1.
James Hasik jhasik@jameshasik.com
[Redacted],
At your request, I have evaluated the likelihood of bankruptcy for Oshkosh Corporation
[NYSE:OSK] over the next year. I have used three generally consulted methods that employ
current accounting information: Altman’s (1968)1, Ohlson’s (1980)2, and Zmijewski’s (1984)3. In
each case, the accounting data is drawn from the preceding year or two. Each approach
depends on logit or probit regression, and so yields an abstract score which must be
transformed through logistic transformation to obtain a probability. These approaches remain
widely cited in the literature and widely used by financial analysts, even though options-pricing
models have been shown to provide greater predictive power. This is largely due to their ease of
use: methods using a transformed Black-Scholes-Merton equation require more than just simple
algebra. I have more on that below.
Altman’s Z-score was the first (1968) serious and empirically valid multivariate model for
predicting bankruptcy:
Z = 1.2
WK
TA
+1.4
RE
TA
+ 3.3
EBIT
TA
+ 0.6
VE
TL
+1.0
R
TA
where! WK! =! working capital
! TA! =! total assets
! RE! =! retained earnings
! EBIT! =! earnings before interest and taxes
! VE! =! market value of the equity
! R! =! revenues
For [REDACTED], using figures in millions of US dollars, the equation becomes
Z = 1.2
1842 −1722
3186
+1.4
−1026
3186
+ 3.3
138
3186
+ 0.6
31
3913
+1.0
6874
3186
= 1.89
After logistic transformation, we have
1 Edward I. Altman, “Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy,” Journal of
Finance, 1968, pp.189-209.
2 J.A. Ohlson, “Financial ratios and the probabilistic prediction of bankruptcy,” Journal of Accounting Research, Vol.
18, No. 1 (1980), pp. 109–131.
3 Mark E. Zmijewski, “Methodological Issues Related to the Estimation of Financial Distress Prediction Models.”
Journal of Accounting Research, 1984, 22 (Studies on Current Econometric Issues in Accounting Research), pp.
59-82.

2.
Pr =
eZ
1+ eZ
=
e1.89
1+ e1.89
= 0.87
Ohlson’s O-score (1980) is similar to Altman’s method, but expands the set of terms to nine:
O = −1.3− 0.407log TA( )+ 6.03
TL
TA
−1.43
WK
TA
+ 0.76
CL
CA
−1.72
1 if TL > TA
0 otherwise
⎧
⎨
⎪
⎩⎪
⎫
⎬
⎪
⎭⎪
− 0.521
NIt − NIt−1
NIt − NIt−1
⎛
⎝
⎜
⎞
⎠
⎟
where! CL! =! current liabilities
! CA! =! current assets
! NI! =! net income, in the current (t) and previous (t-1) years
For Oshkosh, using figures in millions of US dollars, the equation becomes
O = −1.3− 0.407log 3186( )+ 6.03
3913
3186
−1.43
1842
3186
+ 0.76
1722
1824
−1.72 1( )− 0.521
−101− −219( )
−101 − −219
⎛
⎝⎜
⎞
⎠⎟ = 1.51
After logistic transformation, we have
Pr =
eO
1+ eO
=
e1.51
1+ e1.51
= 0.82
Zmijewski’s method came later (1980), but elegantly reduced the number of terms to just four:
X = −4.3− 4.5
NI
TA
+ 5.7
TL
TA
− 0.004
CA
CL
For Oshkosh, using figures in millions of US dollars, the equation becomes
X = −4.3− 4.5
−101
4674
+ 5.7
4212
4674
− 0.004
2452
2137
= 0.93
Again, after logistic transformation, we have
Pr =
eX
1+ eX
=
e0.93
1+ e0.93
= 0.72
Zmijewski’s method, notably, is significantly sensitive to variations in net income. If we instead
use as NI the December 2007-to-December 2008 figure—a loss of $1,080 million—the X score
becomes 1.89, and the probability of bankruptcy within one year rises to 87 percent.
Assessing the probability of bankruptcy for Oshkosh Corporation Monday, March 9, 2009
James Hasik www.jameshasik.com
page 2 of 4

3.
There are, however, limitations to these approaches. Subsequent research has indicated
that the coefficients in all three models, and particularly Ohlson and Zmijewski’s, degrade with
time, and vary from industry to industry. The varying interpretations of accounting rules over
time and between firms contribute considerably to this problem. All the same, the various
scoring methods remain reasonably useful predictors of general financial distress short of
bankruptcy.4
Black-Scholes-Merton seems to provide the best results empirically. Based on the model
developed by Black and Scholes (1973)5 and Merton (1974)6, owning equity is essentially a
holding call option on the value of a company’s assets. When that hits zero, the company is
bankrupt. Thus, the Black-Scholes-Merton (BSM) options pricing model can be transformed to
calculate the probability of that bankruptcy. Robert MacDonald shows that this is given by7
Pr = N −
log
VA
X
+ µ − δ −
σA
2
⎛
⎝⎜
⎞
⎠⎟ T
σA T
⎡
⎣
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
where! N! is! the standard normal cumulative distribution function
! VA! =! market value of all the assets
! X! =! face value of the liabilities (analogous in the model to the strike price)
! μ! =! expected rate of return of the assets
! σA! =! volatility of the asset value
! δ! =! the dividend rate
Note that! !µ = max
VA t( )+ div − VA t −1( )
VA t −1( )
,r
⎡
⎣
⎢
⎤
⎦
⎥ ,
which is the greater of the relative appreciation of the equity and its dividend, or the risk-free
rate, as the expected return of an option cannot be negative.
Note also that!!δ =
div
VA
, or the dividend divided by the market value of the assets.
Assessing the probability of bankruptcy for Oshkosh Corporation Monday, March 9, 2009
James Hasik www.jameshasik.com
page 3 of 4
4 J.S. Grice and M.T. Dugan, "The Limitations of Bankruptcy Prediction Models: Some Cautions for the Researcher,"
Review of Quantitative Finance and Accounting, Vol. 17, No. 2 (2001), pp. 151-166
5 Fisher Black and Myron Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy,
Vol. 7 (1973), pp. 637–54.
6 Robert Merton, “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance, Vol.
29 (1974), pp. 449–70.
7 Robert MacDonald, Derivatives Markets, Addison-Wesley, 2002, p. 604

4.
Continuing reliance on accounting measures for predicting bankruptcy stems from the difficulty
of using the BSM model: neither the total market value of the assets nor the market’s expected
rate of return is actually observable in the market. By Hillegeist et alia,8 however, we can find
these two figures by simultaneously solving the call option equation and the optimal hedge
equation:
VE = VAe−δT
N d1( )− Xe−rT
N d2( )+ 1− e−δT
( )VA , σE =
VAe−δT
N d1( )σA
VE
The system of equations can be solved with an iterative Newton search algorithm, but for that, I
would need a little more time (we needed this work overnight). If the client wanted this, we could
calculate it, but it would probably just confirm what we already know.
Still, bond prices offer a useful heuristic
check of our work.9 Inspection of the table at
left, which shows today’s asking prices for
Oshkosh’s bonds, shows that the market is
reasonably confident that the company will
make its payments due later this week, but
after that, faith falls off fast. Bond prices have
not been shown to correlate systematically
with bankruptcy rates, but this is probably due
to the changing legal vagaries of the
bankruptcy process.
coupon maturity price currency
7.125 15 Mar 2009 96.5 USD
8.750 1 Mar 2012 22 USD
8.125 15 Sep 2015 21 USD
10.375 28 Oct 2018 No ask GBP
4.625 1 Mar 2026 No ask USD
4.625 1 Mar 2012 17 USD
4.000 15 Feb 2027 No ask USD
4.000 15 Feb 2027 17.9370 USD
Assessing the probability of bankruptcy for Oshkosh Corporation Monday, March 9, 2009
James Hasik www.jameshasik.com
page 4 of 4
8 Stephen A. Hillegeist, et al., “Assessing the Probability of Bankruptcy,” Review of Accounting Studies, Vol. 9, No. 1
(2004), pp. 5–34.
9 The data were pulled from Bloomberg on the afternoon of 9 March 2009.