Contents
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Balance sheet fundamentals
Financial ratios
Bankruptcy Models
What is a balance sheet?
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Shows the financial position of an enterprise at a
given point in time
Provides information about what an enterprise
owns(assets), owes (liabilities) and its value to its
inverstors (share holders equity)
Accounting equation
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Assets = Liabilities + stockholders’ equity
Measured at a point in time
Balance Sheet
Balance Sheet terminology
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Asset
 Any item of economic value owned by a
corporation
Liabilities
 A financial claim, debt or potential loss that is
owed by a corporation
Stockholder’s Equity
 Value of the business a corporation generates that
it owes to its shareholders after all its obligations
have been met
Balance Sheet terminology
Continued …
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Basic Accounts Equation
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Asset = Liabilities + Shareholder’s equity
Owners Equity
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Owners claim on the assets
Owners total investment
Prediction of Financial Distress
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Process of estimating the probability of
the bankruptcy of a corporation by
using financial ratios and existing
models.
Models used in the prediction
of financial distress
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Z-Score Model
Vasicek-Kealhofer model
Black- Scholes –Merton Probability
Compensator Model
The Z-score Model
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First developed by Altman in 1968
Uses a specified set of financial ratios
as variables in multidiscriminant
statistical methodology (MDR)
Real world application of the Altman
score successfully predicted 72% of
bankruptcies 2 years prior to their filing
for Chapter 7
Multi Discriminant Analysis
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Used to classify an observation into several groupings
The groupings are based on an observation’s individual
characteristics
MDR is used while making predications in problems where the
variable dependant variable appears in qualitative form. Eg.
Bankrupt and non-bankrupt
Forms a linear equation using characteristics that can be used to
distinguish between the dependant variable groups
Z = V1.X1 + V2.X2 + … +VnXn
V1…Vn = discriminant coeff.
X1…Xn = independent variables
Z = discriminant function
Z-score model :reprise
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Uses five financial ratios
Ratios are objectively weighed and summed
Ratios can be obtained from corporations financial
statements
Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5
X1 = Working Capital/total assets
X2 = Retained Earnings/total assets
X3 = Earnings before interest and taxes/total assets
X4 = Market value equity/book value of total liabilities
X5 = Sales/total assets
Z = Overall index
Z-score constituent ratios
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Working Capital/total assets (WC/TA)
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Retained Earnings/total assets ( RE/TA)
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Working Capital is the difference between the current assets and current
liabilities as obtained from the balance sheet
Retained Earning is also know as the earned surplus
It represents the total amount of reinvested earnings and/or losses of a firm
over its entire life-cyle
Can be obtained from balance sheet
Earnings before interest and taxes/Total assets (EBIT/TA)
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Measure of a corporation’s earning power from ongoing operations
Also know as Operating profit
Watched closely by creditors as it represent the total amount of cash that a
corporation can use to pay off its creditors
Can be obtained for the Income statement
Z-score constituent ratios
Continued…
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Market Value of Equity/Book Value of total liabilities (MVE/TL)
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The market value of equity is the total market value of all of the
stock, both preferred and common
The book value of liabilities is the total value of liabilities both long
term and current
The MVE/TL shows how much the firms assets can decline in value
with increasing liabilities, before the liabilities exceed the assets
Sales/Total Assets (s/TA)
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Also known as capital turnover ratio
Illustrates the sales generating ability of the corporation’s assets
Z score Results
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Based on Z-scores averaged over time, Altman
calculated that a Z-score <2.675 could be classified
as failed
More accurately, Z<1.81 signals bankruptcy within 1
year
Z > 2.99 signals the firm is in good financial health
VK model
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Uses EDF (expected default frequency) credit
measures – the probability that a company will
default within a given timeframe
3 main elements are used to determine the default
probability
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Market Value of assets
Asset Risk
Leverage – Extent of the corporation’s contractual liabilities.
It is the book value of liabilities relative to the market value
of assets
Leverage
Market Value
of Assets
Defaulted
November 2001
Default Point
(Liabilities Due)
Source : www.moodyskmv.com
Default risk increases as the market value of the assets approaches the book value
of the liabilities.
Market net worth
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Market net worth is market value of the company’s
assets minus the default point
Market net worth is considered in context of the
business risk
Food and beverage industries can afford higher
leverage( lower market net worth) than technology
businesses because their asset values are more
stable
Asset Volatility
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It is the standard deviation of the annual percentage
change in the asset value
It is related to the size and nature of the industry
It can be calculated from the value of the increase or
decrease in percentage of asset value upon 1
standard deviation change in the asset value
Distance to Default
Value
Distribution of
asset value at
horizon
Asset Volatility
(1 Std Dev)
Asset
Value
Distance-to-Default =
3 Standard deviations
Default Point
EDF
Today
1 Yr
Source : www.moodyskmv.com
Time
Distance to Default
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Compares the market net worth to the size of a 1
standard deviation move in the asset value
Combines 3 key credit issues:
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Value of firm’s assets
Business and industry risk
leverage
[Dist to default] = [Market value of assets]-[default point]
[Market value of assets][asset volatility]
Determining Default Probability
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3 steps to determine default probability
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Estimate Asset value and volatility:
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Calculate Distance to default:
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Equity is a call option on asset value. Equity holders have the
right but are not obligated to pay off the debt holders
Solve for implied asset value and volatility
Contractual obligations determine Default Point
Number of standard deviations from default
Calculate Default probabilty:
 Assign EDF using actual historical rates
Black-Sholes-Merton Probability
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Volatility is crucial variable in bankruptcy prediction since it captures the likelihood that the
values of firms assets will decline to such an extent that the firm will be unable to repay
its debts
Equity can be viewed as a call option on the value of the firm’s assets. The strike price of
the call option is equal to the face value of the firm’s liabilities and the option expires at
time T when the debt matures.
The BSM equation:
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Where N(d1) and N(d2) are the standard cumulative normal of d1 and d2 and
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VE is the current market value of equity; VA is the current market value of assets; X is the
face value of debt maturing at time T; r is the continuously-compounded risk-free rate; δ
is the continuous dividend rate expressed in terms of VA and ∂A is the std deviation of
asset returns.
Under the BSM model . The probability of bankruptcy is simply the prob that the market
value of assets , VA is less than the face value of the liabilities, X, at time T (i.e VA(T) <
X). The BSM model assumes that the natural log of future asset values is distributed
normally as follows, where ų is the continuously compounded expected return on assets:
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The probability that VA(T) < X is as follows:
This shows the prob of bankruptcy is a function of the distance btw the current value of the firm’s assets
and the face value of the liabilities
adjusted for the expected growth in asset values
relative to the asset volatility
We must estimate the market value of assets, asset volatility and the expected return on assets.
We estimate the values of VA and
by simultaneously solving the call option equation and the
optimal hedge eqn :
We solve the two equations simultaneously for the two unknown variables VA and
.The starting
values are determined by setting VA equal to book value of liabilities plus market value of equity and
In the second step, we estimate the expected market return on assets, ų, based on the actual return on
assets during the previous year, based on the estimates of VA that were computed in the previous step.
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Finally we use these values to calculate the BSM-Prob for each firm year.
Compensator Model
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Based on the assumption of incomplete information : bond investors are not certain abut
the true level of firm value that will trigger default. Coherent integration of structure and
uncertainty is facilitated with compensators.
In reality, default, or at least the moment at which default is publicly known to be inevitable
, usually comes as a surprise. Highlighted in credit market by the prevalence of positive
short-term credit spreads.
Features :
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Structure plus uncertainty – integrate an intuitive, cause-and-effect model with the uncertainty that
surrounds default events
Economic reasonability and flexibility
Unified perspective – broad enough to incorporate intensity based models and traditional structural
models
For t>0 let F(t) be the prob of default before time t. If Γ(w) is the time of default in state w,
then F(t) = P[Γ(w)<=t] which is strictly < 1.
Consider the function: A(t) = -log(1-F(t)) . This is called the pricing trend of the default
process. The pricing trend can be analyzed directly with the mathematical theory of
compensators:
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The difference btw an underlying process and its compensator is a martingale
The compensator is non decreasing
Compensator is predictable even if underlying process is not
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The compensator of the default process is continuous iff the default is completely
unpredictable.
Compensators, and thus pricing trends depend both on the underlying structure that keeps
track of the information acquired as time passes.
How to create compensators without the information structure? – use info generated by
underlying process – survival information structure
Theory can be reworked with an eye to information available – histories of equity prices,
debt outstanding , agency ratings and accounting variables. – Use this information to derive
a pricing trend from which default probability can be estimated.
Now we have the conditional probability of default by time t, given info at time t as F(t,w),
which gives the pricing trend as A(t,w) = -log(1-F(t,w))
F(t) = 1 - E[exp(-A(t,w)]
Alternatively, F(t) = E[F(t,w)]
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Model specification:
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Default triggered when the value of firm falls below barrier
Default barrier is not publicly known
The firm value process is given by a geometric Brownian motion
History of fundamental data and other publicly available info used to model the default barrier and
firm value process