Accounting and financial performance indicators
Accounting and general financial performance indicators are usually expressed as ratios derived from information contained on corporate financial statements. While ratios such as return on assets (ROA), return on equity (ROE), return on capital employed (ROCE), debt equity ratio (DER), net profit margin (NOM), gross profit margin (GPM), and inventory turnover rate (ITR) are fractional ratios that can be expressed as mere fractions or in percentages, others such as earning per share (EPS), receivable turnover ratio (RTR) or average collection period (ACP) and others may be expressed in monetary or time denominated terms as kobo or cents per share or days. The objective of whichever form the ratio takes is to convey a useful information to the recipient of such information.
The knotty point in the use of accounting ratios, however, is the fact that accounting performance data may include different elements in its composition, such as fractional values, days and monetary denominations which must be fused together to obtain the geometric mean. For instance, supposing a researcher wants to study the relationship between a company’s performance as proxied with ROCE, ROA, EPS, and ACP surrogates over a 20-year period, and the personnel (PER), administrative (ADM), financial (FIN), and marketing (MKT) costs; the researcher has the option of studying the relationship between each surrogate of the performance variable and the four independent variables of PER, ADM, FIN, and MKT or combining the four surrogates into one using a geometric mean. If he decides to study them individually, he will end up with four models and four conclusions, which might conflict with one another thereby rendering the process an exercise in futility. However, if he decides to unify them with a mean, he will have to deal with the problem of bringing all the variables under a common denominator since ROCE and ROA will be in fractions while EPS will be either book value or market value denominated, and ACP will be time denominated as ACP is always expressed in days.
To resolve the issue, the EPS and the ACP must be converted to fractions in line with ROCE and ROA. To convert the EPS into a fraction, it is necessary to divide the EPS with the market value of the share of the firm, if it is market regulated or with the par/book value of the share if the firm is not listed or quoted. To convert the ACP to fraction, two steps must be followed – the first step is to divide the ACP with 365, the number of days in a year whilst the second step is to deduct the resulting fraction away from one. This two-prong approach to convert ACP to fraction is necessary because efficiency in credit administration relies much on the shortness of the debtors’ collection period. The shorter the period, the more efficient the firm’s credit administration is adjudged. When a relatively short ACP is converted to a fraction with the first step, it will show a small value which will be suboptimal when used in a regression analysis, but when this value is deducted from one, it will reveal the true fraction or percentage of efficiency achieved in credit administration by the firm. For instance, assuming companies A and B achieved 32- and 45-days ACP respectively, at first step fractional conversion, company A will have ACP fraction of 0.0877 (8.77%) while company B will return ACP fraction of 0.1233 (12.33%) which is indeed confusing and totally incorrect because from the face value of it, company A performed better than B in credit control, and not the other way round. In order to correct this anomaly, it will be necessary to take away the earlier computed fractions from one, such that the new ACP fractions become 0.9123 (91.23%) for company A and 0.8767 (87.67%) for company B which echoes the reality of credit control events in the two firms. Succinctly, the formula for the EPS and ACP fractional conversions are given in equations (1) and (2) below:
EPS (in fraction) = \(\frac{\text{EPS}}{\text{Share\ Price}}\) (1)
ACP (in fraction) = \(1-\ \frac{\text{ACP}}{365}\) (2)
To complete our sample analysis, it is necessary to bring all the four surrogates of the financial performance dependent variable into one using the geometric mean formula as follows:
FP = \(\sqrt[4]{\text{ROCE}}\text{\ x\ ROA\ x\ EPS\ x\ ACP}\) (3)
The number 4 in the formula (equation 3) was used there because the number of elements requiring a geometric mean is four. That is to say that the geometric mean of the product of the four elements is the fourth (4th) root. If the number is five, then the geometric mean will be the fifth (5th) root, and so on.
Where,
FP = Financial Performance ROCE, ROA, EPS, and ACP as previously defined.
With the variables now defined and brought under a uniform measurement platform, we can now fit the ordinary GLM as follows:
FP = β0 + β1PER + β2ADM + β3FIN + β4MKT + ε (4)
With this overall unified dependent variable GLM regression model, it will be easy to predict the impact of each of the four cost elements on the overall fortunes or profitability of the company for the 20-year period under review.