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1


Fixed income
Term Structure and Interest Rate Dynamics:
Forward Rates:
T* = When loan is initiated
T = Tenor of the loan
Forward rate = (when loan is initiated, tenor of loan)
= (time until initiation + tenor) / (tenor of loan)
The forward rate (Breakeven Rate):

Par: The rate to discount multiple cash flows to get the present value of
the bond (market price) this is also the YTM for Coupon paying bonds
Spot: The rate to discount individual cash flows at given maturities – it

is the YTM for a zero coupon bond.
The key that links the spot curve to the par curve is that you have to get
the same price whether you use the par curve or the spot curve
(otherwise, there would be an arbitrage opportunity). The spot curve is
derived from the par curve with this relationship in mind; the process to
derive the spot curve is called bootstrapping.
The first observation is that the forward contract price remains
unchanged as long as future spot rates evolve as predicted by today’s
forward curve

The level movement refers to an upward or downward shift in the yield curve.
The steepness movement refers to a non-parallel shift in the yield curve when either shortterm rates change more than long-term rates or long-term rates change more than short-term
rates.
The curvature movement refers to movement in 3 segments of the yield curve: the short-term
and long-term segments rise while the middle-term segment falls or vice versa.
Principal Component Analysis:
The method to determine the number of factors—and their economic interpretation—begins with
a measurement of the change of key rates on the yield curve, The next step is to try to discover a
number of independent factors (not to exceed the number of variables—in this case, selected
points along the yield curve) that can explain the observed variance/covariance matrix.
PCA creates a number of synthetic factors defined as (and calculated to be) statistically
independent of each other

Zero Spread or Z – Spread: Constant basis point spread that would need to be added to the implied spot yield curve so that the discounted cash flows of a bond is equal to its
current market price. For credit / Liquidity risk

The N square root = the tenor of the loan
f(1,2) is this example is the Breakeven Rate = the rate at
which
an investor

impartial
to investing for 3 years
The
Forward
pricewould
from abeforward
rate:
or for 2 years starting in 1 year. It’s a forward rate which we
derive from the sport rate curve.

Forward Price:

Swap Spread = (Swap Rate – On the run Gov Bond Yield) It’s added on to the Government Bond Yield – covers liquidity and credit risk.
Ted Spread = (Libor – T-bill) this measures the overall credit risk of the economy (related to economic cycles)
Libor–OIS spread is considered an indicator of the risk and liquidity of money market securities / Measure of counterparty risk and risk in banking system
Equilibrium term structure models
One-factor or multifactor models - Assume that a single observable factor (state variable) drives all yield curve movements. Both the Vasicek and CIR models assume a single
factor, the short-term interest rate. Note that because both models model require the short-term rate to follow a certain process, the estimated yield curve may not match
the observed yield curve. But if the parameters of the models are believed to be correct, then investors can use these models to determine mispricing.
Modern Term Structure Models: (Explains how interest rates evolve)

The Cox–Ingersoll–Ross Model: CIR = dr=a(b−r)dt+σ√rd
b = mean reverting level

T* = Period when loan is initiated = this is a discount factor now
T = Tenor of the loan = (this is a discount factor now) = (1/1+r)
Following the same principles above

Bootstrapping:
100 = (coupon / 1+spot1) + (Par and coupon / 1+ spot2^2)

Spot1 = Par1 hence It is given.
Spot2 = [Par + coupon / (1 – coupon/1+spot1)] - 1
Then take nth square root which 2 In this case
Once identified repeat steps to find spot etc…
The coupons will differ as the bonds on the par curve will differ

Assumes Economy has a constant long-run interest rate that the short-term
interest rate converges to over time.
 Interest Rates are non-negative
 Volatility increases with level on interest rates
 Explains interest rate movements in terms of an individual’s preferences for
investment and consumption as well as the risks and returns of the
productive processes of the economy.
 Assuming that an individual requires a term premium on the long-term rate,
the model shows that the short-term rate can determine the entire term
structure of interest rates and the valuation of interest rate–contingent
claims.
 σ√rdz = stochastic or volatility term which follows the random normal
distribution for which the mean is zero, the standard deviation is 1, and the
standard deviation factor is σ√r

Term Structure of the Interest Rate Volatility:
Short End: More linked to uncertainty about monetary policy
Long End: More linked with uncertainty about real economy and
inflation
CIR and Vsicek - both have the same drift tern but differ in terms
of stochastic terms.

The Vasicek Model: dr = a(b – r)dt + σdz Also captures mean reversion
 Interest rates are calculated assuming that volatility remains constant

over the period of analysis. Interest Rates can be negative.
 The stochastic or volatility term, σdz follows the random normal distribution
for which the mean is zero & the standard deviation is 1
σdz = volatility term

Arbitrage-free models, the analysis begins with the observed market prices. An
assumed random process with a drift term and volatility factor is used for the generation
of the yield curve.
This calibration is typically performed via a binomial lattice-based model in which at
each node the yield curve can move up or down with equal probability. This probability is
called the “implied risk-neutral or “risk-neutral probability. Similar to Black-Scholes
Model
Term Structure Model: Explain the shape of the curve at a point in time
 Unbiased expectations theory - Forward rates are an unbiased predictor of future
spot rates. Also known as the pure expectations theory.
 Local expectations theory - Bond maturity does not influence returns for short term
holding periods. Returns for all Bonds are the same over short term.
 Liquidity preference theory - Investors demand a liquidity premium that is positively
related to a bond's maturity. Long-term rates will be higher than investors'
expectations of future rates
 Segmented markets theory - The shape of the yield curve is the result of the
interactions of supply and demand for funds in different market (i.e., maturity)
segments.
o
Segmented markets theory contends that asset/liability
management constraints force investors to buy securities whose
maturities match the maturities of their liabilities.
 Preferred habitat theory - Similar to the segmented markets theory, but recognizes
that market participants will deviate from their preferred maturity habitat if
compensated




2


Arbitrage Free Valuation Framework
The first type of arbitrage opportunity is often called value additivity or, put simply, the value of the whole equals the sum of the values of
the parts.

Binomeial Tree:
Not appropriate for MBS because it is not path dependent

Dominance Arbitrage Opportunity:

Value 1L = (½) [(V2U + C) / (1 + r1L)] + [(V2L + C) / (1 + r1L)]

T0:
T1:
Bond A
100
105
Bond B 200
220
Bond B is dominant as I can sell (2*bond) to finance 1 Bond B which will return 10% at maturity.

High Node = Middle Node x ( e N x volatility)
Low Node = Middle Node / ( e N x volatility)
N = Maturity of Bond
Pathwise Valuation:


Compare current market price vs No Arbitrage price. No Arb price as PV, with coupon = PMT and F = zer0 and N = Maturity

Pathwise valuation calculates the present value of a bond for each possible interest rate path and takes the
average of these values across paths.

One of the benefits of a lognormal distribution is that if interest rates get too close to zero, the absolute change in interest rates becomes
smaller and smaller. Negative interest rates are not possible.

Number of paths = 2 (number of cash flows – 1)

Use Binomial if bonds have options.
Ratchet bonds are floating-rate bonds with both issuer and investor options. Ratchet bonds, in a nutshell:

Coupon rate starts very high: much higher than the borrowing rate for the issuer

There’s a formula for resetting the coupon rate periodically

The rate can remain the same or decrease at a reset date; it cannot increase

Whenever the coupon is reset lower, the bondholder has an option to put the bond at par.
You can think of the reset as a sort of call option: the issuer calls the existing bond and replaces it with another callable bond that has a
lower coupon rate, and the same maturity as the existing bond

Steps:
1. Specify a list of all potential paths through the tree
2. Determine present value of a bond along each potential path
3. Calculate the average PV Bond Price across all possible paths

Monte Carlo Simulation:

Used to simulate sufficinetly large number of intrest rates paths. Use it when cash flows are path dependent e.g.
when the cash flow change depending on where the intres rates are.
In MBS as interest rate drops , prepayment goes up.

Parallel shift in the yield curve will impact the effective duration of a portfolio hence portfolios with the same effective duration should
have the same change in price.

1.Simulate numerous paths based on probability assumption
2.Generate sport rates from the simulation
3.Determine cf for all paths and compute present value
Add a constant to all spot rates at each paths so value = market value

When you have a long position in a forward or futures contract, you have, in essence, already purchased the underlying asset (you simply
haven’t paid for it yet); therefore, you have positive duration. If you have a short position in a forward or futures contract, you have, in
essence, already sold the underlying asset (you simply haven’t been paid for it yet); therefore, you have negative duration. Furthermore, the
duration will be comparable to that of the underlying bonds.
(Slightly different because these contracts don’t transfer ownership of the interim coupon payments, but comparable.)
The same holds true for options: if you’re long calls or short puts, you have positive duration; if you’re short calls or long puts, you have
negative duration. Here, however, the duration will be shorter – possibly much shorter – that that of the underlying bonds; it will depend on
the option’s delta.

3


Valuation: Bonds with embedded options
Convertibles
Forced Conversion:
Issuer will call the bond when the underlying share price increases above the
conversion price in order to avoid paying further coupons.
Conversion Ratio:

Par Value / Conversion Price
Conversion value:
Current Market Share Price × Conversion ratio
Minimum Value of a Convertible Bond:
Conversion value or the option-free straight bond value
Market conversion price:
Current Convertible Bond Market Price / Conversion ratio
Market conversion premium per share:
Market conversion price – Current Market Share Price
Market conversion premium ratio:
Market conversion price / Underlying share price
Premium over straight Value:
Current Convertible Bond Market Price / Straight Bond Price
Underlying Share Price > Conversion Share:
Bond exhibits mostly stock risk–return characteristics. The call on the underlying is
ITM and hence the price movements of the stock have significant impact on the
bond. The bond is more likely to be exercised by the bondholder.

Binominal Calibration:
Iteration of discount rates until the value of the bond = market value of the bond

Soft Put:
The issuer may redeem the convertible bond for cash, common stock, subordinated
notes, or a combination of the three.

What Is Volatility and How Is It Estimated
1. Estimating historical interest rate volatility by using data from the recent past with the assumption that what has happened recently is indicative of
the future.
2. Estimate interest rate volatility is based on observed market prices of interest rate derivatives (e.g., swaptions, caps, floors). This approach is called
implied volatility.


Callable Convertibles:
The issuer may the call option and redeem the bond early if interest rates are falling
or if its credit rating is revised upward and issue new debt at a lower cost.
Busted Convertible = Call is OTM

Constructing the Binomial Interest Rate Tree
Describe the process of calibrating a binomial interest rate tree to match a specific term structure
Assume that volatility

Underlying Share Price < Conversion Share Price. Bond exhibits mostly bond risk–
return characteristics. Call is OTM and hence share price movements have limited
impact. This is stronger when there is less time to maturity.

4


OAS:
Added to the one-period forward rates on the tree to produce a value or price for
a bond OAS = Average spreads over the Treasury spot rate curve.
1.
2.
3.

Identify the impact the change in interest rate volatility will have on
the option and Bond Price at the old and new volatility assumption.
Assuming r is constant (1+r+OAS), compare the OAS that needs to be
added to get market price using (Bond Price / (1+ r) + OAS).
Market Price will be lower because it is discount by (1+r+OAS).


If two bonds have the same characteristics and credit quality, they should have
the same OAS. If not the bond with the largest OAS is likely to be underpriced
relative to the bond with the smallest OAS.
Z-Spread:
= OAS - Option Cost
Option Free Bond = [Credit Spread +Liquidity Spread]
Callable Bond
= [Credit Spread + Liquidity Spread] - Option Cost
Putable Bond
= [Credit Spread+ Liquidity Spread] - Option Cost

As interest rates decline, the value of the straight bond rises, but the rise is
partially offset by the increase in the value of the call option. Call option will be
ITM because it is likely to be called by Issuer.
Rate of Price Rises when Interest Rates Decline:
Straight Bond > Callable Bond > Putable Bond
Rate of Price Rises when Interest Rates Rise:
Straight Bond > Putable Bond > Callable Bond
The decrease in the bond price is partially offset by the put, but net the price of the
putable will decrease.
Shape of Yield Curve:
Flattens/ Invents = call option is ITM and gains in value (Bond is less likely to be
called)
Upward sloping = put is ITM gains in value (Bond is more likely to be put)

The Option cost for a put is negative and the option cost for a call is positive hence
the OAS for all 3 will be the same. It is the change in Option cost that increases or
decreases the Z –spread and hence the discount rate for the Bond.
Estate Puts (Death Puts):
Putable by the heirs after the death of the bondholder Bond Value hence depends

on life expectancy as well as interest rate movements.
A prime example is a sinking fund bond (sinker), which requires the issuer to set
aside funds over time to retire the bond issue, thus reducing credit risk.
From the issuer’s perspective, the combination of the call option and the delivery
option is effectively a long straddle.

One-sided durations—that is, the effective durations when interest rates go up or
down—are better at capturing the interest rate sensitivity of a callable or putable
bond than the (two-sided) effective duration, particularly when the embedded
option is near the money.
Bond will be more sensitive to one direction of interest movement – which is the
direction with the highest durations.
Key rate durations (partial durations), which reflect the sensitivity of the bond’s
price to changes in specific maturities on the benchmark yield curve. Thus, key
rate durations help identify the “shaping risk” for bonds—that is, the bonds
sensitivity to changes in the shape of the yield curve (e.g., steepening and
flattening). Can be -ve
Key rate duration for a Par Bond = rate matching the tenor of the Bond.
So a 10 year par bond would only be affected by 10 year key rate.
Callable Bond = Bond - Call
Puttable Bond = Bond + Put
Callable and Puttable = Bond – Call + Put
Convertible = Bond + Call
Value of floored floater = Value of straight bond + Value of embedded floor
Bondholder option Protects against rate decreases

Positive Convexity:
When interest rates are high and the value of the call option is low, the callable
and straight bond both has positive convexity.
Negative Convexity:

Only call option near the money. The reason is because when interest rates
decline, the price of the callable bond is capped by the price of the call option if it
is near the exercise date.
Putable bonds have more upside potential than otherwise identical callable
bonds when interest rates decline. In contrast, when interest rates rise,
callable bonds have more upside potential than otherwise identical putable
bonds
Zero-volatility spread is a commonly used measure of relative value for MBS
and ABS

Value of capped floater = Value of straight bond - Value of embedded cap
(Issuer option) Protects against rate increases because the coupon rate is capped
at a specific rate
As a consequence, a sinking fund bond benefits the issuer not only if interest rates
decline but also if they rise.
Putable and extendible bonds are equivalent, except that their underlying optionfree bonds are different.

5


Credit Analysis Models
The expected loss is equal to the probability of default multiplied by the loss given default
The present value of the expected loss is the largest price to pay on a bond to a third party (e.g., an insurer) to entirely
remove the credit risk of purchasing and holding the bond. Uses Risk-neutral probability
The present value of the expected loss is the preferred measure because it includes the:
-Probability of default
-Loss given default
-Time value of money
-Risk premium in its computation


Importance
1. PV of expected loss
2. Expected loss
3. Default probability

Traditional Credit Models:
Credit scoring – Ordinal:
Ranks most risky to least risky
Credit Rating- does not provide an estimate of the loan’s default probability
Negative: not explicitly depend on the business cycle
Asset Backed Securities: Do no default when payment is missed.
Unlike corporate debt, an ABS does not go into default when an interest payment is missed.
Structural or Reduced Form or Monte Carlo to Value
The credit risk measures used for corporate or sovereign bonds can be applied: probability of loss, expected loss, and present
value of the expected loss. Probability of Default does not apply
Monte Carlo:
A constant is added to all interest rates on all paths such that the average present value for each benchmark bond equals its
market value.
Structural Models:
Balance sheet structure: 1 debt (zero-coupon bond) and assets
Equity owners: Equivalent to holding a long European call option on firm’s assets
Debt owners: Equivalent to holding risk free bond selling European put on firm’s assets

Reduced Form Models: Nothing is constant
Reduced form models were originated to overcome a key weakness of the structural model the assumption that the
company’s assets trade.

The riskless rate of interest is stochastic

The state of the economy can be described stochastic variables that represent the macroeconomic factors

influencing the economy

Default Probability is also stochastic
The second assumption allows interest rates to be stochastic. Allowing for this possibility is essential to capture the interest rate
risk inherent in the pricing of fixed-income securities. Only the term structure evolution must be arbitrage free.
For a given state of the economy, whether a company defaults depends only on company-specific considerations, because given
the macroeconomic state variables, a company's default represents idiosyncratic risk. A company-specific action could be that
the company’s management made an error in their debt choice in years past, which results in their defaulting now.
Management error is idiosyncratic risk, not economy-wide or systematic risk. The loss given default explicitly depends on the
business cycle through the macroeconomic state variables. This allows, for example, that in a recession the loss given default is
larger than it is in a healthy economy. This assumption is also very general and not restrictive.
(PV expected loss > Expected Loss) = Risk Premium is dominant In other words, in the absence of a risk premium; the present
value of the expected loss will be less than the expected loss.
Can use Historical Estimation = Hazard rate estimation is a technique for estimating the probability of a binary event, like
default/no default. More flexible than implicit estimation
Using the reduced form model, the value of debt is determined by calculating the expected discounted value of debt after
adjusting for risk.
Value of the company’s debt = Expected discounted payoff of company debt, if there is no default
+Expected discounted payoff of debt if default occurs
Historical Estimation: one uses past time-series observations of the underlying asset’s price and standard statistical
procedures to estimate the parameters.

Assumptions

the company’s assets trade in frictionless markets that are arbitrage free,

the riskless rate of interest, r, is constant over time ( means there is no interest rate risk)

the time T value of the company’s assets has a lognormal distribution


Implicit Estimation: also called calibration, uses market prices of the options themselves to find the value of the parameter
that equates the market price to the formula’s price. Uses Black-Scholes model – hence no risk premium has to be estimated.
The problem with implicit estimation, of course, is that if one uses a misspecified model that is inconsistent with the market
structure then the resulting estimates will be biased. This problem can be avoided by historical estimation.

The probability of default depends explicitly on the company’s assumed liability structure. This explicit dependency of the
probability of default on the company’s liability structure is a limitation of the structural model. The fact that one needs to
estimate the markets equity risk premium in the computation of the company default probability is a weakness of the
structural model.

Expected Loss: Notional * 1-e- default density * loss given default * N
Probability of Default: 1 – e- default density * N

Negatives:
- Can’t use historical estimation – because asset prices are not observable (they do not trade)
- Balance sheet will have a liability structure much more complex than zero-coupon bond
- Interest rates are not constant over time
- The asset’s return volatility is constant, independent of changing economic conditions/ business cycles
-Credit risk measures are biased because implicit estimation procedures inherit errors in the model's formulation

6


Credit Default Swaps
Credit Default Swaps:
The designated instrument is usually a senior unsecured obligation, which is often referred to as a senior CDS, but the reference
obligation is not the only instrument covered by the CDS. Any debt obligation issued by the borrower that is pari passu (ranked
equivalently in priority of claims) or higher relative to the reference obligation is covered.
CDS Index:
↑credit correlation = ↑cost of insurance

CDS Spread / Credit Spread:
Periodic payments from buyer to seller ≈ Probability of default x loss given default bps
Long / Short:
Hence, the CDS industry views the credit protection seller as the long and the buyer as the short. This point can lead to confusion
because we effectively say the credit protection buyer is short and the credit protection seller is long.
Credit Events (decided by a committee):
Filing of Bankruptcy
Failure to Pay scheduled interest or principle
Restructuring change in seniority or reduction in coupon / principle forced on the borrower (not a default event in the US)
Succession Event:
Event that changes the debt issuer or structure of the reference entity is and their obligations.
Payout ratio = (1 – Recovery rate (%)
Payout amount = (pay-out ratio × Notional)
(N / N of Index Entities)* Notional = Exposure to Specific Entity
If a firm in the Index defaults, remove (Notional/ N of Index) * Notional from Notional
Index CDS are typically more liquid than single-name CDS

The hazard rate is the probability that an event will occur given that it has not already occurred. Once the event occurs,
there is no further likelihood of its occurrence
Probability of survival: p (%) in year 1 * p (%) in year n
Upfront payment = (PV of protection leg – PV of premium leg)
Upfront premium % ≈ (Credit spread – Fixed coupon) × Duration
= (100 – Price of CDS in currency per 100 Par)
Credit Spread = Upfront Payment / Duration + Fixed Coupon
Price of CDS in currency per 100 par = (100 – Upfront premium %)
Profit for the buyer of protection ≈ (Change in spread in bps * Duration * Notional)
Alternatively % Change in CDS price = (Change in spread in bps × Duration)
The CDS indices also permit some opportunities for a type of arbitrage trade. If the cost of the index is not equivalent to
the aggregate cost of the index components, the opportunity exists to go long the cheaper instrument and short the more
expensive instrument.

Basis Trading: CDS is the base
CDS spread > Bond Credit Spread
Positive Basis = short bond (pay 1.5%) and sell CDS to profit (receive 3%) Profit = ∆
CDS spread < Bond Credit Spread
Negative Basis = long bond (receive 3%) and buy CDS (pay 1.5%) Profit = ∆
Don’t Forget: (Bond Yield – Libor) = Credit Spread of the Bond

CDS:
Sell = long
Buy = short

Curve Trading:
Buying a CDS of one maturity (deteriorating credit) and selling a CDS on the same reference entity with a different
maturity (improving credit)

Cheapest to deliver = Bond trading at lowest of notional meaning where the % par value is the lowest
If bond trades 25% of par and there was another bond trading at 40% of par the 25% of par would be cheapest to deliver. The
maturity is not relevant in choosing the cheapest to deliver it’s the priority if claims that’s important.

index CDS are typically more liquid than single-name CDS

7


INTERCORPORATE INVESTMENTS

AFS
HFT

FVPL


DFV
HTM

Balance Sheet

Income Statement

OCI

Market Value

Interest Payments

Unrecognised P/L
FV – Amortised Value (for debt)

Market Value

Unrecognised P/L and
Interest Payments

Amortised Cost

Effective rate * cost

Equity Method:
ROA and ROE are Higher because Assets and Equity (Denominator is lower)

Liabilities and leverage = Lower


Net Profit Margin, ROE, and ROA = Higher

D/E is also ↓because Equity under Acquisition method includes the non-controlling stake so numerator is ↑

Current Ratio is ↑due to lower denominator
US GAAP:
IFRS
Allows to value at FV under Equity Method
Only Allows FV for VC’s, mutual funds etc
The choice of equity method or proportionate consolidation does not affect reported shareholders’ equity

Consolidation Process:
Non-controlling investments: Reversals are prohibited under both IFRs and US GAAP
Acquirer takes 100% of Targets:

Tangible and Intangible Assets at FV (includes measureable and probable contingent assets and liabilities)

Current Assets at FV

Liabilities at FV

Revenues

Expenses

Remove costs paid for target from cash on Acquirer’s IS

Among the other factors that are considered in determining whether the Group has significant influence are representation on
the board of directors (supervisory board in the case of German stock corporations) and material intercompany transactions.

The existence of these factors could require the application of the equity method of accounting for a particular investment even
though the Groups investment is for less than 20% of the voting stock.
Under US GAAP, an acquirer is identified, but the business combinations are categorized as merger, acquisition, or
consolidation based on the legal structure after the combination

Minority interest = (the proportion not owned of Target) x (Equity of Target)
If Acquirer does not owe 100%, remove proportion of income not owed from Income Statement

Control is present when
1) The investor has the ability to exert influence on the financial and
2) Operating policy of the entity is exposed, or has rights, to variable returns from its involvement with the investee

Assuming Consolidation:
Acquirer Shareholder Equity Post Merger = (Capital Stock + Value of stock paid for target + Retained Earnings)
Value of stock paid for target = Portion bought + non-controlling interest

Contingent Assets and Liabilities:
Both IFRS and US GAAP do not re-measure equity classified contingent consideration; instead, settlement is accounted for
within equity.

Acquisition Method Equity will be higher by the amount of the minority interest. Assets and Liabilities are highest here

Under IFRS, the cost of an acquisition is allocated to the fair value of assets, liabilities, and contingent liabilities. Contingent
liabilities are recorded separately as part of the cost allocation process, provided that their fair values can be measured reliably.
Subsequently, the contingent liability is measured at the higher of the amount initially recognized or the best estimate of the
amount required to settle.

ROA and ROA will be different under Partial Goodwill compared to Full Goodwill. This will change over time as the results of
change in equity
Differences between IFRS and U.S. GAAP treatment of intercorporate investments include:


Unrealized foreign exchange gains and losses on AFS securities are recognized on the IS under IFRS and as OCI
under U.S. GAAP.

IFRS permits either the partial goodwill or full goodwill method to value goodwill and non-controlling interest in
business combinations. U.S. GAAP requires the full goodwill method
Restructuring Cost
IFRS and US GAAP do not recognize restructuring costs that are associated with the business combination as part
of the cost of the acquisition. Instead, they are recognized as an expense in the periods the restructuring costs are
incurred

IFRS

FVPL or FVOCI
HTM

Reclassification from HFT is severely restricted

→

Reclassification from HFT is severely restricted

←

←
→

Under the full method (IFRS and US GAAP), minority interest is (% x Fair Value of Target)
Under the partial method (only IFRS), minority interest is (% x Fair Value of Net Assets)


US GAAP

Off Balance sheet financing:
SPE / SPV have to be consolidated if a firm (sponsor) has significant beneficial interest in the SPE even if no voting
rights

Move gains & loss from OCI into IS on date of transfer
∆ in Value (FV – Amor Cost) reported in IS

←

`

Contingent assets: Measured at the lower of acquisition date fair value or the best estimate of the future settlement amount.

AFS

→
← →

Reclassification from HFT is severely restricted

Previous ∆ in Value from OCI are amortised
using effective rate method in IS
∆ in Value (FV – Amor Cost) reported in OCI

HFT

Under US GAAP, contractual contingent assets and liabilities are recognized and recorded at their fair values at the time of
acquisition. Non-contractual contingent assets and liabilities must also be recognized and recorded only if it is more likely than

not and they meet the definition of an asset or a liability at the acquisition date. Subsequently, a contingent liability is
measured at the higher of the amount initially recognized or the best estimate of the amount of the loss.

Cumulative P/L previously recognized in other OCI is
recognized in IS
Previous ∆ in Value from OCI are amortised using
effective rate method in IS
∆ in Value (FV – Amor Cost) reported in OCI

If an SPE is reversed, on the consolidated balance sheet, the accounts receivable balance will be the same since the
sale to the SPE will be reversed upon consolidation on the balance sheet. Hence consolidating an SPV reverses it
US GAAP only: VIE When below points are present
1. Has to be consolidated when total equity at risk is insufficient to finance equity without outside support
2. Equity investors lack ability to make decisions and lack obligation to absorb losses
Sponsor = party absorbing majority of losses / retains risk of default.
Under IFRS, SPEs cannot be classified as qualifying

8


Acquisition Method Goodwill: Measurement

Goodwill Impairments

IFRS Partial Goodwill
Fair value of consideration
80% of Fair value of identifiable Net assets
Goodwill recognized

800,000

720,000
80

IFRS and US GAAP Full Goodwill
Fair value of entity
Fair value of identifiable Net Assets

1,000,000
900,000

Goodwill recognized

100,000

Partial Goodwill = lower Equity hence higher Debt / Full Goodwill = higher Equity hence lower Debt
Bond Amortisation:
Amortisation of coupon = (Interest Paid – Interest Income)
Interest Paid = (Coupon x begin Par)
Interest Income = (Effective market rate x Cost) what we actually get
If Bond is purchased at a premium, deduct amortisation every year until it reaches par at maturity
If Bond is purchased at a discount, add amortisation every year until it reaches par at maturity
HTM Ending BS Value = Amortised Bond Value
Unrealised P/L = (MV – Amortised Value) which goes into OCI

Effective Interest Rate Method:
Beginning Value of a Bond issued at Premium or Discount after N periods
PMT => Coupon
FV => Notional
I/Y => Effective Rate
N => (Years to maturity at issuance – years gone by since)

PV = Bond Amortised Value at N period after issuance

IFRS: Cash generating Units
Recoverable Amount < Carrying Value = Impairment
Record ∆ and deduct from Goodwill Amount allocated until its zero. Then reduce non-cash assets
US GAAP: Reporting Unit
1. (Fair Value < Carrying Amount) = Impairment
2. (Carrying Amount of Goodwill - Implied FV of Goodwill) = Cash Amount of Impairment
3. (Fair Value – Net Identifiable Assets) = Implied Goodwill

Fair value of reporting unit

1,300,000

Less: net assets

1,200,000

Implied goodwill

100,000

Current carrying value of goodwill

300,000

Less: implied goodwill

100,000


Impairment loss

200,000

After the goodwill of the reporting unit has been eliminated, no
other adjustments are made automatically to the carrying values of
any of the reporting unit’s other assets or liabilities.
Under both IFRS and US GAAP, the impairment loss is recorded as a
separate line item in the consolidated income statement

IFRS and US GAAP recognize in-process research and development acquired in a business combination as a separate intangible asset and
measure it at fair value (if it can be measured reliably)
Reversal of impairments Financial Assets:
IFRS
Available for sale = Equities No reversals
= Debt can be reversed if increase in FV can be objectively related to an event occurring after the impairment loss
HTM
= Reversals allowed up to original value
Reclassification of equity securities under the new standards is not permitted as the initial designation (FVPL or FVOCI) is irrevocable

Equity Method Goodwill in Purchase Price when Investment in Excess of Book Value
Purchase price

100,000.00

- Ownership % * book value of target equity

66,000.00

= Excess purchase price


34,000.00

Attributable to net assets
(MV – BV) of Plant and equipment * % ownership

9,000.00

(MV – BV) of Land * % ownership

6,000.00

Goodwill (residual)

19,000.00

Excess purchase price

34,000.00

This method is used when (BV ≠ MV) and there is an excess over book value.
The additional step is to amortise the value of the excess purchase price over the relevant period and exclude
it from the income that is going to the acquirer. The excess will be attributable to PPE or Land most likely.
Value of Investment in Associate using Equity Method* only time we use amortisation of excess
Purchase Price
+Acquirer share * Net Income
- Acquirer share * dividends paid
-Amortisation of excess (because BV ≠ MV)
Ending BS Value


US GAAP:
No Reversals for Financial Assets
Available for sale = Reversals are allowed but cannot exceed new cost basis on P/l instead any reversals beyond go into OCI
The disappearance of an active market because an entity’s financial instruments are no longer publicly traded is not evidence of impairment.
Impaired Equites:
Significant changes in the technological, market, economic, and or legal environments that adversely affect the investee and indicate that the
initial cost of the equity investment may not be recovered. A significant or prolonged decline in the fair value of an equity investment below its
cost
Business Model Test:
To be measured at amortized cost, financial assets must meet two criteria:

A business model test: The financial assets are being held to collect contractual cash flows; and

A cash flow characteristic test: The contractual cash flows are solely payments of principal and interest on principal
Recycling: Under AFS at sale of assets remove unrecognised P/L from OCI into Income Statement

The shareholders’ equity section of the post-acquisition consolidated balance sheet will consist of the capital stock and retained earnings account
of the parent and the non-controlling interest of the minority shareholders.

9


EMPLOYEE COMPENSATION: POST-EMPLOYMENT and SHARE-BASED
Net Pension Liability = (Beginning PV of the Defined benefit obligation – Beginning FV of Plan Assets)
Funded Status = (Fair value of the plan assets – PV of the Defined benefit obligation) = (Ending funded status – Employer contributions – Beginning funded status)
Total Periodic Pension Cost = Economic Pension Expense = (Change in Funded Status - Contributions) = (Change in Assets - Change in Liability) - Contribution
Periodic Pension Costs under IFRS and US GAAP
IFRS
Service Cost
Past Service Cost

Net Interest Income or Expense
r x net pension liability / asset
Re-measurements
Actual Return - (r x Plan Assets)
Actuarial gains and losses

Assumption

US GAAP

Recognition

Service Cost

Income Statement

Past Service Cost

OCI and amortised
over service life

Interest expense on pension obligation

Income Statement

Expected return on plan assets will reduce the costs

Income Statement

Recognition

Income
Statement
Income
Statement

OCI NOT
Amortised
Actual return – (Plan Assets × Expected return)
Actuarial Gains / Losses

Impact of Assumption on Balance Sheet

OCI or Amortised using
corridor method to P/L

Impact of Assumption

Higher discount rate

↓beginning PBO & ↓Service cost
↑ or↓ Interest cost

Periodic pension costs will typically be lower
because of lower opening obligation and lower
service costs

Higher rate of compensation increase

Higher obligation


Higher service costs

Higher expected return on plan assets

No effect, because fair value of return plan
assets is used on balance sheet

Not applicable for IFRS

PBO Jan
+Current Service Cost
+Past Service Cost
+/- Plan Amendments
+Interest Costs
-Benefits Paid
+/-Actuarial P/L
+Employee Contribution
PBO Dec

Plan Assets Jan
+Actual Return of Plan Assets
+Employer Contribution
+Employee Contribution
-Benefits Paid
Plan Assets Dec

Retroactive curtailment is a form of past service benefit for the frim hence will decrease pension cost
Retroactive benefit i.e. past service cost increases the pension expense
Vested BO < Accumulated BO Stock Option Model Inputs:

Exercise Price
Stock Price
Volatility
Dividend Yield- high values decreases value of option = ↓compensation expense
Risk Free Rate – high value increases value of option = ↑compensation cost
Option Expense:
Expense for the year: N Options granted × (Market Price of Option / vesting period in years)

Lower periodic pension expense (US GAAP)

The vesting date is the date that employees can first exercise the stock options

Classification of Periodic Pension Costs Recognised in P&L
To better reflect the components of periodic pension costs which can be classed as operating from non-operating items, we add the
Total pension cost in P&L to operating income and deduct service cost.

Stock appreciation rights – employee has limited downside risk unlimited upside – no dilution
The potential for risk aversion is limited because employees have limited downside risk and unlimited
upside potential.

This adjustment: 1.Removes the amortisation of past service costs and the amortisation of net actuarial gains and losses from operating income
2. Eliminates the interest expense component and the return on plan assets component from the company’s operating income

Stock Grants: Given to employees outright, with restrictions, or contingent on performance.
Compensation expense is reported on the basis of the fair value of the stock on the grant date
generally the market value at grant date

We then add the interest expense component to interest expense on P&L and Return on Plan Assets is added into non- operating income on P&L
1. Operating Expense + (Total Pension Expense – Service cost)
2. Deduct pension interest costs from Interest expense on P&L

3. Add return on plan assets to Interest income on P&L and deduct expected return

The reclassification of interest expense
would not change net income

Corridor Approach:
If the net cumulative unrecognised actuarial gains losses exceed 10% of the larger of Pension Obligation or FV of Plan Assets, then the excess is
amortised over expected average remaining working lives of the employees in the plan.

Excess = (Employer Contribution > TPPE) = financing use of funds
= equivalent to repayment of loan – use money from CFF to pay for something in CFO
↓CFF and ↑ CFO by the after tax figure
Deficit = (Employer Contribution < TPPE) = financing source of funds
= equivalent to getting a loan – hence take out money from CFO and increase CFF
↑CFF and ↓CFO by the after tax figure
After-tax $ by which the firms contribution exceeds/below total pension cost
Amount = (Company Contributions - Pension Cost) * 1 – tax

10


US GAAP:
If the plan has a surplus, the net pension asset is subject to a ceiling defined as the present value of available refunds and reductions in future contributions
Annual Unit of Credit:
1. Estimated final salary = Current Annual Salary * 1+annual comp increase years of service
2. Lump sum value at retirement = final salary * benefit formula * years of service
3. Annual unit credit (benefit) per service year = (value at retirement / years of life post retirement)
4. Current service cost = PV of annual unit of credit

Year 1

Year 2

Beginning PBO

0

100

Interest

0

100*r = 20

Current service cost

Annual Unit of Credit / (1+r^n) = 100

Annual Unit of Credit / (1+r^n-1) = 150

Ending PBO

100

170

If the employee were to live for 5 years after retirement, he would receive the annual unit of credit every year
for those 5 years. The current service cost is just the PV for the period we are in from retirement. Set annual
credit unit = PMT and compute PV to find the PV at the time of retirement.

*final salary calculation might be bgn or end of period hence adjust ^years of service. Assuming there are no
prior service costs, the bgn PBO is zero* If there are prior service costs then bgn PBO = the PV of prior service
costs.

11


Multinational Operations
Current Rate Method

Temporal Method

Assets
Monetary, such as cash and receivable
Non-monetary

Current rate
Current rate

measured at current value (e.g., marketable securities and
inventory measured at market value under the lower of cost
or market rule)
measured at historical costs, (inventory measured at cost
under the lower of cost or market rule; property, plant &
equipment; and intangible assets)

Historical

US GAAP:
To achieve the objective of translating to the parent’s presentation currency as if

the subsidiary’s transactions had been recorded in that currency.

Current rate

Current rate

Depends on rate used at the time

Monetary, such as accounts payable, accrued expenses, longterm debt, and deferred income taxes

Current rate

The net gain or loss in purchasing power during the period of inflation is included in
net income

Historical

Non-monetary

Current rate

measured at current value
Current rate

Equity
Other than retained earnings
Retained earnings

Historical
Historical

Beginning RE = (Net Income -Dividends) (translated using relevant rate)
Do not translate RE number directly

Income Statement

Expenses

Treatment of the translation adjustment in the parent’s
consolidated financial statements
Current Rate:
Typically net asset BS exposure
IS is calculated first
CTA = plug figure to make (Liability + Equity) = Assets
Assets = (Total Liabilities + Capital Stock + RE) + CTA

US GAAP:
Use Temporal method
Both IFRS and US GAAP require two types of disclosures related to foreign
currency translation:

The amount of exchange differences recognized in net income

The amount of cumulative translation adjustment classified in OCI

A reconciliation of the amount of CTA at the begin & end of the period
US GAAP:
Specifically requires disclosure of the amount of translation adjustment transferred
from stockholders’ equity and included in current net income as a result of the
disposal of a foreign entity.

Average rate

Revenues

Expenses related to assets translated at historical exchange
rate, such as cost of goods sold, depreciation, and
amortization

Hyper Inflation
When inflation over 3 years >100% i.e. compounded at 26% over 3 years.
IFRS:
IFRS require the non-monetary item to be restated for inflation then translated
using the current exchange rate. All Income Statement items are restated.

Liabilities

not measured at current value, such as deferred revenue

IFRS:
The basic concept underlying the current rate method is that the entire investment
in a foreign entity is exposed to translation gain or loss. Therefore, all assets and all
liabilities must be revalued at each successive balance sheet date.

Average rate
Average rate

Historical

Accumulated in OCI

Included as gain or loss in net income

Temporal:
Typically net liability BS exposure
BS is translated 1st so that we have RE
Translation Gain or Loss = (NI – RE – Dividends) using the RE from BS

The amount of exchange differences recognized in net income consists of foreign
currency transaction gains and losses, and translation gains and losses resulting
from application of the temporal method
How to determine functional Currency:

Currency that mainly influences sales prices for goods and services

Currency of the country whose competitive forces and regulations
determine sales prices

Currency that influences labour, material and costs

Currency in which financing activities are generated Currency in which
CFO receipts are retained

Only receivables turnover is the same under both translation methods current rate and temporal. This is the only ratio presented in which there is no difference
in the type of exchange rate used to translate the items that comprise the numerator and the denominator.
Companies often include disclosures about the effect of exchange rates on sales growth in the MD&A. Such disclosures may also appear in other financial
reports, such as company presentations to investors or earnings announcements.

12

Evaluating Quality of Financial Reports
M&A Issues:
The consolidated CFO will include the cash flow of the acquired company, effectively concealing the acquirer’s own cash flow problems. Such an acquisition can provide a one-time boost to CFO that may or may not be sustainable.
Understate Fair Value of assets to increase Goodwill since it’s not amortised, hence no associated amortisation charges. Large accruals for losses (e.g., environmental or litigation-related liabilities) suggest that prior periods’ earnings may have been
overstated because of the failure to accrue losses earlier.
Higher M-scores (i.e., less negative numbers) indicate an increased probability of earnings manipulation.
Days of sales receivables (DSR): The value > one for DSR indicates that receivables as a percentage of sales have increased, may
be due to inappropriate revenue recognition
Gross margin index (GMI): The value > 1 indicates that gross margins were higher last year; deteriorating margins could
predispose companies to manipulate earnings. Last year’s gross margin / this year’s gross margin
Sales growth index (SGI): The value > one for indicates positive sales growth relative to the previous year. Could be manipulate
earnings to manage perceptions of continuing growth and also to obtain capital needed to support growth

Warning Signs:

Declining receivables turnover = revenues are fictitious or recorded prematurely or that the allowance for
doubtful accounts is insufficient. Account Receivables growth > Revenue growth

Declining inventory turnover = obsolescence problems that should be recognized

Net income greater than cash provided by operations could suggest that aggressive accrual accounting policies
have shifted current expenses to later periods

Lessor use of sales-type finance lease classification results in Lessor recognizing the gross profit at inception of
the lease and is a mechanism to overstate

Earnings
Quality

DEPI: The value > one indicates that the depreciation rate was higher in the prior year; a declining depreciation rate can indicate
manipulated earning
AQI (asset quality index) = [1 – (PPEt + CAt)/TAt] / [1 – (PPEt–1 + CAt–1)/TAt–1], where PPE is property, plant, and equipment; CA
is current assets; and TA is total assets. Change in the percentage of assets other than in PPE and CA could indicate excessive
expenditure capitalization
Accruals = (Income before Extraordinary items – CFO / Total Assets) highest values to the model with a coefficient of 4.67
Anything higher than -1.78 indicates earnings manipulation
Probability of Bankruptcy with Altman Z-Score
Z-score = 1.2 (NWCap Inv /Tot Ass)
+ 1.4 (RE/ Tot Ass)
Profitability
+ 3.3 (EBIT/ Tot Ass)
+ 6.1 (MVE /BVL) ---------> Leverage
+ 1.0 (Sales/Tot Ass)
High Z- score is better <1.8 = high probability of bankruptcy
>3 = low probability of bankruptcy
Scores in-between 1.8 < 3 are not a clear indication
Earningst+1 = α + β1Cash flow + β2Accrualst + ε -> Higher coefficient (β1) cash represents more persistent earnings

High Altman Z-Scores and Low M –Scores are Good
High-quality earnings provide an adequate level of return on investment (r ≥ cost of capital) and are sustainable.
Low-quality earnings (they can be of low quality because they do not provide an adequate level of return and/or they are not
sustainable). Derived from non-recurring, one-off activities. In addition, the term “low-quality earnings” can be used when the
reported information does not provide a useful indication of the company’s performance
Remember that even GAAP-compliant financial reports can diverge from economic reality if GAAP allows for biased choices.
Aggressive, premature and fictitious revenue recognition = ↑Revenue =↑ Equity =↑ Assets
Expenses omission = ↓Expenses = ↑ Net Income = (↑ Assets or ↓ Liabilities)
A company that consistently reports earnings that exactly meet or only narrowly beat benchmarks can raise questions about its
earnings quality

Reporting
Quality
Cash flow can be described as “low quality” either because the reported information properly represents genuinely bad
economic performance or because the reported information misrepresents economic reality.
Impairment / Restructuring: How often do they occur?
If regularly then normalise earnings by spreading the costs over the prior and current periods
Sudden increases to allowances or reserves and large accruals for losses indicate past period earnings were over
stated
Sustainable Earnings:
Accruals = (NI – Operating Cash flow) this will consist of normal transactions and discretionary accruals
If NI > CFO on a consistent basis then there may an issue, compare with industry norms
CFO less easily manipulated compared to Net Income
Receivables turnover ratio = Total revenue ÷ Average receivables
Days of sales outstanding (DSO) = 365/Receivables turnover ratio -> (Days it takes to collect revenue)
Inventory turnover ratio = Cost of goods sold ÷ Average inventory
Days of inventory on hand (DOH) = 365/Inventory turnover ratio -> (Days it takes to sell inventory)
Payables turnover ratio = Purchases ÷ Average trade payables
Number of days of payables = 365/Payables turnover ratio
-> (Days it takes to pay for purchases)
Cash conversion cycle (net operating cycle) = (DOH + DSO – N days of payables) (Liquidity Ratio)
Source of Information about Risk

Change in Auditor

MD&A notes on Risks (exposure) and relationships that significantly impact firm

Material events – change of management – legal disputes – change in control (M&A)
Disclosures about pensions and post-employment benefits include information relevant to actuarial risks that could
result in actual benefits differing from the reported obligations based on estimated benefits or investment risks that
could result in actual assets differing from reported amounts based on estimates

Disclosures about financial instruments include information about risks, such as credit risk, liquidity risk, and market
risks that arise from the company’s financial instruments and how they have been managed.

13


Cash flow Quality:
In general, for established companies, high-quality cash flow would typically have most or all of the following
characteristics
Positive OCF
OCF derived from sustainable sources
OCF adequate to cover capital expenditures, dividends, and debt repayments
OCF with relatively low volatility (relative to industry participants)
Classification shifting:
Shifting positive cash flow items from investing or financing to inflate operating cash flows.
A shift in classification does not change the total amount of cash flow, but it can affect investors’ evaluation of a
company’s cash flows and investors’ expectations for future cash flows.
Results in inflation of core or recurring earnings while keeping the total reported income same.
This is used to mislead analysts into using a higher number as a basis for generating forecasts of future earnings and cash
flows. Result in inflated equity and firm valuation.
Measurement and timing issues typically affect multiple financial statement elements
Classification issues typically affect categorization of a specific element in a financial statement.
Capitalizing a lease (finance lease) enhances earnings quality because it’s on the BS and runs through the IS.
An operating lease lowers earnings quality; it’s an off BS item.
With the accrual basis of accounting, revenues are recognized when earned and expenses are recognized when incurred
– costs are allocated over assets life in the IS. Faster mean reversion
With the cash basis of accounting, revenues are recognized when cash is collected and expenses are recognized when
cash is paid – cash flow and revenue may be recorded in different periods. Slower mean reversion
Typical steps involved in evaluating financial reporting quality include:


An understanding of the company’s business and industry in which the company is operating;

Comparison of the financial statements in the current period and the previous period to identify any significant
differences in line items

An evaluation of the company’s accounting policies, especially any unusual revenue and expense recognition
compared with those of other companies in the same industry

financial ratio analysis

Examination of the statement of cash flows with particular focus on differences between net income and operating
cash flows; perusal of risk disclosures; and review of management compensation and insider transactions

Decomposition:
Removing Market Value of subsidiary
Compute Market value of parent
Subtract holding value of the subsidiary once translated into the parent’s currency
Removing Income:
Compute NI of parent
Subtract income contributed by the subsidiary in parent currency. This will be a line item if the holding is under Equity method.
If the holding is consolidated i.e. under acquisition method, we will subtract 100% of the income contribution from subsidiary.
Then subtract any minority interest which was not attributable to the 100% of income removed.

Balance Sheet Quality:
With regard to the balance sheet, high financial reporting quality is indicated by:

Completeness

Unbiased measurement and clear presentation.
High financial results quality (i.e. strong balance sheet) is indicated by:


An optimal amount of leverage

Adequate liquidity and economically successful asset allocation
The use of unconsolidated joint ventures or equity-method investees may reflect off-balance-sheet liabilities. Firms with
stakes in other firms that never go above 50% should be suspicious.
Understatement of impairment charges for inventory; plant, property, and equipment; or other assets not only results in
overstated profits on the income statement but also results in overstatement of the assets on the balance sheet.
Asset impairments are write-downs of assets required when circumstances indicate that the carrying amount of an asset
is excessive compared with the expected future benefits.
The term “restructuring charge” is used under IFRS to indicate a sale or termination of a line of business, closure of
business locations, changes in management structure, and/or a fundamental reorganization. All of these events could
also give rise to the recognition of a liability (e.g., a commitment to make employee severance payments or to make a
payment to settle a lease).
Should be spread over several periods to avoid overstating / understating net income

14


Integration of Financial Statement Analysis Techniques
Accruals Ratio:

Seek granularity and apply disaggregation (e.g. using Du Pont) to look beneath the level of information presented. Granular analysis
will release the sources of company’s earnings drivers.

BS Accrual = (NOA1 – NOA0) / Average NOA
By using the average we adjust for differences in size
CF Accrual = [NI end − (CFO end + CFI end)] / [Average NOA]
Look out concerning ratios < 1

Aggregate Accruals = (NOAt1 – NOAt-1) = simply ∆ in NOA

𝐶𝑎𝑠ℎ 𝑓𝑟𝑜𝑚 𝐶𝐹𝑂
𝐶𝑎𝑠ℎ 𝑓𝑟𝑜𝑚 𝐶𝐹𝑂
=
𝐸𝐵𝐼𝑇
𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑃𝑟𝑜𝑓𝑖𝑡

Other ratio to look out for: (low values or decreasing trends are of concern) Negative Return shows inefficient asset
allocation

Cash flow to reinvestment:

Cash flow to Total Debt:

Balance sheet: Shareholder Equity includes minority interest because parent firm has control over the firm being consolidated.

Working capital account: Liquidity
If there is deleveraging – is it paid from cash account? Not sustainable in the long run and makes liquidity ratios worse
Liquidity ability is just as important as the liquidity i.e being able to access cash quickly.

Cash flow to Interest Coverage:
𝐶𝑎𝑠ℎ 𝑓𝑟𝑜𝑚 𝐶𝐹𝑂
𝐶𝑎𝑠ℎ 𝑓𝑟𝑜𝑚 𝐶𝐹𝑂
=
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝐶𝑜𝑣𝑒𝑟𝑎𝑔𝑒 𝐶𝑎𝑠ℎ 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑃𝑎𝑖𝑑

Is Goodwill unusually large or small?

EBIT / CFO or CFO / Total Assets Make sure this ratio remains >1

Non-Operating Assets:
Assets not needed to operate the business e.g. assets held for long-term investment purposes, marketable securities, or

investment
property.
(Total Assets – Cash and STI) = Operating Assets
(Total Liabilities – LT Debt & Debt in CL) = Operating Liabilities
(Operating Assets - Operating Liabilities) = Net Operating
Assets

What is the rate of growth in Goodwill? If too large it should be further investigated. This will have been a function of acquisitions
mostly. E.g. High intangibles like goodwill combined with low current assets might show the company has been expanding (growth)
through acquisitions. Driving earnings by acquiring isn’t sustainable! Check CFI for large outflows which will confirm the acquisitions.
Cash Conversion Cycle = days in sales + days in inventory – days in payables (liquidity measure) the lower the better
Segment information Revenue, Capex vs Assets:
Identify which areas have the biggest Revenues and EBIT can calculate EBIT Margin (EBIT/Revenue)

PV of lease x r

Interest Coverage Ratio Adjustment:
(EBIT + Previous Lease Rent Expense – Depreciation of lease term) / (Interest Expense + Interest Expense of Lease)
Depreciation of lease term = (PV of lease term/ N) unless more information is provided
Leverage Adjustment (Assets / Equity):
Add PV of Lease to Assets only.
Liabilities are unaffected because there lease payment is much lower than the PV of lease.

D/E and Debt/Capital Adjustment (Debt Ratios):
Add PV of lease to Debt -> will make all ratios worse

Take into account any previous changes in accounting rules that impacted some of the years but not the others? If so restate with

adjustments. This will facilitate an accurate comparison when using Du-Pont.

Has Long Term Debt been rising or falling?
If Leverage is too low the firm may be underleveraged and have capacity to take advantage of opportunity.

𝐶𝑎𝑠ℎ 𝑓𝑟𝑜𝑚 𝐶𝐹𝑂
𝐶𝑎𝑠ℎ 𝑓𝑟𝑜𝑚 𝐶𝐹𝑂
=
𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑏𝑡
𝑆𝑇 + 𝐿𝑇 𝑓𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝐷𝑒𝑏𝑡 + 𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝐷𝑒𝑏𝑡

Adjusting Assets and Liabilities for Capital Lease
Add (PV of lease - depreciation) to Assets
Add (PV of lease + interest on lease for the year - lease payment) to Liability

Effect from Investment in Associates on Net Profit Margin: What is the trend here? Is the contribution to NI from associates
growing year on year? Is it having a larger impact? If so this is bad.

Financial leverage: Does not need to be adjusted for the investment in associates, i.e we do not remove it. We would need to adjust
the asset removed from the capital structure with another asset – the two would cancel each other out and the leverage ratio won’t
change. Simply put if you did not investment in the associates you would have had cash or another asset.

𝐶𝑎𝑠ℎ 𝑓𝑟𝑜𝑚 𝐶𝐹𝑂
𝐶𝑎𝑠ℎ 𝑓𝑟𝑜𝑚 𝐶𝐹𝑂
=
𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑆𝑝𝑒𝑛𝑑𝑖𝑛𝑔 𝐶𝑎𝑝𝑒𝑥 + 𝐸𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 𝑜𝑛 𝐼𝑛𝑡𝑎𝑛𝑔𝑖𝑏𝑙𝑒 𝐴𝑠𝑠𝑒𝑡𝑠

Years to pay debt while remaining current reinvestment policy:
Total Debt / (CFO – Total Reinvestment Spending)

Remove any income and equity from associates that the firm does not have control for

1. Compute: Segment Capex / Total Capex
Segment Assets / Total Assets
2. Compute ratios of (% Sector Capex / % Total Assets)
If the ratio is <1 then we are giving the segment a lower capex and in the future this segment will be lower of importance.
The idea is to have >1 for growing segments.
3. Compare with EBIT Margin i.e. high capex / total assets should equate to high EBIT margin segments – if not then company is not
allocation capex properly. Alternatively the firm could be growing the segment which is currently producing low margins due to high
capex and costs.
Consider segments of the core business e.g. a shoemaker may have largest income from non-core related segment. Is the firm growing
a large EBIT margin segment? If not that’s questionable.
Rank (capex / total assets) by Ebit margin – if a high Ebit margin segment has a below 1 ratio of capex / total assets its likely that the
segment will become less significant.
Compare (CFO before interest and taxes / Ebit) make sure ratio is >1 in order for it to be sustainable.
CFO is adjusted for interest and tax i.e. interest and tax are added back to the CFO figure.

15


RETURN CONCEPTS
Expected alpha = (Expected return – Required return)
Realized alpha = (Actual holding-period return − Contemporaneous required return)
Expected return = required rate of return = (Current expected risk-free return + Equity risk premium)
Geometric Risk Premium < Arithmetic Risk Premium (Arithmetic is favoured by theory of finance e.g. CAPM-> which uses single period
returns)
Target Price consistent with fair value = V0 * (1+ r- div yield)
Vo * r- (dividends)

Calculating Required Returns:

Forward looking (ex-ante) measures are less likely to have non-stationary issues
Required Return = Expected risk-free return + β (Equity risk premium)
Adjusted beta (Blume) = (2/3) (Unadjusted beta) + (1/3) (1.0)  
Beta Estimation for Thinly Traded Stocks and Non-public Companies
Un-lever: Gives me the beta of the Benchmarks Assets

Rfr = Long Term Government Bonds are preferred to Treasury Bills. T – Bill is preferred for short single period returns.
If D/A is given simply apply D / (1-D) to get D/E
Survivorship Bias: When using a series that has such bias, however, the historical risk premium estimate should be adjusted downward.
Historical Return Adjustment:
Positive inflation and productivity surprises = high returns = increase historical mean estimate of the equity risk premium. In such cases, a
forward-looking model estimate may suggest a much lower value of the equity risk premium. To mitigate that concern, the analyst may
adjust the historical estimate downward.

Re-Lever: Now Apply the above beta to the firm in questions Assets

Risk Premium = (↑RM – Rf) = ↑

Multifactor:
R = RF + (Risk prem 1) + (Risk Prem n)
Risk Prem = (risk factor x risk sensitivity)

War & Negative economic influences will bias historical equity risk premium lower. Risk Premium = (↓RM –↑Rf) = ↓

Fama and French:

An artificially low risk-free rate would bias the equity risk premium estimate upward unless the required return on equity was smaller by an
equal amount. The failure to incorporate the return from dividends biases the equity risk premium estimate downward. Risk premiums are
also generally believed to be inversely related to valuation ratios
Gordon Growth Model Equity Risk Premium:

Dividend yield on the index based on year-ahead aggregate forecasted dividends and aggregate market value
+Consensus long-term earnings growth rate
-Current long-term government bond yield
(Div Yield + g) - rf
Ibbotson and Chen:
Equity risk premium = {[(1+eINFL) (1+egEPS) (1+egPE) −1] +eINC] − Expected Rfr

RMRF = (market return in excess of T-bill – Rfr) = Equity Risk Premium
HML = (High P/B – Low P/B)
Use T-Bill i.e short term rate as Rf
DDM Require Rate of Return = D1 / P + g
BIRR: 5 Factors
RF (T-Bill)
+Confidence (∆ in risky corporate bonds and government bonds)
-Time Horizon (∆ change in 20yr bonds - 30 day bills)
-Inflation
+Business Cycle (∆ in business activity)
+Market Timing (residual unexplained)

INFL:
Build up Model: Good for Private Business
Risk-free rate + (Beta x Equity risk premium) + Size Premium +/- Risk Premium
Only use beta if there is a similar listed stock in the industry

Differences in GDP growth rates between countries may exist but this is not an important consideration specific to estimating required rate
of return between the two countries

A weakness of build-up models is that they typically use historical values as estimates that may not be relevant
to current market conditions.
Bond yield plus risk premium method = LTD YTM + Equity Risk Premium of firm

16


Industry and Company Analysis
Income Statement Modelling:
In a top-down approach, analysts may consider such factors as the overall level of inflation or
industry-specific costs before making assumptions about the individual company.
In a bottom-up approach analysts would start at the company level, considering such factors
as segment-level margins, historical cost growth rates, historical margin levels, or the costs of
delivering specific products.
Variable costs are directly linked to revenue growth, and may be best modelled as a
percentage of revenue or as projected unit volume multiplied by unit variable costs
By contrast, increases in fixed costs are not directly related to revenue - they are related to
future investment in PP&E and to total capacity growth
Economies of scale, a situation in which average costs per unit of a good or service produced
fall as volume rises
Testing for Economies of Scale:
Decreasing rations of COGS / Revenue and SGA / Revenue are signs of EOS.
Factors that can lead to economies of scale include:

Higher levels of production

Greater bargaining power with suppliers

Lower cost of capital

And lower per unit advertising expenses
Because COGS has a direct link with sales, forecasting this item as a percentage of sales is
usually a good approach. Analysts should also consider the impact of a company’s hedging

strategy. For example, commodity-driven companies’ gross margins almost automatically
decline if input prices increase significantly because of variable costs increasing at a faster rate
than revenue growth
In contrast to COGS, SG&A expenses have less of a direct relationship with the revenue of a
company. They have a mixture of fixed and variable costs.

Return Measures:
ROIC = (NOPLAT / Invested Capital) = EBIT x (1 – effective tax)
Invested Capital = (Operating Assets – Operating Liabilities)
NOPLAT = Net Operating Profit Less Adjusted Tax
ROIC is a better measure of profitability than return on equity because it is not
affected by a company’s degree of financial leverage because we do not deduct any
interest payments in NOPLAT. In general, sustainably high ROIC is a sign of a
competitive advantage. To increase ROIC, a company must either increase
earnings, reduce invested capital
ROCE = (ROIC before Tax) = (Operating Profit / Capital Employed)
= EBT / (Assets – Liabilities)
Useful for comparing companies in different tax jurisdiction

Customer’s satisfaction can be measure as same store sales growth
rate
Scenario Analysis and Sensitivity Analysis
Either sensitivity analysis or scenario analysis can be used to
determine a range of potential intrinsic value estimates based on a
variety of different assumptions about the future. Analysts can use
either tool to estimate the effect on a company’s valuation of
different assumptions for economic growth, for inflation, for the
success of a particular product, and so on.
Cannibalization
Inflation, Deflation and Costs

The rational efficient markets formulation (Grossman and Stiglitz, 1980) recognizes
that investors will not rationally incur the expenses of gathering information unless
they expect to be rewarded by higher gross returns compared with the free alternative
of accepting the market price.
In an inflationary environment, raising prices too late will result in a profit margin
squeeze but acting too soon could result in volume losses. In a deflationary
environment, lowering prices too soon will result in a lower gross margin but waiting
too long will result in volume losses
Mature companies may be able to accelerate their long-term growth rate through
product innovation and/or market expansion
Average annual growth different from CAGR Forecasting:
When forecasting e.g. a 5% increase in COGS or SGA, the formula is (Current
COGS/Current Sales) x 1.05. For absolute numbers like sales it simple sales x (1+g)
Upward cost pressure = supplier power and buyer power (high quality service)

Cash tax rate ≠ effective tax rate ≠ statutory tax rate
Depends on DTA and DTL and tax management of the firm
Interest income is a key component of revenue for banks and insurance companies, but it is
relatively less significant to most non-financial companies
Depreciation forecasts are usually based on historical depreciation and disclosure about
depreciation schedules, whereas capital expenditure forecasts depend on the analysts’
judgment of the future need for new PP&E
Technological Change:
Usually leads to lower costs – if its proprietary it will sustain cost advantage
If non-proprietary it will have advantage in short run to early adopters

Balance Sheet Modelling:
Build forecast from working capital accounts and efficiency ratios.
If efficiency ratios are held constant, working capital accounts will grow in line with Revenue

(assuming a historical cost relationship)
Non-Current Assets: ∆NCA = (Capex – Depreciation)
Capex should be < Depreciation due to inflation

Downward price pressure = low entry barriers
= High buyer power
= Substitutes
= Fragmented market with intense rivalries
Operating Assets are needed to generate revenue and run the company on a day to
day basis.
Operating Assets
Operating Liabilities
 Cash
Accounts Payable
 Prepaid expenses
Accrued Expenses
 Accounts receivable
Income Tax Payable
 Inventory
 Fixed assets
 Licences needed to manufacture goods
Net Debt = Gross Debt – Cash and equivalent

17


Dividend Discount Model
Gordon Growth Model:

Multi Stage:

The H-Model with linear growth: No need to discount final figure!
Use Dividends Not Earnings

Leading / Forward PE:
When to use H-Model
A firm that has little competition now, but has competition that is expected to increase, is a candidate for the H-model. Growth can be
expected to decline as competitors enter the market. Growth then stabilizes as the industry matures.
Trailing PE:

Du-Pont:

Perpetuity:

PRAT:
PVGO:
V0 = E1 / r - PVGO

B = retention rate

Value = (No Growth + PV of Growth) hence PVGO = (Value – No Growth)
Companies that have good business opportunities and/or a high level of managerial flexibility in responding to
changes in the marketplace should tend to have higher values of PVGO than companies that do not have such
advantages.
g = (b × ROE) = dividend growth rate
b = earnings retention rate (1 – Dividend Payout Ratio)
ROE = return on equity
Sum-of-the-parts analysis is most useful when valuing a company with segments in different industries that
have different valuation characteristics. Sum-of-the-parts analysis is also frequently used to evaluate the value
that might be unlocked in a restructuring through a spin-off, split-off, tracking stock, or equity (IPO) carve-out.

Growth is a function of profit margin (P), retention rate (RR), asset turnover (A), and financial leverage (T)

g can be decomposed in a variety of ways:
ROE = Return on assets × Leverage = first part of Du-Pont
g = Net profit margin × Asset turnover × Leverage = 3 factor Du-Pont
g = EBIT margin × Tax burden × Interest burden × Asset turnover × Leverage = 5 factor Du-Pont
H - Model r:

Conglomerate discount refers to the concept that the market applies a discount to the stock of a company
operating in multiple, unrelated businesses compared to the stock of companies with narrower focuses
Leverage = ROE / ROA
Asset Turnover = ROA/NPM
Disproportionate returns would result when control shareholders increase their returns through above-market
compensation and other actions that reduce the returns available to minority shareholders. For private
companies seeking a liquidity event through an IPO or strategic sale of the entity, the likelihood of actions by a
control group that reduce the earnings of an entity is reduce

r = Dividend Yield x (1+gl + H adjustment) + gl
Sustainable Growth Rate:
The sustainable growth rate model assumes that the growth will be financed with issuance of debt and internally generated equity
When to use 2 Stage
A firm that is expected to have a high rate of growth until patents expire, for example, should be modelled by the two-stage model, with one
rate of growth before the patent expires and another rate thereafter.

18


Free Cash Flow Valuation
Use when Investor has a control perspective
Conceptually FCFE = (Operating Assets + Marketable Securities + Cash) – MVD

FCFF might be better for comparing firms with different financial leverage structures because when FCFE is the change in
leverage is reflected
FCFF = NI + Net NCC + Int(1 – Tax rate) – FCInv – WCInv
FCFE = NI + NCC − FCInv − WCInv + Net borrowing
WCInc = (CA - Cash) – (CL – ST Debt i.e. notes payable & portion of LTD). Cash and cash equivalents are excluded because a
change in cash is what we are trying to explain. Notes payable and the current portion of long-term debt are excluded
because they are liabilities with explicit interest costs that make them financing items rather than operating items. This is
the y-o-y change!!!
FCInv = Net purchase of fixed assets = Increase in gross fixed assets i.e. includes Deprecation! (The y-o-y change)
This can also be net purchase of property, plant, and equipment from CFI
FCInv = change in net fixed assets + depreciation expense
= change in GROSS PPE

FCFF = EBIT (1 – Tax rate) + Dep – FCInv – WCInv (add NB for FCFE)
FCFF = EBITDA (1 – Tax rate) + Dep (Tax rate) – FCInv – WCInv (add NB for FCFE)
Net Income = (EBITDA – Dep – Int) * (1 – Tax rate)
In the calculation of net income, many noncash charges are made after computing EBIT or EBITDA, so they do not need to be
added back when calculating FCFF based on EBIT or EBITDA
In general, a firm has the following alternative uses of positive FCFF:
1) Retain the cash and thus increase the firm’s balances of cash and marketable securities;
2) Use the cash for payments to providers of debt capital (i.e., interest payments and principal payments in excess of new
borrowings)
3) Use the cash for payments to providers of equity capital (i.e., dividend payments and/or share repurchases in excess of new
share issuances).
Similarly, a firm has the following general alternatives for covering negative free cash flows:
o
Draw down cash balances
o
Borrow additional cash
o

Issue equity

FCFF = CFO + Interest (1-tax rate) - FCInv
FCFE = CFO − FCInv + Net borrowing

Forecasting FCFF and FCFE:
FCInv – Dep represents the incremental fixed capital expenditure net of depreciation. By assuming a target DR, we eliminated
the need to forecast net borrowing. Net borrowing = DR*(FCInv – Dep) + DR*(WCInv)
By using this expression, we do not need to forecast debt issuance and repayment on an annual basis to estimate net borrowing.
This will not work if the firm has significant NCC other than depreciation.

CFO incorporates adjustments for noncash expenses (such as depreciation and amortization i.e. they were never deducted
because they are not a cash expense) as well as for net investments in working capital

FCFE = NI – (1 – DR) (FCInv – Dep) – (1 – DR) (WCInv)
= NI − (1−DR) (Net investment in operating assets)

Deferred Taxes:
Generally, if the analyst’s purpose is forecasting and, therefore, identifying the persistent components of FCFF, then the
analyst should not add back deferred tax changes that are expected to reverse in the near future.

FCFF: Can also be used for FCFE by starting with NI
Investment in fixed capital in excess of depreciation (FCInv – Dep) and investment in working capital (WCInv) both bear a
constant relationship to forecast increases in the size of the company as measured by increases in sales.

If a company is growing and has the ability to indefinitely defer its tax liability, adding back deferred taxes to net income
is warranted – i.e. they will not reverse

Free Cash Flow Tied to Sales
EBIT (1 − Tax rate) - Incremental FC - Incremental WC

Incremental FC = (Capex – Dep Expense) / Increase in Sales * Increase in Sales
Incremental WC = Increase in WC / Increase in Sales * Increase in Sales

Net Debt: (New debt issuance – Principal repayments) = ∆ in debt outstanding

FCFE = FCFF – Int(1 – Tax rate) + Net borrowing
Transactions between the company and its shareholders (through cash dividends, share repurchases, and share issuances)
do not affect free cash flow.
Leverage changes, such as the use of more debt financing, have some impact because they increase the interest tax shield
(reduce corporate taxes because of the tax deductibility of interest) and reduce the cash flow available to equity. In the
long run, the investing and financing decisions made today will affect future cash flows.
(FCInv > NCC): Due to inflation FCInv should be larger; if it isn’t then we have just about enough FCInv to support and
maintain current growth
(FCInv
Alternatively its: NI – Incremental FCInv – Incremental WCInv + NB
Net borrowing = (Increase in notes payable + Increase in long-term debt)
When excluding NB from FCFE to get FCFF this figure can be –ve. Hence it will be added.
FCInv using (net PPE t1 - net PPE t0) + accumulated depreciation
Total net payment to equity holders = (Net change in cash – FCFE)
Notes payable represents a short term debt obligation and hence an increase in notes payable would result in an increase in net
borrowings all things being equal
If the company has preferred stock, the FCFE equation is essentially the same. Net borrowing in this case is the total of new
debt borrowing and net issuances of new preferred stock.

19


EBITDA is a poor measure of the cash flow available to the company’s investors because it does not capture depreciation tax
shield and the differences in FC and WC. Even poorer measure for FCFE due to not capturing after tax interest costs or new

borrowing

Application and Processes:
Any departure of market price from the manager’s estimate of intrinsic value is a perceived mispricing
Mispricing = (Intrinsic Value – Market Price) + (estimated Intrinsic Value – Market Price)
=
Alpha
+
Error

Share repurchase and cash dividends on common stock does not affect FCFF or FCFE, which are the amounts of cash available
to all investors or to common stockholders. Change in Leverage impacts FCFE
In the year the debt is issued, it increases the FCFE by the amount of debt issued. After the debt is issued, FCFE is then reduced
by the after-tax interest expense.
To capture preferred stock dividends we add the preferred dividends back to NI
Equity Value = Firm Value – MVD – MV of Preferred Debt
Interest Expense / MVD = Cost of capital
International Application of Require Rate of Return = does not include inflation

λ

Country Return (real)
+Industry Adjustment
+Size Adjustment
+Leverage Adjustment

4 Factor Model

This approach is particularly useful for countries with high or variable inflation rates.
2 Stage FCFF and FCFE

Same principle of multi stage
CFO = NI + Depreciation + (Cash from Equipment Sale – Cash outflow Equipment Bought)
As depreciation increases Ni decreases and CFO increases
Value of firm = Value of operating assets + Value of non-operating assets
If a company has significant non-operating assets, such as excess cash, excess marketable securities, or land held for
investment, then analysts often calculate the value of the firm as the value of its operating assets (e.g., as estimated by FCFF
valuation) plus the value of its non-operating assets:
Free cash flow valuation focuses on the value of assets that generate income or are needed to generate operating cash flows.
In general, if any company asset is excluded from the set of assets being considered in projecting a company’s future cash
flows, the analyst should add that omitted asset’s estimated value to the cash-flows-based value estimate.
Some companies have substantial noncurrent investments in stocks and bonds that are not operating subsidiaries but, rather,
financial investments. These investments should be reflected at their current market value. Those securities reported at book
values on the basis of accounting conventions should be revalued to market values

Fair Market Value – willing buyers / sellers under no compulsion
Market Value – Observable in the market
Intrinsic Value – value calculated by analyst
Investment Value - value to a specific buyer taking account of potential synergies and based on the investor’s requirements
and expectations
The Valuation Process:
1.
Understanding the business. Industry and competitive analysis, together with an analysis of financial statements
and other company disclosures, provides a basis for forecasting company performance.
a.
Cost leadership: being the lowest cost producer while offering products comparable to those of other
companies, so that products can be priced at or near the industry average;
b.
Differentiation: offering unique products or services along some dimensions that are widely valued by
buyers so that the company can command premium prices; and
c.

Focus: seeking a competitive advantage within a target segment or segments of the industry, based on
either cost leadership (cost focus) or differentiation (differentiation focus).
2.
Forecasting company performance. Forecasts of sales, earnings, dividends, and financial position (pro forma
analysis) provide the inputs for most valuation models.
3.
Selecting the appropriate valuation model. Depending on the characteristics of the company and the context of
valuation, some valuation models may be more appropriate than others.
4.
Converting forecasts to a valuation. Beyond mechanically obtaining the “output” of valuation models,
estimating value involves judgment.
5.
Applying the valuation conclusions. Depending on the purpose, an analyst may use the valuation conclusions to
make an investment recommendation about a particular stock, provide an opinion about the price of a transaction,
or evaluate the economic merits of a potential strategic investment
In summary, an effective research report:

contains timely information

is written in clear, incisive language

is objective and well researched, with key assumptions clearly identified

distinguishes clearly between facts and opinions

contains analysis, forecasts, valuation, and a recommendation that are internally consistent;

presents sufficient information to allow a reader to critique the valuation

states the key risk factors involved in an investment in the company; and


discloses any potential conflicts of interests faced by the analyst

The two-stage model is best suited to analysing firms in a high growth phase that will maintain that growth for a specific
period, such as firms with patents or firms in an industry with significant barriers to entry

20


Market Based Valuations: Price and Enterprise Multiples
Comparable (Relative Valuation): Compare vs Benchmark or Peer group PE Forward P/E = (1-b) / r-g
(next year expected eps)
Trailing PE = (1-b) (1+g)/ r-g (most recent 4 q’s eps)
Leading PE > Actual PE = Overvalued
Usually the leading PE is smaller than the training PE because Earnings are grown by G in the trailing PE
Justified PE is not based market price – instead it’s based on the prices which are justified by current fundamental information.
E.g. price calculated from FCFE or based on peer group justified P/B or P/E. Based on intrinsic value of price instead of actual price.
Compare (Benchmark PE * Target EPS) vs (Current Market Price) or Target PE vs Benchmark PE on its own.
Look at historical relationship between (Intrinsic Value & Market Value) or (Target PE vs BM PE).
Have there been changes? If so adjust. PE could have been 80% of BM historically, in that case compare Target PE vs (80% * BM PE)
If not can the differences be explained by differences in fundamentals e.g. asset turnover / profitability or risks (liquidity, leverage)?
A firm with higher growth rates should have higher PE or a firm with higher leverage should have lower PE.
Transitory firm components are expected to be non- recurring and are excluded to calculate core EPS. Analyse carefully.
Use forward looking PE when investment is forward looking or when there have been lots of unusual items distort past earnings.
A predicted P/E, which is conceptually similar to a justified P/E, can be estimated from cross-sectional regressions of P/E on the
fundamentals believed to drive security valuation:
PE
+ve DPR
–ve Beta
+ve Growth

↑P/Es on depressed EPS at the bottom of the cycle and low P/E’s on unusually ↑EPS at the top of the cycle reflect the countercyclical
property of P/E’s known as the Molodovsky Effect. In this case ↑PE = undervalued due to Molodovsky effect
NTM PE = Price / [t/12 x total year EPS] + [12-t / 12 *Next year’s EPS]
Fiscal Year EPS = Subject to firms fiscal year
Current Fiscal Year EPS = only use EPS for quarters in current fiscal year
Next 4 Quarters EPS = Can include both current and next fiscal year EPS

PEG:
Stocks with lower PEGs (>1 over valued and <1 undervalued) are more attractive than stocks with higher PEGs, all else
being equal

PEG does not factor in differences in risk, an important determinant of P/E and does not account for
differences in the duration of growth (how many years will growth be and what happens after that period?)

Assumes linear relationship between PE and growth rate & does not account for the overall growth rate of an
industry / the economy as a whole
Potential drawbacks to using P/Es derive from the characteristics of EPS:

EPS can be zero, negative, or insignificantly small relative to price, and P/E does not make economic sense
with a zero, negative, or insignificantly small denominator.

The ongoing or recurring components of earnings that are most important in determining intrinsic value can
be practically difficult to distinguish from transient components.

The application of accounting standards requires corporate managers to choose among acceptable
alternatives and to use estimates in reporting. In making such choices and estimates, managers may distort
EPS as an accurate reflection of economic performance. Such distortions may affect the comparability of P/Es
among companies.
The Fed Model:

Based on the premise that the two yields should be closely linked, on average, the trading rule based on the Fed Model
considers the stock market to be overvalued when the market’s current earnings yield is less than the 10-year Treasury
bond (T-bond) yield. The intuition is that when risk-free T-bonds offer a yield that is higher than stocks—which are a
riskier investment—stocks are an unattractive investment.
Another drawback to the Fed Model is that the relationship between interest rates and earnings yields is not a linear one.
Critics of the Fed Model point out that it ignores the equity risk premium and inadequately reflects inflation.
The Yardeni Model: Gives a justified P/E (Think of it as 1 / r – g) where (1/ CBY – b x LTEG)
CEY = CBY – b × LTEG + Residual
CBY is the current Moody’s Investors Service A-rated corporate bond yield
LTEG is the consensus five-year earnings growth rate forecast for the market index

Normalized EPS: Calculated as average EPS over the most recent full cycle may not be reflective of current size of the firm due to
information being old.
Average ROE: Calculated as the average return on equity (ROE) from the most recent full cycle, multiplied by current book value per
share. Average ROE x Current BVPS = Normalised EPS
For stocks with comparable relative valuations, the stock with the greatest expected growth rate (or the lowest risk) is, all else equal,
the most attractively valued
Fundamental Factor
Beta
Wacc

Explanation
P/E is a decreasing function of risk ↑Beta = ↓ P/E
Same as above

g

P/E is an increasing function of the growth rate of the company—that is, the higher the expected
growth, the higher the P/E.

Equity risk premium

P/E is a decreasing function of the equity risk premium. An increased equity risk premium increases
the required return, which lowers the price of a stock relative to its earnings.

Does not incorporate an equity risk premium per se. Consistent with valuation theory, in Yardeni’s model, ↑current
corporate bond yields imply a ↓justified P/E and ↑expected long-term growth results in a ↑justified P/E.
P/E and Inflation - For two companies with the same pass-through ability, the company operating in the environment
with higher inflation will have a lower justified P/E; if the inflation rates are equal but pass-through rates differ, the
justified P/E should be lower for the company with the lower pass-through rate.
With less than 100 % cost pass-through, the justified P/E is inversely related to the inflation rate (with complete cost passthrough, the justified P/E should not be affected by inflation)

↑Inflation =↓PE hence ∆ in PE may be justified by ∆in inflation rates or ∆in pass-through rates
PE = 1/ real r + (1- λ) x Inflation
P = real rate of required return = r – I
λ= % of inflation costs that can be passed on
I = Inflation

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P/B: Market Cap / Equity

Enterprise Value Multiples

High P/B is justified by
↓r
↑ROE
↑growth

Typically a pre-interest income measure - Enterprise value multiples are relatively less sensitive to the effects of financial
leverage than price multiples when one is comparing companies that use differing amounts of leverage.

If we are evaluating two stocks with the same P/B, the one with the↑ROE is relatively undervalued

EV/EBITDA is usually more appropriate than P/E alone for comparing companies with different financial leverage (debt), because
EBITDA is a pre-interest earnings figure, in contrast to EPS, which is post interest

This is a re-arranged version of 1 + [(ROE − r) x B0) / (r − g)] to get a Justified P/B
High EBITDA is justified by
↑g
↑ROIC
↓wacc (because it’s firm wide)
Possible drawbacks of P/Bs in practice include the following:

Accounting effects on book value may compromise how useful book value is as a measure of the shareholders’
investment in the company

Intangible Assets e.g. human capital may not be reflected on the BS and hence Book Value

Share repurchases or issuances may distort historical comparisons

For assets measured at net historical cost, inflation and technological change can eventually result in significant
divergence between the book value and the market value of assets

EV = (MVE + MV Preferred Stock + MVD + MV Non-Control) – (Cash Equivalent & Short-term Investments)

Residual Income Model:

ROIC is the relevant measure of profitability because EBITDA flows to all providers of capital.

EBITA Use when amortization related in intangibles is a major expense for companies being compared.
EBIT may be chosen where neither depreciation nor amortization is a major item

P/S: Usually reported on the basis on trailing sales –> the 1+g for the justified P/S
P/S is calculated as price per share divided by annual net sales per share (net sales is total sales minus returns and customer
discounts
Justified P/S:

Equity = (EV + Cash Equivalent, Short-term Investments) - MVD
Cash and Equivalent are subtracted because EV is designed to measure the net price an acquirer would pay for the company as a
whole. The acquirer must buy out current equity and debt providers but then receives access to the cash and investments, which
lower the net cost of the acquisition.

Cross Border Valuations:
Pay attention to Accounting methods, tax regimes, and cultural differences
International considerations:
P/CFO and P/FCFE will generally be least affected by accounting differences.
P/B, P/E, and multiples based on such concepts as EBITDA, which start from accounting earnings, will generally be the most
affected.
Scaled earnings surprise = Surprise / σ of analyst earnings forecast – scaled by analyst forecast

Share price reflects the effect of debt financing on profitability and risk. In the P/S multiple, however, price is compared with
sales, which is a pre-financing income measure—a logical mismatch. Use a ratio of enterprise value to sales because enterprise
value incorporates the value of debt
P/S does not reflect differences in cost structures among different companies and Sales are stable and of particular value
when dealing with cyclical companies.

Standardized Unexpected Earnings: Scaled by the standard deviation in past unexpected earnings
EPSt = actual EPS for time t
E(EPSt) = expected EPS for time t

σ[EPSt – E(EPSt)] = standard deviation of [EPSt – E(EPSt)] over some historical time period
Relative-strength indicators allow comparison of a stock’s performance during a period either with its own past performance
(first type) or with the performance of some group of stocks (second type).

The fact that (Sales) × (Net profit margin) = Net income means that (P/E) × (Net profit margin) = P/S
NPM = (P/S ÷ P/E) hence P/S is an increasing function of NPM and earnings growth rate
High P/S is justified by ↑NPM, ↑g, ↑ROE and ↓r

The rationale for using relative strength is the thesis that patterns of persistence or reversal in returns exist.

P/CF = CF (defined as EPS plus per-share depreciation, amortization, and depletion)

Screening is the application of a set of criteria to reduce an investment universe to a smaller set of investments and is a part of
many stock selection disciplines. In general, limitations of such screens include the lack of control in vendor-provided data of the
calculation of important inputs and the absence of qualitative factors.

The difference between TIC and EV is that EV excludes cash, cash equivalents, and marketable securities. For purpose of
calculating TIC/EBITDA or EV/EBITDA
Compare the dividend yield in combination with r and g.
Does the firm have positive growth and is it paying a sustainable dividend pay-out ratio? i,e. below 100%?
Also compare the total return (div yield + capital appreciation) with the dividend yield.
Dividend Yield = D0/P0 = r-g/1+g

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Harmonic Mean:
The harmonic mean is sometimes used to reduce the impact of large outliers—which are typically the major concern in using the
arithmetic mean multiple—but not the impact of small outliers (i.e., those close to zero).
Harmonic mean

Weighted harmonic mean – most accurate - Avoids outliers

The two best methods are to take median and weighted harmonic mean to calculate industry averages
Harmonic < Arithmetic

Possible drawbacks of using P/S in practice include the following:

A business may show high growth in sales even when it is not operating profitably as judged by earnings and cash
flow from operations. To have value as a going concern, a business must ultimately generate earnings and cash

Share price reflects the effect of debt financing on profitability and risk. In the P/S multiple, however, price is
compared with sales, which is a pre-financing income measure—a logical mismatch.

P/S does not reflect differences in cost structures among different companies

Although P/S is relatively robust with respect to manipulation, revenue recognition practices have the potential to
distort P/S
Possible drawbacks to using EV/EBITDA include the following: *Worst account discrepancies*

EBITDA will overestimate CFO if working capital is growing.

EBITDA also ignores the effects of differences in revenue recognition policy on cash flow from operations

Free cash flow to the firm (FCFF), which directly reflects the amount of the company’s required capital expenditures,
has a stronger link to valuation theory than does EBITDA. Only if depreciation expenses match capital expenditures
do we expect EBITDA to reflect differences in businesses’ capital programs. This qualification to EBITDA
comparisons may be particularly meaningful for the capital-intensive businesses to which EV/EBITDA is often
applied






EPS plus per-share depreciation, amortization, and depletion (CF)
o
Limitation: Ignores changes in working capital and noncash revenue; not a free cash flow concept.
Cash flow from operations (CFO)
o
Limitation: Not a free cash flow concept, so not directly linked to theory.
Free cash flow to equity (FCFE)
o
Limitation: Often more variable and more frequently negative than other cash flow concepts.
Earnings before interest, taxes, depreciation, and amortization (EBITDA)
o
Limitation: Ignores changes in working capital and noncash revenue; not a free cash flow concept.
Relative to its use in P/EBITDA, EBITDA is mismatched with the numerator because it is a pre-interest
concept

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Residual Income
Multistage Residual Income Model:
Premium over BV = Price at ending period – BV at current period
BV0 + PV 0f (Earnings – r x BV0) + (PV of Premium over BV)
BV0 + PV of [ROE – r x (BV0)] + (PV of Premium over BV)
Using a Persistent Factor:

Economic Profit = Economic Value Added = NOPAT – (WACC % × Total Capital)

Residual Income
RI = (ROE –r)* BVo
RI = (NI – Equity Charge)
RI = (NI+OCI) – Equity Charge

(T-1) because it is the PV of
the Terminal Value

Stock Value using Residual Income = (Book value per share) + (Present value of expected future per-share residual income)
RE + Common Stock = Equity
BV0 + PV 0f (Earnings – r x BV0)
BV0 + PV of (Residual Income for each individual Period)
BV0 + PV of [ROE – r x (BV0) / r-g] = Single Stage RI
BV0 + PV of RI + (PV of Perpetuity of Sustainable RI)

Beginning Book Value =

A

EPS

=

B

Dividend

=

C

Equity Charge

=

(Cost of Equity) x A

Ending Book Value

=

A+ (B - C)

Residual Income

=

In practice, because the RI model uses primarily accounting data as inputs, the model can be sensitive to
accounting choices, and aggressive accounting methods (e.g., accelerating revenues or deferring
expenses) can result in valuation errors. Aggressive accounting =↑ book value
Violations of the Clean Surplus Relationship: Violations of this assumption occur when accounting
standards permit charges directly to stockholders’ equity, bypassing the income statement e.g. CTA, P/L
from hedging instrument, unrealised changes in FV instruments.

(B - Equity Charge)

Adjustments:
Deferred taxes are eliminated such that only cash taxes are treated as an expense
Any inventory LIFO reserve is added back to capital
Increase in the LIFO reserve is added in when calculating NOPAT

Because of the adjustments made in calculating EVA, a different numerical result will be zero 

When OCI is not included to arrive at Net Income, growth rate in residual income is generally not equal to
the growth rate of net income or dividends.
How to adjust for OCI in RI when there is a clean surplus violation
BVt0 + NI +E – Div – OCI = BVt1

Market Value Added = (MVD + MVE) – (Accounting Value of Firm)
A company that generates positive economic profit should have a market value in excess of the accounting book value of its capital.
PV of Economic Profit = (Share Price – BVPS) = the relationship that a firm with positive economic profit should have a market value in excess of the
accounting book value of its capital
Justified Price to Book using RI:
1 + [(ROE − r) x B0) / (r − g)]

A persistence factor of one implies that residual income will not fade at all; rather it will continue at the
same level indefinitely (i.e., in perpetuity).
A persistence factor of zero implies that residual income will not continue after the initial forecast
horizon

R&D expenditures are reflected in a company’s ROE, and hence residual income, over the long term.
Productive R&D will increase ROE and RI. Simply put ROE should reflect the productivity of R&D
expenditures without requiring an adjustment.
Expensing R&D = ↓ROE immediately but ↑ROE in future years when the capitalised expenditure is
amortised. Hence Capitalising R&D = ↑ROE

g = r − [B0*(ROE − r)] / (V0 − B0)

Tobins Q: A Firm Value Metric: (MVD + MVE) / Replacement Cost of Total Assets
Tobin’s q is expected to be higher the greater the productivity of a company’s assets. One difficulty in computing Tobin’s q is the lack of information on
the replacement cost of assets. If available, market values of assets or replacement costs can be more useful in a valuation than historical costs.

Intangible assets can have a significant effect on book value. In the case of specifically identifiable
intangibles that can be separated from the entity (e.g., sold), it is generally appropriate to include these in
the determination of book value of equity. If these assets have a finite useful life, they will be amortized
over time as an expense. Intangible assets, however, require special consideration because they are often
not recognized as an asset unless they are obtained in an acquisition.

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Nonrecurring Items

extraordinary items (applicable under US GAAP but not under IFRS)

restructuring charges

discontinued operations

accounting changes
If these changes appear every period = they are classed as ordinary items
International Considerations:
Analysts should expect the model to work best in situations in which earnings forecasts are available, clean surplus violations
are limited, and accounting rules do not result in delayed recognition
The following are some common items to review for balance sheet adjustments

inventory

deferred tax assets and liabilities

operating leases


reserves and allowances (for example, bad debts)

Intangible assets

Additionally, the analyst should examine the financial statements and footnotes for items unique to the subject
company
The strengths of residual income models include the following:

Terminal values do not make up a large portion of the total present value, relative to other models.

RI models use readily available accounting data.

The models can be readily applied to companies that do not pay dividends or to companies that do not have
positive expected near-term free cash flows.

The models can be used when cash flows are unpredictable.

The models have an appealing focus on economic profitability.
The potential weaknesses of residual income models include the following:

The models are based on accounting data that can be subject to manipulation by management.

Accounting data used as inputs may require significant adjustments.

The models require that the clean surplus relation holds, or that the analyst makes appropriate adjustments
when the clean surplus relation does not hold

The residual income model’s use of accounting income assumes that the cost of debt capital is reflected
appropriately by interest expense.

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