Contents

1
Contents

• Balance sheet fundamentals
• Financial ratios
• Bankruptcy Models

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What is a balance sheet?

• 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
• Assets Liabilities stockholders equity
• Measured at a point in time

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Balance Sheet
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Balance Sheet terminology

• Asset
• Any item of economic value owned by a corporation
• Liabilities
• A financial claim, debt or potential loss that is
  owed by a corporation
• Stockholders Equity
• Value of the business a corporation generates
  that it owes to its shareholders after all its
  obligations have been met

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Balance Sheet terminology Continued

• Basic Accounts Equation
• Asset Liabilities Shareholders equity
• Owners Equity
• Owners claim on the assets
• Owners total investment

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Prediction of Financial Distress

• Process of estimating the probability of the
  bankruptcy of a corporation by using financial
  ratios and existing models.

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Models used in the prediction of financial
distress

• Z-Score Model
• Vasicek-Kealhofer model
• Black- Scholes Merton Probability
• Compensator Model

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The Z-score Model

• 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

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Multi Discriminant Analysis

• Used to classify an observation into several
  groupings
• The groupings are based on an observations
  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

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Z-score model reprise

• Uses five financial ratios
• Ratios are objectively weighed and summed
• Ratios can be obtained from corporations
  financial statements

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Z-score constituent ratios

• Working Capital/total assets (WC/TA)
• Working Capital is the difference between the
  current assets and current liabilities as
  obtained from the balance sheet
• Retained Earnings/total assets ( RE/TA)
• 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)
• Measure of a corporations 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

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Z-score constituent ratios Continued

• Market Value of Equity/Book Value of total
  liabilities (MVE/TL)
• 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)
• Also known as capital turnover ratio
• Illustrates the sales generating ability of the
  corporations assets

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Z score Results

• Based on Z-scores averaged over time, Altman
  calculated that a Z-score lt2.675 could be
  classified as failed
• More accurately, Zlt1.81 signals bankruptcy within
  1 year
• Z gt 2.99 signals the firm is in good financial
  health

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VK model

• 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
• Market Value of assets
• Asset Risk
• Leverage Extent of the corporations
  contractual liabilities. It is the book value of
  liabilities relative to the market value of
  assets

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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.

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Market net worth

• Market net worth is market value of the companys
  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

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Asset Volatility

• 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

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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
Time
1 Yr
Today
Source www.moodyskmv.com
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Distance to Default

• Compares the market net worth to the size of a 1
  standard deviation move in the asset value
• Combines 3 key credit issues
• Value of firms assets
• Business and industry risk
• leverage

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Determining Default Probability

• 3 steps to determine default probability
• Estimate Asset value and volatility
• 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
• Calculate Distance to default
• Contractual obligations determine Default Point
• Number of standard deviations from default
• Calculate Default probabilty
• Assign EDF using actual historical rates

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Black-Sholes-Merton Probability

• 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 firms assets. The strike price of
  the call option is equal to the face value of the
  firms liabilities and the option expires at time
  T when the debt matures.
• The BSM equation
• 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 d 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) lt X).
  The BSM model assumes that the natural log of
  future asset values is distributed normally as
  follows, where u is the continuously compounded
  expected return on assets

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• The probability that VA(T) lt X is as follows
• This shows the prob of bankruptcy is a function
  of the distance btw the current value of the
  firms 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, u, 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.

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Compensator Model

• 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
• 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 tgt0 let F(t) be the prob of default before
  time t. If G(w) is the time of default in state
  w, then F(t) PG(w)ltt which is strictly lt 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
• 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 - Eexp(-A(t,w)
• Alternatively, F(t) EF(t,w)

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• Model specification
• 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