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Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at https://about.jstor.org/terms Operational Research Society and Palgrave Macmillan Journals are collaborating with JSTOR to digitize, preserve and extend access to The Journal of the Operational Research Society This content downloaded from 54.84.104.155 on Thu, 18 Jun 2020 17:31:21 UTC All use subject to https://about.jstor.org/terms Journal of the Operational Research Society (2003yf 8 ?2003 Operational Research Society Ltd. All rights reserved. 0160-5682/03 $15.00 www.palgrave-journals.com/jors 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 (DEAyf F D Q D X J P H Q W W K H W U D G L W L R Q D O U D W L R D Q D O \ V L V ' ( A 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 (2003yf G R L S D O J U D Y H M R U V 5 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 (DEAyf L Q Y D U L R X V G H F L V L R Q F R Q W H [ W V V X F K D s 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 *^ This content downloaded from 54.84.104.155 on Thu, 18 Jun 2020 17:31:21 UTC All use subject to https://about.jstor.org/terms 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 (GAAPyf L n the USA mandate that only earnings per share (EPSyf U H O D W H d 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 (ROEyf X V L Q J W K H ' X 3 R Q t model. ROE, measuring the relationship of net income to common equity, can be decomposed as follows: NI S A ROE= - x x (1yf S A B where profit margin = net income (NIyf 6 D O H V 6 \f; asset utilization = sales (Syf 7 R W D O $ V V H W V $ \f; equity multiplier = total assets (Ayf F R P P R Q H T X L W \ ( \f. This decomposition facilitates the examination of ROE in terms of a measure of profitability (profit marginyf O H Y H O R I D V V H W V U H T X L U H G W o generate sales (asset utilizationyf D Q G W K H I L Q D Q F L Q J R f those assets (equity multiplieryf $ V V X F K 5 2 ( H Q F R P S D V V H s measures of sales, net income, total assets, and common equity. The components given above (sales, net income, total assets, and common equityyf G H I L Q H L P S R U W D Q W G L P H Q V L R Q V R f 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 (lossesyf P D \ Q R W E H D S S U R S U L D W H 7 K H O L Q H D U S U R J U D P P L Q g problem of accommodating negative net incomes (net lossesyf F D Q E H D G G U H V V H G E \ G H I L Q L Q J W K H L Q S X W V D V W R W D l 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 equityyf D Q G V K R U W W H U m (costsyf U H V R X U F H V . 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 (1973-1992yf I R U W K H R L l 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 requestyf 7 K e 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 unityf E \ ' 0 8 E D V L V I R U W K H R L O D Q G J D s 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 valueyf D V T X L F N O \ D V R Q H \ H D U 7 K L V L V W K H I D V W H V t 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 This content downloaded from 54.84.104.155 on Thu, 18 Jun 2020 17:31:21 UTC All use subject to https://about.jstor.org/terms 50 Journal of the Operational Research Society Vol. 54, No. 1 Table 1 Descriptive statistics for raw ratios (1973-92yf I R U R L O D Q G J D V L Q G X V W U y Ratio Mean Median a Max Min (ayf / L T X L G L W \ U D W L R s 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 (byf 3 H U I R U P D Q F H U D W L R s 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 (cyf 6 R O Y H Q F \ U D W L R s 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 + Receivableyf & X U U H Q W / L D E L O L W L H V , CSHRAT = (Cash/Current Assetsyf , 1 9 5 $ 7 , Q Y H Q W R U \ & X U U H Q W $ V V H W V & $ ' & 0 $ & D V K / Current Liabilitiesyf O R J & D V K & X U U H Q W $ V V H W V \f, 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 Stockyf & X U U H Q W / L D E / R Q J W H U P ' H E W \f, GMRAT =(Sales - COGSyf 6 D O H ( 4 ) $ 5 = (Preferred Stocks + Common Stocksyf ) L [ H G $ V V H W V 6 ) $ 5 $ 7 6 D O H V ) L [ H G $ V V H W V 6 ( 4 5 $ 7 = Sales/(Preferred Stocks + Common Stockyf 5 7 $ 5 $ 7 5 H W D L Q H G ( D U Q L Q J 7 R W D O $ V V H W V . 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 (2yf 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 (1yf W K H I R U P X O D I R U G H W H U P L Q L Q J W K H G H Y L D W L R Q V \f from the optimum for the DEA efficiency scores is: Dit = 1 - DEAit, (3yf where D stands for deviation for ith firm (DMUyf D W W K e tth year. Similarly for the financial ratios listed in Table 2, we first determine the optimum values (operationally interpreted as maximum valuesyf I R U H D F K R I W K H V H U D W L R V I R U D S D U W L F X O D r 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 (DMUsyf F R Q V W L W X W H W K H X Q L Y H U V H , n other words, the deviation for individual ratios is computed as follows: RDit = Rmax - Rit (4yf where RDit is the deviation for a particular ratio for the ith firm (DMUyf L Q \ H D U W 5 L L V W D N H Q I U R P W K H L Q G L Y L G X D O U D W L R s in Table 2 and Rmax is the maximum (optimumyf Y D O X H R I W K e ratio, which is selected from all of the firms (DMUsyf L Q W K e industry. This content downloaded from 54.84.104.155 on Thu, 18 Jun 2020 17:31:21 UTC All use subject to https://about.jstor.org/terms 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 (ayf / L T X L G L W \ U D W L R s 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 (byf 3 H U I R U P D Q F H U D W L R s 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 (cyf 6 R O Y H Q F \ U D W L R s 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 (xyf \ $ [ $ [ W L \f *CURAT = Current Assets/Current Liabilities, QRAT = (Cash + Receivableyf & X U U H Q W / L D E L O L W L H V , CSHRAT =(Cash/Current Assetsyf , 1 9 5 $ 7 , Q Y H Q W R U \ & X U U H Q W $ V V H W V & $ ' & 0 $ & D V K / Current Liabilitiesyf O R J & D V K & X U U H Q W $ V V H W V \f, 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 Stockyf & X U U H Q W / L D E / R Q J W H U P ' H E W \f, GMRAT = (Sales - COGSyf 6 D O H ( 4 ) $ 5 = (Preferred Stocks + Common Stocksyf ) L [ H G $ V V H W V 6 ) $ 5 $ 7 6 D O H V ) L [ H G $ V V H W V 6 ( 4 5 $ 7 = Sales/(Preferred Stocks + Common Stockyf 5 7 $ 5 $ 7 5 H W D L Q H G ( D U Q L Q J 7 R W D O $ V V H W V . 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(5yf 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 (Diyf F R P S X W H G K H U H D U H W K H R - 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, respectivelyyf where the correlation coefficients (P-valueyf D U H V L J Q L I L F D Q t at 10yb R U O H V V I R U W R R I W K H \ H D U V . 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 DSEQRATyf W K H Q V K R U W H U W H U m ratios appeared more important for the three industries pooled (Table 5, column 5: DCURAT, DQRAT, and DCSHRAyf , Q V K R U W Q R H Y L G H Q W S D W W H U Q R I U D W L R V D U e 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 This content downloaded from 54.84.104.155 on Thu, 18 Jun 2020 17:31:21 UTC All use subject to https://about.jstor.org/terms 52 Journal of the Operational Research Society Vol. 54, No. 1 Tables 1 and 2yf K D G R X W R I V L J Q L I L F D Q W F R U U H O D W L R Q R I V L J Q L I L F D Q W F R U U H O D W L R Q F R H I I L F L H Q W V Z H U H V X P P H G D F U R V s 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 yearsyf certain industries and not others. However, when the number and fourth (29 yearsyf U H V S H F W L Y H O \ . 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 10yb R U O H V V \f 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 - Ratioyf 0 D [ L P X P 5 D W L R 0 L Q L P X P 5 D W L R \f. 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 (continuedyf 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 nThis content downloaded from 54.84.104.155 on Thu, 18 Jun 2020 17:31:21 UTC All use subject to https://about.jstor.org/terms EH Feroz et al-Financial statement analysis 53 Table 3 (continuedyf 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 This content downloaded from 54.84.104.155 on Thu, 18 Jun 2020 17:31:21 UTC All use subject to https://about.jstor.org/terms 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 combinedyf ' 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 10yb R U O H V V \f 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 - Ratioyf 0 D [ L P X P 5 D W L R 0 L Q L P X P 5 D W L R \f. (continuedyf This content downloaded from 54.84.104.155 on Thu, 18 Jun 2020 17:31:21 UTC All use subject to https://about.jstor.org/terms EH Feroz et al-Financial statement analysis 55 Table 4 (continuedyf 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 This content downloaded from 54.84.104.155 on Thu, 18 Jun 2020 17:31:21 UTC All use subject to https://about.jstor.org/terms 56 Journal of the Operational Research Society Vol. 54, No. 1 Table 5 Number of significant correlations (P-value 10yb R U O H V V \f for three industries separately and combined Oil and Pharmaceuticals Primary Totala Threea industries Ratio gas (1yf \f metals (3yf \f pooled (5yf 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 - Rityf 5 P D [ 5 P L Q \f, where R is each ratio in Table 1. DCURAT = (CURATmax - CURATityf & 8 5 $ 7 P D [ - CURATminyf D Q G V R R Q . 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 DMUsyf W K D W H [ K L E L W W K H V D P H P X O W L S O H L Q S X W V D Q G P X O W L S O e 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 caseyf Z K L O H S U R G X F L Q J D V P X F K R X W S X t (salesyf D V S R V V L E O H I U R P W K H J L Y H Q O H Y H O R I L Q S X W F R Q V X P S - tion. Those DMUs that comprise the efficient frontier are efficient, while those DMUs not on the efficient frontier are inefficient (enveloped by the efficient organizationsyf . 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 setyf : PE = (T, XTyf ( L < 7 ; 7 \f; i= 1 /,l Elpi = 1, i=-l iii > o} where i represents the general index of n DMUs comprising the industry and (YjT, Xjyf L V W K H W U D Q V S R V H G Y H F W R U R I R X W S X W s and inputs, for a particular firm under evaluation, denoted as DMUj. The technical efficiency status (efficient or inefficientyf I R r 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 outputsyf will cause an efficient DMU to become inefficient or any minuscule favorable perturbation (decrease in inputs and/or increase in outputsyf Z L O O F D X V H D Q L Q H I I L F L H Q W ' 0 8 W o 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 (DMUyf $ O D U J H V W D Q G D U G G H Y L D W L R Q L Q G L F D W H V O D U J H Y D U L D W L R n 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 (DMUsyf L Q W K H V D P H L Q G X V W U \ R Y H U D S H U L R G R I W L P H . This content downloaded from 54.84.104.155 on Thu, 18 Jun 2020 17:31:21 UTC All use subject to https://about.jstor.org/terms 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 valuesyf F R P S D Q \ L V D O V R \ H D U V F R P S D Q \ V P H D Q L V E D V H G R Q \ H D U V . 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 (GAAPyf D Q G R W K H U P D F U R - 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. This content downloaded from 54.84.104.155 on Thu, 18 Jun 2020 17:31:21 UTC All use subject to https://about.jstor.org/terms 58 Journal of the Operational Research Society Vol. 54, No. 1 References 1 Coase RD (1937yf 7 K H Q D W X U H R I W K H I L U P ( F R Q R P L F D : 386-405. 2 Chames A, Cooper W, Lewin A, and Seiford L (1994yf ' D W a Envelopment Analysis: Theory, Methodology and Applications. Kluwer Academic Publishers: Boston, MA. 3 Feroz EH, Raab R and Haag S (2001yf $ Q L Q F R P H H I I L F L H Q F y model approach to the economic consequences of the OSHA cotton dust regulations. Aust J Mngt 26: 69-90. 4 Beaver WH (1968yf 0 D U N H W S U L F H V I L Q D Q F L D O U D W L R V D Q G W K e prediction of failure. JAcc Res 6: 179-192. 5 Davis HZ and Peles YC (1993yf 0 H D V X U L Q J H T X L O L E U D W L Q J I R U F H s of financial ratios. Acc Rev 68(4yf . 6 Farrell NJ (1957yf 7 K H P H D V X U H R I S U R G X F W L Y H H I I L F L H Q F \ - 5 R y Statist Soc 120: 253-290. 7 Chares A, Cooper WW, Golany B, Seiford L and Stutz J (1985yf ) R X Q G D W L R Q V R I G D W D H Q Y H O R S P H Q W D Q D O \ V L V I R r 'Pareto-Koopmans' efficient empirical production functions. JEconom 30: 91-107. 8 Charnes A, Rousseau JJ and Semple JH (1996yf 6 H Q V L W L Y L W \ D Q d stability of efficiency classification in data envelopment analysis. J Productiv Anal 7: 5-18. Received May 2001; accepted July 2002 after two revisions This content downloaded from 54.84.104.155 on Thu, 18 Jun 2020 17:31:21 UTC All use subject to https://about.jstor.org/terms