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# Probability of bankruptcy for Oshkosh in 2009

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An analysis undertaken on contract in 2009 regarding the probability that Oshkosh Corporation would go bankrupt in the next several years. The short answer: extremely unlikely.

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### Probability of bankruptcy for Oshkosh in 2009

1. 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. 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. 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. 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.