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  Using Combinations of Ratios

Introduction to Using combinations of ratios

The weaknesses of univariate analysis have led researchers to build up models that combine ratios in such type of way like to generate a single index which can be interpreted more visibly. One way to model development, much favoured through researchers, applies multiple discriminate analyses (MDA). Basically, this is a statistical method that is identical to regression analysis and that can be employed to draw a boundary among those businesses which fail and those businesses that do not. This boundary is considered to as the discriminate function. In this situation, MDA attempts to recognize those factors probable to affect financial failure. Though, not like regression analysis, MDA supposes that the observations come from two dissimilar populations (for instance, failed and non-failed businesses) than from a single population.

To demonstrate this approach, let us suppose that we want to test whether two ratios (i.e. the current ratio and the return on capital employed) can assist to predict failure. For this, we can compute these ratios, 1st for a sample of failed businesses and then for a matched sample of non-failed ones. From these two sets of data we can generate a scatter diagram that plots every business as per to these two ratios to generate a single coordinate.

Figure demonstrates this approach.

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Figure: Scatter diagram showing the distribution of failed and non-failed businesses

By using the observations plotted on the figure, we try to recognize the boundary among the failed and the non-failed businesses. This is the diagonal line in Figure.

We can see that those businesses which fall below and to the left of the line are predominantly failed and those which fall to the right are predominantly non-failed ones.

Note:  there is some overlap among the two populations. The boundary generated is not likely, in practice, to eliminate all errors. Some businesses which fail may fall on the side of the boundary along with non-failed businesses. The reverse also occurs. Though, the analysis will minimise the misclassification errors.

The boundary that was displayed in Figure above can be expressed in the form

Z = a + (b × Current ratio) + (c × ROCE)

In which 'a' stands for a constant and b and c are weights to be attached to each ratio. A weighted average or total score (Z) is then derived. The weights provided to the two ratios will rely on the slope of the line and its absolute position. Note: this illustration, using the current and ROCE ratios, is entirely theoretical and only intended to demonstrate the approach.

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