Reading 5: Time Value of Money 1. Interest Rate (i)
• i = Rf + Inf P + Default Risk P + Liquidity P + Maturity P • Nominal Rf i rate = Real Rf i Rate +
Inf P
• i rate as a growth rate = g = !"$"#
% # -1 2. PV and FV of CF = • PV = &'(!"# • PV of Perpetuity = $)*(
• PV (for more than one Compounding per year) = PV= FVN 1 + ( -. /.×1 𝑤ℎ𝑒𝑟𝑒 𝑟7 = 𝑠𝑡𝑎𝑡𝑒𝑑 𝑎𝑛𝑛 𝑖 − 𝑟𝑎𝑡𝑒 • FVN = 𝑃𝑉 1 + 𝑟 1
• FV (for more than one Compounding per year) = FVN = 1 +
( -.
.×1
• FV (for Continuous Compounding) = FVN = 𝑃𝑉𝑒(-×1 • Solving for N = B1 CD ED B1 &'( (where LN = natural log)
4. Stated & Effective Rates • Periodic i Rate =
FGHGIJ KLL M NHGI
1O OP QO.ROSLJMLT $I(MOJ7 ML ULI VIH(
• Effective (or Equivalent) Ann Rate
(EAR = EFF%) = 1 +
𝑃𝑒𝑟𝑖𝑜𝑑𝑖𝑐 𝑖 𝑅𝑎𝑡𝑒 .− 1
• EAR (with Continuous Compounding) = EAR = 𝑒(-− 1
5. PV & FV of Ordinary Annuity • PVOA = LG[& &'($)*Z = 𝑃𝑀𝑇 &/ % %^_ # ( • FVOA = 𝑃𝑀𝑇G 1 + 𝑟 1/G L G[& = 𝑃𝑀𝑇 &'(#/& (
• Size of Annuity Payment = PMT =
$" $" OP KLLSMG` !HaGO( • PV of Annuity Factor = &/ % %^ _-b b×# _-b
6. PV & FV of Annuity Due • PVAD = 𝑃𝑀𝑇 &/ % %^_ # ( + PMT at t = PVOA + PMT • FVAD = 𝑃𝑀𝑇 &'( #/& ( (1 + 𝑟) = FVOA ×(1+r)
Reading 6: Discounted Cash Flow Applications
1. NPV = Q!Z
&'(Z
L
G[& − 𝑐𝑓f
2. IRR (when project’s CFs are perpetuity) = NPV = - IO + gNNQ! = 0 3. HPR = $% /$h' i% $h 4. MMWR = M[f &'gNNZ= 0 (IRR represents the MWR) 5. TWR: • TWR (when no external CF) = rTWR = HPR = rt = )"%)"/)"h h
• TWR (for more than one periods) = rTWR = [(1+rt,1)× (1+rt,2)×… (1+rt,n)] -1
• Annualized TWR (when investment is for more than one year)
= 1 + 𝑅& 1 + 𝑅k… + 1 + 𝑅L %m_1
• TWR (for the year) = rTWR = [(1+R1)×
(1+R2)×… (1+R365)] -1 where R1 =
)"%/)"h
)"h
6. Bank Discount Yield = BDY = rBD =
opf L
$H(/$(MaI
$H( therefore Price = Par
1 −L × (qr
opf
7. Holding Period Yield = HPY = $% /$h' i%
$h
8. Effective Annual Yield = EAY = 1 + 𝐻𝑃𝑌 opu/G− 1 (Rule: EAY > BDY)
9. Money Market Yield (or CD equivalent Yield) rMM:
• rMM = HPY ×
opf G
• rMM = (rBD) ×
!HaI "HwSI OP GxI *(IH7S(` yMww $S(axH7I $(MaI
• rMM = opf/ G (
qr (Rule: rMM>
rBD)
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 up the 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 at L
k
• For Odd no. of obvs locate median at L'&k
9. Mode = obvs that occurs most frequently in the distribution
10. Weighted Mean = 𝑋•= LM[&𝑤M𝑋M =
(w1X1+ w2X2+….+ wnXn)
11. Geometric Mean = GM = m 𝑋&𝑋k… 𝑋L with Xi≥0 for i = 1,2,…n. 12. Harmonic Mean = H.M = 𝑋z= L% ‚ƒ m ƒ„% 13. Population Mean = µ = mƒ…ƒ 1 with 𝑋M> 0 for i = 1,2,.,.,n. 14. Sample Mean = 𝑋 = mƒ…ƒ L where n =
number of observation in the sample 15. Measures of Location:
• Quartiles = iM7G(M|SGMOL‡ • Quintiles = iM7G(M|SGMOLu • Deciles = iM7G(M|SGMOL&f , • Percentiles = Ly = 𝑛 + 1 &ff`
16. Mean Absolute Deviation = MAD =
…Z/… m ƒ„% L 17. Population Var = σ2 = ƒ„% ƒ 1 18. Population S.D = 𝜎k= #ƒ„%…ƒ/ˆ‰ 1 19. Sample Var = s2 = mƒ„%…ƒ/…‰ L/& 20. Sample S.D = s = mƒ„%…ƒ/…‰ L/& 21. Semi-var = …ƒ/…‰ L/& !O( Hww …ƒ‹… 22. Semi-deviation (Semi S.D) = 𝑠𝑒𝑚𝑖𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = …ƒ/…‰ L/& !O( Hww …ƒ‹… 23. Target Semi-var = …ƒ/y‰ L/& !O( Hww …ƒ‹y
where B = Target Value 24. Target Semi-Deviation = 𝑡𝑎𝑟𝑔𝑒𝑡 𝑠𝑒𝑚𝑖𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = …ƒ/y‰ L/& !O( Hww …ƒ‹y 25. Coefficient of Variation = CV = F …
where s= sample S.D and 𝑋 = sample mean
26. Sharpe Ratio = )IHL $O(GPOwMO N/)IHL NP N
F.i OP $O(GPOwMO N
28. Geometric Mean R ≈
𝐴𝑟𝑖𝑡ℎ𝑚𝑒𝑡𝑖𝑐 𝑀𝑒𝑎𝑛 𝑅 −"H(MHLaI OP N
k
Reading 8: Probability Concepts
1. Empirical Prob of an event E = P(E) =
$(O| OP I~ILG • *OGHw $(O|
2. Odds for event E = &/$(O| OP •$(O| OP •
3. Odds against event E = &/$(O| OP •
$(O| OP •
4. Conditional Prob of A given that B has occurred = P(A|B) = $ Ky$ y → P(B) ≠ 0.
5. Multiplication Rule (Joint probability that both events will happen):
P(A and B) = P(AB) = P(A|B) × P(B) P(B and A) = P(BA) = P(B|A) × P(A) 6. Addition Rule (Prob that event A or B will
occur):
P(A or B) = P(A) + P(B) – P(AB)
P(A or B) = P(A) + P(B) (when events are mutually exclusive because P(AB) = 0) 7. Independent Events:
• Two events are independent if: P(B|A) = P(B) or if P(A|B) = P(A)
• Multiplication Rule for two independent events = P(A & B) = P(AB) = P(A)× P(B)
• Multiplication Rule for three independent events = P(A and B and C) = P(ABC) = P(A) × P(B) × P(C)
8. Complement Rule (for an event S) = P(S) + P(SC) = 1 (where SC is the event not S)
9. Total Probability Rule:
P(A) = P(AS) + P(ASC) = P(A|S)×P(S) + P(A|SC)×P(SC)
P(A) = P(AS1) + P(AS2) +….+ P(ASn) =
P(A|S1)×P(S1) + P(A|S2)×P(S2)…
P(A|Sn)×P(Sn)
(where S1, S2, …,Sn are mutually exclusive
and exhaustive scenarios) 10. Expected R = E(wiRi) = wiE(Ri)
11. Cov (Ri Rj) = LM[& 𝑝 𝑅M− 𝐸𝑅M 𝑅”− 𝐸𝑅” Cov (Ri Rj) = Cov (Rj Ri) Cov (R, R) = σ2 (R) 12. Portfolio Var = σ2 (Rp) = 𝑤M𝑤”𝐶𝑜𝑣 𝑅M𝑅” L ”[& L M[& σ2 (Rp) = 𝑤&k𝜎k 𝑅& + 𝑤kk𝜎k 𝑅k + 𝑤ok𝜎k 𝑅o + 2𝑤&𝑤k𝐶𝑜𝑣 𝑅&, 𝑅k + 2𝑤&𝑤o𝐶𝑜𝑣 𝑅&, 𝑅o + 2𝑤k𝑤o𝐶𝑜𝑣 𝑅k, 𝑅o 13. Standard Deviation (S.D) = 𝑤&k𝑅M+ 𝑤kk𝑅k+ 𝑤ok𝑅o
14. Correlation (b/w two random variables Ri,
Rj) = 𝜌 𝑅M𝑅” = QO~ NƒN˜ ™Nƒ×™N˜ 15. Bayes’ Formula = 𝑃 𝐸𝑣𝑒𝑛𝑡|𝑁𝑒𝑤 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 = $ 1I• gLPO(.HGMOL|•~ILG $ 1I• gLPO(.HGMOL × 𝑃 𝑃𝑟𝑖𝑜𝑟 𝑝𝑟𝑜𝑏. 𝑜𝑓 𝐸𝑣𝑒𝑛𝑡
16. Multiplication Rule of Counting = n factorial = 𝑛! = n (n-1)(n-2)(n-3)…1. 17. Multinomial Formula (General formula for
labeling problem) = L!
L%!L‰!…Lž!
18. Combination Formula (Binomial Formula) = L 𝐶( = L( = L/( !(!L!
where n = total no. of objects and r = no. of objects selected.
19. Permutation = L 𝑃(= L/( !L!
Reading 9: Common Probability Distributions 1. Probability Function (for a binomial
random variable) p(x) = p(X=x) = L Ÿ 𝑝Ÿ 1 − 𝑃 L/Ÿ = = L! L/Ÿ !Ÿ!R &/Rm¡ (for x = 0,1,2….n)
• 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 0 𝑓𝑜𝑟 𝑎 ≤ 𝑥 ≤ 𝑏 = F(x) = Ÿ/H |/H 𝑓𝑜𝑟 𝑎 < 𝑥 < 𝑏
3. Normal Density Funct = 𝑓 𝑥 =
& ™ k¥𝑒𝑥𝑝
/(Ÿ/ˆ)‰
k™‰ for − ∞ < 𝑥 < + ∞
4. Estimations by using Normal Distribution: • Approximately 50% of all obsv fall in
the interval 𝜇 ±k
o𝜎
• Approx 68% of all obvs fall in the interval 𝜇 ± 𝜎
• Approx 95% of all obvs fall in the interval 𝜇 ± 2𝜎
• Approx 99% of all obvs fall in the interval 𝜇 ± 3𝜎
• More precise intervals for 95% of the obvs are 𝜇 ± 1.96𝜎 and for 99% of the observations are 𝜇 ± 2.58𝜎.
5. Z-Score (how many S.Ds away from the mean the point x lies) 𝑧 =
𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑛𝑜𝑟𝑚𝑎𝑙 𝑟𝑎𝑛𝑑𝑜𝑚 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 = …/ˆ
™ (when X is normally distributed)
6. Roy’s Safety-Frist Criterion = SF Ratio =
• NE/N´
™E
7. Sharpe Ratio = = • NE/Nµ
™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 + 0.50σ2)
10. Variance (σL2) of a lognormal random
variable = exp (2µ+ σ2) × [exp (σ2) – 1].
11. Log Normal Price = ST = S0exp (r0,T)
Where, exp = e and r0,t = Continuously
compounded return from 0 to T 12. Price relative = End price / Beg price =
St+1/ St=1 + Rt, 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:
rt, t+1= ln(1 + holding period return) or
rt, t+1 = ln(price relative) = ln (St+1 / St) = ln
(1 + Rt,t+1)
14. Continuously compounded return
associated with a holding period from 0 to T:
R0,T= ln (ST / S0) or 𝑟f,*= 𝑟*/&,*+
𝑟*/k,*/&+ ⋯ + 𝑟f,&
Where,
rT-I, T = One-period continuously
compounded returns
15. When one-period continuously compounded returns (i.e. r0,1) are IID
random variables. 𝐸 𝑟f,* = 𝐸 𝑟*/&,* + 𝐸 𝑟*/k,*/& + ⋯ + 𝐸 𝑟f,& = 𝜇𝑇 And 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 𝜎k 𝑟 f,* = 𝜎k𝑇 S.D. = σ (r0,T) = σ 𝑇
16. Annualized volatility = sample S.D. of one period continuously compounded returns × 𝑇
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‰
3. Standard Error of the sample mean: • When the population S.D (σ) is known
= 𝜎… = ™L
• When the population S.D (σ) is not known = 𝑠… = 7L where s = sample
S.D estimate of s = 𝑠𝑎𝑚𝑝𝑙𝑒 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 𝑠k 𝑤ℎ𝑒𝑟𝑒 𝑠k = mƒ„%…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 = 𝑥 ± 𝑧H/k ™L
• CI for normally distributed population with unknown variance = 𝑥 ± 𝑧H/k FL
where S = sample S.D. 7. Student’s t distribution µ = 𝑋 ± 𝑡H/k FL 8. Z-ratio =
Z =
x − µ
σ / n
9. t-ratio =t =
x − µ
s / n
Reading 11: Hypothesis Testing 1. Test Statistic =
𝑺𝒂𝒎𝒑𝒍𝒆 𝑺𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄 𝑯𝒚𝒑𝒐𝒕𝒉𝒆𝒔𝒊𝒛𝒆𝒅 𝑽𝒂𝒍𝒖𝒆 𝒐𝒇 𝒑𝒐𝒑 𝒑𝒂𝒓𝒂𝒎𝒆𝒕𝒆𝒓 𝒔𝒕𝒂𝒏𝒅𝒂𝒓𝒅 𝒆𝒓𝒓𝒐𝒓 𝒐𝒇 𝒔𝒂𝒎𝒑𝒍𝒆 𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄 ∗ *when Pop S.D is unknown, the standard
error of sample statistic is give by 𝑆… =
F
L
*when Pop S.D is unknown, the standard
error of sample statistic is give by 𝜎… = ™
L
2. Power of Test = 1-Prob of Type II Error 3. 𝑧 = …/ˆh
Î m
(when sample size is large or small but pop S.D is known)
4. 𝑧 = …/ˆh
-m
(when sample size is large but pop S.D is unknown where s is sample S.D)
5. 𝑡L/&= …/ˆ- h 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‰ ÏЉ m%' ÏЉ m‰ %/‰ where 𝑆Rk = pooled
estimator of common variance =
L%/& F%‰' L‰/& F‰‰
L%' L‰/k where 𝑑𝑓 = 𝑛&+ 𝑛k−
2.
7. Test Statistic for a test of diff b/wn two pop means (normally distributed, unequal and unknown pop var unknown) t = …%/…‰/ ˆ%/ˆ‰ Ï%‰ m%'m‰Ï‰‰ %/‰ In this df calculated as 𝑑𝑓 = Ï%‰ m% 'ω ‰ m‰ ‰ Ï%‰ m% ‰ m% ' ω‰ m‰ ‰ m‰
8. Test Statistic for a test of mean differences (normally distributed populations,
unknown population variances) • 𝑡 = J/ˆFJÑh
• sample mean difference = 𝑑 = & L 𝑑M L M[& • sample variance = 𝑆Jk= J%/J ‰ m ƒ„h L/&
• sample S.D = 𝑆J
• sample error of the sample mean difference = 𝑠 𝑑 = FÑ
L
8. Chi Square Test Statistic (for test concerning the value of a normal population variance) 𝑋k= L/& F‰
™h‰ where
𝑛 − 1 = 𝑑𝑓 𝑎𝑛𝑑 𝑆k=
𝑠𝑎𝑚𝑝𝑙𝑒 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = mƒ„h…ƒ/…‰
L/&
9. Chi Square Confidence Interval for variance
Lower limit = L = L/& F‰
…Ò/‰‰ and Upper limit
= U = = L/& F‰
…%¡Ò/‰‰
10. F-test (test concerning differences between variances of two normally distributed populations) F = F%‰
F‰‰
𝑆&k= 1𝑠𝑡 𝑠𝑎𝑚𝑝𝑙𝑒 𝑣𝑎𝑟 𝑤𝑖𝑡ℎ 𝑛& 𝑜𝑏𝑠 𝑆&k=
2𝑛𝑑 𝑠𝑎𝑚𝑝𝑙𝑒 𝑣𝑎𝑟 𝑤𝑖𝑡ℎ 𝑛k 𝑜𝑏𝑠
𝑑𝑓&= 𝑛&− 1 𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟 𝑑𝑓
𝑑𝑓k= 𝑛k− 1 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟 𝑑𝑓
11. Relation between Chi Square and F-distribution = 𝐹 = …% ‰ . …‰‰ L where:
• 𝑋&k is one chi square random variable
with one m degrees of freedom
• 𝑋k is another chi square random
variable with one n degrees of freedom
12. Spearman Rank Correlation = 𝑟7
= 1 − 6 𝑑&
k L M[&
𝑛 𝑛k− 1
• For small samples rejection points for the test based on 𝑟7are found using
table.
• For large sample size (e.g. n>30) t-test can be used to test the hypothesis i.e. 𝑡 = 𝑛 − 2
&/k𝑟 7
1 − 𝑟7k &/k
Reading 12: Technical Analysis 1. Relative Strength Analysis =
𝑷𝒓𝒊𝒄𝒆 𝒐𝒇 𝒂𝒔𝒔𝒆𝒕 𝑷𝒓𝒊𝒄𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑩𝒆𝒏𝒄𝒉𝒎𝒂𝒓𝒌 𝑨𝒔𝒔𝒆𝒕
2. Price Target for the
• Head and Shoulders = Neckline – (Head – Neckline)
• Inverse Head and Shoulders = Neckline + (Neckline– Head) 3. Simple Moving Average = 𝑷𝟏'𝑷𝟐'𝑷𝟑….'𝑷𝒏
𝑵
4. Momentum Oscillator (or Rate of Change Oscillator ROC):
• Momentum Oscillator Value M = (V-Vx) ×100
(where V = most recent closing price and Vx = closing price x days ago)
• Alternate Method to calculate M =
" " ×100
5. Relative Strength Index = RSI = 100 − &ff
&'NF where
RS = ÝR axHLTI7
iO•L axHLTI7
6. Stochastic Oscillator (composed of two lines %K and %D):
• %𝐾 = 100 z&‡/B&‡Q/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) = 𝑽𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝑷𝒖𝒕 𝑶𝒑𝒕𝒊𝒐𝒏𝒔 𝑻𝒓𝒂𝒅𝒆𝒅
𝑽𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝑪𝒂𝒍𝒍 𝑶𝒑𝒕𝒊𝒐𝒏𝒔 𝑻𝒓𝒂𝒅𝒆𝒅
8. Short Interest Ratio (Type of Sentiment Indicators) = 𝑺𝒉𝒐𝒓𝒕 𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕
𝑨𝒗𝒆𝒓𝒂𝒈𝒆 𝑫𝒂𝒊𝒍𝒚 𝑻𝒓𝒂𝒅𝒊𝒏𝒈 𝑽𝒐𝒍𝒖𝒎𝒆
9. Arms Index TRIN i.e. Trading Index (Type of Flow of funds Indicator) =
𝐴𝑟𝑚 𝐼𝑛𝑑𝑒𝑥 𝑜𝑟 𝑇𝑅𝐼𝑁 =
1O.OP KJ~HL g77SI7 ÷1O.OP iIawML g77SI7 "OwS.I OP KJ~HL g77SI7÷"OwS.I OP iIawML g77SI7
Reading 13: Demand & Supply Analysis: Introduction
1. Slope of the demand curve =
∆ éê ëìéíî ∆ éê ïðñêòéòó ôîõñêöîö
2. Slope of the supply curve =
∆ éê ëìéíî ∆ 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) = ½ (Base × Height) = ½ (Q0
× P0)
4. Producer Surplus = Total revenue received from selling a given amount of a good – Total variable cost of producing that amount
• Total revenue = Total quantity sold × Price per unit
• Area (for calculating Producer Surplus) = ½ (Base × Height) = ½ {(Q0) × (P0 – intercept point on
y-axis**)}
**where supply curve intersects y-axis 5. Total Surplus = Consumer surplus +
Producer surplus
6. Total Surplus = Total value – Total variable cost
7. Society Welfare = Consumer surplus + Producer surplus
8. Price Elasticity of Demand =
% ∆ éê ïðñêòéòó ôîõñêöîö % ∆ éê ëìéíî
)
(
)
(
P
%
Q
%
2 1 2 1 1 2 2 1 2 1 1 2P
P
P
P
Q
Q
Q
Q
+
−
+
−
=
Δ
Δ
9. Income Elasticity of Demand =
% ∆ éê ïðñêòéòó ôîõñêöîö % ∆ éê úêíûõî =
)
(
)
(
I
%
Q
%
2 1 2 1 1 2 2 1 2 1 1 2I
I
I
I
Q
Q
Q
Q
+
−
+
−
=
Δ
Δ
10. Cross Elasticity = % ∆éê ïðñêòéòó ôîõñêöîö ûü ýûûö þ % ∆ éê ëìéíî ûü ýûûö ÿReading 14: Demand & Supply Analysis: Consumer Demand
1. Marginal Utility = ∆ éê !ûòñù "òéùéòó
∆ éê ïðñêòéòó #ûê$ðõîö
2. Equation of Budget Constraint Line = (PX
× QX ) + (PY × QY)
3. Slope of Budget Constraint Line = ∆ éê ï%
∆ éê ï‚ =
ë‚
ë%
4. Marginal Rate of Substitution = ∆ éê ï%
∆ éê ï‚ = &ñì'éêñù "òéùéòó ûü ýûûö þ
&ñì'éêñù "òéùéòó ûü ýûûö ÿ
Reading 15: Demand & Supply Analysis: The Firm
1. Profit = Total revenue – Total cost 2. Accounting Profit = Total Revenue –
Explicit Costs (or Accounting costs) 3. Economic Profit
• = Total Revenue – Explicit Costs – Implicit Costs or
• = Accounting Profit – Implicit Costs or
• = Total Revenue – Total Economic Costs
4. Economic costs = Explicit costs + Implicit costs
5. Normal Profit = Accounting Profit – Economic Profit
6. Accounting profit = Economic Profit + Normal Profit
7. Economic rent = (New “Higher” Price after ↑ in Demand – Previous Price before ↑ in Demand) × QS before ↑ in Demand
8. Total Revenue (TR): • = Price × Quantity or
• = Sum of individual units sold × Respective prices of individual Units sold = Σ (Pi × Qi)
9. Average Revenue (AR) = !ûòñù )î*îêðîïðñêòéòó
10. Marginal Revenue (MR) = ∆ éê !ûòñù )î*îêðî
∆ éê ïðñêòéòó
11. Total Variable Cost = Variable Cost per unit × Quantity Produced
12. Total Cost = Total Fixed + Total Variable 13. Average total cost (ATC) =
!ûòñù #û$ò
ïðñêòéòó ëìûöðíîö = Avg. Fixed Cost + Avg.
Variable Cost
14. Marginal cost (MC) = ∆ éê !ûòñù #û$ò
∆ éê ïðñêòéòó ëìûöðíîö
15. Marginal Variable Cost =
∆ éê !ûòñù +ñìéñ,ùî #û$ò ∆ 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 è Output level where Price = Average Revenue = Marginal Revenue = Average Total Cost è 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 Costè firm will continue operating. 22. Losses are incurred when there are
Operating profits (Total Revenue ≥ Variable Cost) but Total Revenue < Total Fixed Cost + Total Variable Cost AND when Price = Marginal Cost while losses are < fixed costs è firm will continue operating.
23. Losses are incurred when there are Operating losses (Total Revenue ≤ Variable Cost) AND when losses ≥ fixed costs è firm will shut down.
24. Average Product = !ûòñù ëìûöðíò ïðñêòéòó ûü -ñ,ûì 25. Marginal Product = ∆ éê ïðñêéòó ûü -ñ,ûì = ∆ éê !ûòñù .ðòøðò ∆ éê /û ûü 0ûì1îì$
26. Least-cost optimization Rule:
&ñì'éêñù ëìûöðíò ûü -ñ,ûì ëìéíî ûü -ñ,ûì =
&ñì'éêñù ëìûöðíò ûü ë2ó$éíñù #ñøéòñù
ëìéíî ûü ë2óéíñù #ñøéòñù
27. Profit is maximized when: MRP = Price or cost of the input for each type of resource that is used in the production process 28. Marginal Revenue product = Marginal
Product of an input unit × Price of the Product = Price of the input =
∆ éê !ûòñù )î*îêðî ∆ éê ïðñêòéòó ûü úêøðò îõøùûóîö
29. Surplus value or contribution of an input to firm’s profit = MRP – Cost of an input Reading 16: The firm & Market Structures 1. In perfect competition, Marginal revenue =
Avg. Revenue = Price = Demand 2. Marginal Revenue = Price × 1 −
&
ëìéíî 7ùñ$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
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 ýôë ×100
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 – Investment) – Trade Balance
22. Average propensity to consume (APC) =
8''ìî'ñòî #ûê$ðõøòéûê )îñù úêíûõî
23. Quantity theory of money equation: Nominal Money Supply × Velocity of Money = Price Level × Real Income or Expenditure
24. % ∆ in unit labor cost = % ∆ in nominal wages - % ∆ in productivity
25. Economic growth = Annual % ∆ in real GDP
26. Total Factor Productivity growth = Growth in potential GDP – [Relative share of labor in National Income × (Growth in labor) + [Relative share of capital in National Income × (Growth in capital)]
27. Growth in potential GDP = Growth in technology + (Relative share of labor in National Income × Growth in Labor) + (Relative share of capital in National Income × Growth in capital]
28. Capital share =Corporate profits + net interest income + net rental income + (depreciation/ GDP)
29. Labor share = 7õøùûóîî #ûõøîê$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 %×100
Inflation Rate = ëìéíî úêöî9 ñò òéõî òk
&ff − 1
2. Fisher Index = 𝐼𝑝 ×𝐼𝐿 (where, IL =
Laspeyres index and Ip = Paasche Index)
3. 𝑈𝑛𝑖𝑡 𝑙𝑎𝑏𝑜𝑟 𝑐𝑜𝑠𝑡 (𝑈𝐿𝐶) 𝑖𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟 =
!ûòñù ùñ,ûì íûõøîê$ñòéûê øîì 2ûðì øîì <ûì1îì .ðòøðò øîì 2ûðì øîì <ûì1îì
4. Velocity of money = &ûêîó ÷ðøøùó/ûõéêñù ýôë
Reading 19: Monetary & Fiscal Policy 1. Total Money created = New deposit/
Reserve Req
2. Money Multiplier =
&
)î$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 in
consumption 11. Cumulative multiplier =
íðõðùñòé*î îüüîíò ûê ìîñù ýôë û*îì ò2î ò<û óîñì$ % 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)
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-Sp And,
CA = Sp- I+ Govt surplus (or Govt saving)
= Sp- I+ (T- G- R)Sp + Sg = I + CA
where, Sg = Govt savings
Sp = I + CA – Sg
• Current Account Imbalance CA = Sp + Sg – I
Reading 21: Currency Exchange Rates
1. Foreign price level in domestic currency = Sö/ü×Pü
2. Real exchange rate(ô/ü)= (Sö ü×Pü)/Pö=
Sö ü×(Pü/Pö)
3. Real Exchange Rate öûõî$òéí/üûìîé'ê=
Sö/ü× #ëú#ëúR
S
4. Change in Real Exchange rate = 1 +∆÷S/R ÷S/R × &'∆UR UR &'∆US US − 1
5. Direct Quote = úêöéìîíò ïðûòî&
6. Points on a forward rate quote = Fwd X-rate quote –Spot X-X-rate quote
7. Forward rate = Spot X-rate + Vûì<ñìö øûéêò$
&f,fff
8. Forward premium/discount (in %) = $øûò þ/ìñòî'(üûì<ñìö øûéêò$/&f,fff)$øûò þ/ìñòî − 1
9. To convert spot rate into a forward quote (when points are represented as %) = Spot exchange rate × (1 + % premium or discount)
10. Arbitrage relationship is stated as follows: • 1 + 𝑖J = 𝑆µ
Ñ 1 + 𝑖P
& !µ
Ñ
• In case of indirect quote, Arbitrage relationship is: 1 + 𝑖J = 1/𝑆P/J 1 + 𝑖P 𝐹P/J • 𝐹µ Ñ = 𝑆µ Ñ &'Mµ &'MÑ
• Forward rate as a % of spot rate =
!µ/Ñ Fµ/Ñ=
&'Mµ &'MÑ
11. Return on hedged foreign investment (with a quoted forward rate) = 𝑆P/J 1 +
𝑖P &
!µ/Ñ
12. Expected % change in the spot rate =
FZ^% FZ − 1 = %∆𝑆G'&= Mµ/MÑ &'MÑ • Forward points: 𝐹P/J− 𝑆P/J = 𝑆P/J Mµ/MÑ
&'MÑX 𝜏 (where 𝜏 is quoted
interest rate period)
13. Relationship between the trade balance and expenditure/ saving decisions:
= Ex – Im = (Sav – Inv) + (T – G) where T= taxes net of transfers G= government expenditures) 14. Price elasticity of demand = Ԑ =
% í2ñê'î éê Cðñêòéòó % í2ñê'î éê øìéíî = –
% ∆ ï % ∆ ë
15. Expenditure (R) = Price × Quantity = P × Q
• % ∆ in expenditure = % ∆ R = % ∆ P + % ∆ Q = (1- Ԑ) % ∆ P
16. Basic idea of Marshall-Lerner condition = 𝜔Ÿ𝜀Ÿ+ 𝜔) 𝜀)− 1 > 0 where,
ɷx=share of exports
ԐX=price elasticity of foreign demand for
domestic country exports ɷM=share of imports
ԐM =price elasticity of domestic country
demand for imports
17. Trade balance = Income (GDP) – Domestic expenditure = Absorption Reading 22: Financial Statement Analysis: An Introduction
1. Gross Profit = Revenue – Cost of sales 2. Operating Profit or EBIT = Gross profit –
Operating costs + Other operating income 3. Profit before tax = EBIT – Interest expense 4. Profit after tax = Profit before tax –
Income tax expense
Reading 23: Financial Reporting Mechanics 1. Owner’s Equity = Contributed Capital +
R.E
2. End R.E = Beg R.E + Net income – Dividends
3. Assets = Liabilities + Contributed Capital + Beg R.E + Revenue – Expenses – Dividends
Reading 24: Financial Reporting Standards
Reading 25: Understanding Income Statements 1. Revenue recognized on Prorated basis =
!ûòñù 8õûðêò ûü #û$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$ × 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) = 7$òéõñòîö "$îüðù -éüî#û$ò/)î$éöðñù +ñùðî
9. Annual Depreciation Expense (Declining balance method) = &ff%
"$îüðù ùéüî × Acceleration
factor (say 200% or 2) × Net Book Value 10. Basic EPS = 0'2ò 8*' /û ûü $2ñìî$ ûðò$òñêöéê'/îò úêíûõî/ëìîüîììîö ôé*éöîêö$
11. Diluted EPS for preferred stock =
/îò úêíûõî
0'2ò 8*' /û ûü $2ñìî$ û/$'/î< íûõõûê $2ñìî$ ò2ñò <ûðùö 2ñ*î ,îîê é$$ðîö ñò íûê*îì$éûê
12. Diluted EPS for convertible debt =
/îò éêíûõî '8! M ûê íûê*îìòé,ùî öî,ò/ëìîüîììîö ôé*
0'2ò 8*' ûü $2ñìî$ û/$'8ööéòéûêñù íûõõûê $2ñìî$ ò2ñò <ûðùö 2ñ*î ,îîê é$$ðîö ñò íûê*îì$éûê
13. Diluted EPS using Treasury Stock Method =
(/îò úêíûõî/ëìîüîììîö öé*éöîêö$)
[0'2ò 8*' ûü $2ñìî$'(/î< $2ñìî$ ñò ûøòéûê î9îìíé$î/ ÷2ñìî$ øðìí2ñ$îö <éò2 #ñ$2 ìîíîé*îö ðøûê î9îìíé$î ) ×
(ëìûøûìòéûê ûü ÿì)]
14. Net Profit Margin = /îò úêíûõî
)î*îêðî
15. Gross Profit Margin = ýìû$$ ëìûüéò
)î*îêðî
16. Comprehensive EPS = EPS + Other Comprehensive Income per share Reading 26: Understanding Balance Sheets
1. Percentage of A/C Receivable estimated to be uncollectible =
8ùùû<ñêíî üûì ôûð,òüðù 8/# ýìû$$ ñõûðêò ûü 8/# )îíîé*ñ,ùî
2. Net Identifiable Assets = Fair value of identifiable assets – Fair value of liabilities & contingent liabilities
3. Amortized cost of PPE = Historical cost – Accumulated depreciation – Impairment losses
4. Carrying value for PPE under revaluation model
= Fair value at date of revaluation – Accumulated depreciation (if any)
5. 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
15. Accumulated Dep on equipment sold = Beg balance accumulated dep + Dep expense – 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 – Tax rate) – 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$$îò$ 23. Cash ROE = #V. 8*îìñ'î $2ñìî2ûùöîì$_îCðéòó 24. Cash to income = #V. .øîìñòéê' éêíûõî
25. Cash flow per share =
#V./ëìîüîììîö ôé*éöîêö$ /û ûü íûõõûê $2ñìî$ û/$ 26. Debt Coverage = #V. !ûòñù ôî,ò 27. Interest Coverage = #V.'úêòîìî$ò øñéö'!ñ9î$ øñéö úêòîìî$ò øñéö 28. Reinvestment = #V. #ñ$2 øñéö üûì ùûê'/òîìõ ñ$$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 =
7êö +ñùðî ^î' +ñùðî
%
`a aR bcdeaSf − 1
2. Combined ratio = /îò ëìîõéðõö 7ñìêîö-û$$î$ ñêö 79øîê$î$ 3. Operating ROA = .øîìñòéê' úêíûõî 8*' !ûòñù 8$$îò$ 4. ROA = /îò úêíûõî 8*' !ûòñù 8$$îò$ or ROA = /îò úêíûõî'úêòîìî$ò 79øîê$î &/!ñ9 ìñòî 8*' !ûòñù 8$$îò$
5. Effective Tax Rate = úêíûõî !ñ9
7ñìêéê'$ ,îüûìî !ñ9
6. Vertical common size income statement =
úêíûõî $òñòîõîêò úòîõ )î*îêðî
7. Horizontal common size balance sheet =
^ñùñêíî $2îîò éòîõ éê ÿîñì k ^ñùñêíî $2îîò éòîõ éê ÿîñì &
8. Inventory turnover =
#û$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 = 8*' )îíîé*ñ,ùî$)î*îêðî
11. Days of Sales Outstanding (DSO) =/û ûü ôñó$ 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$ ghi jkl 13. Payables turnover = 8*' òìñöî øñóñ,ùî$ëðìí2ñî$ 14. No of Days of Payables = /û ûü ôñó$ éê øîìéûö ëñóñ,ùî$ !ðìêû*îì 15. WC Turnover = )î*îêðî 8*' 0#
16. Fixed Asset Turnover = )î*îêðî
8*' /îò Vé9îö 8$$îò$
17. Total Asset Turnover = )î*îêðî
8*' !ûòñù 8$$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' úêíûõî8*' .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 = ýìû$$ úêòîìî$ò 7^ú!ô8 33. FFO Interest Coverage =
VV.'úêòîìî$ò ëñéö/.øîìñòéê' -îñ$î 8ömð$òõîêò$ ýìû$$ úêòîìî$ò 34. Return on Capital = 7^ú! 8*' #ñøéòñù = 7^ú! 8*' (7Cðéòó'/ûê íðììîêò öîüîììîö òñ9î$'öî,ò) 35. FFO to Debt = VV. !ûòñù ôî,ò
36. Free Operating CF to Debt =
!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 ùéñ,éùéòéî$&+ ûü $òûí1 + 1.0 × ÷ñùî$ !8 42. Segment margin = ÷î'õîêò ëìûüéò (-û$$) ÷î'õîêò )î*îêðî 43. Segment turnover = ÷î'õîêò )î*îêðî ÷î'õîêò 8$$îò$ 44. Segment ROA = ÷î'õîêò ëìûüéò (-û$$) ÷î'õîêò 8$$îò$
45. Segment Debt Ratio = ÷î'õîêò -éñ,éùéòéî$
÷î'õîêò 8$$îò$
1. NRA = Estimated Selling Price – Estimated Costs of completion and disposal
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 of liability < Tax base of asset
8. Company’s tax expense (or credit) reported on its income statement = Income
tax liability currently payable + ∆ in deferred tax asset / liability
Where,
• Income Tax liability currently payable = Taxable income × Tax rate
• ∆in 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 × Tax rate
• 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
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 interest expense under effective interest rate method = Carrying value of
the bonds at the beginning of the period × Effective interest 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 the lease
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 =
(ûøîìñòéê' #V ,îüûìî 0# í2ñê'î$ – öé*éöîêö$) òûòñù öî,ò
4. )îòñéêîö #V/#ñø î9ø
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$î
9. Remaining useful life of the asset =
/îò ëë7 (êîò ûü ñííðõðùñòîö öîø) 8êêðñù öîø î9øîê$î
10. Avg depreciable life of the assets at installation = 8êêðñù ôîø î9øîê$îýìû$$ ëë7
11. % of asset base that is being renewed through new capital investment =
#ñøî9 ýìû$$ 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 = EBIT + rent exp ∗ −Dep exp ∗
𝑖 payments + 𝑖 expense ∗ * 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 & òñ9î$ ,îüûìî éêòîìî$ò 8*' ^+ ûü úê*$ò
4. PI = ë+ ûü üðòðìî #V$ú. = 1 + /ë+ú.
5. Value of a company = Value of company’s existing invst + Net PV of all of
company’s future invst Reading 36: Cost of Capital
1. WACC = wdrd (1 – t) + wprp + were
2. Debt-to-Equity Ratio conversion into weight (i.e. Debt / (Debt + Equity) =
jcvw xyzew{
&' xyzew{jcvw
3. Optimal Capital Budget is the point where MC of capital = Marginal return from investing
4. After-tax cost of debt = Before-tax Marginal Cost of Debt × (1 – firm’s marginal tax rate)
5. Preferred Stock Price per Share =ëìîü ÷òûí1 ôé* øîì ÷2ñìî#û$ò ûü ëìîü ÷òûí1
6. Expected Return on Stock I (under CAPM) = E (Ri) = RF + βi [E (RM) – RF]
7. Expected Return on Stock I = E (Ri) = RF +
βi1 (Factor risk premium)1 + βi2 (Factor
risk premium)2+…..+βij (Factor risk
premium)j
8. Cost of Equity = 𝐫𝐞=ôë%
h+ g
9. Expected Growth Rate of Dividends g = (1 - ô
7ë÷) × ROE
g = retention rate × ROE
10. Company’s stock returns = Réò= a +
bRõò
11. Unlevered β of Comparable Company = β", íûõøñ= €•, ‚aƒb„d„v…c
&' &/ò‚aƒb„d„v…cj‚aƒb„d„v…c
x‚aƒb„d„v…c
12. Levered β of Project =
𝛽B, R(O”= 𝛽Ý, aO.R 1 + 1 − 𝑡R(O”
𝐷R(O” 𝐸R(O” 13. 𝛽H77IG= ˆ‰Š‹ƒZŒ &' &/Gr• 14. 𝛽I}SMG`= 𝛽H77IG 1 + 1 − 𝑡 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 $û*îìîé'ê ,ûêö &1ò éê 8êê ÷.ô ûü 7Cðéòó éêöî9
òîìõ$ ûü öî*îùûøîö õ1ò íðììîêíó
17. Cost of equity = Ke= RF + β[(E(RM)-RF) +
CRP] 18. Breakpoint =
8õûðêò ûü íñøéòñù ñò <2éí2 $ûðìíî_$ íû$ò ûü íñø ∆
ëìûø ûü êî< íñø ìñé$îö üìûõ ò2î $ûðìíî
19. Cost of Capital (hen flotation costs are in monetary terms = rî= ëô%
h/V + g
20. When FC are in terms of % of the share price: Cost of Equity = rî= ëô%
h/V + g
21. If FC are not tax deductible: NPV = PV of Cash Inflows – IO – (FC in % × New Equity Capital)
22. If FC are tax deductible: NPV = PV of Cash Inflows – IO – [(FC in % × New Equity Capital) × (1 – Marginal Tax Rate)] 23. Asset β = (Debt β × Proportion of Debt) +
(Equity β × Proportion of Equity)
Reading 37: Measures of Leverage
1. Contribution Margin (CM) = (# of units sold) × [(price per unit) - (variable cost per unit)]
2. Per unit CM = Price per unit - Variable cost per unit
3. Operating income = CM – Fixed Operating Costs 4. DOL = % ∆ éê .øîìñòéê' úêíûõî 7^ú! % ∆ éê "êéò$ ÷ûùö or DOL= #& #&/ Vé9îö .øîìñòéê' #û$ò 5. DFL = % ∆ éê .øîìñòéê' úêíûõî% ∆ éê /îò úêíûõî or #&/ Vé9îö .ø #û$ò #&/Vé9îö .ø úêíûõî/Vé9îö Véê #û$ò 6. DTL= % ∆ éê /û ûü "êéò$ ÷ûùö% ∆ éê /îò úêíûõî = DOL × DFL = #& #&/Vé9îö .ø úêíûõî/Vé9îö Véê #û$ò
7. Break-even Revenue = (Variable cost per unit × Break-even Number of Units) + Fixed Operating costs + Fixed Financial Cost
8. Breakeven Number of units =
Vé9îö .øîìñòéê' #û$ò$'Vé9îö Véêñêíéñù #û$ò$ ëìéíî øîì ðêéò/+ñìéñ,ùî íû$ò øîì ðêéò
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$ û/$ ,îüûìî ôé*éöîêö
÷2ñìî$ û/$ 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 =
[(# ûü $2ñìî$ û/$) × (&+ $2ñìî) – #ñ$2 öé*] # ûü $2ñìî$ û/$
12. Post-repurchase share price =
#ûü $2ñìî$ û/$ × (&+ $2ñìî – <ûìò2 ûü ÷2ñìî ìîøðìí2ñ$î]
( # ûü $2ñìî$ û/$/# ûü $2ñìî$ (íñê ,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$î øìéíî ×
opf /û ûü öñó$ òû õñòðìéòó
4. Bond Equivalent Yield =
Vñíî *ñùðî/ëðìí2ñ$î øìéíî ëðìí2ñ$î øìéíî × opu /û ûü öñó$ òû õñòðìéòó 5. Discount-basis Yield = Vñíî *ñùðî/ëðìí2ñ$î øìéíî Vñíî +ñùðî × opf /û ûü öñó$ 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$éò = 8*' ôñéùó Vùûñò
•aw„… •ƒaz‘w aR ’“c‚”f jcbafewcS `a aR j„{f
Where, Float =Amount of money that is in transit b/w payments (by customers) and funds (usable by co)
8. Value of stretching payment = A/c payable × Co's opportunity cost for ST funds 9. Cost of Trade Credit = 1 +
ôé$íûðêò
&/ôé$íûðêò
ghi
‘ − 1
where n = days beyond discount period 10. Cost of Line of Credit =
úêòîìî$ò'#ûõõéòõîêò üîî -ûñê 8õûðêò
11. Bankers Acceptance Cost = úêòîìî$ò
/îò øìûíîîö$ = úêòîìî$ò
12. Commercial Paper Cost =
úêòîìî$ò'ôîñùîì_$ íûõõé$$éûê'^ñí1ðø íû$ò$
-ûñê ñõûðêò/úêòîìî$ò
13. Annualized cost = Cost × 12
Reading 40: The Corporate Governance of Listed Companies
Reading 41: Portfolio Management: An Overview
1. NAV of bond mutual fund =
(*ñùðî ûü îñí2 ,ûêö éê ò2î øûìòüûùéû) /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 be invested 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¡% 3. Dividend Yield = ô• ëh − 1 4. 3-Yr HPR = [(1 + R1) × (1 + R2) × (1 + R3)]1/3 – 1
5. Arithmetic mean (AM) R = 𝑅M= Nƒ%'Nƒ‰'⋯'Nƒ.•¡%'Nƒ• * = & * 𝑅MG * G[&
6. Geometric R for n periods = RDM= 1 + 𝑅& 1 + 𝑅k … 1 + 𝑅L & L− 1
7. IRR = #V ñò !éõî ò
&'ú))w = 0
! 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 × 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) = (&'/ûõéêñù ))
(&'úêü)
16. Var of a Single Asset = 𝜎k= •ƒ„%NZ/ˆ‰
*
17. Sample Variance = sk= •e„%)w/)‰
!/&
18. Cov of R b/w two assets = Cov (Ri,Rj) = ρij× σi × σj
19. Portfolio Var = σëk= ω&kσ&k+ ωkkσkk+ 2ω&ωkCov R&, Rk = ωk&σ&k+ ωkkσkk+ 2ω&ωkρ&kσ&σk
20. Portfolio S.D. = Portfolio Variance 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 ,/< ò<û ñ$$îò$ ÷.ô.ûü ñ$$îò & × ÷.ô.ûü ñ$$îò k
23. 1 + Expected Return =1 + E R = 1 + rìü × 1 + E π × 1 + E RP