2018 finquiz CFA level 2 formula sheet

FinQuiz

Formula Sheet

Reading 9: Correlation & Regression
1.   Sample
 Cov
  X, Y =

r=

!
b1 − b1
•   Test statistic = t =
s b1

0+1
34567
(96 )(97 )

or

5;<()) 5;<(,)

< 0+>
1+
9.

•  

Intercept (b0) = b0 = y − b1 x =
Slope or regression coefficient =
 b1 =
345(O,P)
5;<(O)

0+T+1

SSU+SSR
SSU

8.

𝑦Z

𝑆𝑆𝑅
𝑘

𝑦Z

𝑆𝑆𝐸
𝑛−𝑘−1

Z\1
>

𝑆𝑆𝑅
𝑆𝑆𝐸

[

=
Z\1
>

𝑘

𝑛−𝑘−1

11. Prediction Intervals = Y ± t 3 sm
1

()+))?

0

0+1 9?
6

and

Reading 10: Multiple Regression & Issues in
Regression Analysis
1.   Yi = b0 + b1X1i + b2X2i + … + bkXki + εi,i =
1, 2, … n  
2.   Prediction equation = 𝑌Z = 𝑏u + 𝑏1 𝑋1Z +
𝑏> 𝑋>Z +. . . +𝑏w 𝑋wZ + εy , 𝑖
 

𝑆𝑆𝑇

Total
df = n-1

fgg
)
 
h
ggi
(
)
jkhk/

(

[

=

𝑦Z
Z\1
>

3.   Adjusted R2 = 𝑅 > = 1 −

−𝑦

[+1
[+w+1

1 − 𝑅>

0+T+1

=

VSS
SSU

where, 0 ≤ R2≤ 1

(for single independent variable R2 = r2)
7.

[

=

bce

=
 

s f = s 2f

F

−𝑦

O+O ?

Coefficient of Determination (R2) =
=

MSS

bcd

𝑤ℎ𝑒𝑟𝑒
 sm> = s > 1 + +

𝑆𝑆𝐸
Error
df = n-k-1

- (P +P)?
*./ *

=

SS

−𝑦

O+O P+P

Standard Error of Estimate SEE = SR =
SSR

6.

or =

b1 ± t c s b1

𝑆𝑆𝑅
Regression
df = k

Linear Regression = Yi = b0 + b1Xi + εi,
•  

5.

ANOVA

10. F-Statistic or F-Test =

(df numerator = k = 1)
(df denominator = n – k – 1 = n – 2)

ANOVA (Analysis of variance) =


 t
 distribution
 with
  n −

2 deg. of
 freedom

4.

Confidence Interval =

•  

345(),,)

3.   t-test (for normally distributed variables) =
t=

H1: b1 ≠ 0 (linear relationship does
exist)

•  

*./ )* +) ,* +,

2.   Correlation Coefficient = r), =

Level II 2018

SST = SSE + SSR(or RSS)
Hypothesis Testing:
•   Null and Alternative hypotheses
•   H0: b1 = 0 (no linear relationship)

Source of
Variability

DoF

Sum of
Squares

Mean Sum
of Squares

Regression
(Explained)

1

RSS

MSR =
RSS/1

Error
(Unexplained)

n-2

SSE

MSE =
SSE/n-2

n-1

SST=
RSS +
SSE

Total

4.   Breusch–Pagan test
•   H0 = No conditional
Heteroskedasticity exists
•   HA = Conditional Heteroskedasticity
exists
•   Test statistic = n × R2residuals
5.   Durbin-Waston Test = 𝐷𝑊 =
•
?
~.? }~ +}~k/
• } ?
~./ ~

•  

For Large Sample size DW Statistic
(d) = d ≈ 2 (1 – r)


FinQuiz

Formula Sheet

•  

•  

Level II 2018

Random walk with a drift = xt = b0 + x
t-1 + εt where, b0 ≠ 0 and b1 = 1
By taking first difference yt = xt - x t-1
= b0 + εt

Reading 11: Time Series Analysis
1.   Linear Trend Models = yt = b0 + b1t+ εt
•   Predicted/fitted value of yt in period
(T + 1) =

yˆ t +1 = bˆ0 + bˆ1 (T + 1)

2.   Log-Linear Trend Models =

yt = e b0 +b1t

3.   Autoregressive Time-Series Models:
•   First order autoregressive AR (1) = xt
= b0 + b1 x t-1 + εt
•   pth-order autoregressive AR (p) = xt
= b0 + b1 x t-1 + b2 x t-2 + …..+ bp x t-p
+εt
4.  

b0
Mean reverting level of xt =

1 − b1

5.   Chain Rule of Forecasting:
•   One-period ahead forecast =

xˆt+1 = bˆ0 + bˆ1 xt
•  

Two-period ahead forecast=

xˆt+2

= bˆ0 + bˆ1 xt+1

6.   Random Walks and Unit Roots:
•   Random Walk without drift = xt = x t1 + εt where, b0 = 0 and b1 = 1.
•   Correcting Random Walk = yt = xt - x
t-1

7.   Using Dickey-Fuller Test = xt - x t-1 = b0 +
(b1 -1) x t-1 + εt
8.   Smoothing Past Values with n-Period
Moving Average =

xt + xt −1 + xt −2 + ..... + xt −( n −1)
n
9.   Correcting Seasonality in Time Series
Models:

Reading 13: Currency Exchange Rates

1.   Bid-offer Spread = Offer price – Bid price
2.   Fwd
 rate
  = Spot
 Exchange
 rate
  +

 

†4<‡;<ˆ
 ‰4y0Š9

9‰4Š
 •O3Ž;0••
 <;Š•+(m4<‡;<ˆ
 ‰4y0Š9/1u,uuu)
9‰4Š
 •O3Ž;0••
 <;Š•

5.   Covered interest rate parity:

•  

εˆ 2 t = α 0 + α1εˆ 2 t −1 + µ t

where

1 + i∫

ˆ
1’y∫

1
†∫ /‘

F∫ /ˆ = S∫

•  

Using day count convention:

ˆ

1’y‘

'
! Actual $*
)1+ id #
,=
" 360 &%+
(

µt is

'
! Actual $*' 1 *
,
S f /d )1+ i f #

,)
" 360 &%+)( Ff /d ,+
(

σˆ t2+1 = αˆ 0 + α1εˆt2

Reading 12: Excerpt from ‘Probabilistic
Approaches , Scenario Analysis, Decision Tree
& Simulations’

1 + iˆ = S ∫

•  

an error term
•   Predicting variance of errors in period
t+1 =

−1

4.   To convert spot rate into forward quote:
•   Spot exchange rate × (1 + % premium)
•   Spot exchange rate × (1 - % discount)

•  
For quarterly data = xt = b0 + b1x t-1 +
b2x t-4 + εt
•   For monthly data = xt = b0 + b1x t-1 +
b2x t-12 + εt
10. ARCH model =

1u,uuu

3.   Forward
 premium/discount
 (in
 %)
  =

•  

Ff / d

⎛
⎡ Actual ⎤ ⎞
⎜ 1 + i f ⎢
⎟
360 ⎥⎦ ⎟
⎣
⎜
= S f /d
⎜
⎡ Actual ⎤ ⎟
⎜ 1 + id ⎢
⎟
⎣ 360 ⎥⎦ ⎠
⎝

6.   Uncovered Interest Rate Parity :
•  

i f − %ΔS e f / d = id


FinQuiz

•  
•  
•  

Formula Sheet

%ΔS e f / d = i f − id
Forward premium or discount:
For one year horizon =

Ff /d − S f /d =
"i −i %
S f /d $ f d ' ≅ S f /d (i f − id )
# 1+ id &
•  

Using day count convention:
( " Actual % +
* $
# 360 '& Ff /d − S f /d = S f /d *
(i f − id )
* 1+ i " Actual % *
d$
# 360 '& ,

)

7.   Forward discount or premium as % of spot
rate:

Ff / d − S f / d
S f /d

≅ (i f − id )

If uncovered interest rate parity holds
•  

=

Ff /d − S f /d
= %ΔS ef /d ≅ (i f − id )
S f /d

8.   Purchasing Power parity (PPP)
•   Pf = S f/d × Pd
•   S f/d = Pf / Pd
9.   Relative version of PPP = %∆S f/d = πf – πd
10.   Ex ante version of PPP = %∆Sef/d = πef –
π ed
11.   Real Exchange Rate

qf/d =

⎛ S f / d Pd

⎜
⎜ P
f
⎝

⎞
⎛
⎟ = S f / d ⎜ Pd
⎟
⎜ P
⎠
⎝ f

⎛ CPI d
q f / d = S f / d ⎜
⎜ CPI
f
⎝

Level II 2018

⎞
⎟
⎟
⎠

⎞
⎟
⎟
⎠

or
12.   Fisher effect:
•   id = rd + πεd
•   if = rf + πεf
•   if – id = (rf – rd) + (πεf- πεd)
•   (rf – rd) = (if – id) - (πεf- πεd)
Reading 14: Economic Growth & The
Investment Decision
1.   Economic growth = Annual % ∆ in real
GDP or in real per capita GDP
2.   P = GDP

R

•

“”•

R

3.   Expressing in terms of logarithmic rates:

•   (1/T) % ∆P = (1/T) % ∆GDP + (1/T)
%∆ (E / GDP) + (1/T) % ∆(P / E)

•   % ∆ in stock MV = % ∆ in GDP + %
∆ in share of earnings (profit) in GDP
+ % ∆ in the price-to-earnings
multiple

4.   A two-factor aggregate production
function: Y = AF (K, L)
5.   Cobb-Douglas Production Function = F
(K, L) = Kα L1 - α

6.   Under the Cobb-Douglas production
function:
•   Marginal product of capital = MPK =
α AK α-1 L 1-α = α Y/K
•   α Y/K = r èα = r (K) / Y = Capital
income / Output or GDP
7.

Output per worker or Average labor
productivity (Y/L or y):
•   GDP/Labor input = TFP × capital-tolabor ratio × share of capital in GDP
•   Or y = Y/L = Akα

8.   Contribution of Capital Deepening = Labor
productivity growth rate – TFP
9.   Contribution of Improvement in
technology = Labor productivity growth
rate – Capital Deepening
10.   Growth Accounting based on Solow
Approach = ∆Y /Y = ∆A / A + α ∆K/K +
(1 – α) ∆L/ L
11.   Labor productivity growth accounting
equation
•   Growth rate in potential GDP = LT g
rate of labor force + LT g rate in labor

productivity
12.   Balanced or Steady State Rate of Growth
in Neoclassical Growth Theory:
•   Growth in physical capital stock = ∆K
= sY – δK


FinQuiz

Formula Sheet

13.   In the steady state:
•   Growth rate of capital per worker = ∆k
/ k = ∆y / y = ∆A / A + α ∆k / k =
–—˜
 
1+
 ™

•  

è Steady state growth rate of

labor productivity
Growth rate of Total output = ∆Y / Y
= Growth rate of TFP scaled by labor
force share + Growth rate in the labor
force =

•  

›

=

1

š

•

1+
 ™

+
 𝛿 + 𝑛 =
 𝛹

Gross investment per worker =
š
1+
 ™

•  

1+
 ™

14. During the transition to the steady state
growth path:

•   Growth rates of output per capita = ∆y
/y=

 

š
1+™

š
1+
 ™

+
 𝛼𝑠
 

›
œ

−
 𝛹

=

+ 𝛼𝑠 (y/k – Ψ)

•   Capital-to-labor ratio = ∆k / k =
š
1+
 ™

+
 𝑠
 

›
œ

−
 𝛹

=
 

š
1+™

+s

(y/k – Ψ)

1

knew
•   kold

' ! Y $ *α −1
)# & ,
" K %new ,
=)

)!Y $ ,
)( #" K &%old ,+

y new ⎡ k new ⎤
= ⎢
⎥
y
old
⎣ k old ⎦
•  

α

+n

Steady state Output-to-capital ratio =
œ

•  

š

Level II 2018

15.   Proportional impact of the saving rate
change on the capital-to-labor ratio and per
capita income over time:

16.   Production function in the endogenous
growth model = ye = f (ke) = cke

•   Growth rate of output per capita =
∆ye/ye = ∆ke/ke = sc – δ – n

+
 𝛿 + 𝑛 𝑘

Slope of straight line = [δ + n + θ / (1
– α)]

Reading 15: Economics of Regulation


FinQuiz

Formula Sheet

Level II 2018

Reading 16: Interoperate Investments
1.   Summary of Accounting Treatment of Investments
Income Statement (I.S)

Held-tomaturity

Held
for
trading
security
Designated
at

fair value

Available
-for-sale

§  

i income = Market rate at purchase × Initial fair value (FV) of a
debt security
Ori income = i pmt – Amort
  i pmt = (Coupon rate × Par value)
  Amort = i pmt – i income
§   If debt security is sold: Realized g/l reported on I.S = SP – CV or
Amort cost
§   i income = Market rate × Initial FV
§   Unrealized g/l = FV at the end of Yr t – Amort Cost at end of Yr t
If debt security is sold:
§   Realized g/l reported on I.S= SP – Recorded FV
§   i income = Market rate at purchase × Initial FV
§   Unrealized g/l = FV at the end of Yr t – Amortized Cost at end of
Yr t
If debt security is sold:
§   Realized g/l reported on I.S= SP – Recorded FV
§   i income = Market rate at purchase × Initial Fv
If debt security is sold:
§   Cumulative unrealized g/l is removed from OCI and entire g/l
recognized in P&l statement.
Where, Realized g/l in I.S = (SP – Recorded FV) + Unrealized g/l

Balance Sheet (B.S)

§  
§  

Initially, at FV (IFRS) or initial price paid (US
GAAP)
Subsequently, reported at amort cost at the
subsequent reporting date on B.S.

§  
§  

Initially, at FV.
Subsequently, at FV at subsequent reporting date
on B.S.

§  
§  

Reported at FV at the end of Yr t
Subsequently, at FV at the subsequent reporting
date on B.S

§  
§  

Reported at FV at the end of Yr t
Subsequently, at FV at the subsequent reporting
date on the B.S.

Statement
ofSH’sEq
uity
N/A

Unrealized g/l (net
of tax) = FV at end
of Yr t – Amort Cost
at end of Yr t
•   Unrealized g/l
(net of tax) is
reported as OCI


FinQuiz

Formula Sheet

Level II 2018

2.   Goodwill = Cost of acquisition – investor’s share of the FV of the net
identifiable assets
PP
Xxx
Less: (% of Ownership Interest × BV of Investee’s Net
(xxx)
Assets)
= Excess Purchase Price
Xxx
Less: Attributable to Net Assets:

-Plant & Equipment (% of Ownership Interest × difference
(xxx)
b/wBV & FV)
-Land (% of Ownership Interest × difference b/wBV & FV)
(xxx)
= Residual Amount (Treated as Goodwill)
Xxx

Add: Unamortized excess PP (Excess PP – Amount attributable
to PP&E)
= Investment in Investee
Transactions with Associates:
4.   Upstream Transactions:
Investor’s share of Associate’s reported NI (% of Ownership
Interest × Reported net income)

xxx
xxx

xxx

Less: Amort. of excess purchase price

(xxx)

Less: Unrealized profit (% of Ownership Interest × Profit from
upstream sale in Associate’s NI)

(xxx)

3.   Amort. of Excess PP:
Investment in associate:
PP
Xxx
Add: Investor’s share of Investee’s NI (% of Ownership
Xxx
Interest × Investee’s NI)
Less: Div. received (% of Ownership Interest × Div. paid)
(xxx)
Less: Amort. of excess PP attributable to plant & equipment
(xxx)
(Amount attributable to PP&E* ÷ Remaining life of PP&E)
= Balance in investment in Investee
Xxx
Where, *Amount attributable to Plant & Equipment = % of Ownership
Interest of investor × (FV of P&E – BV of P&E)

= Equity Income to be reported as a line item on Investor’s I.S*

xxx

Beg net assets
Add: NI
Less: Div. paid
= Ending net assets
Investor’s proportionate share of Investee’s recorded net assets
(% of Ownership Interest × Ending net assets)

•   Composition of Investment account:
Investor’s proportionate share of Associate’s net equity = [% of

Ownership Interest × (beg BV of net assets) + (Reported NI of
associate – Profit from upstream sale in Associate’s NI) – Div. paid
by the associate)]
Add: Unamortized excess PP (Excess PP – Amort. of excess PP)

Xxx
Xxx
(xxx)
Xxx
Xxx

Balance in the investment in Associate to be reported at the end of
year:
PP
xxx
Add: Equity income (as calculated above)*
xxx
Less: Div. received (% of Ownership Interest × Div paid)
(xxx)
•  

= Value of Investment in Associate’s company at the end of year

xxx

xxx

xxx

FinQuiz

5.   Downstream Transactions
Investor’s share of Associate’s
reported NI (% of Ownership Interest
× Reported NI)
Less: Amort of excess PP
Less: Unrealized profit (% of
Ownership Interest × Profit from the
downstream sale in Associate’s NI)
= Equity Income to be reported as a
line item on Investor’s I.S

Formula Sheet

xxx

(xxx)
(xxx)

xxx

Unrealized profit = % of goods unsold × Profit
on the sale to investee
Investor’s share of the unrealized profit =
Unrealized profit × % of goods unsold
Investor’s share of associate’s
reported NI (% of Ownership Interest
× Reported NI)
Less: Amort of excess PP

Add: Realized profit (% of goods
unsold × Unrealized profit)
= Equity Income to be reported as a
line item on Investor’s I.S

Level II 2018

Goodwill
9.   Full Goodwill = Total FV of the
Subsidiary – FV of subsidiary’s
identifiable net assets

under acquisition method = BV for A&L
of Investor + FV for A&L acquired from
Acquiree

10.   Partial Goodwill Method:
•   Goodwill = FV of acquisition –
Acquirer’s share of FV of all
identifiable tangible and intangible
assets, liabilities and contingent
liabilities acquired
Or
•   Goodwill = Purchase price – parent’s
(acquirer’s) proportionate share of the
FV of subsidiary’s identifiable net
assets.

xxx

(xxx)
xxx

11.   Under Acquisition method, the allocation
of PP:
FV of the stock issued
xxx
Add: BV of Investee’s net assets
xxx
= Excess PP
xxx

xxx

Business Combinations
6.   Merger = Company X + Company Y
= Company X
7.   Acquisition = Company X + Company Y =
(Company X + Company Y)
8.   Consolidation = Company X + Company
Y = Company Z

FV of the stock issued
Less: FV allocated to identifiable net
assets
= Goodwill

xxx
(xxx)
xxx

12.   Allocation of excess PP: Excess PPP =
Sum of diff b/w FV and BV of identifiable
assets + Goodwill
13.   Combined Assets & Liabilities (A&L)
reported on Consolidated B.S under
acquisition method: Consolidated B.S

14.   Combined Paid-in Capital (PIC) = (FV of
the stock issued to effect the transaction –
Par value of the stock issued) + Additional
PIC of investor
15.   Minority Interest = % of subsidiary not
owned by the Parent × Subsidiary’s Equity
16.   Value of non-controlling interest under full
goodwill method = Non-controlling
interest’s proportionate interest in
subsidiary × FV of subsidiary on
acquisition date
17.   Value of non-controlling interest under
partial goodwill method = Non-controlling
interest’s proportionate interest in
subsidiary × FVof the subsidiary’s
identifiable net assets on acquisition date
Goodwill Impairment:
18. Goodwill Impairment Test under IFRS:
•   Impaired when CA of the Cash-generating
Unit > RA of the Cash-generating Unit
•  

Impairment loss = CA of Cash-generating
Unit - RA of Cash-generating Unit where,
RA = Higher of Net SP and its VIU
Net SP = FV – costs to sell
VIU = PV of expected future CF of
cash-generating unit


FinQuiz

19. Goodwill Impairment Test under U.S.
GAAP (Two Step Approach)
•  
•  

•  

•  

Step 1: Goodwill Impairment Test
Impaired when CV of Reporting Unit
(including Goodwill) > FV of
Reporting Unit (including Goodwill).
Step 2: Measurement of Impairment
loss = CV of Reporting unit’s
Goodwill - Implied FV of Reporting
unit’s Goodwill
Where Implied FV of Reporting unit’s
Goodwill = FV of Reporting Unit –
FV of Reporting unit’s net assets

Formula Sheet

5.   Net i income = Discount rate × Net
Pension asset
6.   Net return on plan assets = Actual return
on plan assets – (Plan assets × i rate)
7.   Actuarial g/l = Actual return – (Plan assets
× Expected return)

8.   Total Periodic Pension Costs =Sum of
components of periodic pension costs
•  

Reading 17: Employee Compensation: Post
Employment & Share-Based
•  
1.   Under DC Plans: Pension exp = Co.’s
annual contribution to plans adjusted for ∆
in yr-end accruals
2.   Funded Status = PV of DB obligations –
FV of plan assets
3.   Period pension cost of a Co.’s DB pension
plan = ∆ in Net pension liability or asset
adjusted for employer’s contributions
4.   Net i exp = Discount rate × Net Pension
liability
where Discount Rate = rate used to
calculate PV of future pension benefits

Total periodic pension cost in a given
period = ∆in Net pension liability or
asset adjusted for employer
contributions
Total Net periodic pension cost (End
Funded Status* – Beg Funded Status*)
– Employer Contribution
where *Pension liability is treated as a
negative

9.   Adjusted Total P&L pension exp (income)
•  

•  

= Current service costs + i costs + (-)
actuarial losses (actuarial gains) + past
service costs (or plan amendments) –
(+) Actual return (loss) on plan assets
Or
= Reported Total P&L pension exp
(income) + Expected return on plan
assets – Actual return on plan assets

Level II 2018

10.   Adjusted Pre-tax Income:
•   = Reported Pre-tax income + (Actual
return on plan assets – Expected return
on plan assets)

Or
•   = Reported Pre-tax income + Total
reported pension and other postretirement benefits - Current service
costs - i exp component of pension
cost + Actual return on plan assets
11.   Adjusted Net Operating Exp=Reported Net
operating exp – Total reported pension and
other post-retirement benefits + Current
service costs
12.   Adjusted i Exp. = Reported i exp. + i exp.
component of pension cost
13.   Adjusted i and investment Income
=Reported i and investment income +
Actual return on plan assets
14.   Compensation exp. = FV of stock on the
Grant Date
16. Compensation
 exp
 recognized
  =
¤0<•34•0y¥•ˆ
 040+
5•9Š•ˆ
 34¦‰•09;Šy40
 •O‰

 
V•¦;y0y0•
 5•9Šy0•
 ‰•

FinQuiz

Formula Sheet

Foreign Subsidiary’s Functional Currency

Reading 18: Multinational Operations
1.   Cumulative Translation Adjustment = CTA = Assets – Liabilities –
Common Stock – Retained Earnings
2.   Balance Sheet Exposure:
B.S Exposure
When assets translated at
current X rate > liabilities
translated at current X rate
When liabilities translated at
current X rate > assets
translated at current X rate

Net Asset B.S
exposure
Net Liability B.S
exposure

Level II 2018

Foreign Currency (FC)
Strengthens
Weakens

+ve
-ve
translation
translation
adj
adj
-ve
+ve
translation
translation
adj
Adj

(X = exchange)

inventories measured at
market value under the lower
of cost or market rule.
ii) Measured at historical
costs e.g. PP&E
LIABILITIES
Monetary liabilities: a/c
payable, LT debt, accrued
exp., and deferred income
taxes.
Nonmonetary liabilities:
i) measured at current value
ii) not measured at current
value i.e. deferred revenue

FC

Parent’s Presentation
Currency

Current rate

Historical rate

Current rate

Current rate

Current rate

Current rate

Current rate

Historical rate

Historical rates

Historical rates

Beg R.E +
translated NI – div.
translated at
historical rate

Beg R.E + translated NI –
div. translated at historical
rate

Average rate

Average rate

Average rate

Average rate

Average rate

Historical rate

Average rate

Mixed (a mix of average
rate & historical rate)

Net Assets or Net
Liabilities

Net monetary assets or Net
monetary liabilities

Accumulated as a
separate component
of equity

Included as g/l in NI

3.   Re-measurement Gain = NI − NI before re-measurement gain
4.   Re-measurement Loss = NI − NI before Re-measurement loss
5.   Rules For Translation Of A Foreign Subsidiary’s FC Financial
Statements (F.Ss) Into Parent’s Presentation Currency Under IFRS &
U.S. GAAP

EQUITY
Other than R.E i.e. Common
Stock
Retained Earnings (R.E)

Foreign Subsidiary’s Functional Currency
FC
Translation Method:

Current Rate
method

Parent’s Presentation
Currency
Temporal Method

X rate at which F.Ss are
translated from foreign
subsidiary’s bookkeeping
currency to parent’s
presentation currency.

ASSETS
Monetary assets: Cash, a/c
receivables
Nonmonetary Assets:
i) Measured at current value
i.e. marketable securities &

Revenues
EXPENSES
Most Expenses
Expenses related to assets
translated at historical X rate
e.g. COGS, Dep.,
& Amort. etc.
NI

Current rate

Current rate

Exposure

Current rate

Current rate

Treatment of translation adj.
in parent’s consolidated F.Ss

FinQuiz

Formula Sheet

TEMPORAL METHOD:

FC
strengthens
relative to
parent’s
presentation
currency

FC weakens
relative to
parent’s
presentation
currency

Net Monetary
Liability Exposure
§  
Rev ↑
§  
Assets ↑
§  
Liabilities ↑

Net Monetary
Asset Exposure

§  
Rev ↑
§  
Assets ↑
§  
Liabilities ↑

CURRENT
RATE
METHOD
§  
§  
§  

Rev ↑
Assets ↑
Liabilities ↑

NI ↑
SH’ equity ↑
Translation
gain

§  
§  

NI ↑
SH’ equity
↑
+ve

Translation
adj.
Rev ↓
Assets ↓
Liabilities ↓

NI ↓
SH’ equity ↓
Translation
loss

§  
§  
§  

§  
§  
§  

Rev ↓
Assets ↓
Liabilities ↓

§  
§  
§  

Rev ↓
Assets ↓
Liabilities ↓

§  
§  
§  

§  
§  
§  

NI ↑
SH’ equity ↑
Translation
gain

§  
§  
§  

NI ↓
 
SH’ equity ↓
Translation
loss

§  

§  
§  
§  

§  

§  
§  

Net Income
↓
SH’ equity ↓
-ve
Translation
adj.

Level II 2018

7.   Restatement Factor =

©ª<<•0Š
 P<« 9
 ‰  y0ˆ•O
¬y9Š4  
 ‰  y0ˆ•O

8.   Restated Capital Stock = Capital stock original value ×
©ª<<•0Š
 P<« 9
 ‰  y0ˆ•O

 4<
 ˆ;Š•
 4m
 340Š  y9
 -;Š•<
¬y9Š4  ‰  y0ˆ•O

9.   Restated Revenue = Revenue original value ×

©ª<<•0Š
 P<« 9
 ‰  y0ˆ•O
¯5•.‰  y0ˆ•O

10.   Loss from holding beg balance in cash = -Beg balance in cash ×
©ª<<•0Š
 P<« 9
 ‰  y0ˆ•O
 –¬y9Š4  ‰  y0ˆ•O
¬y9Š4  ‰  y0ˆ•O

11.   Loss from increase in cash during the yr = -Increase in cash ×
©ª<<•0Š
 P<« 9
 ‰  y0ˆ•O+¯5•
 ‰  y0ˆ•O
¯5•
 ‰  y0ˆ•O

12.   Gain from holding note payable = Notes payable ×
©ª<<•0Š
 P<« 9
 ‰  y0ˆ•O+¬y9Š4  ‰  y0ˆ•O
¬y9Š4  ‰  y0ˆ•O

6. Impact of Changing Exchange Rates on Exposure
Foreign Currency
Strengthens
Weakens
CURRENT RATE METHOD:
Net Assets
Net Liabilities

TEMPORAL METHOD:
Net Monetary Assets
Net Monetary Liabilities

Hyperinflationary Economy

Gain
Loss

Loss
Gain

Gain
Loss

Loss
Gain

13.   Avg. effective tax rate =

U;O
 RO‰

 •<•Š;O
 ¯334ª0Šy0•
 •<4myŠ9

14.   Organic sales growth = Net sales growth + Foreign X impact +
Acquisition/Divestiture impact.

FinQuiz

Reading 19: Evaluating Quality of Financial
Reports
1. DSR (days sales receivable index) =
(Receivablest/Salest) / (Receivablest
1/Salest1)
2. GMI (gross margin index) = Gross
margint1 / Gross margint
3. AQI (asset quality index) = [1 (PP&Et+
CAt)/TAt ] / [1 (PP&Et1+ CAt-1)/TAt-1]
4.

SGI (sales growth index) = Salest/Salest1

5. DEPI (depreciation index) = Dep ratet
1/Dep ratet
where, Dep rate = Dep/(Dep + PP&E)
6. SGAI (sales, general, and admin exp
index) = (SGAt/Salest) / (SGAt1/Salest1)
7. Accruals = (Income before extraordinary
items Cash from operations)/TA
8. LEVI (leverage index) = Leveraget /
Leveraget1 where, Leverage = Debt /
Assets
9. Earnings t+1 = + (1 ì Earnings t) +
10. Account receivable turnover = (365/DSO)

Formula Sheet

11. Z-score = 1.2
ì

3.3
ì

1.0
ì


RảãU

U
S;-9



â


+ 1.4
ì


U

+ 0.6
ì

Level II 2018

V.R

U

.ằ
4m
RẳêyP
ả.ằ
4m
-y;đy-yy9

+

+


U.

(Cash t + ST invstmnt. t)} {Total liab
t (Total LT debt t + Debt in current
liab.)}]
B. S
based
Accruals
Ratio =
ề~ +ề~k/
ề~ ề~k/

Reading 20: Integration of Financial Statement
Analysis
1. DuPont Analysis:
ROE = Tax Burden ì Interest
Burden ì EBIT margin ì TATO ì
Financial Leverage
ROE = NI/EBT ì EBT/EBIT ì
EBIT/Sales ì Sales/Assets ì
Assets/Equity
ROE = Net profit margin ì asset
turnover ì leverage
Adjusted Asset base = Adjusted Total
Assets = Total Assets of the company
Investments in Associates
Adjusted NI = NI of Co NI from
Associates
Adjusted
Tax
Burden =

>

3. CF based aggregate accruals:
Aggregate Accruals = NI t (CFO t +
CFI t)
CF
based
Accruals
Ratio =

ã +(âề âã )
(ề ềk/ )
>




Op. CF before interest and taxes = Op.
CF + cash i paid + cash taxes paid
Op income adjusted for accounting
= Profit before i& taxes + amort. of
goodwill

4. Cash
Return
on
Assets =

ề.â
5
U.

5. Cash Flow to Reinvestment =
ề.â
3;y;-
O0yê<9

ã+RẳêyP
y034Ư

RảU



6. Cash Flow to Total Debt =

Adjusted
TATO =

ặ
ầẩkặ
ẫấ.ậ-èẻ-.ẽẫ-
ầẩkẫ-
ẫấ.ậ-èẻ-

ề.â
đm4<
y0<9
&
ễếệì
U.

>

7. Capacity to pay debt (in years)
Accruals and Earnings Quality
2. B.S based aggregate accruals
Aggregate Accrualst = NOAt NOAt-1
where, NOAt = Net operating Assets t
= Op Assets t Op Liab t = [{TA t

=

U.
ề.â+â;y;-
RO0yê<9

8. CF Interest Coverage =

ề.â
đm4<
Z&
ễếệì
Z
;y



FinQuiz

Formula Sheet

Decomposition and Analysis of the Co’s
Valuation:
9.   Parent Co. pro-rata share of
subsidiary/affiliates = (Subsidiary’s share
price in FC× Shares held by Parent Co. ×
X- rate)/Parent Co. total market
capitalization
10.   Implied Value of Parent Co. (excl.

subsidiary/affiliates) = Parent Co.’s Mkt
Cap - Value of subsidiary/affiliate holdings
11.   P/E ratio of Parent Co =

•;<•0Š
 ©4.’9
 ¦TŠ
 ©;‰
²·
 4m
 
 •;<•0Š
 ©4.

12.   Implied P/E ratio of Parent Co. =
Implied
 Value
 of
 Parent
 Co.
(excluding
 subsidiary/affiliates)
 
NI
 of
 
 Parent
 Co. −Equity
 Income
 from

 
subsidiary/affiliates
13.   Discount to Benchmark =
ß
É

Reading 21: Capital Budgeting
1.   Depreciable Basis = Purchase price + any
Shipping or handling or installation costs

Off-Balance Sheet Leverage from Operating
Leases
14.   Adj. Fin Lev =

U.¯
 ’
 •»
 4m
 -•;9•
 ‰;P¦•0Š9

15.   Adj. D-to-E ratio =

U.R
 
U.”’•»
 4m
 -•;9•
 ‰;P¦•0Š9

16.   Adj. i-coverage Ratio =
R¶·U+”•‰
 •O‰’V•0Š
 RO‰
Z
 •O‰’¯99ª¦•ˆ
 Z
 •O‰
 40
 -•;9•9

U.R

9.   Profitability index = PI = 1 + (NPV/Initial
investment)
when PI > 1, invest and when PI < 1, do
not invest.

Expansion Project
2.   Initial Outlay = FCInv + NWCInv
NWCInv = ∆non-cash current assets –
∆non-debt current liabilities= ∆NWC

10.   CAPM = ri = R F + βi [E (R M) – R F]

3.   Annual after-tax operating cash flow = CF
= (S – C – D) (1 – T) + D or CF = (S – C)
(1 – T) + TD

12.   Economic Income = AT CF from

investment + ∆ in MV = AT CF from
investment + (End MV – Beg MV)
OR
= AT CF from invstmnt. – (Beg MV – End
MV)= AT CF from invstmnt. – Eco. Dep

4.   Terminal year after-tax non-operating cash
flow = TNOCF = Sal T + NWCInv – T (Sal
T – B T)
Replacement Project
5.   Initial Outlay = FCInv + NWCInv – Sal 0 +
T (Sal 0 – B0)

¶•03Ž¦;  •;<•0Š
 ©4.•/R
¶•03Ž¦;  •/R

Level II 2018

6.   Annual after-tax operating cash flow
(incremental)
•   CF = (∆S – ∆C – ∆D) (1 – T) + ∆D or
•   CF = (∆S – ∆C) (1 – T) + T∆D
7.   Terminal year after-tax non-operating cash
flow = TNOCF = ∆Sal T + NWCInv – T
(∆Sal T – ∆B T)
8.  

(1 + Nominal rate) = (1 + Real rate) (1 +
Inf rate)

Economic and Accounting Income
11.   Accounting income = Rev – Exp

13.   Economic Profit (EP) = NOPAT– $WACC
where,
NOPAT = net operating profit after tax
i.e. EBIT (1 – Tax rate)
EBIT = earnings before interest and taxes
$WACC= dollar cost of capital = WACC
× capital
Capital (after Year 1) = investment =
Initial Investment – depreciation
14.   MVA
 or
 NPV =

R•Í
á
Š\1 (1’³¯©©)Í

15.   Total value of Co. = original investment +
NPV
16.   Residual income (RI) = NI – Equity
Charge
•   RI t = NI t – (re × B t-1)

FinQuiz

Formula Sheet

where,



Vã
ỏ
\1 1<


V=D+E=
ã0<9
;PƯ09
40
đ




MVA =



Total value of Co. = NPV (PV of RI)
+ Original Equity investment +
Original Debt investment

Reading 23: Dividends & Share Repurchases
Analysis

+

â49
4m
đ
(RảãU

y0<9
;PƯ09
40
đ)
â49
4m
ẳêyP

8. Systematic Risk = a =

Claims Valuation
17. Total value of Co. = value of liabilities +
value of equity

Level II 2018

ằ

d +


R

ằ


e


e = a + (a d) (D/E)

9. AT cost of debt = BT cost of debt ì (1
Marginal tax rate)

Reading 22: Capital Structure
1. WACC = rââ =
R
ằ


ằ

10. MM Proposition I with Taxes: Co.s value
is maximized at 100% Debt

V L = V U + (t ìD)
Value
of
Unlevered all
equity Co. =

ìr ì 1 t +

ìr


VU =

2. Total value of Co. = V = D + E

3. WACC

ằ

without

ìr +

R
ằ

taxes

=

rââ =

ã0<9
;PƯ09
40
đ



â49
4m
đ
(RảãU

y0<9
;PƯ09
40
đ)


R

+

11. MM Proposition II with Taxes: WACC is
minimized at 100% Debt


R

+

re = r0 + (r0 rd)(1 t)


R

(r0 rd)(1-t) = Slope coefficient *
*(r0- r d)(1 t) < (r 0 - r d)






6. According to MM proposition I: V L = V
and E = V D



7. According to MM proposition II:
Cost
of
Equity = r = ru + (ru
r )

â49
4m
đ

(RảãU

y0<9
;PƯ09
40
đ)(1

)
â49
4m
ẳêyP

4. Cost
of
Equity = r = ru + (ru r )

â49
4m
ẳêyP

<ổẩỗỗ
ã0<9
;PƯ09
40
đ

V=D+E=

ìr

5. V = D + E =

RảãU
1





Share is sold (after share goes ex-div.)
2. CF from Sale = Sale price cap gains tax
(owed on sale) + AT amount of div. = Px
(Px Pb) (TCG) + D (1 TD)
3. When Px = Pw then Pw (Pw Pb) (TCG) =
Px (Px Pb) (TCG) + D (1 TD)
P PO = D

1+Uố
1+Uỗộ

or P = D

1+Uố
1+Uỗộ

where, P = in price when the stock
goes from with div to ex-div
4. Double Taxation Method: ETR= Corp. tax
rate + {(1 Corp. tax rate) (Indiv. tax
rate)}

WACC with taxes: rWACC = ìrdì (1
R

U

Share is sold just before it goes ex-dividend:
1. Cash flow from Sale = Sale price capital
gains tax owned on the sale = Pw (Pw
Pb)(TCG)
where, Pw = price with the right to receive
dividend
Pb = purchase price where b is for buy
TCG = marginal tax rate on capital gains

ằ

t)+ ìre
ằ

12. Static trade-off theory of capital structure
VL = V U + tD PV(Costs of financial
distress)

5. Dividend imputation tax system: ETR =
SHs Marginal Tax Rate
6. Split tax system: ETR = Corp. tax rate on

div + {(1 Corp. tax rate on div.)
(personal tax rate)}


FinQuiz

Formula Sheet

Payout Policies:
7. Stable Div. Policy
Expected in Div. = (Expected
Earnings ì Target payout ratio
Previous dividend) ì Adj. factor
Adj. factor = 1/no. of yrs. over which
adj. in div. will take place

Reading 26: Mergers & Acquisitions

8. Residual Div. Policy
Div. = Earnings (Capital budget ì

4. New shares issued by Acquirer =

Equity % in capital structure) or


Div. = Zero, whichever is greater.

9. Div. Payout Ratio =

y5.
ã

10. Div. Coverage Ratio =

ã


1. Statutory Merger = Co. X + Co. Y= Co. X
2. Subsidiary Merger = Co. X +Co. Y=(Co.
X + Co. Y)

Level II 2018




Unlevered NI = EBIT ì (1- tax rate)
NOPLAT = Unlevered NI + in
deferred taxes

11. FCF = NOPLAT + NCC in Net WC
Capex

3. Consolidation = Co. X + Co. Y = Co. Z

T
3;
4m
U;<

943T
4m
3ẳêy<<

5. Post-merger no. of shares outstanding =
Acquirers pre-merger total shares
outstanding + new shares issued by
Acquirer

12. FCF = NI + net interest after-tax + in
deferred taxes + net noncash charges in
NWC Capex
Terminal Value:
13. Using constant growth formula
Terminal
ValueU =

âầ (1)
(ââúụừè +)

y5.

6. Post-Merger EPS =
11. FCFE Coverage Ratio =

14. Using Market Multiple

3ẳêy<<ô 9
<

Ư<<
R;<0y09U;<ô 9
<
Ư<<
R;<0y09


âR


49
Ư<<
0êƯđ<
4m
9;<9
4ê9;0y0

Terminal
ValueU = FCFU ì


â

[y5.S;<
Vê<3;99]

FCFE = CFO FCInv + Net Borrowings
Reading 24: Corporate Performance,
Governance & Business Ethics

Reading 25: Corporate Governance
1. Share Overhang =

7. Post merger P/E (if market is efficient)
=

<
Ư<<
943T
4m
3ẳêy<<
49
Ư<<
RS


8. No. of acquirer shares received by each
shareholder (in target Co.) = No. of target
shares he/she owns ì X ratio
9. HHI =
100

cếỡì
ớợ
ớùễùễ
ớủ
Zợũ
Z
[

Z ớễếỡ
cếỡì
ớợ
ớùễùễ
ớủ
ũếợwìễ

ì

2

4.4m
9;<9
<<90
đP

ềy409
U4;-
04.4m
9;<9
4ê9;0y0

15. EV =MV of debt + MV of equity cash &
cash equivalents

10. Unlevered NI = NI + Net Interest after-tax
Net interest after-tax = (i exp i
income) ì (1 Tax rate) Or

16. Takeover Premium = takeover (deal price)

per share (of target Co.) current stock
price of target Co. =


+
S
c

17. Estimated takeover price of Target =
Estimated stock price of Target based on
Comparables + Estimated takeover
premium


When takeover premium is given in
%, Estimated takeover price of Target


FinQuiz

= (Estimated stock price of Target
based on Comparables) × (1 +
Takeover premium in %)
18.   Target Shareholders’ gain = Premium = P T
–VT
where,
P T = price paid for target company
V T = pre-merger value of target
company

Formula Sheet

•  
•  

V–P: True Mispricing
VE–V: Valuation Error
where,VE = estimated value
P = market price
V = intrinsic value

2.   Residual Income Model = NI – (cost of
equity × Beg value Equity)

7.   IRR:
•   Intrinsic value= D1 / (k-g)
•   If asset (fairly priced), market price =
intrinsic value: k = (D1 / P0) + g

9.   GGM Intrinsic value = D1/ (k-g)

20.   Post-merger value of the combined
company = V A* = V A + V T + S – C
where,
V A = pre-merger value of the acquirer
C = cash paid to target SH i.e. cash paid =
cash price paid per share of target co. × no.
of shares outstanding of target co.

2.   Price appreciation R = (PH-P0)/P0

1.   Mispricing = VE – P = (V- P) + (VE –
V)
•   VE–P: Mispricing

{(V0 – P0)/P0} = estimate of return
from convergence over period

Reading 28: Return Concepts
1.   Dividend yield or investment income =
(DH/P0)

Reading 27: Equity Valuation: Applications &
Processes

•  

8.   Req ROE = Rf + ERP

19.   Acquirer’s gain = Synergies – Premium =
S – (P T – V T)

21.   In Stock offer = P T = (N × P AT)
where,
P T = price paid for target co.
N = No. of new shares target receives
P AT = price per share of combined firm
after merger announcement

Level II 2018

3.   HPR = r = {(DH + PH) / P0} – 1 OR r =
{(P1 – P0+CF1) / P0
4.   Expected Alpha = Exp. R – Req. R
5.   Realized Alpha (Ex-post alpha) = (Actual
HPR) – (Contemporaneous Req. R)
6.   Expected HPR:
•   When an asset’s intrinsic value ≠
market price, the investor expects to
earn = RR + return from the
convergence of price to value
•   When an asset’s intrinsic value =
price, the investor expects to earn RR
only.
•   E (RT) ≈ rT + {(V0 – P0) / P0}
where,rT = periodic required RoR,

Macroeconomic Model Estimates (Supply side
models):
10.   ERP = [{(1+EINFL) (1+EGREPS)
(1+EGPE)-1} +EINC]-Expected Rf R
•   where EINFL= expected inf.(
forecasted as) {(1+YTM of 20-yr Tbonds) / (1+YTM of 20-yr TIPS)} –
1.
•   EGREPS = expected growth rate in
real EPS.
•   Real GDP growth rate = labor
productivity growth + labor supply
growth rate
Labor supply growth rate = population

growth rate + increase in labor force
participation rate
•   EGPE = expected growth rate in P/E
ratio. (For efficient markets 1+EGPE
= 1+0 = 1.


FinQuiz

•  

EINC = expected income component
(includes dividend yield &
reinvestment R)

11.   CAPM: Required Return on share i =
Current expected Rf R + Bi (ERP)
•   where ERP = Expected R on mkt
portfolio – RF R
•   Beta = Cov of returns with mkt R /mkt
portfolio var.
12.   Adjusted Beta = (2/3) (Unadjusted beta) +
(1/3) (1.0)
13.   Beta Estimation for Thinly Traded Stocks
and Nonpublic Companies
•   Bu ≈ [1/ {1+ (D/E)}] ×Be
•   Be’ ≈ [1+ (D’/E’)] ×Bu
14.   Multifactor Models = r = Rf+ (RP)1 +
(RP)2 + … + (RP)k
•   RPi = (Factor sensitivity)i × (Factor

RP)i.
15.   The Fama-French Model (FFM): ri =Rf +
Bimarket × RMRF + Bisize× SMB + Bivalue ×
HML
•  
•  

RMRF = RM –Rf
SMB(small minus big) = Avg. R on 3
small-cap portfolios – avg. R on 3
large-cap portfolios.

Formula Sheet

•  

HML (high minus low) = Avg. R on 2
high Book-to-market portfolios – avg.
R on 2 low book-to-market portfolios.

16.   Pastor-Stambaugh Model (PSM): ri = Rf +
Bimarket×RMRF + Bisize× SMB + Bivalue ×
HML+ BiLiq× LIQ
17.   5-factor BIRR Model: ri = T-bill rate +
(sensitivity to confidence risk × confidence
RP)–(sensitivity to time horizon × time
horizon RP) – (sensitivity to inf. risk × inf.
RP) + (sensitivity to business cycle risk ×
business cycle RP) + (sensitivity to mkt.
timing risk × mkt. timing RP)

Level II 2018

Reading 29: Industry & Company Analysis
1.   % of sales (specific geographic region) =
Sales of a particular region / Total sales of
a co.
2.   Co.’s projected Rev. growth = Projected
mkt. share × Projected sales of a given
product mkt.
3.   Forecasted variable costs = % of rev. Or =
Unit volume × Unit variable costs
4.   COGS =Raw materials + Direct labor +
Overhead (in producing the goods)

18.   Build-Up Approaches for Private Business
Valuation: ri = rf + ERP + Size premi
+Specific Co. premi

5.   Finance costs = (Fixed i rate on debt ×
Gross debt at beg. of period) – (i income
rate × cash position at beg of period)

19.   Bond yield Plus RP (BYPRP) cost of
equity = YTM on the co.’s LT debt + RP

6.   Gross debt = LT financial debt + ST
financial debt + Accrued interest

Country Spread Model

20.   ERP estimate = ERP for a developed mkt
+ Country prem.
•   Country Prem. = yield on emerging
mkt bonds (denominated in currency
of developed market) – yield on
developed mkt. govt. bonds

7.   Net debt = Gross debt – Cash and cash
equivalents
8.   Effective i rate = i exp / Avg gross debt

21.   Cost of Capital = WACC = {D/(D+E)}rd
(1-Tax rate) + {E / (D+E)}rE

9.   i rate on avg cash position =i income / Avg
cash position
10.   i rate on avg. net debt = Net i exp / Avg.
net debt


FinQuiz

Formula Sheet

11.   Deferred tax asset/liability = Profit and
loss (reported) tax amount – Cash tax
amount

18.   Post cannibalization revenue =Precannibalization revenue – Estimated
impact on rev. from cannibalization

12.   Projected A/C receivable = Forecasted
annual sales (assuming all credit sales) ×
(Assumed DSO/ 365)

19.   Overall organic rev. growth = [(1 +
volume growth) (1 + % of price/mix
contribution to rev. growth)] -1

13.   Projected inventory = Assumed COGS /
Assumed Inventory TO ratio

20.   Construction of Pro Forma I.S:
Sales
Less: COGS
= Gross profit
Less: Admin. exp.
Less: Distrib. Exp.
Add: Other income from operation
= EBIT
Add (Less): Other operating income
(exp.)
Less: Finance costs & other financial
exp.
= Profit before tax
Less: Income Tax
Add: Income from associates
= Profit from continuing
operations
Add (Less): Profit (loss) from

discontinued operations
= Net profit for the year
Less: Non-controlling interests
= Owners of the co.

14.   ROIC= NOPLAT / Invested Capital = EBI
/ (Operating assets – Operating liab.)
15.   ROCE = Op. profit / Capital employed (i.e.
debt and equity capital)
16.   Rev. loss for co. due to cannibalization of
demand = Projected no. of units of product
cannibalized by the new substitute product
× Estimated ASP
Where,
•   Average selling price (ASP) =
©4¦‰;0P« 9
 •9Šy¦;Š•ˆ
 ;5•.
 
 <•5.
©4¦‰;0P« 9
 •9Šy¦;Š•ˆ
 9Žy‰¦•0Š9
 4m
 ‰<4ˆª3Š
 

•  

No of units of a product cannibalized

by the new substitute product =
Expected no. of product shipments ×
% representation of each category
(e.g. consumer & non-consumer) ×
Cannibalization factor for the category

17.   Post cannibalization shipments =Precannibalization shipments – Expected
cannibalization

21.   EBITDA = EBIT + Dep. & amort. exp.

Level II 2018

22.   Forecasted CF Statement
CF from operating activities:
NI (profit after taxes)
Adj. to determine CF:
Add:
dep.
↓
 in a/c receivable
↓ in inventory
↑ in a/c payable
Total adjustments
Net CF from operating activities
CF from investing activities:
𝐴𝑑𝑑: ↓ in plant and equipment
Net CF from investing activities
CF from financing activities:
↑ in notes payable

↑ in LTD
Less: Dividends paid
Net CF from financing activities
Forecasted ↑ in cash
23.   Forecasted B.S
PP&E
Add: Investment in associates
Add: Other financial assets
Add: Deferred tax assets
= Total non-current assets
Inventories
Add: Trade and other receivables
Add: Cash & cash equivalents
Add: Other current assets
=Total current assets
Total assets = Total non-current +
Total current assets
Share capital


FinQuiz

Add: Share premium
Less: Treasury shares
Add: Consolidated reserves+Net profit
to co. owners
Plus: Translation reserve
+/-: Profit or loss recorded in equity
= Equity attributable to
shareholders

Plus: Non-controlling interest
= Equity
LT financial debt
Add: Provision for employee benefits
Add: LT provisions for liabilities and
charges
Add: Deferred tax liabilities
= Total non-current liabilities
ST financial debt and accrued interest
Add: Trade and other payables
Add: Income tax payable
Add: ST provisions for liabilities and
charges
Add: derivative financial instruments
Add: Liabilities held for sale
= Current liabilities
24.   FCFF:
Normalized operating profit
Less: Taxes
= Normalized operating
profit after tax
Add: Dep. & amort.
∆ in WC
Less: Capital expenditures
= FCFF

Formula Sheet

Level II 2018

Reading 30: Discounted Dividend Valuation

6.   GGM for Preferred stock (fixed rate
perpetual preferred stock) = Vu =

1.   Asset’s value is PV of its expected future
©†Í
0
Š\1 1’< Í

CFs i.e. Vu =

2.   RI = NI – (cost of equity × Beg. BV of
common equity)
3.   In RI Model: Value of stock = BVPS at t =
0 + PV of expected future residual
earnings
•   where, BVPS = common SHs’ equity /
no. of common shares outstanding
•   RI model (assumes Clean Surplus
Accounting holds) i.e. BV t = BVt-1 +
NIt – Divt
4.   DDM
•   With Single HP = Value of Stock =
PV of expected Div. + PV of expected
Selling Price at the end of year one =
Vu =
•  

”/

(1’<)/

+

•/
(1’<)/

”/

+

”?
(1’<)?

+

•?

8.   Actual value of a company’s share = Vu =
R/
<

•  

•  
•  

+ PVGO
where,
PVGO =Sum of PV of expected

profitable opportunities of reinvesting
the earnings.
E1/r = no-growth value per share
When P0 = V0 then. PVGO = Pu −

”Í

1
<

+

0
Š\1 1’< Í

For n-HPs = Vu =

•  

When HP is extended into indefinite
future: Vu =

+

R/

R/

•

<


 or
  =
R

•»“Ò
R/

•

•ù

R

R/

=

”/

R/
<+•

1’< -

”Í
á
Š\1 (1’<)Í

 or
 

•ù

R/

where, 1/r = value of P/E for nogrowth company.
PVGO/E1 = component of P/E value
that represents growth opportunities.

•-

•  

»ù

Can be restated as

9.   Leading ratio =

(1’<)?

<

7.   GGM ERP = 1-yr. forecasted div. yield on
market index + consensus LT earnings
growth rate – LT govt. bond yield

Value of stock for 2 years HP = Vu =
(1’<)/

”

10.   Trailing
 P/E
 ratio =
 

•ù
Rù

=

=

1+®
<+•

”ù (1’•)
(<+•)

Rù

=

(1+®)(1’•)
(<+•)

5.   Gordon Growth Model (GGM) = Vu =
”ù × 1’•
<+•

or =

”/
<+•

11.   GGM can be used to derive required RoR
=r=

”ù (1’•)
•ù

+g=

”/
•ù

+g


FinQuiz

Formula Sheet

SŽ;<•Ž4-ˆ•<9« •¼ªyŠP
U4Š;-

 ¯99•Š9

12.   Two-Stage Div Discount Model = Vu =
”Í
0
Š\1 (1’<)Í

+

»-

SŽ;<•Ž4-ˆ•<« 9
 •¼ªyŠP
²·

(1’<)-

=

where,
•  

V0 =

•  

Vu =

²·

15.   ROE
  =

”ù × 1’•ü - 1’•ý

²·

=

U4Š;-
 ¯99•Š9

S;-•9

S;-•9
U4Š;-
 ¯99•Š9
U4Š;-
 ¯99•Š9

×

×

=

SŽ;<•Ž4-ˆ•<9« •¼ªyŠP

<+•ý

”ù (1’•ü )Í
0
Š\1
(1’<)Í

×

Level II 2018

= Net profit margin × Asset
Turnover × Leverage

+

”ù ×(1’•ü )- ×(1’•ý )
1’< - (<+•ý )

Reading 31: Free Cash Flow Valuation

13.   H-Model
•  

Vu =

•  

Vu =

1.   PV of FCFF = Firm
 Value =

”ù × 1’•ý
” ×¬× •ü +•ý
+ ù
or
<+•ý
<+•ý
”ù × 1’•ý ’ ”ù ׬×(•ü +•ý )


 

14.   Estimating Sustainable Growth Rate = g =
b × ROE
•  

g=

²·+”y5yˆ•0ˆ9

²·
U4Š;-
 ¯99•Š9

×

²·
S;-•9

×

S;-•9
U4Š;-
 ¯99•Š9

×

SŽ;<•Ž4-ˆ•<9« R¼ªyŠP

•  
•  

7.   CF from operating activities = CFO = NI +
NCC – WCInv.

†©††Í
á
Š\1 (1’³¯©©)Í
 

(<+•ý )

where,
gL= normal LT div. growth rate after
year 2H
gS= initial ST div. growth rate
H = half-life in years of the highgrowth period i.e. high growth period
= 2H years

g = PRAT i.e..

g = profit margin (P) × retention rate
(R) × asset turnover (A) × financial
leverage (T)

2.   WACC
  =
 
Tax
 rate

º»
 4m
 ”
º»
 4m
 ”’º»
 4m
 R
º»4m
 R

+
 

× rˆ
 × 1 −

º»4m
 ”’º»4m
 R

× r•

3.   PV of FCFE = Equity
 value =

á †©†RÍ
Š\1 (1’<)Í
 

4.   Constant-Growth FCFF valuation Model =
Firm
 Value = Vu =

†©††/
³¯©©+•

=

†©††ù ×(1’•)
³¯©©+•

5.   Constant-Growth FCFE valuation Model =
Equity
 Value = Vu =

†©†R/
<+•

FCInv = End gross PPE – Beg. gross

PPE
b)  When LT assets are sold during the yr:
FCInv = Capital expenditures –
proceeds from sale of LT assets or
FCInv = (End. gross PPE – Beg. gross
PPE) - Proceeds from sale of LT
assets
WCInv = ∆ in Current assets excl. cash
& cash equivalents – ∆ in Current liab.
excl. ST debt

=

†©†Rù ×(1’•)
<+•

6.   Computing FCFF from NI = FCFF = NI +
NCC + Int × (1 – Tax rate) + Preferred
stock div. – FCInv – WCInv
a)   When no LT assets are sold during the
yr:

8.   Computing FCFE from FCFF
•   FCFE = FCFF – Int ×(1 – Tax rate) –
preferred stock dividends + Net
Borrowing + issuance of preferred
stocks – redemption of preferred stock
•   FCFE = NI + NCC – FCInv – WCInv
+ Net Borrowing + issuance of
preferred stocks – redemption of

preferred stock
•   FCFE = CFO – FCInv + Net
Borrowing + issuance of preferred
stocks – redemption of preferred stock
•   Total value of Equity (common) =
Total Firm value – Market value of
Debt – Preferred stock
9.   Finding FCFF and FCFE from EBIT or
EBITDA
•   FCFF = EBIT (1 – Tax rate) + Dep –
FCInv – WCInv


FinQuiz

FCFF = EBITDA (1 – Tax rate) + Dep
(Tax rate) – FCInv – WCInv
•   FCFE = FCFF – Int (1 – Tax rate) +
Net borrowing + issuance of preferred
stocks – redemption of preferred stock
10.   Forecasted FCFF = Forecasted [EBIT ×(1
– Tax rate) – FCInv – WCInv]

Formula Sheet

Required rate of return (real) [in %]

•  

11.   Incremental fixed capital expenditures as a

proportion of sales increases =
©;‰yŠ;-
 •O‰+”•‰
 •O‰
·03<•;9•
 y0
 9;-•9

12.   Incremental working capital expenditures
as a proportion of sales increases =
·03<•;9•
 y0
 ³©
·03<•;9•
 y0
 9;-•9

13.   FCFE = NI – (FCInv – Dep) – WCInv +
Net borrowing
where,
Net borrowing = DR×(FCInv – Dep) +
DR×(WCInv) Or
FCFE = NI – (FCInv – Dep) – WCInv
+ (DR) ×(FCInv – Dep) + (DR)
×(WCInv) Or
FCFE = NI - (1-DR) ×(FCInv – Dep)
– (1 – DR) ×(WCInv)

Level II 2018

15.   Single-Stage FCFF and FCFE Model for
International Valuation:
FCFFu ×(1 + g <•;- )
Value
 of
 firm = Vu =
WACC<•;- − g <•;FCFF1
=
WACC<•;- − g <•;-

Reading 32: Market based Valuation: Price &
Enterprise Value Multiples
1.   Trailing P/E or Current P/E =
©ª<<•0Š
 ºTŠ
 •  ‰•<
 9Ž;<•
¦49Š
 <•3•0Š
 ÿ
 !ª;<Š•<9« R•S

2.   Forward P/E or Leading P/E or Prospective
P/E =

Value
 of
 Stock = Vu
FCFEu ×(1 + g <•;- )

=
r<•;- − g <•;FCFE1
=
r<•;- − g <•;16.   Two-stage FCFF valuation model equation
is:
•  

Firm
 Value =
†©††-Ï/
(³¯©©+•)

•  

×

†©††Í
0
Š\1 (1’³¯©©)Í
1

†©†R-Ï/
(<+•)

×


 

U4Š;-

 R;<0y0•9
³•ŽŠˆ
 ¯5•
 04.4m
 9Ž;<•9
 ;3Šª;--P
 4/9
 ˆª  ŠŽ•
 ‰•
4.   Diluted EPS =

 

U4Š;-
 R;<0y0•9
²4.4m
 9Ž;<•9
 4/9
 ‡Ž•0
 Ž4-ˆ•<9
 4m
 
•O3•<3y9•ˆ
 ŠŽ•y<
 
 4‰Šy409
 Š4
 4®Š;y0

 34¦¦40
 9Š43T

5.   Justified Forward P/E = P0/E1 =

(1’³¯©©)-

+

3.   Basic EPS =

+

Two-stage FCFE valuation model
equation = Equity
 Value =
0 †©†RÍ
Š\1 (1’<)Í

©ª<<•0Š
 º;  •  ‰•<
 9Ž;<•
²•OŠ
 ,•;<« 9
 RO‰•3Š•ˆ
 R;<0y0•9
 

1
(1’<)-

17.   Excess Cash = Total
 Cash
 Available −

6.   Justified Trailing P/E = P0/E0 =
=

1+® ×(1’•)
<+•

è/
É/

<+•

=

1+®
<+•

”ù (1’•)/Rù
<+•

where

P = price; E = earnings; D = dividends; r =
required rate of return; and g = dividend

growth rate

Total
 Assets
 of
 Firm×
14.   Modified Build-Up method to estimate real
discount rate:
Country return (Real) [in %]
+/ - Industry Adjustment [in %]
+/ - Size Adjustment [in %]
+/ - Leverage Adjustment [in %]

º•ˆy;0
 -•5•-
 4
 m
 ·0ˆª9Š  3;9Ž
º•ˆy;0
 -•5•-
 4m
 ·0ˆª9Š  U4Š;-
 ¯99•Š

7.   PEG ratio =

SŠ43T« 9
 •/R

RO‰•3Š•ˆ
 R;<0y0•9
 “<4‡ŠŽ
 V;Š•
 y0
 %

8.   Yardeni Model CEY = CBY – (b × LTEG)
+ Residual
where,


FinQuiz

Formula Sheet

CEY = current earnings yield on the mkt.
index i.e. E/P.
CBY = current Moodys Investors Service
A-rated corporate bond yield.
LTEG = consensus 5-year earnings growth
rate forecast for the mkt index.
b = coefficient (measures weight, the mkt
gives to 5-year earnings projections).


By taking inverse:


R

=

1
âả,+đ
ì
"UR

9. Own Historical P/E: Justified price =
Benchmark value of own historical P/Es ì
Most recent EPS
10. Terminal Value (T.V) based on
Fundamentals:
T.V in yr n = (justified trailing P/E) ì
(forecasted earnings in year n)
T.V in year n = (justified leading P/E)
ì (forecasted earnings in year n+1)
11. Terminal Value based on Comparables:
T.V in yr n = (Benchmark trailing
P/E) ì (forecasted earnings in year n)
T.V in yr n = (Benchmark leading
P/E) ì (forecasted earnings in year
n+1)
12. P/B =


<
S;<

ả44T
ằ;-ê
<
S;<

where

04.4m
34ƯƯ40
943T
9;<9
4/9

* It includes preferred stock and div.
in arrears on preferred stock.
BVPS for whole company =
4;-
;999

4;-
-y;đy-yy9


=

Sơô 9ô ẳêyP

4;-
ẳêyP
5;-ê

3-;yƯ9

;
;<
90y4<
4
34ƯƯ40
943T
#
4m
â.S
9;<9
4/9

19. Dividend Yield =


13. Justified P/B = P0/B0 =



VềR+

=

y5
<
9;<
<

9;<

Trailing Div Yield =
Leading Div Yield =
4<3;9
y5
<
9;<
45<

0O
P<

<+

âê<<0
ƯT.

<
9;<

ằ
4m
O3
mêê<
<9yê;-
;<0y09

20. Div Yield (by using GGM) = Justified Div

Yield =

ảu

15. P/S =



âê<<0
ƯT
<
9;<

14. Justified P/B based on RI model = P0/B0 =
1+



y5y0
V;

0êƯđ<
4m

9;<9
4ê9;0y0

u
u

=

<+
1

<
9;<
00ê;-
0
9;-9
<
9;<

where Net Sales = Total Sales
returns customer discounts
16. P/S ( in terms of Gordon Growth Model =
Justified P/S =

ự
Sự

ẫự
ỹự

=

1+đ (1)
(<+)

where, E0/S0 = Businesss profit
margin
17. g = Retention rate (b) ì ROE
g = b ì PM0 ì
U4;-
999

S;-9
U4;-
999

ì

S;<4-<9ô RẳêyP

where, PM0 = Profit Margin at t = 0
18. Price To Cash Flow

BVPS for equity shareholders =
U

U"

.S




Level II 2018

=



=



=



=

<
9;<
R;<0y09
-ê9
0403;9
3;<9
<
9;<
â;9
m-4
m<4Ư

ề<;y409
<
9;<
âR
<
9;<
RảãU

Or

Or

21. EV = MV of Common equity + MV of
preferred stock* + MV of debt Cash &
Short-term Investments
MV of Common equity = No. of
shares o/s ì Price per share
Cash & Investments = cash, cash
equivalents, short term investments
etc.
*If minority interest exists and it is not
included elsewhere, then it should be
added back.
22. ROIC =

ề<;y0
<4my
;m<

;O
U4;-
y059
â;y;-

23. Total Invested Capital = TIC = MV of
Common equity + MV of preferred stock +
MV of debt

Or
24. Earnings surprise UEt = EPS t E (EPS t)
where,
UEt= unexpected earnings for quarter t


FinQuiz

•  

Formula Sheet

EPSt= reported/actual EPS for quarter
t
E(EPSt) = expected EPS for the
quarter
Percent Earning Surprise =

•  

R;<0y0•9

 Sª<‰
•  

RO‰•3Š•ˆ
 R•S

•  

Scaled Earnings Surprise =
R;<0y0•9
 Sª<‰S.”
 4m
 ;0;-P9Š9%
 •;<0y0•9
 m4<•3;9Š

•  

Level II 2018

=NOPAT – Total Capital Charge =
NOPAT – Debt Charge – Equity
Charge = NOPAT – (AT cost of debt
× Debt Capital) – (cost of equity ×
Equity Capital)
RI (with preferred stock) = NI –
Equity Charge – Preferred Stock Div
RI = (ROIC – Effective Capital

Charge) × Beg. Capital

•  

=

R•SÍ
 +R
 (R•SÍ )
&
 [R•SÍ
 +R
 (R•SÍ )]

where,
EPSt= reported/actual EPS for time t
E (EPSt) = expected EPS for the time t
σ [EPSŠ
  − E
 (EPSŠ )] = S.D of [EPSŠ
  −
E
 (EPSŠ )] over some historical time period.
26.   Relative strength indicator
=

SŠ43T« 9
 ‰•••  4m

 ;0
 R¼ªyŠP
 ·0ˆ•O

27.   Harmonic Mean = XH=

0
- (/)
*./ 6
*

Reading 33: Residual Income Valuation
1.   End. BV of equity = Beg. BV of equity +
Earnings – Div.
B t = B t-1 + E t – Dt &
D t = E t - (B t - B t-1) = E t + B t-1 - B t

3.   EVA = NOPAT – (C% × TC)
Or = [EBIT (1 – t)] – (WACC × invested
capital)
where,
C% = cost of capital
TC = Total capital
WACC × invested capital = dollar cost of
capital
Invested capital = net WC + net fixed
assets = BV of LT debt + BV of equity
4.   MVA = MV of Co. – Accounting BV of
total capital = MV of Co – (BV of Debt +
BV of Equity)

á
Š\1 (1’<)Í

•  

Vu = Bu +

V·/
(1’<)/

+

V·?
(1’<)?

+

V·'
(1’<)'

+

⋯
6.   RI Model (general) = Vu = Bu +
á VÒRÍ +< ׶Ík/
Š\1
1’< Í
•

•ù

¶

¶ù

7.   Justified =

=
 

VÒR+•
<+•

=
 1 +

VÒR+<
<+•

where, Justified Price is the stock’s
Intrinsic value i.e. P0 = V0
BV of equity = B0 = Total assets –
total liab.
8.

Tobin’s q =

º»
 4m

 ”•®Š
 ;0ˆ
 R¼ªyŠP
V•‰-;3•¦•0Š
 349Š
 4m
 U4Š;-
 ¯99•Š9

9.   Single-Stage RI Valuation = Vu = Bu +
VÒR+<
<+•

•  

×Bu

Implied Growth rate in RI = g = r −
¶ù VÒR+<
»ù +¶ù

5.   RI model
•   RIt = E t – (r × B t-1) = (ROE – r) × B t-1
•   Two components of intrinsic value of
stock/equity
i.   Current BV of Equity that is B0.
ii.   PV of expected future RI

2.   Residual Income (RI)
•   = NI – Equity Charge = NI – (Equity

Capital × Cost of Equity Capital)

= Bu +

RÍ +<¶Ík/

25.   Standardized Unexpected Earnings = SUE
t

V·Í
á
Š\1 1’< Í

Vu = Bu +

V·?
(1’<)?

+

V·'
(1’<)'

+⋯

V·/
(1’<)/

10.   Multi-Stage RI Valuation = V0 = B0 + (PV
of interim high-growth RI) + (PV of

continuing RI)
•   PV of continuing RI in year T–1
=

+
•  

V·Ç
where,
1’<+* 1’< Çk/

ω=

persistence factor, 0 ≤ ω ≤ 1
Assumptions about Continuing RI:


FinQuiz

Formula Sheet

o RI is at +ve level currently and
will persist at this level in the
future indefinitely:
PV of continuing RI in year T-1
=

Vãầ

=

1<+*

Vãầ
1<+1

=

Vãầ
<

o RI will become 0 from the
terminal yr forward.
PV of continuing RI in year T-1
=

Vãầ
1<+* 1< ầk/
Vãầ

1<+u 1< ầk/

=

To value Equity directly = V =

â/
<+

2. Excess Earnings or RI = Normalized

earnings [(RR on WC ì value of WC) +
(RR on fixed assets ì value of fixed
assets)]

1< ầk/

Vãầ
1<+* 1< ầk/

o RI declines to long-run mean
level of mature industry.
Where premium over book value is assumed at
the end of time horizon T (PT Bt), current
value (V0) =

(ROEt r )Bt 1 + PT BT
B0 +
(1 + r )T
(1 + r )T
t =1
T

1
1â40<4-
<ƯyêƯ

â/
ââ++

Value of Equity = Vf MV of Debt

1 + +
1 +

5. Lack of Marketability Discount =
DLOM =

1 + +



5. Yield Curve Movement and the Forward
Curve


F (T*, T) =


ằ;-ê
4m
";Ư40P"
ê
4y40

P* (T) = ễ
ễ
F*(t, T*, T) =

++ễ
ễ

5;-ê
4m
943T
đm4<
;0P
"ề

6. Total Discount = [1 (1 DLOC in %) ì
(1 DLOM in %)]

F*(t, T*, T) =

.
(~ẽ
ẽk~)
.
(~)
.
(~ẽ
k~)
.
(~)

=

(
)

()

=

F (T*, T)
Reading 35: The Term Structure & Interest
Rate Dynamics


1. Discount Factor = P (T) =

1
1ớễợếễì

Active Bond Portfolio Management
6. 1-yr. HPR =
=



1ợ
()

Reading 34: Private Company Valuation

1. Capitalized CF to the firm = Vm =

DLOC = 1

1

Where PT =BT ì (forecasted
P/B ratio)

Forward rate model can be expressed as:

= 1 + ,

4. Calculation of Lack of Control Discount =

Vãầ

r (T) = {[ 1 + r (1)] [1 + f (1,1)] [1 + f
(2,1)] [1 + f (3,1)] [1 + f (T 1,1)]} (1/T)
-1

3. MVIC = MV of Debt + MV of Equity

=

o RI declines to 0 as ROE
approaches r over time (& RI will
become 0 eventually). i.e. 0
1
PV of continuing RI in year T-1=

Level II 2018



2. Forward pricing model: P (T* + T) = P
(T*) ì F (T*,T)



3. Forward rate model = [1 + r (T* + T)] (T* + T)
= [1 + r (T*)] T* ì [1 + f (T*, T)] T
4. Spot rate for a security, having maturity of
T > 1


1ợ 1 ẽ/
1ủ 1,

=
1 + (1)

(when the spot curve one year from today
is todays forward curve)
7. Return of the 2-year zero-coupon bond
over 1-yr HP =

4m
;
>+P<
Ơ<4+34ê40
đ40
1
P<
m<4Ư
4;P
ê<3;9
4m
đ40

1




FinQuiz

•  

Formula Sheet


 
15.   Interest rate volatility for a security with

Price of a 2-yr zero-coupon bond 1 yr
from today =
˜Õî/Õìï×íñ0í[1

maturity T at time t = σ (t, T) =

(1’—21îÕÔ×ñíî13î0í[113îñîíòÔí1Õ3)

•  

Price of a 3-yr zero-coupon bond 1 yr
from today =
˜Õî/Õìï×íñ0í[1
(1’—21îÕÔ×ñíîÔ2í3î0í[113×ÕîñîíòÔí1Õ3)
˜Õî/Õìï×íñ0í[1


 

=

<

∆=
 (~.•)
=
 (~,•)

∆Ô

 

Reading 36: The Arbitrage Free Valuation
Framework

1’ñ 1,>

8.   Swap Spread = Fixed-rate of an interest
rate swap – Interest rate on “on-the-run”
Govt. security
•
 (–)
–
Ô\1 1’î Ô Í

•  

Level II 2018

+
 

1
1’î – •

↓
𝑓𝑖𝑥𝑒𝑑𝑟𝑎𝑡𝑒𝑙𝑒𝑔

=1

↓
𝑓𝑙𝑜𝑎𝑡𝑖𝑛𝑔𝑟𝑎𝑡𝑒𝑙𝑒𝑔

9.   TED spread = LIBOR - T-bill rate of
matching maturity
 

 
10.   Libor–OIS spread = Libor - Overnight
indexed swap (OIS) rate
 

 
11.   Local expectations theory =

1
˜
 (Ô,–)

=

1 + 𝑟 1 1 + 𝑓 1,1 1 + 𝑓 2,1
𝑓 3,1 … [1 + 𝑓 𝑇 − 1,1 ]
 

1+

12.   Cox–Ingersoll–Ross (CIR) Model = dr = a
(b – r) dt + σ 𝑟𝑑𝑧
 

 
13.   Vasicek Model = dr = a(b – r)dt + σdz
 

 
14.   Ho-Lee model = drt = θtdt + σdzt
 

Reading 37: Valuation & Analysis: Bonds with
Embedded Options
1.   Value of callable bond = Value of straight
bond – Value of issuer call option
2.   Value of issuer call option = Value of
straight bond – Value of callable bond
3.   Value of putable bond = Value of straight
bond + Value of investor put option
4.   Value of investor put option = Value of
putable bond – Value of straight bond
5.   The rate in the up state = Ru = Rd × e2σ 𝑡
where, Rd = Rate in the down state
σ = Interest rate volatility
t = Time in years between “time slices”
6.   Duration =
 

»k +»Ï

8.   Effective

∆@ïî/× ? × ˜?ù


 

10.   Value of capped floater = Value of straight
bond – Value of embedded cap
11.   Value of floored floater = Value of straight
bond + Value of embedded floor
Analysis of a Convertible Bond
12.   Conversion Ratio (CR) = No. of shares of
C.stock from exercising call option
 

 
13.   Conversion Price (or stated conversion
price) = Par value of convertible bond ÷
CR
 

 
14.   Conversion Value (or Parity) = Market
price of C.stock × CR
 

 
15.   Straight Value or Investment Value =
Market value of a security without
conversion option
 

 
16.   Min. Value of a Convertible Security is
(greater of conversion value or straight
value)
 

 
17.   Market Conversion Price or Conversion
Parity Price =
©V

»Ï ’»k + >×»ù

>×
 »ù × ∆, ?
•»k + •»Ï
Duration =
>× ∆©ª<5• × •»>

˜?k ’ ˜?Ï + >× ˜?ù

º;  •  4m
 ©405•<Šy®-•
 S•3ª
>×»ù × ∆,

7.   Convexity =
 

9.   Effective Convexity =


 

18.   Market Conversion Premium per share =
Market Conversion Price – Current Market
Price


FinQuiz

Formula Sheet

19.   Premium Payback Period =
º;  ©405•<9y40
 ‰<•¦yª¦
 ‰•<
 9Ž;<•
†;54<;®-•
 ·034¦•
 ”ymm•<•0Šy;-
 ‰•<
 9Ž;<•

20.   Favorable Income Differential per share =

©4ª‰40
 y0Š•<•9Š+ ©V
 ×©.9Š43T
 ”y5.‰•<
 9Ž;<•
©V

21.   Premium over straight value =
º;  •  4m
 ©405•<Šy®-•
 ¶40ˆ
SŠ<;y•ŽŠ
 »;-ª•

–1

2.   Credit spread = Yield to maturity of a risky
bond – Yield to maturity of a Govt. bond
 

 
3.   Put option’s price = Value of risky debt –
Value of riskless debt
 

 
4.   Black-Scholes Option pricing Formula =

St = At N(d1 ) − ke−r(T −1) N(d2 )
 
Where,

⎛ A ⎞
1
ln⎜⎜ t ⎟⎟ + r (T − t ) + σ 2 (T − t )
K
2
d1 = ⎝ ⎠
σ T −1

22.   Non-callable/Non-putable Convertible
security value = Straight value + Value of
Call option on stock
23.   Callable Convertible bond value = Straight
value + Value of call option on stock –
Value of call option on bond
24.   Callable & Putable Convertible bond value
= Straight value + Value of call option on
stock – Value of call option on bond +
Value of Put option on bond
25.   Value of Call Option – Value of Put
Option = PV (Forward price of bond on
exercise date – Exercise price)
Reading 38: Credit Analysis Models

 
1.   Expected loss = Full amount owed –
Expected recovery or = Loss given default

× Probability of default

d2 = d1 – σ T − 1
5.   Value of debt = D (t, T) = PV of payoff on
co.’s debt if default occurs + PV of payoff
on co.’s debt if default does not occur =

At N (−d1 ) + Ke − r (T −1) N (d 2 )
•  

where, N (d2) = Risk neutral
probability of the co.’s debt not
defaulting

6.   Credit Risk Measures
 
•   Probability of the debt defaulting =
Prob. (AT< K) = 1 – Prob. (AT ≥ K) =
1 – N(e2)
Where,

Level II 2018

•  

⎛ A ⎞
1
ln⎜⎜ t ⎟⎟ + u (T − t ) + σ 2 (T − t )
K
2

e1 = ⎝ ⎠
σ T −t

•   e2 = e1 - σ T − 1
7.   Co.’s asset R in CAPM (a static one-period
model):
Co.’s asset R = Rf + β of co.’s asset
(Expected R per year on Mkt. portfolio –
R f)
= Rf+ (β of co.’s asset × Mkt.’s ERP)
8.   Price of debt𝐷 𝑡, 𝑇 =

 𝐸

œ
1’î/ ∆ 1’î/Ï∆ … 1’î•Ï∆


 


 
9.   Credit risk measures in reduced form
model:
 
•   Default probability over [0,T] = Prob
𝑡 ≤𝑇 =1−
𝐸
 
•  

Ô BC œ
1’D Bù ∆ ’ 1’D B∆ … 1’D B•k∆ ∆

Expected loss =
–+∆
𝐸Ô\u

•  


 

Ô BC œ
1’D Bù ∆ ’ 1’D B∆ … 𝜆
1’D BC ∆

𝑋Z ∆
 

Present value of the expected loss = K
P (t,T) – D (t,T)

10.   Historical Estimation
 
•   Probability of default over [t, t+∆] =

1

Prob (t) =

N

1+ e

−α − ∑ bi X i t
i =1