Financial Management

Financial Statement Analysis: A Data Envelopment Analysis Approach

Author(s): E. H. Feroz, S. Kim and R. L. Raab

Source: The Journal of the Operational Research Society , Jan., 2003, Vol. 54, No. 1 (Jan., 2003), pp. 48-58

Published by: Palgrave Macmillan Journals on behalf of the Operational Research Society

Stable URL: http://www.jstor.com/stable/822748

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Journal of the Operational Research Society (2003) 54, 48-58 ?2003 Operational Research Society Ltd. All rights reserved. 0160-5682/03 $15.00

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Financial statement analysis: A data envelopment analysis approach

EH Ferozl*, S Kim2 and RL Raab1

1University of Minnesota, Duluth, MN, USA; and 2Rutgers University, Camden, NJ, USA, and Singapore Management University, Singapore

Ratio analysis is a commonly used analytical tool for verifying the performance of a firm. While ratios are easy to compute, which in part explains their wide appeal, their interpretation is problematic, especially when two or more ratios provide conflicting signals. Indeed, ratio analysis is often criticized on the grounds of subjectivity, that is the analyst must pick and choose ratios in order to assess the overall performance of a firm.

In this paper we demonstrate that Data Envelopment Analysis (DEA) can augment the traditional ratio analysis. DEA can provide a consistent and reliable measure of managerial or operational efficiency of a firm. We test the null hypothesis that there is no relationship between DEA and traditional accounting ratios as measures of performance of a firm. Our results reject the null hypothesis indicating that DEA can provide information to analysts that is additional to that provided by traditional ratio analysis. We also apply DEA to the oil and gas industry to demonstrate how financial analysts can employ DEA as a complement to ratio analysis. Journal of the Operational Research Society (2003) 54, 48-58. doi:10.1057/palgrave.jors.2601475

Keywords: accounting; data envelopment analysis; finance

Introduction

Financial analysts commonly use ratio analysis to measure the performance of firms. Finance and accounting texts devote a section to ratio analysis as a summary of accumu- lated knowledge necessary for the preparation of financial statements that are designed to report the performance of the entities to the stakeholders. During the late 1970s and early 1980s, the methodology of ratio analysis was considered suspect, especially by the advocates of the strong form of the efficient market hypothesis. However, in the wake of the stock market crash of 1987, the level of faith in the informational efficiency of the market waned, and ratio analysis again seemed to gain ground in academic literature.

*Correspondence: EH Feroz, 137 School of Business and Economics, University of Minnesota, Duluth, 412 Library Drive, Duluth, MN 55812-2496, USA. E-mail: [email protected]

Please do not quote without the permission of the authors. The algo- rithms used in this paper have provided a basis for Invention Disclosure with the University of Minnesota Patent Office.

Earlier versions of this paper were presented before the annual meeting of the Operational Research Society OR43; Accounting-Finance workshop of the University of Wisconsin-Milwaukee; Annual Meetings of the Amer- ican Accounting Association, Dallas, Texas; Annual Meetings of the Financial Management Association, New York; and the Western Economic Association Meetings, Vancouver, B.C.

In the Coasian tradition of the theory of the firm and related transaction cost analysis,' surviving firms indicate that there may be some firm-specific production or manage- rial efficiencies that are unlikely to be replicated by other firms in the same industry and the market, or those firms would not have survived in the first place. Earlier studies have demonstrated the general usefulness of Data Envelop- ment Analysis (DEA) in various decision contexts2 such as evaluating the income efficiency implications of the OSHA health and safety regulations.3 In this paper, we argue that DEA can complement traditional ratio analysis especially if the goal is to provide information regarding the operating and technical efficiency of the firm. Indeed, we demonstrate that there is a correspondence between the measurement of efficiency using ratios and the direction of the relative efficiency trends of firms as captured by DEA. Our null hypothesis is that there is no relationship between the DEA efficiency scores and those of financial ratios. Our empirical results demonstrate that there is a relationship between the deviations from the optimum DEA efficiency scores and the deviations from the optimum financial ratios.

The rest of the paper is structured as follows. The next section articulates the relationship between DEA and tradi- tional ratio analysis. The following sections revisit the ratio methodology in order to demonstrate the usefulness of DEA as a composite tool of financial statement analysis. A further

*^

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EH Feroz et al-Financial statement analysis 49

section illustrates the application of DEA to the oil and gas industry. The last section offers some conclusions.

Financial statement analysis: A DEA approach

Financial statement analysis has traditionally been per- formed using a set of ratios to highlight the relative performance of a firm as compared to its industry. The number of ratios that can be computed on the basis of financial data is constrained only by the imagination of the analyst. However, only a subset of the potentially infinite number of ratios can be meaningfully interpreted. Currently, the Generally Accepted Accounting Principles (GAAP) in the USA mandate that only earnings per share (EPS) related ratios be reported in the financial statements. Financial analysts, however, consider many other ratios. Two pro- blems with the traditional financial statements analysis are the one ratio at a time approach and the subjective choice of specific ratios to assess the overall health of a firm. So, we propose a more integrative model incorporating much of the information contained in financial ratios.

DEA can be applied to revenue-producing organizations by converting financial performance indicators to their technical efficiency equivalents. One such approach is to disaggregate Return on Equity (ROE) using the DuPont model. ROE, measuring the relationship of net income to common equity, can be decomposed as follows:

NI S A ROE= - x x (1)

S A B

where profit margin = net income (NI)/Sales (S); asset utilization = sales (S)/Total Assets (A); equity multiplier = total assets (A)/common equity (E). This decomposition facilitates the examination of ROE in terms of a measure of

profitability (profit margin), level of assets required to generate sales (asset utilization), and the financing of those assets (equity multiplier). As such, ROE encompasses measures of sales, net income, total assets, and common equity.

The components given above (sales, net income, total assets, and common equity) define important dimensions of the technical efficiency of a revenue-producing organization. That is, sales, total assets, and common equity can be minimized as inputs, and net income can be maximized as an output. This view identifies a technically efficient firm as

using a minimum of resources yet producing a maximum of net income. Because DEA does not work with negative numbers, the approach of explicitly modelling net income (losses) may not be appropriate. The linear programming problem of accommodating negative net incomes (net losses) can be addressed by defining the inputs as total assets, common equity, and costs, and defining the output as total revenues. This latter approach is used in this paper. In this way, financial ratios, commonly used to assess the financial performances of a firm, are systematically

incorporated into an operational definition of efficiency; revenues are maximized subject to the constraints from employing long-term (assets and equity) and short-term (costs) resources.

Review of ratio methodology

Best cases favoring the validity of ratios can be found in Beaver4 and Davis and Peles.5 Davis and Peles suggest that financial ratios do have equilibrium values; that is, they adjust to target values that may be managerially predeter- mined or may be simply an industry average. Davis and Peles distinguish ratios in terms of their differential rates of

adjustment to their equilibrium values. They predict that some of the ratios such as liquidity ratios are more likely to adjust faster than others.

The rows of Table 1 show the descriptive statistics for the three groups of the most commonly used ratios. The first group represents five liquidity ratios for the 29 COMPU- STAT firms over a 20-year period (1973-1992) for the oil and gas industry. The oil and gas industry is used as an example in this portion of the paper and comparable tables for the pharmaceuticals and primary metals are not included here (but are available from the authors upon request). The three unrelated industries were selected to test the null

hypothesis since ratio analysis is quite subjective and indus- try specific. The second and third group of ratios comprise five commonly used performance measures and six com- monly used solvency ratios for these COMPUSTAT firms over the same period of time. Table 1 contains the descriptive statistics of the financial ratios for the oil and gas industry. The mean and median ratios appear to have quite conven- tional values and generally are representative of COMPU- STAT firms and industries. Very small differences between the mean and median values of the ratios are evident. More-

over, these ratios are computed for 29 firms over 20 years comprising between 565 and 580 observations per ratio.

Table 2 provides the serial correlation coefficients of the first differences and lagged first differences of the dated financial ratios, which have been aggregated on a DMU (decision making unit) by DMU basis for the oil and gas industry. For the 20 years of data, 19 first differences were computed and 18 pairs of values were used to compute these serial correlation coefficients. This procedure resulted in a sample of 29 correlation coefficients per ratio. If mean reversion occurs in period one, then the coefficient should be -0.5. The mean reversion process occurs when a financial ratio reverts back to an original value (i.e., an equilibrium value) as quickly as one year. This is the fastest speed of adjustment and the serial correlation will approach a value of -0.5.

On the other hand, in a random walk, the mean reversion process does not occur, and the correlation coefficient will approach zero. Consistent with the Davis and Peles results, the serial correlation coefficients for liquidity ratios and

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50 Journal of the Operational Research Society Vol. 54, No. 1

Table 1 Descriptive statistics for raw ratios (1973-92) for oil and gas industry

Ratio Mean Median a Max Min

(a) Liquidity ratios CURAT* 1.414 1.340 0.515 7.782 0.000

QRAT 0.933 0.880 0.459 6.940 0.000 CSHRAT 0.214 0.190 0.150 0.910 0.001 INVRAT 0.292 0.280 0.134 0.690 0.000 CADCMA -0.278 -0.300 0.088 0.000 -0.370

(b) Performance ratios PEPS 2.070 1.990 3.530 19.000 -51.000 EPSPI 2.914 2.060 3.826 37.600 -51.000 EPSPX 2.050 2.010 3.244 16.500 -51.000 ROS 0.173 0.150 0.132 0.800 0.000 ROA 0.164 0.160 0.072 0.510 0.001

(c) Solvency ratios EQDRAT 0.948 0.875 0.485 0.339 0.000 GMRAT 0.263 0.240 0.178 0.950 0.160

EQFAR 0.691 0.680 0.356 2.410 -4.500 SFARAT 2.361 1.865 1.742 14.100 0.180

SEQRAT 3.394 2.720 2.505 20.500 0.260 RTARAT 0.295 0.320 0.161 0.670 -0.740

*CURAT = Current Assets/Current Liabilities, QRAT = (Cash + Receivable)/Current Liabilities, CSHRAT = (Cash/Current Assets), INVRAT = Inventory/Current Assets, CADCMA = - (Cash/ Current Liabilities) * log (Cash/Current Assets), PEPS = Primary Eps, EPSPI = Peps including Extraordinary & Discontinued Items, EPSPX = Peps excluding Extraordinary & Discontinued Items, ROS = Operating Income/Sales, ROA = Operating Income/Total Assets, EQDRAT = (Pref. Stocks + Common Stock)/(Current Liab + Long-term Debt), GMRAT =(Sales - COGS)/Sale, EQFAR= (Preferred Stocks + Common Stocks)/Fixed Assets, SFARAT= Sales/Fixed Assets, SEQRAT = Sales/(Preferred Stocks + Common Stock), RTARAT = Retained Earning/Total Assets.

performance measures are generally higher than the sol- vency ratios. Similar values between mean and median coefficients also confirm the symmetry of the distribution of the coefficients. Thus we conclude that the three indus-

tries that we analysed have mean reversion processes similar to the more general group of firms comprising the Davis and Peles sample.

Relationship between accounting ratios and DEA efficiency scores

In this study we stipulate that if DEA is a complement to the traditional accounting ratios, then there will be a relationship between the ratios and DEA efficiency scores. However, if DEA efficiency scores have incremental information content over and above traditional ratios, we will expect that the relationship between ratios and DEA scores will not be a perfect one.

In order to test our null hypothesis that there is no relationship between accounting ratios and DEA, we first compute the deviations from the optimum both for the individual ratios and the DEA efficiency scores. The DEA efficiency score is defined as:

eTYp + eTXp DEA = P+ P (2) eTy + eTXp + eTS+ + eTS-

where Yand X represent the efficient projections of output and input vectors. Since the optimum value for a DEA efficiency score is

one (1), the formula for determining the deviation(s) from the optimum for the DEA efficiency scores is:

Dit = 1 - DEAit, (3)

where D stands for deviation for ith firm (DMU) at the tth year.

Similarly for the financial ratios listed in Table 2, we first determine the optimum values (operationally interpreted as maximum values) for each of these ratios for a particular year and then determine the deviation from optimum values for individual ratios. In determining the optimum value for a

ratio for a particular year, we define the industry as the population in order to be consistent with our DEA notion that the group of firms (DMUs) constitute the universe. In other words, the deviation for individual ratios is computed as follows:

RDit = Rmax - Rit (4)

where RDit is the deviation for a particular ratio for the ith firm (DMU) in year t, Ri is taken from the individual ratios in Table 2 and Rmax is the maximum (optimum) value of the ratio, which is selected from all of the firms (DMUs) in the industry.

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EH Feroz et at-Financial statement analysis 51

Table 2 Descriptive statistics for serial correlation coefficients for oil and gas industrya

Ratio Mean Median a Max Min

(a) Liquidity ratios CURAT* -0.160 -0.154 0.182 0.173 -0.591 QRAT -0.189 -0.200 0.181 0.181 -0.591 CSHRAT -0.217 -0.232 0.221 0.326 -0.616 INVRAT -0.107 -0.089 0.210 0.251 -0.649 CADCMA -0.265 -0.266 0.171 0.071 -0.548

(b) Performance ratios PEPS -0.284 -0.270 0.204 0.079 -0.622 EPSPI -0.242 -0.269 0.201 0.150 -0.640 EPSPX -0.180 -0.202 0.195 0.183 -0.487 ROS -0.064 -0.056 0.205 0.363 -0.501 ROA -0.190 -0.213 0.183 0.254 -0.213

(c) Solvency ratios EQDRAT -0.111 -0.104 0.223 0.411 -0.591 GMRAT -0.016 -0.016 0.189 0.391 -0.490 EQFAR -0.073 -0.041 0.203 0.385 -0.546 SFARAT -0.013 -0.004 0.23 0.315 -0.427 SEQRAT -0.176 -0.173 0.238 0.354 -0.556 RTARAT -0.075 -0.058 0.213 0.403 -0.485

aSerial correlation coefficients are calculated for each ratio (x); y(Ax, Axt+i) *CURAT = Current Assets/Current Liabilities, QRAT = (Cash + Receivable)/Current Liabilities, CSHRAT =(Cash/Current Assets), INVRAT = Inventory/Current Assets, CADCMA =-(Cash/ Current Liabilities) * log (Cash/Current Assets), PEPS= Primary Eps, EPSPI = Peps including Extraordinary & Discontinued Items, EPSPX = Peps excluding Extraordinary & Discontinued Items, ROS = OperatingIncome/Sales, ROA = OperatingIncome/TotalAssets, EQDRAT = (Pref. Stocks + Common Stock)/(Current Liab + Long-term Debt), GMRAT = (Sales - COGS)/Sale, EQFAR = (Preferred Stocks + Common Stocks)/Fixed Assets, SFARAT = Sales/Fixed Assets, SEQRAT = Sales/(Preferred Stocks + Common Stock), RTARAT = Retained Earning/Total Assets.

Once we have computed the deviations of the individual ratios from the optimum, we transformed them to a 0-1 scale by using the following formula:

RD. t R(5) Rmax - Rmin

Note that this scaling was necessary in order to make the deviations of individual ratios comparable to the deviations of the DEA scores, which range from 0-1. It is also noteworthy that the deviations (Di) computed here are theo- retically more justifiable and not the same as the speed of adjustment computed in Davis and Peles. Unlike the present study, the Davis and Peles managerially determined targets are not identifiable benchmarks. Our deviations are closer to

the industry-determined targets in the sense that we define industry as the population in order to determine the opti- mum value for a particular ratio.

As Table 3 summarised in column 1 Table 5 indicates, there is a correlation between the deviations of the ratios and

the DEA efficiency deviations. Particularly noteworthy are relationships between DEA deviations and DSFARAT, DROS, DGMRAT, and DSEQRAT (scaled versions of SFARAT, ROS, GMRAT, and SEQRAT, respectively)

where the correlation coefficients (P-value) are significant at 10% or less for 14 to 19 of the 20 years.

If the DMUs of the three industries are combined and a

considerably larger "n" results for each of the 20 years, a somewhat different pattern of significant correlation coeffi-

cients results. If longer term ratios appeared more important for the total of the industries (Table 4 summarised in Table 5, column 4: DSFARAT and DSEQRAT), then shorter term ratios appeared more important for the three industries pooled (Table 5, column 5: DCURAT, DQRAT, and DCSHRA). In short, no evident pattern of ratios are highly correlated between particular industries or the totals of the three industries, or even when the three industries are

pooled. This result is expected since ratios often are criti- cized for their lack of temporal stability, general applicabil- ity, and industry specificity. A specific ratio, measuring a specific dimension of firm behavior, may be applicable only to a specific industry over a limited period of time.

Table 5 summarizes the number of significant correlation coefficients for the three industries. Not unexpectedly, the significant ratios, with respect to statistical significance and income efficiency, for the oil and gas industries may or may not be significant in the pharmaceuticals or primary metals industries. For example, DROS (scaled version of ROS in

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52 Journal of the Operational Research Society Vol. 54, No. 1

Tables 1 and 2) had 14 out of 20 significant correlation of significant correlation coefficients were summed across coefficients for oil and gas, but only 1 out of 20 for industries, DSFARAT seemed to be fairly significant for 43 pharmnaceuticals and only 6 out of 20 for primary metals. of the 60 possible years, followed by DSEQRA with It appears that certain ratios are appropriate for analysing 35 years; DROA and DCSHRA are the third (31 years) certain industries and not others. However, when the number and fourth (29 years), respectively.

Table 3 Correlation coefficient between the deviations of ratios and DEA deviation scores for the oil and gas industry'

1973 1974 1975 1976 1977 1978 1979 1980 1981

-0.019

0.92 25

-0.025

0.89

25

0.089

0.66

25

0.327

0.11

24

0.196

0.34

25

-0.093

0.66

25

0.270

0.19

28

-0.139

0.51

25

0.447

0.02

25

0.484

0.01

25

0.273

0.18

25

0.388

0.05

25

0.124 0.54

28

0.303

0.13

28

0.247

0.22

25

-0.005

0.82

25

0.228

0.58

28

-0.481

0.01

28

0.295

0.14

28

-0.595

0

26

0.117

0.57

28

0.449

0.02

28

0.293

0.14

28

0.422

0.03

25

0.3 17 0.11 28

0.25 1 0.21 28

0.238 0.24 28

0.045 0.81

25

0.123 0.55 28

-0.474 0.01 28

0.28 0.150

28

-0.567 0

26

0.27 0.18 28

0.401 0.04 26

0.308 0.12 28

0.294 0.15 25

0.168 0.41 28

0.06 0.77 28

-0.342 0.06 28

0.004 0.99 25

0.201 0.32 28

-0.549 0

28

0.3 16 0.11

28

-0.607 0

26

0.41

0.03 28

0.508 0

28

0.336

0.9 28

0.176 0.38 28

0.267

0.18 28

0.211 0.31 25

-0.373 0.08 25

0.015

0.94 26

0.153

0.45 28

0.293 0.14

26

0.120

0.56

26

0.258 0.21

26

0.31 0.12 26

0.215

0.29 28

0.253 -0.03 1

0.21 0.88

26 26

'Significant correlation coefficients (P-value 10% or less) are in bold numbers.

bDCURA~T DQRAT, etc., are scaled ratios of CURAT and QRAT, respectively, in Tables 1 and 2.

1-0 scale as follows: (Maximum Ratio - Ratio)/(Maximum Ratio - Minimum Ratio).

0.107

0.61 25

0.124

0.58 24

0.072 0.73 24

0.023 0.74 24

-0.166 0.43 24

-0.006 0.97 25

-0.001 0.99 24

0.119 0.57 24

0.403 0.06 24

0.354 0.08 24

0.254

0.23 24

-0.061 0.77 24

-0.132 0.51 26

-0.488 0.01 25

-0.019 0.92 25

0.272 0.17

28

0.15 0.47 25

-0.709 0

25

0.306 0.13

25

-0.484 0.01 .26

0.338 0.09 25

0.347 0.08 26

0.415

0.03 25

0.438 0.02 25

-0.036 0.86 26

-0.144 0.49 25

0.196 0.34 25

-0.024

0.91 28

0.327 0.09 25

-0.823 0 24

0.042 0.84 25

-0.51 0 26

0.405 0.04 25

0.418 0.03 26

0.402

0.04 25

0.427 0.03 25

Each variable per year is scaled do,wn to

(continued)

DCURATb P-value n

0.367 0.07 25

0.332

0.09

25

0.185

0.37

25

0.05 1

0.81

24

0.137

0.51

24

-0.07

0.74

25

0.398

0.06

25

-0.056

0.79

25

0.557

0.79

25

0.575

0

25

0.339

0.04

25

0.347

0.06

25

DQRAT P-value n

DCSHRA P-value n

DINVRAT P-value n

DEQRAT P-value n

DROS P-value n

DROA P-value n

DGMRAT P-value

n

DEQFAR P-value n

DSFARAT P-value

n

DSEQRA P-value n

DRTARA P-value n

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EH Feroz et al-Financial statement analysis 53

Table 3 (continued)

1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992

-0.077 0.273 0.047 0.031 0.015 0.162 0.219 0.537 0.108 -0.008 -0.094 0.71 0.17 0.82 0.88 0.84 0.38 0.29 0 0.81 0.97 0.66 25 26 25 25 25 25 25 25 25 25 24

-0.358 0.037 -0.329 -0.318 -0351 -0.032 0.174 -0.586 -0.038 -0.136 -141 0.06 0.85 0.11 0.12 0.09 0.88 0.38 0 0.85 0.51 0.51 24 25 24 24 24 24 25 25 25 25 24

-0.541 -0.388 -0.459 -0.541 -0.485 -0.139 0.153 -0.497 -0.119 -0.2 -0.262 0 0.05 0.02 0 0.01 0.51 0.48 0.01 0.57 0.33 0.21 24 25 24 24 24 24 25 24 24 25 24

0.258 0.352 0.261 0.033 0.269 0.136 0.021 0.134 0.264 0.12 0.211 0.21 0.07 0.19 0.87 0.17 0.52 0.92 0.53 0.19 0.56 0.32 25 28 25 24 24 24 24 24 24 25 24

0.201 0.235 0.083 0.054 0.058 -0.116 -0.268 -0.184 -0.048 0.178 -0.07 0.34 0.25 0.69 0.79 0.79 0.58 0.19 0.38 0.81 0.39 0.74 25 25 24 24 25 25 25 25 25 25 24

-0.849 -0.788 -0.831 -0.881 -0.51 -0.272 0.701 -0.717 -0.137 -0.442 -0.585 0 0 0 0 0.01 0.19 0 0 0.51 0.02 0 25 25 24 23 25 23 26 26 26 26 25

-0.202 -0.007 -0.251 0.208 0.374 -0.363 -0.701 0.200 0.566 0.304 -0.061 0.34 0.97 0.23 0.34 0.08 0.21 0 0.32 0 0.13 0.77 25 25 24 23 22 23 26 26 26 26 25

-0.473 0.437 -0.426 -0.302 0.116 -0.362 -0.782 -0.37 -0.371 -0.502 -0.545 0.01 0.02 0.03 0.14 0.58 0.08 0 0.08 0.08 0 0 25 26 25 25 24 25 26 26 26 26 25

0.511 0.567 0.403 0.333 0.411 0.044 0.229 -0.171 0.073 -0.089 0.009 0.01 0 0.05 0.11 0.04 0.83 0.26 0.41 0.72 0.86 0.97 24 25 24 24 24 24 26 26 28 28 25

0.498 0.465 0.538 0.422 0.539 0.412 0.502 0.492 0.47 0.641 0.533 0.01 0.01 0 0.03 0 0.04 0 0.01 0.01 0 0 25 26 25 25 25 24 26 26 26 26 25

0.464 0.371 0.596 0.56 -0.02 0.474 0.645 0.698 0.416 0.522 0.394 0.02 0.06 0 0 0.91 0.01 0 0 0.03 0 0.05 25 25 24 24 24 24 26 25 26 26 24

-0.092 -0.256 -0.182 0.477 -0.396 -0.299 0.358 -0.225 -0.145 -0.181 -0.094 0.68 0.22 0.41 0.02 0.06 0.17 0.08 0.31 0.51 0.39 0.66 25 24 22 23 23 22 24 22 24 26 23

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54 Journal of the Operational Research Society Vol. 54, No. I

Table 4 Correlation coefficient between the deviations of ratios and DEA deviation scores (Three industries combined)'

1973 1974 1975 1976 1977 1978 1979 1980 1981

DCURATb P-value n

DQRAT P-value n

DCSHRA P-value n

DINVRAT P-value

n

DEQRAT P-value n

DROS

P-value n

DROA P-value n

DGMRAT P-value

n

DEQFAR P-value n

DSFARAT P-value

n

DSEQRA P-value n

DRTARA P-value

n

-0.343 0.00 73

-0.237 0.03 76

-0.121

0.29 75

-0.173 0.14

73

-0.118 0.31 73

-0.016 0.88 72

0.026 0.82

72

0.137

0.23 77

0.117 0.32 73

-0.129 0.25

78

0.133 0.25 75

0.331 0.01

59

-0.144 0.20 80

-0.047

0.67 82

0.055

0.62 79

-0.070 0.53

78

0.098 0.39 78

-0.069 0.55

73

0.110 0.35

74

0.027

0.8 81

0.139 0.34 48

0.212 0.05

80

0.08 1 0.45 80

0.222 0.07 64

-0.226 0.04 80

-0.052 0.64 81

-0.313 0 76

-0.074 0.52

77

-0.173 0.12

78

0.040 0.73 72

0.282 0.01 73

0.760

0.5 78

0.4 13 0.21

78

0.323 0.00 77

0.379 0.00

79

0.126 0.32 64

-0.167 0.14 78

-0.161

0.15 78

-0.081

0.49 74

0.002 0.98

77

-0.290 0.01 73

-0.204 0.08 71

-0.152 0.20

70

-0.028

0.81 78

-0.190 0.09

78

-0.005 0.95

79

0.113 0.32 76

-0.183 0.12

64

-0.264 0.01 80

-0.208 -0.05

82

-0.114 0.31 79

-0.020 0.85

78

-0.105 0.35

79

-0.172 0.13

77

-0.170 0.13 77

-0.171 0.12 82

0.217 0.05 79

0.233 0.03 79

0.437

0.00 80

0.320 0.00

71

-0.303 0.00 77

-0.275 0.01 76

0.057 0.62 75

-0.011 0.92

75

-0.050 0.66 75

0.128 0.29 70

-0.183 0.13 68

0.100

0.38 76

0.240

0.03 74

0.417

0.00

73

0.387 0.00 74

0.205 0.10

64

-0.449 0.00 74

-0.494

0 75

-0.036 0.76 74

-0.010 0.92 71

-0.018 0.87

75

0.212 0.08

66

0.12 1 0.33

68

0.044

0.7 74

0.185

0.11 74

0.318

0.00 72

0.105 0.36 75

0.247 0.04

67

-0.221 0.05 74

-0.158 0.15

74

-0.158 0.15 73

0.003 0.97

72

0.029 0.80 73

0.049 0.88 59

0.150 0.21

70

-0.200 0.08 76

0.112

0.34 73

0.297

0.01 72

0.401 0.00 73

0.120 0.32 70

-0.200 0.07 79

-0.191 0.08 77

-0.096 0.4 77

-0.077 0.51

75

-0.069 0.58 77

0.061 0.61 69

-0.081 0.50 69

0 0.990

79

0.307 0.00

77

0.363 0.00 77

0.143 0.21 78

0.25 0.03 72

'Significant correlation coefficients (P-value 10% or less) are in bold numbers. bDCURAT, DQRAT, etc., are scaled ratios of CURAT and QRAT, respectively, in Tables 1 and 2. Each variable per year is scaled down to 1-0 scale as follows (Maximum Ratio - Ratio)/(Maximum Ratio - Minimum Ratio).

(continued)

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EH Feroz et al-Financial statement analysis 55

Table 4 (continued)

1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992

-0.356 -0.438 0.091 -0.019 0.255 0.107 -0.194 -0.303 -0.294 -0.216 0.005 0.00 0.00 0.45 0.87 0.03 0.38 0.11 0.01 0.01 0.07 0.95 76 74 69 67 66 68 67 89 68 68 64

-0.193 -0.111 -0.013 -0.198 0.090 -0.352 -0.485 -0.312 -0.454 -0.223 -0.382

0.1 0.35 0.91 0.11 0.47 0 0 0 0 0.06 0

73 72 67 66 64 68 67 89 89 85 59

0.042 -0.142 0.037 -0.247 -0.107 -0.137 -0.228 -0.197 -0.213 -0.255 -0.107

0.72 0.23 0.76 0.04 0.39 0.27 0.06 0.1 0.07 0.02 0.39

73 72 66 65 65 66 66 69 69 68 64

-0.192 -0.074 -0.081 -0.100 -0.069 -0.268 -0.176 -0.048 0.107 -0.113 -0.170

0.10 0.53 0.50 0.42 0.58 0.03 0.15 0.69 0.39 0.36 0.18

71 72 68 66 65 65 66 67 66 67 63

-0.127 0.008 0.089 -0.280 -0.047 0.435 0.439 0.003 -0.122 -0.159 0.200

0.28 0.95 0.46 0.03 0.70 0.00 0.00 0.97 0.31 0.19 0.11

73 72 58 66 54 88 66 59 68 68 64

0.010 -0.375 -0.255 -0.269 -0.182 -0.404 -0.480 -0.563 -0.634 -0.498 -0.560

0.93 0.00 0.03 0.01 0.12 0.00 0.00 0.00 0.00 0.00 0.00

66 85 65 66 64 67 87 68 68 67 57

0.160 0.026 0.038 -0.050 0.002 -0.303 -0.159 -0.151 -0.008 -0.095 -0.454

0.29 0.83 0.75 0.68 0.98 0.01 0.15 0.21 0.94 0.43 0.00

45 66 66 66 64 67 67 68 68 67 57

-0.102 -0.182 -0.163 -0.078 0.035 -0.470 -0.120 -0.103 -0.226 -0.078 -0.034

0.39 0.12 0.18 0.52 0.77 0.7 0.33 0.39 0.060 0.52 0.78

71 72 68 68 86 86 68 69 69 88 64

0.444 0.287 0.188

0.00 0.01 0.12

73 73 69

0.233 0.001 -0.081 -0.032 0.034

0.06 0.88 0.50 0.79 0.77

65 64 68 66 69

0.05 1

0.67

69

0.215 0.416

0.07 0.00

68 64

0.099 0.233 0.190 0.103 -0.086 0.070 -0.002 0.115

0.38 0.04 0.11 0.40 0.48 0.56 0.98 0.34

74 74 69 67 66 68 67 69

-0.116 0.120 0.309

0.33 0.30 0.01

71 73 68

0.18

0.14

68

0.12 1

0.33

65

0.002 0.335 0.1l7 5

0.98 0.00 0.16

6 9 6 8 64

0.091 0.134 -0.129 0.045 0.246 -0.076

0.45 0.28 0.70 0.70 0.04 0.02

68 56 69 89 87 64

0.257 0.336 0.304 0.152 0.048 -0.040 0.064 -0.010 -0.010 -0.001 -0.078 0.03 0.00 0.01 0.22 0.70 0.74 0.61 0.93 0.93 0.99 0.55 68 69 65 65 62 67 64 65 65 65 81

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56 Journal of the Operational Research Society Vol. 54, No. 1

Table 5 Number of significant correlations (P-value 10% or less) for three industries separately and combined

Oil and Pharmaceuticals Primary Totala Threea industries Ratio gas (1) (2) metals (3) (4) pooled (5)

DCURATb 2 9 3 14 13 DQRAT 5 15 3 23 12 DCSHRA 7 18 4 29 6 DINVRAT 2 16 4 22 2

DEQRAT 1 12 3 16 4 DROS 14 1 6 22 11 DROA 4 14 13 31 3 DGMRAT 14 5 5 24 2

DEQFAR 9 11 5 25 9 DSFARAT 19 14 10 43 9

DSEQRA 14 18 3 35 7 DRTARA 8 4 2 14 9

aColumn 4 is the sum of columns 1, 2, and 3. Column 5 is based on pooling of the three industries before the correlation coefficients were computed. b(Rmax - Rit)/(Rmax - Rmin), where R is each ratio in Table 1. DCURAT = (CURATmax - CURATit)/(CURATmax- CURATmin), and so on.

An illustrative DEA application to oil and gas industry

As we have argued, DEA is an analytical tool for evaluating the relative technical efficiency of a firm or a set of firms (or

DMUs) that exhibit the same multiple inputs and multiple outputs. As a linear programming implementation of Farrell's6 notion of technical efficiency, DEA is an 'extremal' approach to efficiency evaluation, constructing an efficient frontier composed of those DMUs that consume as little input as possible (total assets, common equity, and costs of goods sold in our case), while producing as much output (sales) as possible from the given level of input consump- tion. Those DMUs that comprise the efficient frontier are efficient, while those DMUs not on the efficient frontier are

inefficient (enveloped by the efficient organizations). In this illustration, we employ the additive model of Charnes et al.7 The basic formulation of the additive model of DEA utilizes the convex hull input consumption and output production for all of the observed DMUs. A particular DMU's input consumption and output production represents that DMU's component vector. The component vectors for all DMUs examined are combined to form the

empirical production possibility set (reference set):

PE = (T, XT)= E i(YT XT); i= 1 /,l

Elpi = 1, i=-l

iii > o}

where i represents the general index of n DMUs comprising the industry and (YjT, Xj) is the transposed vector of outputs and inputs, for a particular firm under evaluation, denoted as DMUj.

The technical efficiency status (efficient or inefficient) for each DMU is determined by comparing its component vector to PE. If no other component vector, observed or hypothetical, in PE consumes the same or less input while

simultaneously producing more or the same output, with at least one strict inequality, then the DMU is deemed techni- cally efficient. Those DMUs not meeting the above criteria are deemed technically inefficient.

Chares et al8 developed a sensitivity analysis technique based on the oo-norm measure of a vector that defines the

necessary simultaneous perturbations to the component vector of a given DMU to cause it to move to a state of 'virtual' efficiency. Virtual efficiency is defined as a point of the efficient frontier where any minuscule detrimental perturbation (increase in inputs and/or decreases in outputs) will cause an efficient DMU to become inefficient or any minuscule favorable perturbation (decrease in inputs and/or increase in outputs) will cause an inefficient DMU to become efficient. Once the stability index is known for each DMU, the DMUs can be ranked from most robustly technically efficient to most robustly inefficient. To do so, the stability indexes for inefficient DMUs are first negated. Then the DMUs can be rank ordered from highest to lowest based on their stability index values.

As an illustration, descriptive statistics for DEA stability index values are shown for the oil and gas industry in Table 6. Cross-section DEA stability indexes were calculated for each year for a maximum of 26 firms. The means of the stability indexes over the 20 years are shown in the third column. Exxon's large positive value indicates a robustly efficient firm (DMU). A large standard deviation indicates large variation in predominantly positive stability index scores for the 20 years. On the other hand, Wainoco Oil Corporation's largest negative mean stability index value represents robust inefficiency and has the lowest efficiency, being in the 26th ranking. Wainoco's high standard deviation indicates a large variation in predominantly negative stability scores for the 20 years. By using this procedure, the stability index rank- ings, an analyst can obtain a composite measure for verifying the performance of a particular firm as compared to other firms (DMUs) in the same industry over a period of time.

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EH Feroz et al-Financial statement analysis 57

Table 6 DEA stability index rankings by firm for oil and gas industry

Stability Mean of stability of index for Standard deviation of stability index rankings Firm 20 years" index for 20 yearsa

8 Amerada Hess Corp 0.0298 0.1476 20 Amoco Corp -0.0014 0.0141 3 Ashland Oil Inc 0.1404 0.0545 11 Atlantic Richfield 0.0272 0.1334 16 Chevron -0.0073 0.0139 9 Crown Central 0.0286 0.0426 1 Exxon Corp 0.4117 0.0467 22 Fina Inc -0.0212 0.0163 6 Holly Corp 0.0968 0.2186 24 Kerr-McGee Corp -0.0303 0.0251 13 Louisiana Land 0.0100 0.0854 17 Mapco Inc -0.0089 0.0193 6 Mobil Corp 0.0540 0.0353 25 Murphy Oil Corp -0.0369 0.0359 12 Pennzoil Co 0.0127 0.1153 14 Phillips Petroleum 0.0061 0.0458 23 Quaker State Crop -0.0265 0.0245 15 Royal Dutch Pet -0.0004 0.0084 19 Shell Tran Trade -0.0099 0.0101 21 Sun Co Inc -0.0203 0.0188 7 Tesoro Petroleum 0.0367 0.0803 9 Texaco Inc 0.0286 0.0446 2 Tosco Corp 0.1728 0.2034 5 Total Petroleum 0.0908 0.3032 21 Unocal Corp -0.0140 0.0149 26 Wainoco Oil Corp -0.0516 0.2065

aOr less if negative equity should occur in a given year. Three of the 27 firms showed negative equity for a total of nine years: Company 20's mean is based upon 18 years (or tau values); company 22 is also 18 years; company 24's mean is based on 15 years. In 24 other firms the mean was based on 20 observations.

Summary and limitations

In this paper we demonstrate that DEA can complement traditional accounting ratios used as a tool for financial statement analysis. In order to demonstrate the relevance of DEA as a tool for financial statement analysis, we revisited the financial ratio based analysis of Davis and Peles. Our replication results indicate that our initial analysis is con- sistent with those of Davis and Peles so that we can establish

a benchmark for comparing DEA with the accounting ratios. Although our null hypothesis stipulated that there will be no relationship between deviations from optimum DEA effi- ciency scores and deviations from optimum values of financial ratios, our results in Tables 3-5 indicate that the financial ratios provide only an ad hoc and partial evaluation of firm performance. We then demonstrate how financial analysts can employ the stability index rankings to obtain a consistent measure of the overall performance of firm using the rest of the industry as a consistent norm.

As with other empirical research, our analysis could be suffering from the time-period effects, caused by the changes in the accounting convention (GAAP) and other macro- economic variables. A compensating factor, however, would be the practice of restating earnings and relevant financial

statement numbers for some of the changes implemented after the inception of the Financial Accounting Standard Board in 1973.

We believe that these results demonstrate that DEA can

complement traditional ratios as a composite tool for finan-

cial statement analysis, especially since it avoids the pitfalls of the one-ratio-at-a-time approach common to ratio analy- sis. Availability of user-friendly DEA software makes this approach particularly attractive from the point of view of financial analysts. We certainly hope that financial analysts looking for a reliable tool of analysis will find the DEA approach outlined in this paper sufficiently easy to replicate in a practice setting. We have demonstrated that the DEA approach simultaneously measures efficiency, while ratios can only provide ad hoc or anecdotal information. Our research findings indicate that DEA deviations and ratio deviations are somewhat correlated, but not in a systematic way. This indicates that DEA efficiency scores have incre- mental information contents over and above the information

generated by ratios. Future research might devise a truly independent test, which would hopefully be an advancement over our somewhat modest claim that DEA can augment the traditional ratio analysis.

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58 Journal of the Operational Research Society Vol. 54, No. 1

References

1 Coase RD (1937). The nature of the firm. Economica 4: 386-405.

2 Chames A, Cooper W, Lewin A, and Seiford L (1994). Data Envelopment Analysis: Theory, Methodology and Applications. Kluwer Academic Publishers: Boston, MA.

3 Feroz EH, Raab R and Haag S (2001). An income efficiency model approach to the economic consequences of the OSHA cotton dust regulations. Aust J Mngt 26: 69-90.

4 Beaver WH (1968). Market prices, financial ratios and the prediction of failure. JAcc Res 6: 179-192.

5 Davis HZ and Peles YC (1993). Measuring equilibrating forces of financial ratios. Acc Rev 68(4): 725-747.

6 Farrell NJ (1957). The measure of productive efficiency. J Roy Statist Soc 120: 253-290.

7 Chares A, Cooper WW, Golany B, Seiford L and Stutz J (1985). Foundations of data envelopment analysis for 'Pareto-Koopmans' efficient empirical production functions. JEconom 30: 91-107.

8 Charnes A, Rousseau JJ and Semple JH (1996). Sensitivity and stability of efficiency classification in data envelopment analysis. J Productiv Anal 7: 5-18.

Received May 2001; accepted July 2002 after two revisions

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