Web Extension 22A

Multiple Discriminant Analysis

What is MDA, and how can it be used to predict bankruptcy?

Multiple discriminant analysis (MDA) is a statistical technique similar to multiple regression.

It identifies the characteristics of firms that went bankrupt in the past.

Then, data from any firm can be entered into the model to assess the likelihood of future bankruptcy.

MDA Illustration

Assume you have the following 2009 data for 12 companies: Current ratio Debt ratio

Six of the companies (marked by Xs) went bankrupt in 2010 while six (marked by dots) remained solvent.

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X

X

X

XX Bankrupt

Firms

Debt Ratio

SolventFirms

Current Ratio Discriminant Boundary

X

X = Bankrupt

■■

■■

■■

■ = Solvent

The discriminant boundary, or Z line, statistically separates the bankrupt and solvent companies.

Note that two companies have been misclassified by the MDA program: One bankrupt company falls on the solvent (left) side and one solvent company falls on the bankrupt (right) side. (More...

)

Assume the equation for the boundary line is

Z = -2 + 1.5(Current ratio) - 5.0(Debt ratio).

Furthermore, if Z = -1 to +1, the future of the company is uncertain. If Z > 1,bankruptcy is unlikely; if Z < -1, bankruptcy is likely to occur.

Using MDA To Predict Bankruptcy Suppose Firm S has CR = 4.0 and DR =

0.40. Then,Z = -2 + 1.5(4.0) - 5.0(0.40) =

+2.0,and firm is unlikely to go bankrupt.

Suppose Firm B has CR = 1.5 and DR = 0.75. Then,

Z = -2 + 1.5(1.5) - 5.0(0.75) = -3.5,and firm is likely to go bankrupt.

Some Final Points The most well-known bankruptcy

prediction model is Edward Altman’s five factor model.

Such models tend to work relatively well, but only for the near term.

The more similar the historical sample to the firm being evaluated, the better the prediction.