Amortization of Premium
8. Amount of Bonds payable reported on the balance sheet = Historical cost +/-Cumulative amortization (or amortizationcost)
9. Amount of Bonds payable initiallyreported on the balance sheet under IFRS =Sales proceeds – Issuance costs
10. Amount of Bonds payable initiallyreported on the balance sheet under USGAAP = Sales proceeds
11. Bond interest expense under effectiveinterest rate method = Carrying value of
the bonds at the beginning of the period ! Effective interest rate
12. Bond Interest Payment under effectiveinterest rate method = Face value of the
bonds ! Contractual (coupon) rate
13. Amortization of the discount or premiumunder effective interest rate method =Bond interest expense – Bond interest
payment
14. Bond Discount/Premium Amortizationunder Straight-line Method =^ ûêö ôé $íûðêò ûì øìîõéðõ
/ û ûü úêòîìî $ò ëîìéûö $
15. No of shares subscribed when warrants are
exercised = 8'' ìî ' ñòî øìéêíéøñù ñõûðêò ûü öî , ò
ëñì *ñùðî ûü ñ ùûò
! shares subscribed per lot
16. Carrying amount of the leased asset =Initial recognition amount – Accumulateddepreciation
17. Accumulated depreciation = Prior year’saccumulated depreciation + Current year’s
depreciation expense
18. Interest expense = Lease liability at the begof the period ! interest rate implicit in thelease
19. Sales revenue = lower of the fair value ofthe asset and PV of the min lease payments
20. Cost of sales = Carrying amount of theleased asset – PV of the estimatedunguaranteed residual value
21. Interest Revenue = Lease receivable at the beg of the period ! Interest rate
22. Net interest expense = Beg Net pensionliability ! Discount rate
23. Net Interest income = Beg Net Pensionasset ! Discount rate
24. Reported pension expense = Pension costs – Expected return on Pension plan assets
25. Funded Status = PV of the Defined benefit
obligations – Fair value of the plan assets
Reading 33: Financial Reporting Quality
Reading 34: Financial Statement Analysis:Applications
1. Company’s sales = Projected market share! Projected total industry sales
2. Forecast amount of profit for a given period = Forecasted amount of sales ! Forecast of the selected profit margin
3. Retained CF (RCF) / Total debt =cûøîìñòéê ' #V , îüûìî 0# í 2 ñê ' î $ o öé*éöîêö $d
òûòñù öî , ò
4. ) îòñéêîö #V/ # ñø î 9ø! ûòñù ôî , ò
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FinQuiz Formula Sheet CFA Level I 2016
5. Inventory value adjusted to FIFO basis =End Inventory value under LIFO + EndLIFO reserve balance
6. COGS adjusted to a FIFO basis = COGSunder LIFO – (End LIFO reserve – BegLIFO reserve)
7. Useful life of the company’s overall asset
base that has passed = 8 ííðõðùñòîö ôîø
ýìû $$ ëë 7
8. Avg age of the asset base =8 ííðõðùñòîö ôîø
8 êêðñù ôîø î 9øîê $î
9. Remaining useful life of the asset =/ îò ëë 7 cêîò ûü ñííðõðùñòîö öîød
8 êêðñù öîø î 9øîê $î
10. Avg depreciable life of the assets at
installation = ýìû $$ ëë 7
8 êêðñù ôîø î 9øîê $î
11. % of asset base that is being renewedthrough new capital investment =
# ñøî 9
ýìû $$ ëë 7 ' # ñøî 9
12. Adjusted BV = Total stockholders’ equity – Goodwill
13. Adjusted Price to BV ratio =ëìéíî õñì 1 îò íñøéòñùé pñòéûê
8 ö mð $òîö ^+
14. Tangible B.V = Total stockholders’ equity – Goodwill – Other intangible assets
15. Price to tangible BV ratio = ëìéíî
! ñê ' é, ùî ^+
16. Adjusted debt-to-equity ratio =) îøûìòîö öî , ò'ë + ûü ûøîìñòéê ' ùîñ $î
) îøûìòîö 7Cðéòó
17. Adjusted debt-to-asset ratio =) îøûìòîö öî , ò'ë + ûü ûøîìñòéê ' ùîñ $î
) îøûìòîö 8$$ îò' ë + ûü ûøîìñòéê ' ùîñ $î
18. Adjusted Asset Turnover ratio =÷ñùî $
) îøûìòîö 8*' òûòñù ñ$$îò $'ë + ûü ûøîìñòéê ' ùîñ $î
19. PV of future operating lease payments =
ë + ûü íñøéòñù ùîñ $î øñóõîêò $! ûòñù # ñøéòñù - îñ $î øñóõîêò $! Total Future
Operating Lease Payments
20. Interest expense = Interest ! PV of thelease payments
21. Depreciation expense estimated onstraight-line basis =
ë + ûü ò2 î ùîñ $î øñóõîêò $/ û ûü óì $ ûü üðòðìî ùîñ $î øñóõîêò $
22. Adjusted Interest Coverage ratio =Qqrs , ¨ 6B? 6OGÌ ? t6G 6OGÌ
>GN@A6B?J, > 6OG6BJ6Ì
* associated with the operating leaseobligations
Reading 35: Capital Budgeting
1. Incremental CF = CF with a decision - CFwithout that decision
2. NPV = PV of cash inflows - IO =
NPV =
t = 1
n
! AT CFs at time t
1 + Req RoR( )t " IO
3. Avg Accounting RoR (AAR) =8*' / ú ñüòîì öîø u òñ9î $ , îüûìî éêòîìî $ò
8*' ^+ ûü úê*$ò
4. PI = ë + ûü üðòðìî #V$ú.
= 1 + / ë +ú.
5. Value of a company = Value of company’sexisting invst + Net PV of all ofcompany’s future invst
Reading 36: Cost of Capital
1. WACC = w dr d (1 – t) + w pr p + w er e
2. Debt-to-Equity Ratio conversion intoweight (i.e. Debt / (Debt + Equity) =
jcvwxyzew{
&'jcvw
xyzew{
3. Optimal Capital Budget is the point whereMC of capital = Marginal return frominvesting
4. After-tax cost of debt = Before-taxMarginal Cost of Debt ! (1 – firm’smarginal tax rate)
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FinQuiz Formula Sheet CFA Level I 2016
5. Preferred Stock Price per Share
=ëìîü ÷òûí 1 ôé * øîì ÷ 2 ñìî
# û $ò ûü ëìîü ÷òûí 1
6. Expected Return on Stock I (under CAPM)
= E (R i) = R F + , i [E (R M) – R F]
7. Expected Return on Stock I = E (R i) = R F +, i1 (Factor risk premium) 1 + , i2 (Factorrisk premium) 2+…..+ , i j (Factor risk
premium) j
8. Cost of Equity = | } 8 ô %
ë h, F
9. Expected Growth Rate of Dividends
g = (1 -ô
7 ë÷ ) ! ROEg = retention rate ! ROE
10. Company’s stock returns = Méò 8 N,~Mõò
11. Unlevered • of Comparable Company =
• " – íûõøñ 8€ –‚aƒb„d„v…c
&' &/ò ‚aƒb„d„v…cj ‚aƒb„d„v…cx ‚aƒb„d„v…c
12. Levered • of Project =
†B– R(O” 8 †Ý– aO.R + , + ? : R(O”‡ R(O”
“ R(O”
13. †H77IG 8 ˆ ‰Š‹ƒZŒ
&' &/G r
14. †I}SMG` 8 †H77IG + , + ? : i
15. Sovereign yield spread = Govt bond yield(denominated in developed country’scurrency) – T.B yield on a similar maturity
bond in developed country
16. Country equity premium = Sovereign yield
spread ! 8 êê ÷•ô ûü 7Cðéòó éêöî 98 êê ÷•ô ûü $û * îìîé ' ê , ûêö &1 ò éêòîìõ $ ûü öî * îùûøîö õ 1ò íðììîêíó
17. Cost of equity = K e= R F + , [(E(R M)-R F) +CRP]
18. Breakpoint =8 õûðêò ûü íñøéòñù ñò <2 éí 2 $ûðìíî _$ íû $ò ûü íñø è
ëìûø ûü êî < íñø ìñé $îö üìûõ ò 2 î $ûðìíî
19. Cost of Capital (hen flotation costs are in
monetary terms = ¨ î 8 ô %
ë h / V , F
20. When FC are in terms of % of the share
price: Cost of Equity = ¨ î 8 ô %
ë h / V , F
21. If FC are not tax deductible: NPV = PV of
Cash Inflows – IO – (FC in % ! NewEquity Capital)
22. If FC are tax deductible: NPV = PV ofCash Inflows – IO – [(FC in % ! NewEquity Capital) ! (1 – Marginal Tax Rate)]
23. Asset • = (Debt • ! Proportion of Debt) +(Equity • ! Proportion of Equity)
Reading 37: Measures of Leverage
1. Contribution Margin (CM) = (# of unitssold) ! [(price per unit) - (variable cost perunit)]
2. Per unit CM = Price per unit - Variablecost per unit
3. Operating income = CM – Fixed OperatingCosts
4. DOL = Þ è éê . øîìñòéê ' úêíûõî 7^ ú!Þ è éê " êéò$ ÷ûùö
or
DOL= #&#& / Vé9îö . øîìñòéê ' # û $ò
5. DFL = Þ è éê / îò úêíûõî
Þ è éê . øîìñòéê ' úêíûõî or
#& / Vé9îö . ø # û $ò
#& / Vé9îö . ø úêíûõî/ Vé9îö Véê # û $ò
6. DTL= Þ è éê / îò úêíûõî
Þ è éê / û ûü " êéò$ ÷ûùö = DOL ! DFL =
#&#& / Vé9îö . ø úêíûõî/ Vé9îö Véê # û $ò
7. Break-even Revenue = (Variable cost perunit ! Break-even Number of Units) +Fixed Operating costs + Fixed FinancialCost
8. Breakeven Number of units =Vé9îö . øîìñòéê ' # û $ò$' Vé9îö Véêñêíéñù # û $ò$
ëìéíî øîì ðêéò/ + ñìéñ , ùî íû $ò øîì ðêéò
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FinQuiz Formula Sheet CFA Level I 2016
Reading 38: Dividends & Share Repurchases:Basics
1. Company’s payout for the year = Cashdividends + Value of shares repurchased inany given year
2. Dividend Payout ratio =# ûõõûê $2 ñìî íñ $2 öé*éöîêö $
/ îò úêíûõî ñ *ñéùñ, ùî òû íûõõûê $2 ñìî $
3. EPS after Dividend = EPS before Dividend
! ÷2 ñìî $ ûv$ , îüûìî ôé *éöîêö
÷2 ñìî $ ûv $ ñüòîì ôé *éöîêö
4. Stock Price after Dividend = Stock Price before Dividend ! EPS after Dividend
5. Total Market Value after Dividend =Shares outstanding after Dividend ! Stock
price after Dividend
6. Stock price after 2-for-1 stock split =÷òûí 1 øìéíî , îüûìî $òûí 1 $øùéò
k
7. EPS after 2-for-1 stock split =7 ë÷ , îüûìî $òûí 1 $øùéò
k
8. DPS after 2-for-1 stock split =ôë÷ , îüûìî $òûí 1 $øùéò
k
9. EPS after buyback =7 ñìêéê '$ / 8 üòîì òñ 9 # û $ò ûü Vðêö $÷2ñìî $ . ðò$òñêöéê ' ñüòîì ^ ðó , ñí 1
10. Ex-dividend value of share = Stock price –
Dividend per share
11. Market value of Equity after distribution ofcash dividends =\cŽ ûü $2 ñìî $ ûv$d 0 c &+ $2 ñìîd o # ñ$2 öé*]
Ž ûü $2 ñìî $ ûv $
12. Post-repurchase share price =Žûü $2 ñìî $ ûv $ 0 c &+ $2 ñìî o < ûìò 2 ûü ÷2 ñìî ìîøðìí 2 ñ$î ]
c Ž ûü $2 ñìî $ ûv$/ Ž ûü $2 ñìî $ cíñê , î ìîøðìí 2ñ$îö , ó ñ # û
Reading 39: Working Capital Management
1. Operating cycle = No of days of inventory+ No of days of receivables
2. Net operating cycle = No of days ofinventory + No of days of receivables – Noof days payables
3. Money Market Yield =Vñíî *ñùðî/ëðìí 2 ñ$î øìéíî
ëðìí 2ñ$î øìéíî 0
opf
/ û ûü öñó $ òû õñòðìéòó
4. Bond Equivalent Yield =Vñíî *ñùðî/ëðìí 2 ñ$î øìéíî
ëðìí 2ñ$î øìéíî0
opu
/ û ûü öñó $ òû õñòðìéòó
5. Discount-basis Yield =Vñíî *ñùðî/ëðìí 2 ñ$î øìéíî
Vñíî + ñùðî0
opf
/ û ûü öñó $ òû õñòðìéòó
6. Wght Avg collection period = wghts ! Avg no of days to collect accounts withineach aging category
Where, Weights = % of total receivables ineach category
7. Float Factor = 8*' ôñéùó Vùûñò
8*' ôñéùó ôîøû $éò =
8*' ôñéùó Vùûñòaw„… ƒaz‘w aR ’“c‚”f jcbafewcS
`a aR j„{f
Where, Float =Amount of money that is intransit b/w payments (by customers) andfunds (usable by co)
8. Value of stretching payment = A/c payable! Co's opportunity cost for ST funds
9. Cost of Trade Credit = + ,
ôé $íûðêò
&/ôé $íûðêò
ghi‘
? + where n = days beyond discount period
10. Cost of Line of Credit =úêòîìî $ò' # ûõõéòõîêò üîî
- ûñê 8 õûðêò
11. Bankers Acceptance Cost = úêòîìî $ò/ îò øìûíîîö $
=úêòîìî $ò
- ûñê ñõûðêò/úêòîìî $ò
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FinQuiz Formula Sheet CFA Level I 2016
12. Commercial Paper Cost =úêòîìî $ò'ôîñùîì _$ íûõõé $$éûê' ^ ñí 1ðø íû $ò$
- ûñê ñõûðêò/úêòîìî $ò
13. Annualized cost = Cost ! 12
Reading 40: The Corporate Governance ofListed Companies
Reading 41: Portfolio Management: AnOverview
1. NAV of bond mutual fund =c*ñùðî ûü îñí 2 , ûêö éê ò 2 î øûìòüûùéûd
/ û ûü $2 ñìî $
2. New Shares that need to be c reated =8 õûðêò òû , î úê * î $òîö éê ò 2 î Vðêö
/8+ ûì ! ûòñù *ñùðî ûü ñ & ðòðñù Vðêö
3. New NAV of the Fund = NAV or Totalvalue of a Mutual Fund + Amount to beinvested in the Fund
4. No of shares need to be retired =8 õûðêò òû , î < éò2öìñ < ê üìûõ ò 2 î Vðêö
/8+ ûì ! ûòñù *ñùðî ûü ñ & ðòðñù Vðêö
Reading 42: Risk Management: AnIntroduction
Reading 43: Portfolio Risk & Return: Part I
1. Total Return = Capital Gain (or Loss) +Dividend Yield
2. Capital Gain = ë w/ë w¡%
ë w¡%
3. Dividend Yield = ô
ë h? +
4. 3-Yr HPR = [(1 + R 1) ! (1 + R 2) ! (1 +R 3)]1/3 – 1
5. Arithmetic mean (AM) R = YM 8Nƒ%'N ƒ‰'¶'N ƒ• ¡% 'N ƒ
* 8
&*
YMG*G[&
6. Geometric R for n periods = MDM 8
+ , Y & + , Y k l + , Y L& L ? +
7. IRR = #V ñò ! éõî ò
&'ú )) w 8 j!ò[f
8. Annual Return (Ann R):
• Ann R = (1 + Quarterly R) 4 – 1
• Ann R = (1 + Monthly R) 12 – 1
• Ann R = (1 + Weekly R) 52 – 1
• Ann R = (1 + Daily R) 365 – 1
• Weekly R = (1 + Daily R) 5 – 1
• Weekly R = (1 + Annual R) 1/52 – 1
9. Portf R (for Two Assets) = (Wght of Asset1 ! R of Asset 1) + (Wght of Asset 2 ! Rof Asset 2)
10. Gross R = R – Trading exp – other expdirectly related to the generation of returns.
11. Net R = Gross R - All managerial andadministrative exp
12. After-tax nominal R = Total R - Anyallowance for taxes on realized gains
13. (1 + Nominal R) = (1 + Real Rf R) ! (1 +Inf) ! (1 + RP)
14. (1 + Real R) = (1 + Real Rf R) ! (1 + RP)
15. (1 + Real R) = c&' / ûõéêñù ) d
c&'úêüd
16. Var of a Single Asset = Š k 8 NZ/ˆ ‰
ƒ„%
*
17. Sample Variance = Jk 8 ) w/ ) ‰
e„%
! /&
18. Cov of R b/w two assets = Cov (Ri,Rj) =
- ij! %i ! % j
19. Portfolio Var = – ëk 8 —&
k –&k , —k
k –kk ,
¬—&—k T§H M&–Mk 8 —&k –&
k , —kk –k
k ,¬—&—k ˜ &k–&–k
20. Portfolio S.D. = 3§¨ ? ¦§ >4§ =N̈ 4NB56
21. Cov b/w asset 1 & asset 2 = Correlation ofReturn b/w two assets ! S.D. of asset 1 ! S.D. of asset 2
22. Correlation of Return b/w two assets =# û *ñìéñêíî ûü ) îòðìê , v< ò< û ñ $$îò $
÷•ô•ûü ñ $$îò & 0 ÷•ô•ûü ñ $$îò k
23. 1 + Expected Return = + , Q M 8+ , ¨ ìü 0 + , Q ™ 0 + , Q M3
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FinQuiz Formula Sheet CFA Level I 2016
1. Total return to a Leveraged Stock Purchase
= ) îõñéêéê ' 7Cðéòó/ú .
ú. where,
Remaining Equity = IO – Purchase
commission + (-) Trading g(l) – Margin i paid + Div received – Sales commission paid
ORRemaining Equity = Proceeds on sale –Payoff loan – Margin i paid + Div received
– Sales commission paid
2. ROE (based on leverage alone)= Leverage (in times) ! stock price return(in %)
3. Price of stock below which a margin callwill take place (P):
úêéòéñù õñì ' éê ª 'cë/ úêéòéñù ÷òûí 1 ëìéíîd
ë8
ŸN4B?6BNB56 ŸN¨F4B M6«K4̈6A6B? cÞd
4. Total cost of placement to the issuing firmin IPO ($)
= Gross proceeds received by the issuingfirm – Net proceeds received by the issuing
firm
5. Total cost of placement to the issuing firm
in IPO (%) =cýìû $$ øìûíîîö $ ìîíîé * îö , ó úV/
/ îò øìûíîîö $ ìîíîé * îö , ó úV/ îò øìûíîîö $ ìîíîé * îö , ó úV
where IF = Issuing firm
6. Max leverage ratio = &ffÞ
Þ ûü 7Cðéòó
7. Max leverage ratio for position financed bymin margin requirement =
&
& éê õñì ' éê ìî Cðéìîõîêò
Reading 47: Security Market Indices
1. Value of a price return index =
VPRI = D
P n N
i
ii!= 1
For Single Period:2. % Change in value of Price return of
index Portfolio = PR I = 0
01
PRI
PRI PRI
V
V V !
3. Price Return (Ind constituent security):PR I
=0
01
i
ii
P
P P !
4. Price return of the index : PR I =
!=
""#
$%%&
' ( N
i i
iii
P
P P w
1 0
01
5. % è in value of Total return of Index
0
01
PRI
I PRI PRI
V
IncV V +!
6. Total return of each security = TR i =
i
iii
P
Inc P P
0
01 +!
Total Re turn wi
P1 i ! P
0 i + Inci
P0 i
"
#$
%
&'
i = 1
N
(
Over Multiple Time Periods:7. Value of Price Return index at time t =
VPRIT = V PRI0 (1 + PR I1) (1 + PR I2) … (1 +PR IT)
8. Value of Total Return index at time t =VTRIT = V TRI0 (1 + TR I 1) (1 + TR I 2) … (1 +TR I T)
9. Weight of security i under price weighting
= ëìéíî ûü $îíðìéòó é
÷ðõ ûü ñùù øìéíî $ ûü íûê $òéòðîêò $îíðìéòéî $
10. Weight of security i under equal weighting
= &/ û ûü $îíðìéòéî $ éê ò2 î éêöî 9
11. Weight of security i under market-cap
weighting =/ f ûü $2 ñìî $ ûv$ ûü ÷é 0 ÷ 2ñìî øìéíî ûü ÷é
/ û ûü $2 ñìî $ ûv$ ûü ÷é 0 ÷ 2 ñìî øìéíî ûü ÷é`e
Where Si = Security i
12. Weight of Si under Mkt Cap weighting =Vìñíòéûê ûü $2 ñìî $ ûv$ õ 1ò üùûñò 0 ûü $2 ñìî $ ÷é 0
÷2ñìî øìéíî ûü $îíðìéòó écVìñíòéûê ûü $2 ñìî $ ûv $ &1 ò üùûñò 0 ûü $2 ñìî $ ûv$ ûü ÷é 0
÷2 ñìî øìéíî ûü $îíðìéòó éd
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FinQuiz Formula Sheet CFA Level I 2016
13. Fundamental weight on security i =Vðêöñõîêòñù $épî õîñ $ðìî ûü íûõøñêó éÌ
cVðêöñõîêòñù $épî õîñ $ðìî ûü íûõøñêó éd`e
*Book value, cash flow, revenues, earnings,
dividends, & number of employees.
Reading 48: Market Efficiency
Reading 49: Overview of equity Securities
1. Equity security’s Total Return =÷ñùî ë ûü ñ $2 ñìî/ëðì 2 ñ$î ëûü ñ $2 ñìî'íñ $2 v$òûí 1 ôé *
ëðìí 2 ñ$î øìéíî ûü ñ $2 ñìî
2. ROE in yr t =/ ú cüûì . ìöéêñìó ÷ 2 ñìî 2 ûùöîì $d éê óì ò
8*' ! ûòñù ^+ ûü 7Cðéòó
OR
ROE = / ú cüûì . ìöéêñìó ÷ 2 ñìî 2ûùöîì $d éê óì ò
÷2 ñìî 2 ûùöîì $_î Cðéòó ñò , î ' ûü óì ò
3. MV of equity = Mkt price per share ! Shares O/s
4. BV of equity per share = ! ûòñù ÷n _î Cðéòó
÷2 ñìî $ ûv $
5. Price-to-book ratio = & ñì 1 îò øìéíî øîì $2 ñìî
^+ ûü î Cðéòó øîì $2 ñìî
6. ROE = Net profit margin ! Asset turnover
! Financial leverage = / îò îñìêéê '$/ îò $ñùî $
0/ îò $ñùî $
8*' òûòñù ñ$$îò $ 0 8*' òûòñù ñ$$îò $
8*' íûõõûê î Cðéòó
Reading 50: Introduction to Industry &Company Analysis
Reading 51: Equity Valuation: Concepts &Basic Tools
1. Value of a share of stock today =79 øîíòîö öé *éöîêö éê óì ò
c&'ìî Cðéìîö ).) ûê $òûí 1d¬òò[&
If an investor intends to buy and hold a sharefor 1 yr:
2. Value of a share of stock today =79 øîíòîö ôé * éê & óì ' 79 øîíòîö $îùùéê ' øìéíî éê & óîñì
c&'ìî C ) û ) ûê $òûí 1d¬&
3. Value of a share of stock for n holding period or investment horizon =
79 øîíòîö ôé * éê óì ò
&'ìî C ) ûê $òûí 1 w ,LG[&
79 øîíòîö øìéíî éê ê øîìéûö $
&'ìî C ) ûê $òûí 1 ‘
4. CFO = NI + Non-cash exp – Invst in WC
5. FCFE = CFO – FCInv + Net Borrowing
6. Value of a share for a non-div-paying
stock = V#V7 éê óîñì ò
&'ìî C ) ûê $òûí 1 wò[&
7. Req RoR on share i = Current expected Rfrate + Beta i [MRP]
8. Value of a pref stock (non-callable, non-convertible) =
( ) ( )r
D
r
D
g r
g DV 000
00
011=
!+
=!
+=
9. Value of a pref stock (non-callable, non-
convertible) with maturity at time n =Af 8
‡ f
c+ , 5d G ,L
G/&
Ô+ , 5 L
Gordon Growth Model:10. Value of a share of stock =
( )r g
g r
D
g r
g DV <
!=
!+
= ,1 10
0
11. Sustainable dividend growth rate =
g = ROE ! b
where b = earnings retention rate = (1 - Dividend payout ratio)
Two-stage valuation model:12. Value of share today = V0 =
Af 8‡ f + , Ž 7
G
c + , 5 d G ,AL
c + , 5 d L
L
M[&
AL 8‡ L'&
5 ? Ž B
‡ L'& 8 ‡ f c + , Ž 7dL + , Ž B
13. Justified P/E = ëf
7 &8 ô %v7 %
ì/ ' 8 ø
ì/ '
14. EV = MV of stock + MV of debt – Cashand cash Equivalents
15. Asset-based value = Value of Equipmentand inventory – Value of Liabilities
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Reading 52: Fixed Income Securities: DefiningElements
1. Inf adj Principal amount of a zero-coupon-indexed bond= [Par value ! (1 + CPI)]
2. Inf adj coupon payment for an interest-indexed bond= [(coupon rate ! Par value) ! (1+CPI)]
3. Inf adj Principal amount of a capital-indexed bond= [Par value ! (1 + CPI)]
4.
Inflation adjusted coupon payment for acapital-indexed bond= [Par value ! (1 + CPI)] ! coupon rate
Reading 53: Fixed Income Markets: Issuance,Trading & Funding
Reading 54: Introduction to Fixed IncomeValuation
1. Amount of discount below par value =Present value of deficiency
2. Present value of deficiency =# ûðøûê ìñòî/ & ñì 1 îò öé $íûðêò ìñòî 0ëñì *ñùðî
&' & ñì 1 îò öé $íûðêò ìñòî wêò[&
3. Bond price =
PV =PMT
(1 + r )1 +
PMT
(1 + r )2 + ... +
PMT + FV
(1 + r ) N
4. % Price change =/ î < øìéíî/ . ùö øìéíî
. ùö øìéíî
5. Bond price (given sequence of spot rates)= PV =
PMT
(1 + Z 1 )1
+PMT
(1 + Z 2 )2
+ ... +PMT + FV
(1 + Z N )
N
6. Full price of bond = Flat price of bond +
Accrued interest
7. Accrued interest = ›r 8 G*
0@\]
8. Full price of a fixed-rate bond betweencoupon payments = PV Full
=PMT
(1 + r )1! t /T +
PMT
(1 + r )2! t /T + ... +
PMT + FV
(1 + r ) N ! t /T
9. Full price of a fixed-rate bond between
coupon payments
PV ! (1 + r )t /T
10. Interpolated yield (say for 3-year, givenmarket discount rates for 2 and 5 yrs) =
(Average yield for 2 year bonds) + o/k
u/k !
(average yield for 5 year bonds – averageyield for 2 year bonds)
11. 1 + APR
m
m
!"#
$%&
m
= 1 + APR
n
n
!"#
$%&
n
12. Current yield =÷ðõ ûü íûðøûê øñóõîêò $ ìîíîé * îö û * îì ò 2 î óîñì
Vùñò øìéíî
13. Price of Floating-rate note = PV=
( I + Qm ) ! FV m
1 + I + DM
m
"#$
%&'
1 +
( I + QM ) ! FV m
1 + I + DM
m
"#$
%&'
2 + ... +
( I + QM ) ! FV m
+ FV
1 + I + DM
m
"#$
%&'
N
14. Price of Money Market Instrument =
PV = FV ! 1 " DaysYear
! DR#$% &'(
15. Market Discount Rate =
DR = Year Days( )! FV " PV
FV
#$%
&'(
16. Price of Money Market Instrument =
PV =FV
1 + DaysYr ! AOR"#$ %&'
17. Add-on rate =
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FinQuiz Formula Sheet CFA Level I 2016
AOR =
Yr Days
!
"#
$
%&' FV ( PV
PV
!"#
$%&
Relation b/w two spot rates and Implied
Forward Rate:
18. (1 + z A)A ! (1 + IFR A,B-A )B-A = (1 + z B)B
Z-spread over the benchmark spot curve:Price of a bond =
PV =PMT
(1 + z1+ Z )1
+PMT
(1 + z2 + Z )2
+ ... +PMT + FV
(1 + z N + Z ) N
19. OAS = Z-spread – Option value (bps per
year)
20. G-spread = Yield-to-maturity on Corporate bond – Yield-to-maturity on a government bond
21. Interpolated Spread = I-spread = Yield tomaturity of the bond - Linearlyinterpolated yield to the same maturity onan appropriate reference curve
Reading 55: Introduction to Asset BackedSecurities
1. Loan-to-value ratio (LTV) =ëìûøîìòó _$ øðìí 2 ñ$î øìéíî
8 õûðêò ûü & ûìò ' ñ ' î
2. Monthly CF for a MPS = Monthly CF ofunderlying pool of mortgages - Servicingfee - Other fees
3. Pass-through rate = Mortgage rate on theunderlying pool of mortgages – ServicingFee - Other fees
4. SMM = Pre-pmt for month ÷ (Begmortgage balance for month – Scheduled
principal re-pmt for month)
5. CPR = 1 0 (1 0 SMM) 12
6. CF Construction (Monthly CF for MPS):
•
Net interest = (Beg mortgage balance ! Pass-through rate) / 12• Scheduled principal re-pmt =
Mortgage pmt – Gross i- pmt• Gross i- pmt = (Beg mortgage
balance ! WAC) / 12• Pre-pmt for month = SMM !
(Beg mortgage balance for month – Scheduled principal re-pmt formonth)
• Total principal re-pmt =Scheduled principal re-pmt +Prepayment
• Beg mortgage balance for thefollowing month = Beg mortgage
balance for the month – TotalPrincipal Pmt
• Projected CF for MPS = Net i- pmt + Total principal re-pmt
7. DSC ratio = ëìûøîìòó ®$ ñêêðñù /. ú
ôî , ò $îì *éíî
Reading 56: Understanding Fixed Income Risk& Return
1. Interest-on-interest gain fromcompounding = Future value of reinvestedcoupons - Total amount of coupon
paymentsWhere,FV of Reinvested Coupons = [CR ! (1+RR) n-1] + [CR ! (1+RR) n-2] +…+ [CR ! (1+RR) n-n]Total Amount of Coupon Pmt = CR ! Parvalue ! No of periods
RR = Re-invstmnt rate per periodCR = coupon rate
2. Realized RoR on Bond=
÷ðõ ûü ) îéê * î $òîö # ûðøûê $') îöîõøòéûê ûü ëìéêíéøñù ñò & ñòðìéòó
^ ûêö ëìéíî
%m
? +
3. Carrying value of bond (if bond purchased
below par) = Purchase price + Amortizedamount of Discount
4. Carrying value of a bond (if bond purchased above par) = Purchase price –Amortized amount of Premium
5. Amortized amount for 1 st year = BondPrice after 1-yr - Initial bond price
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FinQuiz Formula Sheet CFA Level I 2016
6. Capital g / (l) = Sale price of Bond after nyears – Carrying value of Bond after nyears
7. Macaulay Duration =
MacDur = 1 ! t / T ( )
PMT
1 + r( )1! t /T
PV Full
"
#
$$$$
%
&
''''
+ 2 ! t / T ( )
PMT
1 + r( )2 ! t /T
PV Full
"
#
$$$$
%
&
''''
+ ... + N ! t / T ( )
PMT + FV
1 + r( ) N ! t /T
PV Full
"
#
$$$$
%
&
''''
(
)**
+**
,
-**
.**
OR
MacDur =1 + r
r!
1 + r + N " c ! r( )#$ %&c " 1 + r( )
N
! 1#$
%&+ r
'()
*)
+,)
-)! (t / T )
8. Modified D =& ñíôðì
&'ì
9. Annualized Modified D =&ûöéüéîö ôðìñòéûê
ëîìéûöéíéó ûü øñóõîêò éê ñ óîñì
10. % 1 PV Full = - AnnModDur ! 1 Yield
11. Approx Modified D =
(PV ! ) ! (PV
+ )
2 " (# Yield ) " (PV 0 )
12. Approx Mac Dur = Approx Mod Dur ! (1+ r)
13. Effective D =(PV
! ) ! (PV + )
2 " (# Curve ) " (PV 0 )
14. Macaulay D for a Zero-coupon bond = 1/G
*
15. Macaulay D for a Perpetual bond = (1+ r) /r
16. Avg Mod D for the Portf =
Ÿ §I t §¦ q §BI + 0 &+ ûü ^ ûêö &
! ûòñù &+ ûü ëûìòü
+ Ÿ§I t §¦ q §BI ¬ 0 &+ ûü ^ ûêö k
! ûòñù &+ ûü ëûìòü +
…+ Ÿ§I t §¦ q§BI ¯ 0 &+ ûü ^ ûêö /! ûòñù &+ ûü ëûìòü
17. Money D = Annualized Mod D ! FullBond Price
18. * Full price of Bond (in currency units) # -Money D ! è in annual YTM
19. PVBP =(PV ! ) ! (PV
+ )2
20. Basis Point Value (BPV) = Moneyduration ! 0.0001 (1 bp)
21. Bloomberg’s Risk Statistic = PVBP ! 100
22. %* PV Full = (-AnnModDur ! * Yield) +&
k 0 == W= 4£>:° 0cèt>4³<d k
Or%* PV Full = (-AnnModDur ! * Yield) +
&
k 0 == W= 4£>:° 0cèt>4³<d k
23. Approx. Convexity Adjustment =
(PV ! ) + (PV
+ ) ! [2 " (PV 0 )]
(# Yield )2 " (PV 0 )
24. Convexity of a zero coupon bond =
N ! (t / T )[ ]" N + 1 ! (t / T )[ ](1 + r )2
25. Money Convexity vs Money Duration =
* PV Full # - (MoneyDur ! * Yield) + [ &
k !
MoneyCon ! (* Yield) 2]
26. Money Convexity of bond = AnnualConvexity ! Full Price
27. Effective Convexity =
PV !( )+ PV
+( )! 2 " (PV 0 )[ ]#$ %&
' Curve( )2" PV
0 )( )
28. Duration Gap = Bond’s MacaulayDuration – Investment Horizon
Reading 57: Fundamentals of Credit Analysis
1. Expected Loss = Default Probability ! Loss Severity given Default
2. Operating Profit Margin = . øîìñòéê ' úêíûõî) î * îêðî
3. EBITDA = Operating Income + Dep +Amort
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4. FCF = CFO – Cap exp– Div
5. Capital expenditures = Additions to P&E +Additions to product rights & intangibles –Proceeds of sale of P&E
6. Total debt = ST debt + Current portion ofLT debt + LT debt
7. Capital = Debt + Equity
8. Yield on Corp Bond = Rf rate + ExpectedInf rate + Maturity P + Liquidity P+ Creditspread
9.
Yield spread = Liquidity P + Credit spread
10. Return impact for smaller spread *# % * in price # -Modified Duration ! * Spread
11. Return impact for larger spread * # % * in price # - (Modified D ! * Spread) +&
kConvexity ! (* Spread) 2
12. Secured debt leverage = ! ûòñù $îíðìîö öî , ò
7^ ú! ô 8
13. Senior unsecured leverage =÷îíðìîö öî , ò'÷îêéûì ðê $îíðìîö öî , ò
7^ ú! ô 8
14. Total Leverage = ! ûòñù öî , ò
7^ ú! ô 8
15. Net Leverage = ! ûòñù öî , ò/ # ñ$27^ ú! ô 8
Reading 58: Derivatives Markets andInstruments
1. Value of the contract to the ‘Long’ atexpiration = S T – F 0(T)
2. Value of the contract to the ‘Short’ atexpiration = F 0(T) – S T
3. Margin % in stock market =&+ ûü ÷òûí 1 / &+ ûü ôî , ò
&+ ûü ÷òûí 1
4. Margin Call:• Long position: Price ± that would
trigger a margin call = IM req – MM
req• Short position: Price ( that would
trigger a margin call = IM req – MMreq
5. TED spread = LIBOR – T-Bill rate
6. At expiration (for option Buyer):• Value of Call option =
CT = Max (0, S T - X)
• Profit from Call option =Max (0, S T - X) – C 0
• Value of Put option = P 0 =Max (0, X- S T)
• Profit from Put option =Max (0, X- S T) – P 0
7. At expiration (for option Seller):• Profit from Call option =
– Max (0, S T - X) + C 0 • Profit from Put option =
– Max (0, X- S T) + P 0
8. To eliminate arbitrage opportunity:Forward Price should be = Spot Price0 + , > 5;:4 Þ G
Reading 59: Basics of Derivative Pricing &Valuation
1. Pricing of risky assets = S 0 = 7 c÷! d
&'ì' ²
2. Commodity = F 0, T = S 0 e (r – 2)T
where, 2 = Convenience yield 0 Cost ofcarry
3. S0 = 7 c÷! d
&'ì' ² – 3 + 4
where, 3 (theta) = Present value of thecosts and 4 (gamma) = Present value of
benefits
4. Arbitrage and Derivatives = Underlyingasset + Opposite position in derivative =Underlying payoff – Derivative payoff =Rf return
5. Pricing and Valuation of ForwardContracts:• At Expiration F (0, T) = S 0 (1 + r) T or
S0 = F (0, T) / (1 + r) T • Value of forward (long) during
contract life (where t < T) = V t (0, T)= S t – F (0, T) / (1 + r) (T – t)
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FinQuiz Formula Sheet CFA Level I 2016
• Value of forward (short) duringcontract life (where t < T ) = V t (0, T) = F (0, T) / (1 + r) (T – t) - S t
• Value of forward (long) at expiration(where t = T) = V T (0, T) = S T - F (0,T)
• Value of forward (long) at initiation(where t = 0) = V t (0, T) = S 0 – F (0,T) / (1 + r) T = 0
• Forward price of an asset with benefitsand/or costs = (S 0 – 4 + 3) (1 + r) T =S0 (1 + r) T – (4 - 3) (1+ r) T
• Value of Forward contract with benefits and/or costs during the life ofthe contract = S t – (4 - 3) (1 + r) T - F
(T) / (1 + r)(T – t)
6. FRAs: An example of 3 ! 9 FRA (read asthree by nine):• Contract expires in 90 days• Underlying loan settled in 270 days• Underlying rate is 180-day LIBOR• For Synthetic FRA (take long position
in a 300-day Euro$ T.D and short position in a 30-day Euro$ T.D
•
For synthetic forward position in a 90-day zero-coupon that begins in 30 day(buy 120 day & sell 30 day (zerocoupon bonds)
7. Pricing and Valuation of Swap Contract (afixed for floating swap contract):
• Fixed Periodic rate =
RN
=1 - Z
N
Z1
+ Z2
+ .... + ZN
• Where Z n are n period zero coupon
bonds (i.e. $1 discount factors)
)360/(1 1
Z n days Ln !+
=
• Value of a fixed rate side (per $1 NP)
= V fixed rate = [Fixed payment ! (Z
1+ Z
2 + .... + Z
N )] + ($1 ! Z N)
• Value of a floating rate side (per $ 1 NP) = V floating rate = ($1 + 1 st floating pmt) ! Z1
Pricing and valuation of Options:
8. Payoff of Call options:
• At expiration call option = c T = Max(0, S T –X)
• Profit (call buyer) = Max (0, S T – X) –c0
• Profit (call seller) = -Max (0, S T – X)+ c0
9. Payoff of Put options:
• p T = Max (0, X- S T)• Profit (put buyer) = Max (0, X-S T) – p 0 • Profit (put seller) = - Max (0, X – S T) +
p0
10. Max Profit/Loss for Option writer/holder:
• Max profit of option seller/writer ! Option premium.
• Max loss of option seller/writer ! unlimited.
• Max loss of option holder ! Option premium
Put-Call Parity
11. Protective Put• Value PP = p 0 + S 0 • Payoff at expiration (put out-of-the-
money) = S T.• Payoff at expiration (put in-the-
money) = (X-S T) + S T = X.
12. Fiduciary Call
• Value FC = c 0 + X / (1+r) T • Payoff at expiration (when call out-of-
the-money) = X.• Payoff at expiration (call in-the-
money) = X + (S T – X) = S T.
13.
Put-Call Parity (to avoid arbitrage) = c 0 +X / (1+r) T = p 0 + S 0
• Synthetic long position in a call =
C = p 0+ S 0 ! X
(1 + r )T
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• Synthetic long position in a put =
p 0= c 0
! S 0 + X
(1 + r )T
• Synthetic long position in an
underlying = S 0 = c 0+ X
(1 + r )T ! p0
• Synthetic long position in a riskless
bond = X
(1 + r )T = p 0
+ S 0 ! c0
14. Put-Call-Forward Parity = F 0(T) / (1 + r) T + p 0 = c 0 + X/(1 + r) T
15. Valuing a callable bond using Binomial
Model:
• R u = R d ! e2% : • Value at time 0 = V 0 = hS 0 0 c0
• Value at time 1 will either V 1+ = hS 1
+ -c1
+ or V 1- = hS 1
- - c1-
• If the portfolio was hedged, then V + would equal V -.
• Value of the call =
• Value of the put =
Reading 60: Risk Management Applications ofOption Strategies
1. For Call Option Buyer• cT = max (0, S T –X)• When S T ( X " cT = 0• When S T > X " cT = S T – X• Value at expiration = c T • Profit = c T – c 0 • Maximum profit = 5 ! no upper limit• Maximum loss = c 0 • Breakeven = S T* = X + c 0
2. For Call Option Seller
• cT = max (0, S T –X)• When S T ( X " cT = 0• When S T > X " cT = S T –X• Value at expiration = -c T • Profit = –c T+ c 0 • Maximum profit = c 0
• Maximum loss = 5 ! no upper limit• Breakeven = S T* = X +c 0
3. For Put Option Buyer
• pT = max (0, X - S T)• When S T < X " pT = X - S T • When S T " X " pT = 0• Value at expiration = p T
• Profit = p T – p 0 • Maximum profit = X – p 0 • Maximum loss = p 0 • Breakeven = S T* = X –p 0
4. For Put Option Seller
• pT = max (0, X –S T)• When S T < X " pT = X – S T • When S T " X " pT = 0• Value at expiration = –p T • Profit = –p T + p 0 • Maximum profit = p 0 • Maximum loss = X - p 0 • Breakeven = S T* = X - p 0
5. Covered Call = Long stock position +Short call position
• Value at expiration = V T = S T – max(0, S T – X)
• When S T ( X " VT = S T • When S T > X " VT = S T - ST +X = X• Profit = V T – S 0 + c 0 • Maximum Profit = X – S 0 + c 0 • Maximum Loss = S 0 – c 0 • Breakeven =S T* = S 0 – c 0
6. Protective Put = Long stock position +Long Put position
• Value at expiration: V T = S T + max (0,X - S T)
• When S T ( X " VT = S T + X - S T = X• When S T > X " VT = S T
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• Profit = V T – S 0 - p 0 • Maximum Profit = 5 • Maximum Loss = S 0 + p 0 – X• Breakeven =S T* = S 0 + p 0
Reading 61: Introduction to AlternativeInvestments
1. Total Return = Alpha R + Beta R
2. Asset Based Valuation = Co value = Co’sassets value – Co’s liabilities value
Real Estate Valuation3. Direct Cap Approach " Valuation of a
property = 1UgQHRMGHwM³ HGMOL NHGI where
NOI = Gross potential income –Estimatedvacancy losses – Estimated collectivelosses – Insurance – Property Taxes –Utilities – Repairs, maintenance exp.
4. Income Based Approach " FFO = NI +Dep exp on R.E + Def Tax charges – Gainsfrom sales of R.E + losses from sale of R.E
5. AFFO = FFO – Recurring Cap exp
6. Asset based Approach " REIT’s NAV =Estimated MV of REIT’s total assets –Value of REIT’s total liabilities.
7. Pricing of Commodity Futures Contracts:Futures price # Spot price (1 +r) + Storagecosts – Convenience yield
8. Roll yield = Spot price of a commodity –Futures contract price orRoll yield = Futures contract price withexpiration date ‘X’– Futures contract price
with expiration date ‘Y.
9. Returns on a passive investment incommodity futures= Return on the collateral + RP orconvenience yield net of storage costs.
10. Sharpe ratio = (Investment return – Rfreturn) / S.D. of return
11.
Sortino Ratio = (Annualized RoR –Annualized Rfe rate)/Downside Deviation
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