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8/17/2019 l 1 Formula Sheet June 2016
http://slidepdf.com/reader/full/l-1-formula-sheet-june-2016 1/31
8/17/2019 l 1 Formula Sheet June 2016
http://slidepdf.com/reader/full/l-1-formula-sheet-june-2016 2/31
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 & Market
Returns
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 of
Observations (obvs) in a given class
interval
4. Relative Frequency =K|7OwSGI !(I}SILa`
*OGHw 1O OP U|~7
5.
Cumulative Absolute Frequency = Add up
the 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 observations
are arranged in ascending/descending
order)
• For Even no of obvs locate
median atL
k
• For Odd no. of obvs locate
median atL'&
k
9.
Mode = obvs that occurs most frequently
in the distribution
10. Weighted Mean = € 8 2M €MLM[& =
(w1X1+ w2X2+….+ wnXn)
11. Geometric Mean = GM = €& €k l €Lm
with Xi"0 for i = 1,2,…n.
12.
Harmonic Mean = H.M = €z 8 L%
‚ƒ
mƒ„%
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 = Ly = = , + `
&ff
16.
Mean Absolute Deviation = MAD =…Z/…m
ƒ„%
L
17.
Population Var = !2 =…ƒ/ˆ ‰#
ƒ„%
1
18. Population S.D = Šk=…ƒ/ˆ ‰#
ƒ„%
1
19.
Sample Var = s2 = …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 € = sample
mean
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)
=&
|/H
j 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 © ªk
oŠ
• Approx 68% of all obvs fall in the
interval © ª Š
•
Approx 95% of all obvs fall in the
interval © ª«Š
• Approx 99% of all obvs fall in the
interval © ª¬Š
•
More precise intervals for 95% of the
obvs are © ª +•®Š and for 99% of the
observations are © ª «•¯°Š•
5. Z-Score (how many S.Ds away from the
mean the point x lies) ± 8
9:;=<;5< =W5Œ;² 5;=<WŒ ;5>;œ²4 8
…/ˆ
™ (when X is normally distributed)
6. Roy’s Safety-Frist Criterion = SF Ratio = NE /N³
™E
7.
Sharpe Ratio = = NE /N´
™E
8. Value at Risk = VAR = Minimum $ loss
expected over a specified period at a
specified prob level.
9. Mean (µL) 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 = ST = S0exp (r 0,T)
Where, exp = e and r 0,t = Continuously
compounded return from 0 to T
12. Price relative = End price / Beg price =
St+1/ St=1 + R t, t+1
where,
Rt, t+1 = holding period return on the stock from t to t + 1.
13. Continuously compounded return
associated with a holding period from t to t
+ 1:
r t, t+1= ln(1 + holding period return) or
r t, t+1 = ln(price relative) = ln (S t+1 / St) = ln
(1 + R t,t+1)
14. Continuously compounded return
associated with a holding period from 0 to
T:
R 0,T= ln (ST / S0) or 5f–* 8 5*/&–* ,
5*/k–*/& , µ , 5f–&
Where,
r T-I, T = One-period continuously
compounded returns
15. When one-period continuously
compounded returns (i.e. r 0,1) are IID
random variables.
“ 5f–* 8 “ 5*/&–* , “ 5*/k–*/& ,
µ , “ 5f–& 8 ©] And
A;5>;=X4 8 Šk 5f–* 8 Š k]
S.D. = % (r 0,T) = % ]
16.
Annualized volatility = sample S.D. of
one period continuously compounded
returns ! ]
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 not
known = 9… 87
L where s = sample
S.D estimate of s =
9;Œ’²4 ;5>;=X4 8
9k 23454 9k =…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 population
with known variance = ¢ ª ±Hvk™
L
• CI for normally distributed population
with unknown variance = ¢ ª ±Hvk
F
L where S = sample S.D.
7.
Student’s t distribution
µ = € ª :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» ¶¼·¼½¾¼½¿ ÀÁ¹Â¼Ã»¾½Ä»Å Æ·ºÇ» ÂÈ ¹Â¹ ¹·É·¸»¼»É
¾¼·ÊÅ·ÉÅ »ÉÉÂÉ ÂÈ ¾·¸¹º» ¾¼·¼½¾¼½¿ Ë
*when Pop S.D is unknown, the standard
error of sample statistic is give by Ì… 8
F
L
*when Pop S.D is unknown, the standard
error of sample statistic is give by Š… 8
™
L
2. Power of Test = 1-Prob of Type II Error
3. ± 8…/ˆh
Í
m
(when sample size is large or
small but pop S.D is known)
4. ± 8…/ˆh
-
m
(when sample size is large but
pop S.D is unknown where s is sample
S.D)
5. :L/& 8…/ˆh
-
m
(when sample size is large or
small and pop S.D is unknown and pop
sampled is normally or approximately
normally distributed)
6. Test Statistic for a test of diff b/w two pop
means (normally distributed, pop var
unknown but assumed equal)
t =
…%/…‰ / ˆ%/ˆ‰
Îω
m%'
Îω
m‰
%v‰ where ÌR
k
= 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 distributed, unequal
and unknown pop var unknown)
t = …%/…‰ / ˆ%/ˆ‰
Î%‰
m%'
Ή‰
m‰
%v‰ In this df calculated as
<e 8
Î%‰
m% '
Ή‰
m‰
‰
Î%‰
m%
‰
m%'
Ή‰
m‰
‰
m‰
8. Test Statistic for a test of mean differences
(normally distributed populations,
unknown population variances)
•
: 8J/ˆÐh
FJ
• sample mean difference = < 8
&
L<M
LM[&
• sample variance = ÌJ
k 8J%/J ‰m
ƒ„h
L/&
• sample S.D = ÌJ
k
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FinQuiz Formula Sheet CFA Level I 2016
• sample error of the sample mean
difference = 9 < 8FÐ
L
8. Chi Square Test Statistic (for test
concerning the value of a normal
population variance) €k 8 L/& F‰
™h‰ where
= ?+ 8 <e ;=< Ìk 8
9;Œ’²4 ;5>;=X4 8…ƒ/… ‰m
ƒ„h
L/&
9. Chi Square Confidence Interval for
variance
Lower limit = L =L/& F‰
…Ñv‰‰ and Upper limit
= U = =
L/& F‰
…%ÒÑv‰‰
10. F-test (test concerning differences between
variances of two normally distributed
populations) F =F%
‰
F‰‰
Ì&k 8 +9: 9;Œ’²4 ;5 2>:3 =& Wœ9 Ì&
k 8
«=< 9;Œ’²4 ;5 2>:3 =k Wœ9
<e& 8 =& ? + =ӌ45;: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 of
freedom
12. Spearman Rank Correlation = 57
8 + ?® <&
kLM[&
= =k ? +
•
For small samples rejection points for
the test based on 57are found using
table.
•
For large sample size (e.g. n>30) t-test
can be used to test the hypothesis i.e.
: 8= ? « &vk57
+ ? 57k &vk
Reading 12: Technical Analysis
1.
Relative Strength Analysis =Õɽ¿» ÂÈ ·¾¾»¼
Õɽ¿» ÂÈ ¼Ã» ֻʿø·É× Ø¾¾»¼
2. Price Target for the
• Head and Shoulders = Neckline –
(Head – Neckline)
• Inverse Head and Shoulders =
Neckline + (Neckline– Head)
3. Simple Moving Average =ÕÙ'ÕÚ'ÕÛl•'ÕÊ
Ü
4. Momentum Oscillator (or Rate of Change
Oscillator ROC):
• Momentum Oscillator Value M = (V-
Vx) 0+jj
(where V = most recent closing price
and Vx = closing price x days ago)
• Alternate Method to calculate M ="
"0+jj
5.
Relative Strength Index = RSI = +jj ?
&ff
&'NF where
RS =ÝR axHLTI7
iOL axHLTI7
6. Stochastic Oscillator (composed of two
lines %K and %D):
•
Þß 8 +jjQ/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) =ƺǸ» ÂÈ ÕǼ ๼½Âʾ áÉ·Å»Å
ƺǸ» ÂÈ â·ºº ๼½Âʾ áÉ·Å»Å
8. Short Interest Ratio (Type of Sentiment
Indicators) = ¶ÃÂɼ ãʼ»É»¾¼ Øä»É·å» æ·½ºÁ áɷŽÊå ƺǸ»
9. Arms Index TRIN i.e. Trading Index (Type
of Flow of funds Indicator) =
5Œ ›=<4¢ W5 ]Y›š 81O•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 a
consumer places on units consumed –
Price paid to buy those units
• Area (for calculating Consumer
Surplus) = & (Base ! Height) = & (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) = & (Base ! Height) = & {(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
8. Price Elasticity of Demand =Þ è éê ïðñêòéòó ôîõñêöîö
Þ è éê ëìéíî
)(
)(
P%
Q%
2121
12
2121
12
P P
P P
+
!
+
!
=
"
"
9. Income Elasticity of Demand =Þ è éê ïðñêòéòó ôîõñêöîö
Þ è éê úêíûõî=
)(
)(
I%
Q%
2121
12
2121
12
I I
I I
+
!
+
!
=
"
"
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$ðõîö
2. Equation of Budget Constraint Line = (PX
! QX ) + (PY ! QY)
3. Slope of Budget Constraint Line =è éê ï%
è éê ï‚ =
ë‚
ë%
4.
Marginal Rate of Substitution =
è éê ï%
è éê ï‚ =&ñì'éêñù "òéùéòó ûü ýûûö þ
&ñì'éêñù "òéùéòó ûü ýûûö ÿ
Reading 15: Demand & Supply Analysis: The
Firm
1. Profit = Total revenue – Total cost
2. Accounting Profit = Total Revenue –
Explicit Costs (or Accounting costs)
3.
Economic Profit
• = Total Revenue – Explicit Costs –
Implicit Costs or
• = Accounting Profit – Implicit Costs
or
• = Total Revenue – Total Economic
Costs
4. Economic costs = Explicit costs + Implicit
costs5. Normal Profit = Accounting Profit –
Economic Profit
6.
Accounting profit = Economic Profit +
Normal Profit
7. Economic rent = (New “Higher” Price
after ( in Demand – Previous Price before
( in Demand) ! QS before ( in Demand
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FinQuiz Formula Sheet CFA Level I 2016
8. Total Revenue (TR):
• = Price ! Quantity or
•
= Sum of individual units sold !
Respective prices of individual Units
sold = ' (Pi ! Qi)
9.
Average Revenue (AR) =!ûòñù )î*îêðî
ïðñêòéòó
10. Marginal Revenue (MR) =è éê !ûòñù )î*îêðî
è éê ïðñêòéòó
11.
Total Variable Cost = Variable Cost per
unit ! Quantity Produced
12. Total Cost = Total Fixed + Total Variable
13. Average total cost (ATC) =!ûòñù #û$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 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
21. Profits occur when Total Revenue (TR) "
Total Cost (TC) & 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 ANDwhen 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.
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 0ûì1îì$
26. Least-cost optimization Rule:&ñì'éêñù ëìûöðíò ûü -ñ,ûì
ëìéíî ûü -ñ,ûì8
&ñì'éêñù ëìûöðíò ûü ë2ó$éíñù #ñøéòñù
ëìéíî ûü ë2óéíñù #ñøéòñù
27.
Profit is maximized when: MRP = Price or
cost of the input for each type of resource
that is used in the production process
28. Marginal Revenue product = Marginal
Product of an input unit ! Price of the
Product = Price of the input =è éê !ûòñù )î*îêðî
è éê ïðñêòéòó ûü úêøðò îõøùûóîö
29. Surplus value or contribution of an input to
firm’s profit = MRP – Cost of an input
Reading 16: The firm & Market Structures
1. In perfect competition, Marginal revenue =
Avg. Revenue = Price = Demand
2. Marginal Revenue = 3§456 0 + ?
&
ëìéíî 7ùñ$òéíéòó ûü ôîõñêö
3.
Concentration Ratio =÷ðõ ûü $ñùî$ *ñùðî$ ûü ò2î ùñì'î$ò &f üéìõ$
!ûòñù &ñì1îò ÷ñùî$
4. Herfindahl-Hirshman Index = Sum of the
squares of the market shares of the top N
companies in an industry
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FinQuiz Formula Sheet CFA Level I 2016
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 / GDP
deflator) ÷ 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 payments
8.
GDP = National income + Capital
consumption allowance + Statistical
discrepancy
9. National Income = Compensation of
employees + 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 business
taxes – Corp income taxes – Undistributed
Corp 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 – Inves tment) – Trade
Balance
22. Average propensity to consume (APC) =8''ìî'ñòî #ûê$ðõøòéûê
)îñù úêíûõî
23. Quantity theory of money equation:
Nominal Money Supply ! Velocity of
Money = Price Level ! Real Income or
Expenditure
24. % è in unit labor cost = % è in nominal
wages - % è in productivity
25. Economic growth = Annual % è in real
GDP
26.
Total Factor Productivity growth = Growthin potential GDP – [Relative share of labor
in National Income ! (Growth in labor) +
[Relative share of capital in National
Income ! (Growth in capital)]
27. Growth in potential GDP = Growth in
technology + (Relative share of labor in
National Income ! Growth in Labor) +
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FinQuiz Formula Sheet CFA Level I 2016
(Relative share of capital in National
Income ! Growth in capital]
28. Capital share =Corporate profits + net
interest income + net rental income +
(depreciation/ GDP)
29.
Labor share =7õøùûóîî #ûõøîê$ñòéûê
ýôë
Reading 18: Understanding Business Cycles
1. Price index at time t2 ="HwSI OP GxI QO.7S.RGMOL yH7{IG HG G ‰
"HwSI OP GxI QOL7S.RGMOL yH7{IG HG G %0+jj
Inflation Rate =ëìéíî úêöî9 ñò òéõî òk
&ff? +
2. Fisher Index = ›’ 0›: (where, IL =
Laspeyres index and I p = Paasche Index)
3.
;=>: ²;œW5 XW9: c;:d >=<>X;:W5 8!ûòñù ùñ,ûì íûõøîê$ñòéûê øîì 2ûðì øîì <ûì1îì
.ðòøðò øîì 2ûðì øîì <ûì1îì
4. =6>¦54?@ ¦¥ A¦B6@ 8/ûõéêñù ýôë
&ûêîó ÷ðøøùó
Reading 19: Monetary & Fiscal Policy
1. Total Money created = New deposit/
Reserve Req
2. Money Multiplier =&
)î$îì*î )îC ûì ìî$îì*î ìñòéû
3. Narrow money = M1= currency held
outside banks + checking accounts +
traveller’s check
4.
Broad money = M2 = M1 + time deposits
+ saving deposits
5. M3 = M2 + deposits with non-bank
financial institution
6. Quantity Theory of Money = M ! V = P !
Y where,
M = Quantity of money
V = Velocity of circulation of money
P = Average price level
Y = Real output
7. Neutral Rate = Trend Growth + Inflation
Target
8. Impact of Taxes and Government
Spending: The Fiscal Multiplier
The net impact of the government sector
on AD:
• G – T + B = Budget surplus or Budget
deficit
where, G = government spending , T
=taxes, B =transfer benefits
•
Disposable income = Income – Net
taxes = (1 – t) Income
where, Net taxes = taxes – transfer
payments, t = net tax rate
9. Fiscal Multiplier (in the absence of taxes)
= 1/(1 - MPC)
• MPS = 1 – MPC.
• Total increase in income and spending
= Fiscal multiplier ! G
10. Fiscal Multiplier (in the presence of taxes)
• MPC (with taxes) = MPC ! (1 - t)
• Fiscal multiplier =
&
&/)$Q &/G
• Total ( in income and spending =
Fiscal multiplier ! G
• Initial ( in consumption due to
reduction in taxes = MPC ! tax cut
amount
• Total or cumulative effect of tax cut =
multiplier ! initial change inconsumption
11. Cumulative multiplier =íðõðùñòé*î îüüîíò ûê ìîñù ýôë û*îì ò2î ò<û óîñì$
Þ OP Di$
Reading 20: International Trade & Capital
Flows
1. Terms of trade =ëìéíî ûü î9øûìò$
ëìéíî ûü éõøûìò$
2. Terms of Trade (as an index number) =8*' øìéíî ûü î9øûìò$
8*' øìéíî ûü éõøûìò$
3. Net exports = Value of a country's (exports
–imports)
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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- 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 + Sg = I + CA
where, Sg = Govt savings
S p = I + CA – Sg
• Current Account Imbalance CA = Sp
+ Sg – I
Reading 21: Currency Exchange Rates
1. E¦§64FB G§456 >6H6> 4B I¦A6J?45 5K§§6B5@ 8
Lövü 03ü
2.
M6N> 6O5PNBF6 §N?6côvüd 8 cLö ü 03ü dv3ö 8
Lö ü 0c3ü v3öd
3. M6N> QO5PNBF6 MN?6 öûõî$òéívüûìîé'ê 8
Lövü 0 #ëúR
#ëúS
4. TPNBF6 4B M6N> QO5PNBF6 §N?6 8
+ ,è÷SvR
÷SvR 0
&'èUR UR
&'èUSUS
? +
5.
Direct Quote = &úêöéìîíò ïðûòî
6. Points on a forward rate quote = Fwd X-
rate quote –Spot X-rate quote
7. Forward rate = Spot X-rate +Vûì<ñìö øûéêò$
&f–fff
8. E¦§WN§I G§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 %) = Spot
exchange rate ! (1 + % premium or
discount)
10. Arbitrage relationship is stated as follows:
•
+ , >J 8 Ì ´
Ð
+ , >P&
!´Ð
• In case of indirect quote, Arbitrage
relationship is: + , >J 8
+vÌPvJ + , >P ÔPvJ
•
Ô´
Ð
8 Ì ´
Ð
&'M´
&'MÐ
•
Forward rate as a % of spot rate =!´vÐ
F´vÐ8
&'M´
&'MÐ
11. Return on hedged foreign investment
(with a quoted forward rate) = ÌPvJ + ,
>P&
!´vÐ
12.
Expected % change in the spot rate =FZ^%
FZ? + 8 ÞèÌG'& 8
M´/MÐ
&'MÐ
• Forward points: ÔPvJ ? ÌPvJ 8
ÌPvJ
M´/MÐ
&'MÐX Y (where Y is quoted
interest rate period)
13. Relationship between the trade balance and
expenditure/ saving decisions:
= Ex – Im = (Sav – Inv) + (T – G)
where T= taxes net of transfers
G= government expenditures)
14. Price elasticity of demand = ) =Þ í2ñê'î éê Cðñêòéòó
Þ í2ñê'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,
+x=share of exports
)X=price elasticity of foreign demand for
domestic country exports
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+M=share of imports
)M =price elasticity of domestic country
demand for imports
17.
Trade balance = Income (GDP) –
Domestic expenditure = Absorption
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 +
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 8õûðêò ûü #û$ò
!éõî ûü ò2î íûêòìñíò
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 =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 of
ending inventory
8. Annual Depreciation Expense (using
Straight-Line Method) =#û$ò/)î$éöðñù +ñùðî
7$òéõñòîö "$îüðù -éüî
9. Annual Depreciation Expense (Declining
balance method) =&ffÞ
"$îüðù ùéüî ! Acceleration
factor (say 200% or 2) ! Net Book Value
10. Basic EPS =/îò úêíûõî/ëìîüîììîö ôé*éöîêö$
0'2ò 8*' /û ûü $2ñìî$ ûðò$òñêöéê'
11.
Diluted EPS for preferred stock =/îò úêíûõî
0'2ò 8*' /û ûü $2ñìî$ ûv$'/î< íûõõûê $2ñìî$ ò2ñò
<ûðùö 2ñ*î ,îîê é$$ðîö ñò íûê*îì$éûê
12. Diluted EPS for convertible debt =/îò éêíûõî '8! M ûê
íûê*îìòé,ùî öî,ò/ëìîüîììîö ôé*0'2ò 8*' ûü $2ñìî$ ûv$'8ööéòéûêñù íûõõûê $2ñìî$
ò2ñò <ûðùö 2ñ*î ,îîê é$$ðîö ñò íûê*îì$éûê
13. Diluted EPS using Treasury Stock Method
=c/îò úêíûõî/ëìîüîììîö öé*éöîêö$d
\0'2ò 8*' ûü $2ñìî$'c/î< $2ñìî$ ñò ûøòéûê î9îìíé$î/
÷2ñìî$ øðìí2ñ$îö <éò2 #ñ$2 ìîíîé*îö ðøûê î9îìíé$î d 0
cëìûøûìòéûê ûü ÿìd]
14.
Net Profit Margin =/îò úêíûõî
)î*îêðî
15.
Gross Profit Margin =ýìû$$ ëìûüéò
)î*îêðî
16. Comprehensive EPS = EPS + Other
Comprehensive Income per share
Reading 26: Understanding Balance Sheets
1. Percentage of A/C Receivable estimated to
be uncollectible =8ùùû<ñêíî üûì ôûð,òüðù 8v#
ýìû$$ ñõûðêò ûü 8v# )îíîé*ñ,ùî
2. Net Identifiable Assets = Fair value of
identifiable assets – Fair value of liabilities
& contingent liabilities
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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. Amortized cost of PPE = Historical cost –
Accumulated depreciation – Impairment
losses
6.
Carrying value for PPE under revaluation
model
= 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 $2îîò 8õûðêò
!ûòñù 8$$îò$
10.
Current ratio =#ðììîêò 8$$îò$
#ðììîêò -éñ,éùéòéî$
11.
Quick (acid test) =#ñ$2'&ñì1îòñ,ùî $îíðìéòéî$')îíîé*ñ,ùî$
#ðììîêò -éñ,éùéòéî$
12. Cash ratio =#ñ$2'&ñì1îòñ,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 7Cðéòó
15. Total Debt =!ûòñù ôî,ò
!ûòñù 8$$îò$
16.
Financial Leverage =!ûòñù 8$$îò$
!ûòñù 7Cðéòó
Reading 27: Understanding Cash Flow
Statements
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 from
customers
3.
Cash received from customers = Revenue – Increase in a/c receivable
4. Purchases from suppliers = COGS +
Increase in inventory
5.
Cash paid to suppliers = Cogs + Increase
in 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 and
wages expense – Increase in salary and
wages payable
9. End salary and wages payable = Beg 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
11.
Cash paid for interest = Interest expense +
Decrease in interest payable
12. End Interest Payable = Beg 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 = Beg
balance equipment + Equipment purchased
– End balance equipment
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FinQuiz Formula Sheet CFA Level I 2016
17. Total Asset Turnover =)î*îêðî
8*' !ûòñù 8$$îò$
18. Pretax margin =7ñìêéê'$ ,îüûìî òñ9 ,ðò ñüòîì éêòîìî$ò
)î*îêðî
19.
Return on Total Capital =7^ú!
÷2ûìò ñêö ùûê' òîìõ öî,ò ñêö îCðéòó
20. ROE =/îò úêíûõî
8*' !ûòñù 7Cðéòó
• ROE = ROA ! Leverage
•
ROE = Tax Burden ! Interest Burden
! EBIT Margin ! Total Asset
Turnover ! Leverage
21. Return on Common Equity =/îò úêíûõî/ëìîüîììîö ôé*éöîêö$
8*' #ûõõûê 7Cðéòó
22. Coefficient of Variation of Operating
Income =÷•ô ûü .øîìñòéê' úêíûõî
8*' .øîìñòéê' úêíûõî
23. Coefficient of Variation of Net Income =÷•ô ûü /îò úêíûõî
8*' /îò úêíûõî
24. Coefficient of Variation of Revenues =÷•ô ûü )î*îêðî
8*' )î*îêðî
25. Monetary Reserve Requirement (Cash
Reserve Ratio) =)î$îì*î$ 2îùö ñ$ #îêòìñù ^ñê1
÷øîíéüéîö ôîøû$éò -éñ,éùéòéî$
26. Liquid Asset Requirement =)îñöéùó &ñì1îòñ,ùî ÷îíðìéòéî$
÷øîíéüéîö ôîøû$éò -éñ,éùéòéî$
27. Net Interest Margin =/îò úêòîìî$ò úêíûõî
!ûòñù úêòîìî$ò 7ñìêéê' 8$$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$$ úêòîìî$ò
32. EBITDA Interest Coverage =7^ú!ô8
ýìû$$ úêòîìî$ò
33. FFO Interest Coverage =VV.'úêòîìî$ò ëñéö/.øîìñòéê' -îñ$î 8ömð$òõîêò$
ýìû$$ úêòîìî$ò
34. Return on Capital =7^ú!
8*' #ñøéòñù
=
7^ú!
8*' c7Cðéòó'/ûê íðììîêò öîüîììîö òñ9î$'öî,òd
35. FFO to Debt =VV.
!ûòñù ôî,ò
36. Free Operating CF to Debt =#V./#ñø 79ø
!ûòñù ôî,ò
37. Discretionary CF to Debt =#V./#ñø î9ø/ôé*éöîêö$ øñéö
!ûòñù öî,ò
38.
Net CF to Capital expenditures =VV./ôé*éöîêö$
#ñø î9ø
39.
Debt to EBITDA =!ûòñù öî,ò
7^ú!ô8
40.
Total Debt to total debt plus Equity =!ûòñù öî,ò
!ûòñù öî,ò'7Cðéòó
41.
Z-Score = 1.2 ! #8/#-
!8 + 1.4 !
)•7
!8 +
3.3 ! 7^ú!
!8 + 0.6 !
&+ ûü $òûí1
^+ ûü ùéñ,éùéòéî$ + 1.0
! ÷ñùî$
!8
42. Segment margin =÷î'õîêò ëìûüéò c-û$$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
1. NRA = Estimated Selling Price –
Estimated Costs of completion and
disposal
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2. Inventory amount net of valuation
allowance = 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 "$îüðù -éüî =
né$òûìéíñù #û$ò/7$òéõñòîö )î$éöðñù $ñù*ñ'î + ñùðî
7$òéõñòîö "$îüðù -éüî
2. Dep Exp under Units-of-Production
Method = Depreciable Cost ! ëìûöðíòéûê éê ò2î ëîìéûö
7$òéõñòîö ëìûöðíòé*î #ñøñíéòó
3. Carrying amount under cost model =
Historical Cost – Accumulated Dep or
Amortization
4. Carrying amount under revaluation model
= Fair value at the date of revaluation –
Any subsequent Accumulated Dep 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 CFs
6. Impairment Loss (US GAAP) = Asset’s
Fair Value – Carrying Amount …….If
Carrying amount > Undiscounted Expected
Future Cash Flows
Reading 31: Income Taxes
1. Deferred tax asset = Company’s taxable
income > Accounting profit
2. Tax base of revenue received in advance =
Carrying amount – Any amount of revenue
that will not be taxed at a future date
3.
Reported Effective Tax Rate =úêíûõî !ñ9 î9øîê$î
ëìî òñ9 éêíûõî ûì 8ííûðêòéê' ëìûüéò
4. Deferred tax liability = Carrying amount
of asset > Tax base of asset
5.
Deferred tax asset = Carrying amount of
asset < Tax base of asset
6. Deferred tax asset = Carrying amount of
liability > 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 in
deferred tax asset / liability
Where,
• Income Tax liability currently
payable = Taxable income ! Tax
rate
•
èin deferred tax asset / liability =
Diff b/w the balance of the
deferred tax asset / liability for the
current period and the balance of
the 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 = (carrying
amount – tax base) ! tax rate
• Deferred tax asset = (tax base –
carrying amount) ! tax rate
10. Tax base of a liability = Carrying amount
of the liability – Amounts that will be
deductible for tax purposes in the future
Reading 32: Non-current (Long-term)
Liabilities
1. Annual Interest Payment = Face Value !
Coupon Rate
2. Sale proceeds of bond = Sum of PV of
Interest Payments + PV of Face value of
Bond
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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 Discount
7.
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 amortization
cost)
9. Amount of Bonds payable initially
reported on the balance sheet under IFRS =
Sales proceeds – Issuance costs
10.
Amount of Bonds payable initially
reported on the balance sheet under US
GAAP = Sales proceeds
11. Bond i-exp. under effective i-rate method
= Carrying value of the bonds at the beg.
of the period ! Effective i-rate
12. Bond Interest Payment under effective
interest rate method = Face value of the
bonds ! Contractual (coupon) rate
13.
Amortization of the discount or premium
under effective interest rate method =
Bond interest expense – Bond interest
payment
14. Bond Discount/Premium Amortization
under 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 – Accumulated
depreciation
17. Accumulated depreciation = Prior year’s
accumulated depreciation + Current year’s
depreciation expense
18.
Interest expense = Lease liability at the beg
of the period ! interest rate implicit in thelease
19. Sales revenue = lower of the fair value of
the asset and PV of the min lease payments
20. Cost of sales = Carrying amount of the
leased asset – PV of the estimated
unguaranteed residual value
21. Interest Revenue = Lease receivable at the
beg of the period ! Interest rate
22. Net interest expense = Beg Net pension
liability ! Discount rate
23. Net Interest income = Beg Net Pension
asset ! 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# í2ñê'î$ o öé*éöîêö$d
òûòñù öî,ò
4. )îòñéêîö #V/#ñø î9ø
!ûòñù ôî,ò
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5. Inventory value adjusted to FIFO basis =
End Inventory value under LIFO + End
LIFO reserve balance
6.
COGS adjusted to a FIFO basis = COGS
under LIFO – (End LIFO reserve – Beg
LIFO reserve)
7. Useful life of the company’s overall asset
base that has passed =8ííðõðùñòîö ôîø
ýìû$$ ëë7
8. Avg age of the asset base =8ííðõðùñòîö ôîø
8êêðñù ôîø î9øîê$î
9.
Remaining useful life of the asset =/îò ëë7 cêîò ûü ñííðõðùñòîö öîød
8êêðñù öîø î9øîê$î
10. Avg depreciable life of the assets at
installation =ýìû$$ ëë7
8êêðñù ôîø î9øîê$î
11. % of asset base that is being renewed
through new capital investment =#ñøî9
ýìû$$ ëë7' #ñøî9
12. Adjusted BV = Total stockholders’ equity
– Goodwill
13. Adjusted Price to BV ratio =ëìéíî õñì1îò íñøéòñùépñòéûê
8ömð$òîö ^+
14.
Tangible B.V = Total stockholders’ equity
– Goodwill – Other intangible assets
15. Price to tangible BV ratio =ëìéíî
!ñê'é,ùî ^+
16. Adjusted debt-to-equity ratio =)îøûìòîö öî,ò'ë+ ûü ûøîìñòéê' ùîñ$î
)îøûìòîö 7Cðéòó
17. Adjusted debt-to-asset ratio =)îøûìòîö öî,ò'ë+ ûü ûøîìñòéê' ùîñ$î
)îøûìòîö 8$$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 the
lease payments
21.
Depreciation expense estimated on
straight-line basis =ë+ ûü ò2î ùîñ$î øñóõîêò$
/û ûü óì$ ûü üðòðìî ùîñ$î øñóõîêò$
22.
Adjusted Interest Coverage ratio =
Qqrs , §6B? 6OG Ë ?t6G 6OG Ë
> GN@A6B?J , > 6OG6BJ6 Ë
* associated with the operating lease
obligations
Reading 35: Capital Budgeting
1.
Incremental CF = CF with a decision - CF
without 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’s
existing invst + Net PV of all of
company’s future invst
Reading 36: Cost of Capital
1. WACC = wdr d (1 – t) + w pr p + wer e
2. Debt-to-Equity Ratio conversion into
weight (i.e. Debt / (Debt + Equity) =jcvw
xyzew{
&'jcvw
xyzew{
3. Optimal Capital Budget is the point where
MC of capital = Marginal return from
investing
4. After-tax cost of debt = Before-tax
Marginal Cost of Debt ! (1 – firm’s
marginal tax rate)
5. Preferred Stock Price per Share
=ëìîü ÷òûí1 ôé* øîì ÷2ñìî
#û$ò ûü ëìîü ÷òûí1
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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 (Factor
risk premium)2+…..+,i j (Factor risk
premium) j
8. Cost of Equity = |} 8 ô%
ëh, F
9.
Expected Growth Rate of Dividends
g = (1 -ô
7ë÷) ! ROE
g = 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…c
j‚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’s
currency) – T.B yield on a similar maturity
bond in developed country
16.
Country equity premium = Sovereign yield
spread ! 8êê ÷•ô ûü 7Cðéòó éêöî9
8êê ÷•ô ûü $û*îìîé'ê ,ûêö &1ò éê
òîìõ$ ûü öî*îùûøîö õ1ò íðììîêíó
17.
Cost of equity = K e= R F + ,[(E(R M)-R F) +
CRP]
18. Breakpoint =8õûðêò ûü íñøéòñù ñò <2éí2 $ûðìíî_$ íû$ò ûü íñø è
ëìûø ûü êî< íñø ìñé$îö üìûõ ò2î $ûðìíî
19. Cost of Capital (hen flotation costs are in
monetary terms = §î 8 ô%
ëh/V , F
20. When FC are in terms of % of the share
price: Cost of Equity = §î 8 ô%
ëh/V , F
21.
If FC are not tax deductible: NPV = PV of
Cash Inflows – IO – (FC in % ! New
Equity Capital)
22. If FC are tax deductible: NPV = PV of
Cash Inflows – IO – [(FC in % ! New
Equity 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 units
sold) ! [(price per unit) - (variable cost per
unit)]
2.
Per unit CM = Price per unit - Variable
cost per unit
3. Operating income = CM – Fixed Operating
Costs
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 #û$ò/Vé9îö Véê #û$ò
6.
DTL=Þ è éê /îò úêíûõî
Þ è éê /û ûü "êéò$ ÷ûùö = DOL ! DFL =
#&
#&/Vé9îö .ø #û$ò/Vé9îö Véê #û$ò
7. Break-even Revenue = (Variable cost per
unit ! Break-even Number of Units) +
Fixed Operating costs + Fixed Financial
Cost
8. Breakeven Number of units = QBE =Vé9îö .øîìñòéê' #û$ò$'Vé9îö Véêñêíéñù #û$ò$
ëìéíî øîì ðêéò/+ñìéñ,ùî íû$ò øîì ðêéò
9. Operating Breakeven = QOBE =!MŸIJ URI(HGMLT QO7G
$(MaI RI( SLMG/"H(MH|wI aO7G RI( SLMG
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Reading 38: Dividends & Share Repurchases:
Basics
1. Company’s payout for the year = Cash
dividends + Value of shares repurchased in
any given year
2. Dividend Payout ratio =#ûõõûê $2ñìî íñ$2 öé*éöîêö$
/îò úêíûõî ñ*ñéùñ,ùî òû íûõõûê $2ñìî$
3. EPS after Dividend = EPS before Dividend
! ÷2ñìî$ ûv$ ,îüûìî ôé*éöîêö
÷2ñìî$ 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 =÷òûí1 øìéíî ,îüûìî $òûí1 $øùéò
k
7. EPS after 2-for-1 stock split =7ë÷ ,îüûìî $òûí1 $øùéò
k
8.
DPS after 2-for-1 stock split =ôë÷ ,îüûìî $òûí1 $øùéò
k
9. EPS after buyback =7ñìêéê'$/8üòîì òñ9 #û$ò ûü Vðêö$
÷2ñìî$ .ðò$òñêöéê' ñüòîì ^ðó,ñí1
10. Ex-dividend value of share = Stock price –
Dividend per share
11. Market value of Equity after distribution of
cash dividends =
\cŽ ûü $2ñìî$ ûv$d 0 c&+ $2ñìîd o #ñ$2 öé*]
Ž ûü $2ñìî$ ûv$
12. Post-repurchase share price =
Žûü $2ñìî$ ûv$ 0 c&+ $2ñìî o
<ûìò2 ûü ÷2ñìî ìîøðìí2ñ$î]
c Ž ûü $2ñìî$ ûv$/Ž ûü $2ñìî$ cíñê ,î ìîøðìí2ñ$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 of
inventory + No of days of receivables – No
of days payables
3.
Money Market Yield =Vñíî *ñùðî/ëðìí2ñ$î øìéíî
ëðìí2ñ$î øìéíî 0
opf
/û ûü öñó$ òû õñòðìéòó
4. Bond Equivalent Yield =Vñíî *ñùðî/ëðìí2ñ$î øìéíî
ëðìí2ñ$î øìéíî0
opu
/û ûü öñó$ òû õñòðìéòó
5. Discount-basis Yield =Vñíî *ñùðî/ëðìí2ñ$î øìéíî
Vñíî +ñùðî0
opf
/û ûü öñó$ òû õñòðìéòó
6. Wght Avg collection period = wghts !
Avg no of days to collect accounts within
each aging category
Where, Weights = % of total receivables in
each category
7.
Float Factor =8*' ôñéùó Vùûñò
8*' ôñéùó ôîøû$éò =
8*' ôñéùó Vùûñò
aw„… ƒaz‘w aR ’“c‚”f jcbafewcS
`a aR j„{f
Where, Float =Amount of money that is in
transit b/w payments (by customers) and
funds (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 8õûðêò
11. Bankers Acceptance Cost =úêòîìî$ò
/îò øìûíîîö$ =
úêòîìî$ò
-ûñê ñõûðêò/úêòîìî$ò
12. Commercial Paper Cost =úêòîìî$ò'ôîñùîì_$ íûõõé$$éûê'^ñí1ðø íû$ò$
-ûñê ñõûðêò/úêòîìî$ò
13. Annualized cost = Cost ! 12
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Reading 40: The Corporate Governance of
Listed Companies
Reading 41: Portfolio Management: An
Overview
1. NAV of bond mutual fund =c*ñùðî ûü îñí2 ,ûêö éê ò2î øûìòüûùéûd
/û ûü $2ñìî$
2. New Shares that need to be created =8õûðêò òû ,î úê*î$òîö éê ò2î Vðêö
/8+ ûì !ûòñù *ñùðî ûü ñ &ðòðñù Vðêö
3. New NAV of the Fund = NAV or Total
value of a Mutual Fund + Amount to beinvested in the Fund
4. No of shares need to be retired =8õûðêò òû ,î <éò2öìñ<ê üìûõ ò2î Vðêö
/8+ ûì !ûòñù *ñùðî ûü ñ &ðòðñù Vðêö
Reading 42: Risk Management: An
Introduction
Reading 43: Portfolio Risk & Return: Part I
1. Total Return = Capital Gain (or Loss) +
Dividend Yield
2. Capital Gain =ëw/ëwÒ%
ëwÒ%
3. Dividend Yield =ô
ëh? +
4. 3-Yr HPR = [(1 + R 1) ! (1 + R 2) ! (1 +
R 3)]1/3 – 1
5. Arithmetic mean (AM) R = YM 8Nƒ%'Nƒ‰'µ'Nƒ•Ò%'Nƒ
*
8 &
*
YMG*G[&
6. Geometric R for n periods = MDM 8
+ , Y& + , Yk l + , YL&
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 Asset
1 ! R of Asset 1) + (Wght of Asset 2 ! R
of Asset 2)
10. Gross R = R – Trading exp – other exp
directly related to the generation of returns.
11. Net R = Gross R - All managerial and
administrative exp
12. After-tax nominal R = Total R - Any
allowance 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 = Šk 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 ,
«—&—kT¦H M&– Mk 8 —&k–&k , —kk–kk ,«—&—k˜&k–&–k
20. Portfolio S.D. = 3¦§? ¥¦>4¦ =N§4NB56
21. Cov b/w asset 1 & asset 2 = Correlation of
Return 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$$îò k
23. 1 + Expected Return =+ , Q M 8
+ , §ìü 0 + , Q ™ 0 + , Q M3
24. Utility of an Invest = Expected Return -&
k 0M4Jš ›H6§J4¦B T¦6¥¥ 4546B? 0
=N§ ¦¥ rBH6J?
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Remaining Equity = Proceeds on sale –
Payoff loan – Margin i paid + Div received
– Sales commission paid
2.
ROE (based on leverage alone)
= Leverage (in times) ! stock price return
(in %)
3. Price of stock below which a margin call
will take place (P):úêéòéñù õñì'éê ª 'cë/ úêéòéñù ÷òûí1 ëìéíîd
ë8
ŸN4B?6BNB56 ŸN§F4B M6«K4§6A6B? cÞd
4. Total cost of placement to the issuing firm
in IPO ($)
= Gross proceeds received by the issuing
firm – Net proceeds received by the issuing
firm
5. Total cost of placement to the issuing firm
in IPO (%) =
cýìû$$ 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 by
min margin requirement =&
&éê õñì'éê ìîCðéìîõîêò
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 =
!=
""#
$%%&
' ( N
i i
ii
i
P
P P w
1 0
01
5. % èin value of Total return of Index
0
01
PRI
I PRI PRI
V
IncV V +!
6. Total return of each security = TR i =
i
iii
P
Inc P P
0
01 +!
TotalRe turn wi
P1i ! P
0i + Inc
i
P0i
"
#$
%
&'
i=1
N
(
Over Multiple Time Periods:
7. Value of Price Return index at time t =
VPRIT = VPRI0 (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 ò2î éêöî9
11. Weight of security i under market-cap
weighting =/f ûü $2ñìî$ ûv$ ûü ÷é 0 ÷2ñìî øìéíî ûü ÷é
/û ûü $2ñìî$ ûv$ ûü ÷é 0 ÷2ñìî øìéíî ûü ÷é`e
Where Si = Security i
12. Weight of Si under Mkt Cap weighting =Vìñíòéûê ûü $2ñìî$ ûv$ õ1ò üùûñò 0 ûü $2ñìî$ ÷é 0
÷2ñìî øìéíî ûü $îíðìéòó é
cVìñíòéûê ûü $2ñìî$ ûv$ &1ò üùûñò 0 ûü $2ñìî$ ûv$ ûü ÷é 0
÷2ñìî øìéíî ûü $îíðìéòó éd
13.
Fundamental weight on security i =Vðêöñõîêòñù $épî õîñ$ðìî ûü íûõøñêó éË
cVðêöñõîêòñù$épî õîñ$ðìî ûü íûõøñêó éd`e
*Book value, cash flow, revenues, earnings,
dividends, & number of employees.
Reading 48: Market Efficiency
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Reading 49: Overview of equity Securities
1. Equity security’s Total Return =÷ñùî ë ûü ñ $2ñìî/ëðì2ñ$î ëûü ñ $2ñìî'íñ$2v$òûí1 ôé*
ëðìí2ñ$î øìéíî ûü ñ $2ñìî
2. ROE in yr t =/ú cüûì .ìöéêñìó ÷2ñìî2ûùöîì$d éê óì ò
8*' !ûòñù ^+ ûü 7Cðéòó
OR
ROE =/ú cüûì .ìöéêñìó ÷2ñìî2ûùöîì$d éê óì ò
÷2ñìî2ûùöîì$_îCðéòó ñò ,î' ûü óì ò
3. MV of equity = Mkt price per share !
Shares O/s
4.
BV of equity per share =
!ûòñù ÷n_îCðéòó
÷2ñìî$ ûv$
5. Price-to-book ratio =&ñì1îò øìéíî øîì $2ñìî
^+ ûü îCðéòó øîì $2ñìî
6. ROE = Net profit margin ! Asset turnover
! Financial leverage =/îò îñìêéê'$
/îò $ñùî$ 0
/îò $ñùî$
8*' òûòñù ñ$$îò$ 0
8*' òûòñù ñ$$îò$
8*' íûõõûê îCðéòó
Reading 50: Introduction to Industry &
Company Analysis
Reading 51: Equity Valuation: Concepts &
Basic Tools
1. Value of a share of stock today =79øîíòîö öé*éöîêö éê óì ò
c&'ìîCðéìîö ).) ûê $òûí1d¬ò
ò[&
If an investor intends to buy and hold a share
for 1 yr:
2. Value of a share of stock today =79øîíòîö ôé* éê & óì '79øîíòîö $îùùéê' øìéíî éê & óîñì
c&'ìîC )û) ûê $òûí1d¬&
3. Value of a share of stock for n holding
period or investment horizon =79øîíòîö ôé* éê óì ò
&'ìîC ) ûê $òûí1 w ,L
G[&
79øîíòîö øìéíî éê ê øîìéûö$
&'ìîC ) ûê $òûí1 ‘
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
&'ìîC ) ûê $òûí1 wò[&
7. Req RoR on sharei = Current expected Rf
rate + Beta i [MRP]
8.
Value of a pref stock (non-callable, non-
convertible) =
( ) ( )r
D
r
D
g r
g DV
000
0
0
011=
!
+
=
!
+
=
9. Value of a pref stock (non-callable, non-
convertible) with maturity at time n =
Af 8‡f
c + , 5 dG ,
L
G/&
Ô
+ , 5 L
Gordon Growth Model:
10. Value of a share of stock =
( )r g
g r
D
g r
g DV <
!
=
!
+
= ,1
10
0
11.
Sustainable dividend growth rate =
g = ROE ! b
where b = earnings retention rate = (1 -
Dividend payout ratio)
Two-stage valuation model:
12. Value of share today = V0 =
Af 8‡f + , Ž7
G
c + , 5 dG ,
AL
c + , 5 dL
L
M[&
AL 8‡L'&
5 ? ŽB
‡L'& 8 ‡fc + , Ž7dL + , ŽB
13. Justified P/E =ëf
7&8
ô%v7%
ì/' 8
ø
ì/'
14. EV = MV of stock + MV of debt – Cash
and cash Equivalents
15. Asset-based value = Value of Equipment
and inventory – Value of Liabilities
Reading 52: Fixed Income Securities: Defining
Elements
1. Inf adj Principal amount of a zero-coupon-
indexed bond
= [Par value ! (1 + CPI)]
2.
Inf adj coupon payment for an interest-
indexed bond
= [(coupon rate ! Par value) ! (1+CPI)]
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3. Inf adj Principal amount of a capital-
indexed bond
= [Par value ! (1 + CPI)]
4.
Inflation adjusted coupon payment for a
capital-indexed bond
= [Par value ! (1 + CPI)] ! coupon rate
Reading 53: Fixed Income Markets: Issuance,
Trading & Funding
Reading 54: Introduction to Fixed Income
Valuation
1.
Amount of discount below par value =Present value of deficiency
2. Present value of deficiency =#ûðøûê ìñòî/&ñì1îò öé$íûðêò ìñòî 0ëñì *ñùðî
&'&ñì1îò 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 8G
*0@\]
8. Full price of a fixed-rate bond between
coupon payments = PVFull
=
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 – average
yield 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 ò2î 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" Days
Year! DR
#
$%
&
'(
15. Market Discount Rate =
DR = Year Days( )! FV " PV
FV
#
$%
&
'(
16. Price of Money Market Instrument =
PV = FV
1+ Days
Yr! AOR
"
#$
%
&'
17.
Add-on rate =
AOR =Yr
Days
!
"#
$
%&'
FV ( PV
PV
!
"#
$
%&
Relation b/w two spot rates and Implied
Forward Rate:
18. (1 + zA)A ! (1 + IFR A,B-A)B-A = (1 + zB)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
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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 = YTM of
the bond - Linearly interpolated yield to
the same maturity on an appropriate
reference curve
Reading 55: Introduction to Asset Backed
Securities
1.
Loan-to-value ratio (LTV) =8õûðêò ûü &ûìò'ñ'î
ëìûøîìòó +ñùðî
2. Monthly CF for a MPS = Monthly CF of
underlying pool of mortgages - Servicing
fee - Other fees
3. Pass-through rate = Mortgage rate on the
underlying pool of mortgages – Servicing
Fee - Other fees
4. SMM = Pre-pmt for month ÷ (Beg
mortgage 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 for
month)
•
Total principal re-pmt =
Scheduled principal re-pmt +
Prepayment
• Beg mortgage balance for the
following 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 $îì*éíî
Reading 56: Understanding Fixed Income Risk
& Return
1.
Interest-on-interest gain fromcompounding = Future value of reinvested
coupons - Total amount of coupon
payments
Where,
FV of Reinvested Coupons = [CR !(1+
RR)n-1
] + [CR !(1+RR)n-2
] +…+ [CR !(1+
RR)n-n
]
Total Amount of Coupon Pmt = CR ! Par
value ! No of periods
RR = Re-invstmnt rate per period
CR = coupon rate
2. Realized RoR on Bond=
÷ðõ ûü )îéê*î$òîö #ûðøûê$'
)îöîõøòéûê ûü ëìéêíéøñù ñò &ñòðìéòó
^ûêö ëìéíî
%
m
? +
3. Carrying value of bond (if bond purchased
below par) = Purchase price + Amortized
amount of Discount
4.
Carrying value of a bond (if bond purchased above par) = Purchase price –
Amortized amount of Premium
5. Amortized amount for 1st year = Bond
Price after 1-yr - Initial bond price
6. Capital g / (l) = Sale price of Bond after n
years – Carrying value of Bond after n
years
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 )
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8. Modified D =&ñíôðì
&'ì
9. Annualized Modified D =&ûöéüéîö ôðìñòéûê
ëîìéûöéíéó ûü øñóõîêò éê ñ óîñì
10.
% 1 PVFull = - AnnModDur ! 1Yield
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 ! Full
Bond 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) = Money
duration ! 0.0001 (1 bp)
21. Bloomberg’s Risk Statistic = PVBP ! 100
22. %*PV Full = (-AnnModDur ! *Yield) +&
k 0==W=4¢>:° 0cèt>4²<dk
Or%*PV Full = (-AnnModDur ! *Yield) +
&
k 0==W=4¢>:° 0cèt>4²<dk
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 = Annual
Convexity ! Full Price
27. Effective Convexity =
PV !( )+ PV +
( )! 2" (PV 0 )[ ]#$ %&
'Curve( )2" PV 0 )( )
28.
Duration Gap = Bond’s Macaulay
Duration – 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
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 of
LT debt + LT debt
7.
Capital = Debt + Equity
8. Yield on Corp Bond = Rf rate + Expected
Inf rate + Maturity P + Liquidity P+ Credit
spread
9. Yield spread = Liquidity P + Credit spread
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FinQuiz Formula Sheet CFA Level I 2016
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 $îíðìîö öî,ò
7^ú!ô8
13. Senior unsecured leverage =÷îíðìîö öî,ò'÷îêéûì ðê$îíðìîö öî,ò
7^ú!ô8
14. Total Leverage =!ûòñù öî,ò
7^ú!ô8
15. Net Leverage =!ûòñù öî,ò/#ñ$2
7^ú!ô8
Reading 58: Derivatives Markets and
Instruments
1.
Value of the contract to the ‘Long’ at
expiration = ST – F0(T)
2. Value of the contract to the ‘Short’ at
expiration = F0(T) – ST
3. Margin % in stock market =&+ ûü ÷òûí1/&+ ûü ôî,ò
&+ ûü ÷òûí1
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 – MM
req
5. TED spread = LIBOR – T-Bill rate
6. At expiration (for option Buyer):
• Value of Call option =
CT = Max (0, ST - X)
• Profit from Call option =
Max (0, ST - X) – C0
•
Value of Put option = P0 =
Max (0, X- ST)
• Profit from Put option =
Max (0, X- ST) – P0
7.
At expiration (for option Seller):
• Profit from Call option =
– Max (0, ST - X) + C0
•
Profit from Put option =
– Max (0, X- ST) + P0
8. To eliminate arbitrage opportunity:
Forward Price should be = Spot Price
0 + , > 5;:4 Þ G
Reading 59: Basics of Derivative Pricing &
Valuation
1.
Pricing of risky assets = S0 =7 c÷!d
&'ì'²
2. Commodity = F 0, T = S0 e(r – 2)T
where, 2 = Convenience yield 0 Cost of
carry
3. S0 =7 c÷!d
&'ì'² – 3 + 4
where, 3 (theta) = PV of the costs and 4
(gamma) = PV of benefits
4.
Arbitrage and Derivatives = Underlyingasset + Opposite position in derivative =
Underlying payoff – Derivative payoff =
Rf return
5. Pricing and Valuation of Forward
Contracts:
• At Expiration F (0, T) = S0 (1 + r)
Tor
S0 = F (0, T) / (1 + r) T
• Value of forward (long) during
contract life (where t < T) = Vt (0, T)
= St – F (0, T) / (1 + r) (T – t)
• Value of forward (short) during
contract life (where t < T ) = Vt
(0, T) = F (0, T) / (1 + r) (T – t) - St
• Value of forward (long) at expiration
(where t = T) = VT (0, T) = ST - F (0,
T)
•
Value of forward (long) at initiation
(where t = 0) = Vt (0, T) = S0 – F (0,
T) / (1 + r) T
= 0
•
Forward price of an asset with benefitsand/or costs = (S0 – 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 of
the contract = St – (4 - 3) (1 + r) T - F
(T) / (1 + r) (T – t)
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6. FRAs: An example of 3 ! 9 FRA (read as
three 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 (zero
coupon bonds)
7. Pricing and Valuation of Swap Contract (a
fixed for floating swap contract):
•
Fixed Periodic rate =
RN =
1 - ZN
Z1+Z
2 + ....+Z
N
• Where Zn are n period zero coupon
bonds (i.e. $1 discount factors)
)360/(1
1Zn
days Ln !+
=
• Value of a fixed rate side (per $1 NP)
= V fixed rate = [Fixed payment ! (
Z1
+Z2
+ ....+ZN )] + ($1 ! Z N)
• Value of a floating rate side (per $ 1
NP) = V floating rate = ($1 + 1st floating
pmt) ! Z1
Pricing and valuation of Options:
8. Payoff of Call options:
• At expiration call option = c T = Max
(0, ST –X)
•
Profit (call buyer) = Max (0, ST – X) –
c0
• Profit (call seller) = -Max (0, ST – X)
+ c0
9. Payoff of Put options:
• p T = Max (0, X- ST)
•
Profit (put buyer) = Max (0, X-ST) – p0
• Profit (put seller) = - Max (0, X – ST) +
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 = p0 + S0
• Payoff at expiration (put out-of-the-
money) = ST.
• Payoff at expiration (put in-the-
money) = (X-ST) + ST = X.
12.
Fiduciary Call
• Value FC = c0 + X / (1+r) T
• Payoff at expiration (when call out-of-
the-money) = X.
• Payoff at expiration (call in-the-
money) = X + (ST – X) = ST.
13. Put-Call Parity (to avoid arbitrage) = c0 +
X / (1+r) T = p0 + S0
• Synthetic long position in a call =
C = p 0+S 0!
X
(1+ r)T
• Synthetic long position in a put =
p0= 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 = F0(T) / (1 + r)T
+ p0 = c0 + X/(1 + r) T 15. Valuing a callable bond using Binomial
Model:
•
R u = R d! e2% :
• Value at time 0 = V0 = hS0 0 c0
• Value at time 1 will either V1+ = hS1
+ -
c1+ or V1
- = hS1- - c1
-
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FinQuiz Formula Sheet CFA Level I 2016
• If the portfolio was hedged, then V+
would equal V-.
• Value of the call =
• Value of the put =
Reading 60: Risk Management Applications of
Option Strategies
1.
For Call Option Buyer•
cT = max (0, ST –X)
• When ST ( X"cT = 0
• When ST > X"cT = ST – X
• Value at expiration = cT
•
Profit = cT – c0
• Maximum profit = 5! no upper limit
• Maximum loss = c0
• Breakeven = ST* = X + c0
2. For Call Option Seller
•
cT = max (0, ST –X)
• When ST ( X"cT = 0
•
When ST > X"cT = ST –X
• Value at expiration = -cT
•
Profit = –cT+ c0
• Maximum profit = c0
• Maximum loss = 5! no upper limit
• Breakeven = ST* = X +c0
3. For Put Option Buyer
•
pT = max (0, X - ST)
•
When ST < X" pT = X - ST
• When ST " X" pT = 0
• Value at expiration = pT
•
Profit = pT – p0
• Maximum profit = X – p0
• Maximum loss = p0
• Breakeven = ST* = X –p0
4. For Put Option Seller
• pT = max (0, X –ST)
•
When ST < X" pT = X – ST • When ST " X" pT = 0
• Value at expiration = –pT
• Profit = –pT + p0
• Maximum profit = p0
• Maximum loss = X - p0
• Breakeven = ST* = X - p0
5. Covered Call = Long stock position +
Short call position
•
Value at expiration = VT = ST – max
(0, ST – X)
•
When ST ( X"VT = ST
• When ST > X"VT = ST - ST +X = X
•
Profit = VT – S0 + c0
• Maximum Profit = X – S0 + c0
• Maximum Loss = S0 – c0
• Breakeven =ST* = S0 – c0
6. Protective Put = Long stock position +
Long Put position
•
Value at expiration: VT = ST + max (0,X - ST)
• When ST ( X"VT = ST + X - ST = X
• When ST > X"VT = ST
•
Profit = VT – S0 - p0
• Maximum Profit = 5
•
Maximum Loss = S0 + p0 – X
• Breakeven =ST* = S0 + p0
Reading 61: Introduction to Alternative
Investments
1.
Total Return = Alpha R + Beta R
2. Asset Based Valuation = Co value = Co’s
assets value – Co’s liabilities value
Real Estate Valuation
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3. Direct Cap Approach " Valuation of a
property =1Ug
QHRMGHwM³HGMOL NHGI where
NOI = Gross potential income –Estimated
vacancy losses – Estimated collective
losses – Insurance – Property Taxes –Utilities – Repairs, maintenance exp.
4.
Income Based Approach" FFO = NI +
Dep exp on R.E + Def Tax charges – Gains
from 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) + Storage
costs – Convenience yield
8. Roll yield = Spot price of a commodity –
Futures contract price
or
Roll yield = Futures contract price with
expiration date ‘X’– Futures contract pricewith expiration date ‘Y.
9.
Returns on a passive investment in
commodity futures
= Return on the collateral + RP or
convenience yield net of storage costs.
10. Sharpe ratio = (Investment return – Rf
return) / S.D. of return
11. Sortino Ratio = (Annualized RoR –
Annualized Rfe rate)/Downside Deviation