Un modello evoluto per lo studio della redditività - Pt. 1

An Advanced Model for the Study of Profitability - Pt. 1

The most important of the profitability indicators is undoubtedly the ROE ( Return On Equity ) , an economic index that measures the profitability of equity capital.

We will take a real journey inside this indicator, breaking it down into increasing levels of depth , starting from its classic formulation, given by:

1ST LEVEL OF ANALYSIS

Like other profitability indicators, ROE compares economic quantities (the result of the financial year) with patrimonial quantities (the equity ), so it expresses in a certain sense the yield (economic value) of a specific factor used (patrimonial value).

In other words, ROE answers the question “ how much does the capital contributed by the shareholders yield? ”.

Its popularity derives from the fact that it provides – with a single piece of data – not only an opinion on the quality of the management's work, but also a summary of the company's profitability as a whole: the numerator, in fact, being the last line of the Profit and Loss Statement, includes not only the result of the company's operational management (current management and investment management), but also of the non-operational one (financial, extraordinary and fiscal management).

Wanting to be more precise in its formulation, in the presence of significant changes in the Net Worth from one financial year to the next, to determine more truthfully the profitability of equity in year t , the average value of Equity could be used in the denominator, in this way:

For our discussion, we will ignore this particular consideration and develop all our calculations on the classical formula seen previously, without any loss of significance in the conclusions we will draw.

Through the DuPont scheme (named after the American chemical company DuPont Corporation, which was the first to use this performance measure back in 1914 on the initiative of its CFO Donaldson Brown), it is possible to break down the ROE into multiple indices, in order to better understand the company dynamics that influence its value and allow:

  • comparisons over time (e.g. investigating the causes of the reduction in profitability between year t – 2 and year t );
  • sector analysis (for example, comparing your performance with that of your direct competitors).

The first breakdown that we can carry out, starting from the original ROE formula, is the following (multiply the numerator and denominator by the Total Employment):

2nd LEVEL OF ANALYSIS

That is, in terms of indicators:

ROE = ROA x Equity Multiplier

In this 2nd level, ROE can be seen as the result of two indices:

  • ROA ( Return On Assets ) , a measure of the profitability of the company's activities, obtained by comparing the net result with the total company assets (a ROA of 10% means that every euro of capital invested in the company yields 10 cents);
  • the Equity Multiplier , obtained by comparing the uses to the risk capital; given that the total assets (Uses) is equal to the total Sources, that is:

Uses (= Sources) = Equity + Onerous Debt

By dividing all the factors by Equity , this multiplier can be rewritten as:

which represents a measure of the degree of leverage adopted by the company. All this is consistent with the fact that, as we will see shortly, under certain conditions, namely:

ROI > Cost of Debt

the level of debt has a positive leverage effect on ROE.

Regarding the leverage effect and its repercussions on the profitability of equity, it should be remembered that the ROE can be appropriately rewritten, after a series of simple steps, in the following way:

MODIGLIANI–MILLER FORMULA

Where:

  • ROI ( Return On Investments ) = EBIT / Total loans
  • i = cost of onerous debt
  • t = tax rate
  • s = incidence of extraordinary management

This formula demonstrates what was stated previously, that is, that in the case of a positive spread between ROI and the cost of debt , it is possible to use financial leverage to increase the return on equity. In fact, the Modigliani–Miller formula highlights how, with a ROI greater than the cost of debt, as the financial leverage increases ( onerous debt/Equity ), the ROE also increases proportionally, giving rise to what is commonly called the leverage effect (it is clear that the financial risk associated with debt and its excessive use must always be kept in mind!).

On the contrary, in the case of ROI lower than the cost of debt , it is necessary to try not to use – or at least to do so as little as possible – the use of debt and to instead favor the use of equity capital, in order not to risk seriously endangering the economic equilibrium of the company.

We have seen so far the first two levels of the DuPont model, and the Modigliani–Miller formula, necessary to understand a very important concept linked to ROE and its breakdown into subsequent levels: that of financial leverage .

In the next contributions we will continue to break down the ROE formula into ever greater levels of depth, and finally we will see a practical case to better understand the analysis potential of the DuPont scheme.

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