2018 FinQuiz CFA Level 2 Formula Sheet

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Reading 9: Correlation & Regression

3. t-test (for normally distributed variables) = t =< 0+>

8. Hypothesis Testing:

• Null and Alternative hypotheses • H0: b1 = 0 (no linear relationship)

Variability DoF

Sum of

Reading 10: Multiple Regression & Issues in Regression Analysis

4. Breusch–Pagan test • H0 = No conditional

Heteroskedasticity exists

• HA = Conditional Heteroskedasticity

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Reading 11: Time Series Analysis

1. Linear Trend Models = yt = b0 + b1t+ εt

• Predicted/fitted value of yt in period

(T + 1) =

y

ˆ

_t₊₁

=

b

ˆ

₀

+

b

ˆ

₁

(

T

+

1 )

2. Log-Linear Trend Models =

y

_t

=

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. Mean reverting level of

1

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

• Two-period ahead forecast=

ˆ

6. Random Walks and Unit Roots:

• Random Walk without drift = xt = x

t-8. Smoothing Past Values with n-Period Moving Average =

n

9. Correcting Seasonality in Time Series Models:

• Predicting variance of errors in period t+1 =

σ

ˆ

2tt+1

=

α

ˆ

0

+

α

1

ε

ˆ

2 t

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

Reading 13: Currency Exchange Rates

1. Bid-offer Spread = Offer price – Bid price

2. Fwd rate = Spot Exchange rate +

†4<‡;<ˆ ‰4y0Š9_1u,uuu

3. Forward premium/discount (in %) =

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

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

5. Covered interest rate parity:

• 1 + iˆ = S∫

6. Uncovered Interest Rate Parity :

• f d d

e

f

S

i

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• f d f d

• Forward premium or discount: • For one year horizon =

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

If uncovered interest rate parity holds

=

F

f/d

−

S

f/d

S

_f_/_d

=

%

Δ

S

e

f/d

≅

(

i

f

−

i

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 –

πed

11. Real Exchange Rate

qf/d =

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-to-labor 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:

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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 + n

• Steady state Output-to-capital ratio =

› œ=

1 •

š

1+ ™ + 𝛿 + 𝑛 = 𝛹

• Gross investment per worker =

š

1+ ™ + 𝛿 + 𝑛 𝑘

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

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

• Growth rates of output per capita = ∆y / y = _{1+ ™}š + 𝛼𝑠 _œ›− 𝛹 =

š

1+™ + 𝛼𝑠 (y/k – Ψ)

•

Capital-to-labor ratio = ∆k / k =

š 1+ ™ + 𝑠

›

œ− 𝛹 =

š 1+™ + s

(y/k – Ψ)

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

• k

new

k

old

=

Y

K

!

"

#

$

%

&

new

Y

K

!

"

#

$

%

&

old

'

(

)

*

+

,

1 α−1

•

α

⎥

⎦

⎤

⎢

⎣

⎡

=

old new

k

y

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

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Reading 16: Interoperate Investments

1. Summary of Accounting Treatment of Investments

Income Statement (I.S) Balance Sheet (B.S) Statement

ofSH’sEq uity

Held-to-maturity

§ 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

§ Initially, at FV (IFRS) or initial price paid (US GAAP)

§ Subsequently, reported at amort cost at the subsequent reporting date on B.S.

N/A

Held for trading security

§ 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

§ Initially, at FV.

§ Subsequently, at FV at subsequent reporting date on B.S.

Designated at

fair value

§ 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

§ Reported at FV at the end of Yr t

§ Subsequently, at FV at the subsequent reporting date on B.S

Available -for-sale

§ 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

§ Reported at FV at the end of Yr t

§ Subsequently, at FV at the subsequent reporting date on the B.S.

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

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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 Assets)

(xxx)

= Excess Purchase Price Xxx Less: Attributable to Net Assets:

-Plant & Equipment (% of Ownership Interest × difference b/wBV & FV)

(xxx)

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

3. Amort. of Excess PP: Investment in associate:

PP Xxx

Add: Investor’s share of Investee’s NI (% of Ownership Interest × Investee’s NI)

Xxx

Less: Div. received (% of Ownership Interest × Div. paid) (xxx) Less: Amort. of excess PP attributable to plant & equipment

(Amount attributable to PP&E* ÷ Remaining life of PP&E)

(xxx)

= 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)

Beg net assets Xxx

Add: NI Xxx

Less: Div. paid (xxx)

= Ending net assets Xxx

Investor’s proportionate share of Investee’s recorded net assets (% of Ownership Interest × Ending net assets)

Xxx

Add: Unamortized excess PP (Excess PP – Amount attributable to PP&E)

xxx

= Investment in Investee xxx

Transactions with Associates: 4. Upstream Transactions:

Investor’s share of Associate’s reported NI (% of Ownership Interest × Reported net income)

xxx

Less: Amort. of excess purchase price (xxx)

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

(xxx)

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

• 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)]

xxx

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5. Downstream Transactions Investor’s share of Associate’s reported NI (% of Ownership Interest × Reported NI)

xxx

Less: Amort of excess PP (xxx) Less: Unrealized profit (% of

Ownership Interest × Profit from the downstream sale in Associate’s NI)

(xxx)

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

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)

xxx

Less: Amort of excess PP (xxx) Add: Realized profit (% of goods

unsold × Unrealized profit)

xxx

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

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

Goodwill

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

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.

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

FV of the stock issued xxx

Less: FV allocated to identifiable net assets

(xxx)

= Goodwill 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

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

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

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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

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

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

• 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

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 post-retirement 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 =

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Reading 18: Multinational Operations

1. Cumulative Translation Adjustment = CTA = Assets – Liabilities – Common Stock – Retained Earnings

2. Balance Sheet Exposure:

Foreign Currency (FC)

B.S Exposure Strengthens Weakens

When assets translated at current X rate > liabilities translated at current X rate

Net Asset B.S When liabilities translated at

current X rate > assets translated at current X rate

Net Liability B.S exposure

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

Foreign Subsidiary’s Functional Currency

FC Parent’s Presentation

Currency

Translation Method: Current Rate

method

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 &

Current rate

Foreign Subsidiary’s Functional Currency

FC Parent’s Presentation

Currency inventories measured at

market value under the lower of cost or market rule. ii) Measured at historical costs e.g. PP&E

Current rate Historical rate

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

Current rate

Retained Earnings (R.E)

Historical rates

Beg R.E + translated NI – div.

translated at historical rate

Historical rates

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

rate

Revenues Average rate Average rate

EXPENSES

Most Expenses

Expenses related to assets translated at historical X rate

e.g. COGS, Dep.,

rate & historical rate)

Exposure Net Assets or Net

Liabilities

Net monetary assets or Net

monetary liabilities

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

Accumulated as a separate component

of equity

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TEMPORAL METHOD: CURRENT RATE METHOD Net Monetary

Liability Exposure

Net Monetary Asset Exposure FC

strengthens relative to

parent’s presentation

currency

§ Rev ↑

§ Assets ↑

§ Liabilities ↑

§ NI ↓

§ SH’ equity ↓

§ Translation

loss

§ Rev ↑

§ Assets ↑

§ NI ↑

§ SH’ equity ↑

§ Translation

gain

§ Rev ↑

§ Assets ↑

§ NI ↑

§ SH’ equity

↑

§ +ve Translation adj. FC weakens

relative to parent’s presentation

currency

§ Rev ↓

§ Assets ↓

§ Liabilities ↓

§ NI ↑

§ SH’ equity ↑

§ Translation

gain

§ Rev ↓

§ Assets ↓

§ NI ↓

§ Translation

loss

§ Rev ↓

§ Assets ↓

§ Net Income

↓

§ -ve Translation adj.

6. Impact of Changing Exchange Rates on Exposure Foreign Currency

Strengthens Weakens

CURRENT RATE METHOD: Net Assets

Net Liabilities

Gain Loss

Loss Gain TEMPORAL METHOD:

Net Monetary Assets Net Monetary Liabilities

Gain Loss

Loss Gain

Hyperinflationary Economy

7. Restatement Factor = _{¬y9Š4<y3;- ‰<y3• y0ˆ•O}

8. Restated Capital Stock = Capital stock original value ×

©ª<<•0Š P<«_{9 ‰<y3• y0ˆ•O 4< ˆ;Š• 4m 340Š<y®ªŠy40,‡Žy3Ž•5•< y9 -;Š•<} ¬y9Š4<y3;- ‰<y3• y0ˆ•O

9. Restated Revenue = Revenue original value × ©ª<<•0Š P<_{¯5•.‰<y3• y0ˆ•O}«9 ‰<y3• y0ˆ•O

10. Loss from holding beg balance in cash = -Beg balance in cash ×

©ª<<•0Š P<«9 ‰<y3• y0ˆ•O –¬y9Š4<y3;- ‰<y3• y0ˆ•O ¬y9Š4<y3;- ‰<y3• y0ˆ•O

11. Loss from increase in cash during the yr = -Increase in cash ×

©ª<<•0Š P<«_{9 ‰<y3• y0ˆ•O+¯5• ‰<y3• y0ˆ•O} ¯5• ‰<y3• y0ˆ•O

12. Gain from holding note payable = Notes payable ×

©ª<<•0Š P<«9 ‰<y3• y0ˆ•O+¬y9Š4<y3;- ‰<y3• y0ˆ•O ¬y9Š4<y3;- ‰<y3• y0ˆ•O

13. Avg. effective tax rate =_{•<•Š;O ¯334ª0Šy0• •<4myŠ9}U;O RO‰

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Reading 19: Evaluating Quality of Financial Reports

1. DSR (days sales receivable index) = (Receivablest/Salest) / (Receivablest–

1/Salest–1)

2. GMI (gross margin index) = Gross margint–1 / Gross margint

3. AQI (asset quality index) = [1 – (PP&Et+

CAt)/TAt ] / [1 – (PP&Et–1+ CAt-1)/TAt-1]

4. SGI (sales growth index) = Salest/Salest–1

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) / (SGAt–1/Salest–1)

7. Accruals = (Income before extraordinary items – Cash from operations)/TA

8. LEVI (leverage index) = Leveraget /

Leveraget–1 where, Leverage = Debt /

Assets

9. Earnings t+1 = α + (β1 × Earnings t) + ε

10. Account receivable turnover = (365/DSO)

11. Z-score = 1.2 × _U¯ + 1.4 × _U¯ +

3.3 × R¶·U _U¯ + 0.6 × _{¶.» 4m -y;®y-yŠy•9}º.» 4m R¼ªyŠP +

1.0 × S;-•9

U.¯

Reading 20: Integration of Financial Statement Analysis

1. DuPont Analysis:

• ROE = Tax Burden × Interest Burden × EBIT margin × TATO × Financial Leverage

• ROE = NI/EBT × EBT/EBIT × EBIT/Sales × Sales/Assets × Assets/Equity

• ROE = Net profit margin × asset turnover × 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 =

²·+R¼ªyŠP y034¦• R¶U

• Adjusted TATO =

ÂÃÄ

ÅÃÆ ÇÈkÅÃÆ ÉÊ.Ë-ÄÌÍÎ-Í.ÏÉ-‘ ÇÈkÉ-‘ ÉÊ.Ë-ÄÌÍÎ-Í >

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 –

(Cash t + ST invstmnt. t)} – {Total liab

t – (Total LT debt t + Debt in current

liab.)}]

• B. S based Accruals Ratio =

²Ò¯_~+²Ò¯_~k/ ²Ò¯~’²Ò¯~k/

>

3. CF based aggregate accruals:

• Aggregate Accruals = NI t – (CFO t +

CFI t)

• CF based Accruals Ratio =

²·Í+(©†ÒÍ’©†·Í) (²Ò¯_Í’²Ò¯_Ík/)

>

• 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 =_{¯5• U.¯}Ò‰.©†

5. Cash Flow to Reinvestment =

Ò‰.©† 3;‰yŠ;- •O‰•0ˆyŠª<•9

6. Cash Flow to Total Debt =

Ò‰.©† ®•m4<• y0Š•<•9Š & ÔÕÖ×• U.”

7. Capacity to pay debt (in years) =_{Ò‰.©†+©;‰yŠ;- RO‰•0ˆyŠª<•9}U.”

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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 =

¶•03Ž¦;<T«₉ß

É+ •;<•0Š ©4.•/R ¶•03Ž¦;<T«_{9 •/R}

Off-Balance Sheet Leverage from Operating Leases

14. Adj. Fin Lev = U.¯ ’ •» 4m -•;9• ‰;P¦•0Š9_U.R

15. Adj. D-to-E ratio = U.”’•» 4m -•;9• ‰;P¦•0Š9_U.R

16. Adj. i-coverage Ratio =

R¶·U+”•‰ •O‰’V•0Š RO‰ Z •O‰’¯99ª¦•ˆ Z •O‰ 40 -•;9•9

Reading 21: Capital Budgeting

1. Depreciable Basis = Purchase price + any Shipping or handling or installation costs

Expansion Project

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

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

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)

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)

9. Profitability index = PI = 1 + (NPV/Initial investment)

when PI > 1, invest and when PI < 1, do not invest.

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

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

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

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 = áŠ\1_{(1’³¯©©)}R•Í Í

15. Total value of Co. = original investment + NPV

16. Residual income (RI) = NI – Equity Charge

(13)

where,

• MVA = _1’<V·Í

ÃÍ á Š\1

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

Claims Valuation

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

Reading 22: Capital Structure

1. WACC = r³¯©©=

”

» ×rˆ× 1 − t +

R » ×r•

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

3. WACC without taxes = r³¯©©= ”

»×rˆ + R »×r•

4. Cost of Equity = r•= ru+ (ru− rˆ)

” R

5. V = D + E =·0Š•<•9Š ‰;P¦•0Š9 40 ˆ•®Š _{©49Š 4m ˆ•®Š} +

(R¶·U – y0Š•<•9Š ‰;P¦•0Š9 40 ˆ•®Š) ©49Š 4m •¼ªyŠP

6. According to MM proposition I: V L = V U

and E = V – D

7. According to MM proposition II:

• Cost of Equity = r•= ru+ (ru−

rˆ)

” R

• V = D + E =

·0Š•<•9Š ‰;P¦•0Š9 40 ˆ•®Š ©49Š 4m ˆ•®Š +

(R¶·U – y0Š•<•9Š ‰;P¦•0Š9 40 ˆ•®Š)_{©49Š 4m •¼ªyŠP}

8. Systematic Risk = βa = ”_» βd + _» R βe • βe = βa + (βa – βd) (D/E)

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

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

• V L = V U + (t ×D)

• Value of Unlevered all equity Co. =

VU =R¶·U 1 – Š_<

æÈçç

• V = D + E =·0Š•<•9Š ‰;P¦•0Š9 40 ˆ•®Š_{©49Š 4m ˆ•®Š} +

(R¶·U – y0Š•<•9Š ‰;P¦•0Š9 40 ˆ•®Š)(1 – Š) ©49Š 4m •¼ªyŠP

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

• re = r0 + (r0 –rd)(1 – t) ” R

(r0 –rd)(1-t) = Slope coefficient *

*(r0- r d)(1 – t) < (r 0 - r d)

• WACC with taxes: rWACC = ”

» ×rd× (1 –

t)+R_»×re

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

distress)

Reading 23: Dividends & Share Repurchases Analysis

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

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+U_è

1+Uçé or ∆P = D 1+U_è 1+Uçé

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)}

5. Dividend imputation tax system: ETR = SH’s Marginal Tax Rate

(14)

Payout Policies: 7. Stable Div. Policy

• Expected ↑ in Div. = (Expected Earnings × Target payout ratio – Previous dividend) × Adj. factor • Adj. factor = 1/no. of yrs. over which

adj. in div. will take place

8. Residual Div. Policy

• Div. = Earnings – (Capital budget × Equity % in capital structure) or

• Div. = Zero, whichever is greater. 9. Div. Payout Ratio = ”y5._²·

10. Div. Coverage Ratio = _”y5.²·

11. FCFE Coverage Ratio =

†©†R

[”y5.’SŽ;<• V•‰ª<3Ž;9•9]

FCFE = CFO – FCInv + Net Borrowings

Reading 24: Corporate Performance, Governance & Business Ethics

Reading 25: Corporate Governance

1. Share Overhang =

²4.4m 9Ž;<•9 <•‰<•9•0Š•ˆ ®P ŠŽ• Ò‰Šy409 U4Š;- 04.4m 9Ž;<•9 4ªŠ9Š;0ˆy0•

Reading 26: Mergers & Acquisitions

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

X + Co. Y)

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

4. New shares issued by Acquirer =

ºTŠ 3;‰ 4m U;<••Š 9Š43T ‰<y3• 4m ¯3¼ªy<•<

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

6. Post-Merger EPS =

¯3¼ªy<•<«9 ‰<• ¦•<••< R;<0y0•9’U;<••Š«9 ‰<• ¦•<••< R;<0y0•9 •49Š ¦•<••< 0ª¦®•< 4m 9Ž;<•9 4ªŠ9Š;0ˆy0•

7. Post merger P/E (if market is efficient) =•<• ¦•<••< 9Š43T ‰<y3• 4m ¯3¼ªy<•<_{•49Š ¦•<••< R•S}

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

9. HHI = [ _{–íÔÕì cÕì×• íî íïÔðïÔ íñ òÕîw×Ô}cÕì×• íî íïÔðïÔ íñ —Zîò Z ×

Z

100 2

10. Unlevered NI = NI + Net Interest after-tax • Net interest after-tax = (i exp – i

income) × (1 – Tax rate) Or

• Unlevered NI = EBIT × (1- tax rate) • NOPLAT = Unlevered NI + ∆ in

deferred taxes

11. FCF = NOPLAT + NCC – ∆ in Net WC – Capex

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=

†©†Ç(1’•) (³¯©©_{ó‘ôõÌÍÃ‘}+•)

14. Using Market Multiple

Terminal ValueU= FCFU×

• †©†

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

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

(15)

= (Estimated stock price of Target based on Comparables) × (1 + Takeover premium in %)

18. Target Shareholders’ gain = Premium = P T

– V T

where,

P T = price paid for target company

V T = pre-merger value of target

company

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

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.

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

Reading 27: Equity Valuation: Applications & Processes

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

V)

• VE–P: Mispricing

• 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)

Reading 28: Return Concepts

1. Dividend yield or investment income = (DH/P0)

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

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,

• {(V0 – P0)/P0} = estimate of return

from convergence over period

7. IRR:

• Intrinsic value= D1 / (k-g)

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

8. Req ROE = Rf + ERP

9. GGM Intrinsic value = D1/ (k-g)

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 T-bonds) / (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

(16)

• 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.

• 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)

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

+Specific Co. premi

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

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

21. Cost of Capital = WACC = {D/(D+E)}rd

(1-Tax rate) + {E / (D+E)}rE

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)

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

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

7. Net debt = Gross debt – Cash and cash equivalents

8. Effective i rate = i exp / Avg gross debt

9. i rate on avg cash position =i income / Avg cash position

(17)

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

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

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

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 =Pre-cannibalization shipments – Expected cannibalization

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

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

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.

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

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

(18)

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

Reading 30: Discounted Dividend Valuation

1. Asset’s value is PV of its expected future CFs i.e. Vu= 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 =

• When HP is extended into indefinite future: Vu= áŠ\1_(1’<)”Í Í

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

” <

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

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

< + PVGO

where,

• PVGO =Sum of PV of expected profitable opportunities of reinvesting the earnings.

that represents growth opportunities.

(19)

12. Two-Stage Div Discount Model = Vu= ”_Í

(1’<)Í 0

Š\1 +

» -(1’<)

-where,

• V0=

”ù× 1’•ü -1’•ý <+•_ý

• Vu=

”ù(1’•ü)Í (1’<)Í 0

Š\1 +

”ù×(1’•ü)-×(1’•ý) 1’<-_(<+•

ý)

13. H-Model

• Vu=

”ù× 1’•ý <+•ý +

”ù×¬× •ü+•ý <+•ý or

• Vu=

”_ù× 1’•_ý ’ ”_ù×¬×(•_ü+•_ý) (<+•ý)

where,

gL= normal LT div. growth rate after

year 2H

gS= initial ST div. growth rate

H = half-life in years of the high-growth period i.e. high high-growth period = 2H years

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

• g =²·+”y5yˆ•0ˆ9_²· ×_S;-•9²· ×_{U4Š;- ¯99•Š9}S;-•9 ×

U4Š;- ¯99•Š9 SŽ;<•Ž4-ˆ•<9«_R¼ªyŠP

• g = PRAT i.e..

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

15. ROE =_{SŽ;<•Ž4-ˆ•<9}_«_•¼ªyŠP=_{U4Š;- ¯99•Š9}×

U4Š;- ¯99•Š9 SŽ;<•Ž4-ˆ•<«_{9 •¼ªyŠP}

=_S;-•9²· ×_{U4Š;- ¯99•Š9}S;-•9 ×

U4Š;- ¯99•Š9 SŽ;<•Ž4-ˆ•<9«_•¼ªyŠP =

= Net profit margin × Asset Turnover × Leverage

Reading 31: Free Cash Flow Valuation

1. PV of FCFF = Firm Value =

†©††Í

(1’³¯©©)Í á

Š\1

2. WACC = _{º» 4m ”’º» 4m R}º» 4m ” × rˆ × 1 −

Tax rate + º»4m R

º»4m ”’º»4m R× r•

4. Constant-Growth FCFF valuation Model =

Firm Value = Vu=

†©††_/ ³¯©©+•=

5. Constant-Growth FCFE valuation Model =

Equity Value = Vu=

†©†R/ <+• =

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:

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

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

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

(20)

• 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]

11. Incremental fixed capital expenditures as a proportion of sales increases =

12. Incremental working capital expenditures as a proportion of sales increases =

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)

14. Modified Build-Up method to estimate real discount rate:

Country return (Real) [in %] +/ - Industry Adjustment [in %]

+/ - Size Adjustment [in %] +/ - Leverage Adjustment [in %]

Required rate of return (real) [in %]

15. Single-Stage FCFF and FCFE Model for International Valuation:

Value of firm = Vu=

FCFFu×(1 + g<•;-)

WACC<•;-− g

<•;-= FCFF1

WACC<•;-− g

<•;-Value of Stock = Vu

=FCFEu×(1 + g<•;-)

r<•;-− g

<•;-= FCFE1

r<•;-− g

<•;-16. Two-stage FCFF valuation model equation is:

0 Š\1

1 (1’³¯©©)

-• Two-stage FCFE valuation model equation = Equity Value =

†©†RÍ (1’<)Í+

1 (1’<) -0

Š\1

17. Excess Cash = Total Cash Available − Total Assets of Firm×

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

Reading 32: Market based Valuation: Price & Enterprise Value Multiples

1. Trailing P/E or Current P/E =

3. Basic EPS =

_{³•ŽŠˆ ¯5• 04.4m 9Ž;<•9 ;3Šª;--P 4/9 ˆª<y0• ŠŽ• ‰•<y4ˆ}U4Š;- R;<0y0•9

4. Diluted EPS =

_{²4.4m 9Ž;<•9 4/9 ‡Ž•0 Ž4-ˆ•<9 4m}U4Š;- R;<0y0•9

•O3•<3y9•ˆ ŠŽ•y< 4‰Šy409 Š4 4®Š;y0 34¦¦40 9Š43T

5. Justified Forward P/E = P0/E1 = è/ É/ <+• =

1+® <+•

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

”_ù(1’•)/R_ù <+•

= 1+® ×(1’•)_<+• where

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

7. PEG ratio = _{RO‰•3Š•ˆ R;<0y0•9 “<4‡ŠŽ V;Š• y0 %}SŠ43T«9 •/R

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

(21)

CEY = current earnings yield on the mkt. index i.e. E/P.

CBY = current Moody’s Investors Service A-rated corporate bond yield.

LTEG = consensus 5-year earnings growth rate forecast for the mkt index.

"UR“

9. Own Historical P/E: Justified price = Benchmark value of own historical P/Es × Most recent EPS

10. Terminal Value (T.V) based on Fundamentals:

• T.V in yr n = (justified trailing P/E) × (forecasted earnings in year n) • T.V in year n = (justified leading P/E)

× (forecasted earnings in year n+1)

11. Terminal Value based on Comparables: • T.V in yr n = (Benchmark trailing

P/E) × (forecasted earnings in year n) • T.V in yr n = (Benchmark leading

P/E) × (forecasted earnings in year n+1)

12. P/B =_{¶44T »;-ª• ‰•< SŽ;<•}•<y3• ‰•< SŽ;<• where • BVPS for equity shareholders =

U¯ – U" – •.S

04.4m 34¦¦40 9Š43T 9Ž;<•9 4/9= S¬«₉«_{•¼ªyŠP – Š4Š;- •¼ªyŠP 5;-ª• 3-;y¦9}

* It includes preferred stock and div. in arrears on preferred stock. • BVPS for whole company =

Š4Š;- ;99•Š9 – Š4Š;- -y;®y-yŠy•9 0ª¦®•< 4m 9Ž;<•9 4ªŠ9Š;0ˆy0•

13. Justified P/B = P0/B0 = VÒR+•

<+•

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

1+•» 4m •O‰•3Š•ˆ mªŠª<• <•9yˆª;- •;<0y0•9_¶u

15. P/S =_{¯00ª;- 0•Š 9;-•9 ‰•< 9Ž;<•}•<y3• ‰•< 9Ž;<•

where Net Sales = Total Sales – returns– customer discounts

16. P/S ( in terms of Gordon Growth Model =

Justified P/S =•_Sù

ù = Éù

üù 1+® (1’•) (<+•)

where, E0/S0 = Business’s profit

margin

17. g = Retention rate (b) × ROE g = b × PM0 ×

S;-•9 U4Š;- ¯99•Š9 × U4Š;- ¯99•Š9

SŽ;<•Ž4-ˆ•<9«_R¼ªyŠP

where, PM0 = Profit Margin at t = 0

18. Price To Cash Flow

• =_{R;<0y0•9 ‰-ª9 0403;9Ž 3Ž;<••9}•<y3• ‰•< 9Ž;<• Or • = _{©;9Ž m-4‡ m<4¦ Ò‰•<;Šy409}•<y3• ‰•< 9Ž;<• Or • = •<y3• ‰•< 9Ž;<•_†©†R Or

• = •<y3• ‰•< 9Ž;<•_R¶·U”¯

19. Dividend Yield =”_•=_{•<y3• ‰•< 9Ž;<•}”y5 ‰•< 9Ž;<•

• Trailing Div Yield =

• Leading Div Yield =

20. Div Yield (by using GGM) = Justified Div Yield = ”u_•u = <+•_1’•

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 × 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 =Ò‰•<;Šy0• ‰<4myŠ ;mŠ•< Š;O_{U4Š;- y05•9Š•ˆ}

24. Earnings surprise UEt = EPS t – E (EPS t)

where,

(22)

EPSt= reported/actual EPS for quarter

t

E(EPSt) = expected EPS for the

quarter

• Percent Earning Surprise =

R;<0y0•9 Sª<‰<y9• RO‰•3Š•ˆ R•S

• Scaled Earnings Surprise =

R;<0y0•9 Sª<‰<y9• S.” 4m ;0;-P9Š9% •;<0y0•9 m4<•3;9Š

25. Standardized Unexpected Earnings = SUE

t =

R•SÍ +R (R•SÍ)

& [R•S_Í +R (R•S_Í)]

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 =_{••<m4<¦;03• 4m ;0 R¼ªyŠP ·0ˆ•O}SŠ43T«9 ‰•<m4<¦;03•

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

2. Residual Income (RI)

• = NI – Equity Charge = NI – (Equity Capital × Cost of Equity Capital)

• =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

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)

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 _(1’<)V·/_/+

V·_? (1’<)?+

V·'

(1’<)'+⋯

• Vu= Bu+ _1’<ÍÍ= á

Š\1 Bu+

R_Í+<¶_Ík/ (1’<)Í á Š\1

• Vu= Bu+

V·_/ (1’<)/+

V·_? (1’<)?+

V·'

(1’<)'+

⋯

6. RI Model (general) = Vu= Bu+ VÒR_Í+< ×¶_Ík/

1’<Í á

Š\1

7. Justified_¶•=•ù

¶_ù=

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 =_{V•‰-;3•¦•0Š 349Š 4m U4Š;- ¯99•Š9}º» 4m ”•®Š ;0ˆ R¼ªyŠP

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

<+• ×Bu

• Implied Growth rate in RI = g = r −

¶_ùVÒR+< »ù+¶ù

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 =_1’<+ V·Ç

* 1’<Çk/where, ω=

(23)

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

= V·Ç

terminal yr forward.

PV of continuing RI in year T-1

= V·Ç

approaches r over time (& RI will become 0 eventually). i.e. 0 ≤ ω ≤ 1

PV of continuing RI in year T-1=

V·Ç 1’<+* 1’<Çk/

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

Reading 34: Private Company Valuation

+

• Value of Equity = Vf – MV of Debt

• To value Equity directly = V = _<+•/

2. Excess Earnings or RI = Normalized earnings – [(RR on WC × value of WC) + (RR on fixed assets × value of fixed assets)]

3. MVIC = MV of Debt + MV of Equity

4. Calculation of Lack of Control Discount =

5. Lack of Marketability Discount = DLOM =»;-ª• 4m _{5;-ª• 4m 9Š43T ®•m4<• ;0P ”}";Š–ŠŽ•–¦40•P" ‰ªŠ 4‰Šy40

"Òº

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

Reading 35: The Term Structure & Interest Rate Dynamics

4. Spot rate for a security, having maturity of T > 1

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

Forward rate model can be expressed as:

1 + 𝑟 𝑇∗_{+ 𝑇}

5. Yield Curve Movement and the Forward Curve

Active Bond Portfolio Management

6. 1-yr. HPR = 1’î –’1_{1’ñ 1,–}•Ï/_• = 1 + 𝑟(1)

(when the spot curve one year from today is today’s forward curve)

7. Return of the 2-year zero-coupon bond over 1-yr HP =

•<y3• 4m ; >+P< ¥•<4+34ª‰40 ®40ˆ 1 P< m<4¦ Š4ˆ;P •ª<3Ž;9• ‰<y3• 4m ®40ˆ −

(24)

• Price of a 2-yr zero-coupon bond 1 yr from today =

˜Õî/Õìï×íñ0í[1

(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/_{1’ñ 1,>}Õìï×íñ0í[1

8. Swap Spread = Fixed-rate of an interest rate swap – Interest rate on “on-the-run” Govt. security

•

• (–) 1’î Ô Í+

1 1’î –• –

Ô\1

↓ 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 = _{˜ (Ô,–)}1 =

1 + 𝑟 1 1 +𝑓 1,1 1 +𝑓 2,1 1 +

𝑓 3,1 …[1 +𝑓 𝑇 − 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

15. Interest rate volatility for a security with maturity T at time t = σ (t, T) = <

∆= (~.•)

= (~,•) ∆Ô

Reading 36: The Arbitrage Free Valuation Framework

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

ù× ∆,

7. Convexity = »Ï_{>× »}’»k+ >×»ù

ù× ∆,?

>

9. Effective Convexity = k_∆ Ï ù

@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 =

(25)

19. Premium Payback Period =

20. Favorable Income Differential per share =

21. Premium over straight value =

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

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 =

S

_t

=

A

_t

N

₍

d

₁

₎

−

ke

−r(T−1)

N

₍

d

₂

₎

co.’s debt if default occurs + PV of payoff on co.’s debt if default does not occur =

)

probability of the co.’s debt not defaulting

6. Credit Risk Measures

• Probability of the debt defaulting = Prob. (AT< K) = 1 – Prob. (AT ≥ K) =

(Expected R per year on Mkt. portfolio – Rf)

9. Credit risk measures in reduced form model:

10. Historical Estimation

(26)

• Parameters estimation: arbitrage and frictionless markets)

BG (t) =

∑

zero-coupon bond – Avg. yields on riskless zero-coupon bond

Or

= [Average yields on the risky zero-coupon bond – Average yields on riskless zero-coupon bond] + Liquidity premium or

= Expected % loss per year on the risky zero-coupon bond + Liquidity Premium

13. PV of expected loss = PV of CF of riskless debt – PV of CF of risky debt = [P (t,T) – D (t,T)] XT

Where, XT = Promised CF at T of a risky

Co.

Reading 39: Credit Default Swaps

1. Upfront premium = Credit spread – Standard rate

2. Expected Credit Loss (%) = Payout ratio = 1 – Recovery rate (%)

3. Expected Credit Loss Amount or Payout amount = Payout ratio × Notional amount

4. Loss Given Default:

• Expected loss = Full amount owed – Expected recovery

• Expected loss = Loss given default × Probability of default

• Prob. of default (at some point during T years) = 1 – Prob. of no default during T years

5. Value of protection leg = Expected payoff of bond/loan with credit risk - Expected payoff of bond/loan with no credit risks

6. Value of premium leg = PV of pmts. made by the protection buyer to the protection seller

7. Upfront pmt = PV of protection leg – PV of premium leg

8. Credit spread ≈ Prob. of default × Loss given default (%)

9. Credit spread Pricing Conventions

• Upfront premium = PV of credit spread – PV of fixed coupon Or = (Credit spread – Fixed coupon) × D of the CDS

• PV of credit spread = Upfront prem. + PV of fixed coupon

• Credit spread ≈ (Upfront prem./D) + Fixed coupon

• Upfront premium in % = 100 – Price of CDS in currency per 100 par • Price of CDS in currency per 100 par

*Bond’s Credit spread = Yield on bond - Investor’s cost of funding

Bond yield = Rf rate + Funding spread +

Credit spread

where, Rf + Funding spread = LIBOR