# What is the use of Discriminant Analysis in Credit Score Model?

## What is Discriminant Analysis?

Apart from using a numerical scoring model, a firm may use discriminant analysis in credit scoring models.

Discriminant analyses for credit scoring are divided into two sections. They are as follows −

• Simple Discriminant Analysis

• Multiple Discriminant Analysis Models.

Discriminant models are objective methods of finding the differences between good and bad customers. By applying discriminant analysis, the lending firms can discriminate good credit customers from the bad ones.

## Simple Discriminant Analysis Model

As mentioned above, the simple discriminant analysis model is an objective method to separate the bad credit customers from the good ones. The lenders often look for a solid method that can identify bad customers via using data from the customer’s financial statements. In that way, using simple discriminant analysis goes a long way in providing a dependable solution to the lenders.

• Simple discriminant analysis models are objective.

For example, their empirical analysis may show that the ratio of EBDIT (Earnings before depreciation, interest, and tax) to sales is a good discriminating factor to separate bad customers from the good ones.

• However, to use such a model, the cut-off EBDIT to sales ratio must be obtained.

To do this, first, the good and bad customers are arranged by their EBDIT to sales ratios.

Secondly, a cut-off point is selected to differentiate the array into two parts. This differentiation must be done with minimum misclassifications. The cut-off point has to be selected by visual inspection. Now, the lenders can offer credit to those customers who are above the cut-off point.

• Instead of using only one factor as mentioned above, the lenders can use two factors to make the model more accurate.

For example, two ratios EBDIT to sales and cash flow to sales ratios can be used to discriminate the bad customers and the good ones. A combination of these two factors can be plotted on a graph for paying and non-paying customers.

A straight line can separate the two factors maintaining a minimum misclassification. The straight line will indicate how much importance to be paid to each of the ratios. This will be given by the discriminant index that can be selected from the graph.

• Furthermore, the discriminant index will also indicate which customers are good and which are not.

So, depending on the simple discriminant analysis model, the lenders can differentiate between good and bad customers.

## Multiple-Discriminant Analysis Model

The multiple-discriminant analysis model offers a composite score to each customer and depending on the score, lenders may decide which is the minimum score to consider for separating the good customers from the bad ones. The simple discriminant analysis model mentioned above uses only two factors. However, in practical terms, there may be many factors that affect the analysis of credit scores. These factors will interact with each other.

To include such interactions which may not be excluded from simple discriminant analysis, the multiple-discriminant analysis model gives due weight age to each factor that may impact the credit scoring model.

Depending on the attributes of the firms, Altman predicted the potential bankruptcy of firms via a multiple-discriminant analysis index.

The function derived by Altman was −

$$\mathrm{z=0.012\left(\frac{NWC}{TA}\right)+0.014\left(\frac{RE}{TA}\right)+0.033\left(\frac{EBIT}{S}\right)+0.006\left(\frac{MV}{D}\right)+0.010\left(\frac{S}{TA}\right)}$$

Where,

$$\mathrm{NWC \:= \:Net \:Working \:Capital}$$

$$\mathrm{TA \:= \:Total\: Assets}$$

$$\mathrm{RE\:= \:Retained \:Earnings}$$

$$\mathrm{EBIT \:= \:Earnings\: before \:interest \:and\: taxes}$$

$$\mathrm{MV\:= Market \:value \:of\: equity }$$

$$\mathrm{S \:= \:Sales}$$

$$\mathrm{D\:= \:Book \:value\: of \:debt}$$

With the use of statistical analysis, Altman predicted the cut-off Z score to be 2.675. Firms that had score of 2.675 or higher were considered financially sound whereas firms that had a score lower than 2.675 were prone to bankruptcy and therefore bad debt.

## Conclusion

Discriminant analysis is an effective method for multivariate analysis to extract relevant information from huge amounts of data. Loan processing speed has increased rapidly due to this scoring system.