UP College of Business Administration Discussion Papers DP No. 1006 June 2010 Degrees of Operating and Financial Leverage of Philippine Firms: 1997-2008 by
Rodolfo Q. Aquino*
*Professor, UP College of Business Administration  cba@up.edu.ph  +63 2 928 4571 to 75  +63 2 920 7990 http://www.upd.edu.ph/~cba
Degrees of Operating and Financial Leverage of Philippine Firms: 1997‐2008 Rodolfo Q. Aquino This paper asks whether the degree of operating leverage (DOL) and the degree of financial Leverage (DFL) are useful as external measures of the riskiness of a firm’s business operations, as they are applied to Philippine data. Two popular methods of estimating DOL and DFL are applied to data from 1998 to 2008: the Mandelker and Rhee method and its modification by O’Brien and Vanderheiden. The results of the empirical study are not very encouraging, casting doubts on the usefulness of DOL and DFL as external measures of operating and financial leverage. Further research is indicated in the direction of improving the estimation methods and in applying these to more accurate financial data. The influence of DOL and DFL on capital structure can also be looked into within the framework of competing capital structure theories. Key Words: Operating Leverage; Financial leverage; Business Risk; Capital Structure 1
Introduction The issue examined in this paper is whether the degree of operating leverage (DOL) and the degree of financial Leverage (DFL) are useful as external measures of the riskiness of a firm’s business operations, as they are applied to Philippine firm data. Two popular methods of estimating DOL and DFL are applied to published financial data from 1998 to 2008. The first was introduced by Mandelker and Rhee in 1984 which is denoted herein as the MR method. The second was a modification of the MR method for growing firms by O’Brien and Vanderheiden (1987) denoted here as the OV method. The next section discusses the two measures of leverage and reviews selected literature. The succeeding section then discusses the data and methodology used, followed by sections presenting the empirical results. The last section is a concluding section. Leverage Measures Finance textbooks (e.g., Brigham and Houston, 1996) define business risk as the riskiness of the firm’s operations assuming no debt. On the other hand, financial risk is the additional risk placed on the equity holders as a result of debt. Alternatively, business risk is defined as the uncertainty inherent in expected returns on assets and is claimed to be the single most important determinant of capital structure. Business risk is often measured by the firm’s operating leverage, i.e., the extent to which costs are fixed. A common measure of operating leverage, the break‐even chart was developed in the early 1900s by Professor Walter Rautenstrauch of the Industrial Engineering Department of Columbia University (Mansfield, 1966, p. 93). The reasoning is that the higher the level of fixed cost and the higher is the degree of operating leverage, a relatively small change in revenues will result in a relatively large change in operating income or earnings before interest and taxes (EBIT). This also means that the firm’s break‐even point is relatively high. The traditional break‐even chart assumes linear relations between revenues and total costs. Stated differently, fixed costs are, of course, fixed regardless of volume and revenue and variable cost per unit are constant (see Chart 1). The analysis is usually implemented by an account‐by‐account classification of costs and a straightforward computation of the break‐even point. However, this approach can only be done within the firm and not by an outsider looking only at published financial reports of firms. Thus, another measure was used defining the degree of operating leverage as the percentage change in EBIT per percentage point change in sales, in other words, the point elasticity of EBIT with respect to sales or, in terms of derivatives: d (EBIT)
DOL  EBIT d (S)
S
(1) 2
where S = total sales or revenues. Assuming linearity, finance textbooks give a simple formula for the degree of operating leverage: DOL 
S  VC
EBIT  F
F

 1
S  VC  F
EBIT
EBIT
(2) where VC =total variable costs, and F = fixed cost. As long as the firm has a positive contribution margin from sales (S – VC) this is greater than one and, starting at infinity, progressively declines at higher sales level. Thus, the farther away current revenues are from the break‐even point, the less business risk the firm is exposed to. Microeconomic theory (see, for example, Poblador, 1998), however, allows for nonlinear cases and assumes only that in general the second derivatives d2S < 0 and d2C > 0 (where C = total cost), that is, marginal revenue is declining with volume while marginal cost is increasing with volume (see Chart 2 for the break‐even chart under these assumptions). Assuming profit maximization, DOL ex ante should be zero as d(EBIT) in equation (1) will be zero. Past the optimal profit maximization point, DOL will turn negative as additional volume will only lead to reduced profits. Financial leverage magnifies the effect on net income to equity holders after interest and taxes of changes in the level of sales. The degree of financial leverage (DFL) is defined as the point elasticity of net income after interest and taxes with respect to EBIT. Again assuming linearity, this can be shown as: DFL 
EBIT
EBIT  Int
(3) where Int=Total Interest Expense. For positive EBIT, DFL is greater than one and increases as interest expense, due to higher debt, increases. A combine leverage measure, the degree of total leverage (DTL), is the product of DOL and DFL which in the linear case, simplifies to: DTL 
EBIT  F
EBIT  Int
(4) DTL, assuming linearity in revenues and costs, is always greater than one past the break‐even point and also increases as higher debt burden is assumed. The problem with DOL in equation (2) is that, like break‐even analysis, knowledge of the firm’s fixed cost and variable cost is required. Thus, for external analysis, recourse to other measurement techniques is needed. Using time series data, Mandelker and Rhee(1984) estimate equation (1) using econometric methods used in elasticity analysis (see, for example Gujarati, 1995, p. 165) with the regression equation: ln(EBITt )  cons tan t   ln(S t )   t , (5) 3
where β is the MR estimate of DOL which we denote here as DOL1 and μt is a disturbance term. The inherent assumptions in this method are that the product mix of firms are stable, inflation affects revenues and cost neutrally, and firm operations hover at a stable level from break‐even point. Mandelker and Rhee, using first differences in place of derivatives, show that equation (1) at time t is: EBIT t
EBIT t  EBIT t  1
1
EBIT t  1
EBIT t  1

DOL1t 
St
St  St  1
1
St  1
St  1
(6) O’Brien and Vanderheiden interpret St‐1 = E(St) and EBITt‐1 = E(EBITt) in equation (6), that is, the expected value of sales and EBIT in period t is adjusted to the level of their past realizations in the immediate past period, as in an adaptive expectations model. Generalizing this idea: EBIT t
1
E(EBIT t )
. DOL 2 
Rt
1
E(R t )
(7) Based on this re‐interpretation and further assuming that the expected values both grow at constant rates, the OV methodology involves estimating these rates of growth by running the following regressions: ln(EBIT t )  cons tan t   x T   xt (8) ln(S t )  cons tan t   S T   St (9) where T is a period counter. Then, a third regression is run on the residuals μxt and μst:
 xt   st   t (10) Note that the regression has no constant term as the residuals in equations (8) and (9) have zero means. The regression coefficient λ = DOL2 is precisely the ratio of deviations in equation (7) in the OV method. Data and Methodology The financial data from 1997 to 2008 used in this study are from the Business World Top 1000 Corporations published annually. Companies reported in the 2008 listing with at least five years of profitable operations are selected. This resulted in a sample of 143 firms, 17 of which are listed in the Philippine Stock Exchange. 4
Unfortunately, EBIT as such is not reported. Thus, this has to be estimated from the reported net income after taxes data by working backwards using imputed costs of borrowing and corporate income taxes. Interest expenses are imputed using the bank average lending rates for that particular year as reported by the Bangko Sentral ng Pilipinas. Income tax rates for corporations were 35% in 1997, 34% in 1998. 33% in 1999, 32% in 2000 to October 31, 2005, and 35% thereafter (it was again reduced to 30% effective January 1, 2009). This is a limitation of the study. DOL1 is estimated under the MR method using equation (5). DOL2 is estimated under the OV method using equations (8) to (10). By analogy, DFL1 and DFL2 are estimated using similar methods. Empirical results The estimates of DOL1 and DOL2 are summarized in Chart 3 and Table 1. It can be noted from the chart that a significant number of the computed DOLs are below 1 and even negative, contrary to the predictions of the linear break‐even model. One of the criticisms against the use of time series methods is that they tend to produce DOL estimates of less than one (see, for example, Lord, 1998). In an empirical study of 245 firms in the U.S., Dugan and Shriver (1992) have roughly 85% of the sample firms with DOL less than one using the MR methodology and 45% using the OV methodology. In this study, 65% of the sample firms have DOL less than one using the MR method and 53% using the OV method. In a simulation study, Lord attributes this to the high sensitivity of the methodologies to fluctuations in the firm’s operating parameters. He also cautions against the potential hazards in using simple linear or curvilinear proxies for underlying leverage constructs. Note, however, that the values obtained are consistent with the more general break‐even model depicted in Chart 2. It can also be noted from the chart the existence of a positive linear relationship between the estimates using the MR and OV methods with an R2 of 0.02 which is significant at the 0.90 significance level. On the other hand, running a regression of the difference between the two DOL estimates against past growth rates in revenues does not produce statistically significant results although the sign of the regression coefficient is consistent with theory. Table 1 summarizes the means and standard deviations of the estimated DOL1 and DOL2 for listed vs. non‐listed firms, by growth rates and by industry. Using paired observations, the hypothesis that the estimates of degrees of operating leverage using the two alternative methods are equal is not rejected in almost all groupings. The only exception is for the group where past growth rates in revenues range from 5% to 10% where the hypothesis of equality of means is rejected at the 95% confidence level. The estimates of DFL1 and DFL2 are summarized in Chart 4. Here, the positive linear relationship between the two estimators is more pronounced and statistically very significant. Other Measures of Leverage Other measures of operating leverage include the ratio of fixed assets to total assets (FA/TA) and asset turnover or the ratio of gross revenues to total assets (GR/TA). O’Brien and Vanderheiden call 5
these proxy measures of operating leverage1. We can add to these the standard deviation of past return on total assets (SD_ROTA) and the standard deviation of gross return on sales (SD_GROS). Shown below is the correlation matrix for these measures of operating leverage – DOL1, DOL2, FA/TA, SD_ROTA, and GR/TA. 0.14
DOL1  1.00

1.00
DOL2  0.14
FA / TA  0.05  0.12

 .10
GR / TA  0.07
0.08
SD _ ROTA  0.02

0.01
SD _ GROS  0..03
 0.05 0.07
0.02
0.03 
 0.12 0.10
0.08
0.01 
1.00  0.20  0.04  0.02
  0.20 1.00  0.06  0.35
 0.04  0.06 1.00
0.26 

 0.02  0.35 0.26
1.00 
Of the correlation coefficients, only those between DOL1 and DOL2, between FA/TA and GR/TA, and between SD_GROS and SD_ROTA are significant at 0.95, 0.90 and 0.95 significance levels, respectively. The correlation matrix of DFL1 and DFL2 with the debt to asset ratio (DRATIO)2, standard deviation of return on equity (SD_ROE), and standard deviation of net return on sales (SD_NROS) as alternative measures of financial leverage is shown below. 0.62
0.12
 0.3
0.18 
DFL1  1.00
 0.62
1.00
0.14  0.02 0.13 
DFL2 
DRATIO  0.12
0.14
1.00
0.08  0.02 

SD _ ROE  0.03  0.02 0.08
1.00
0.18 
SD _ NROS  0.18
0.13  0.02 0.18
1.00 
Of the correlation coefficients, only those between DFL1 and DFL2, between DFL2 and DRATIO, between DFL2 and SD_NROS, and between SD_ROE and SD_NROS are statistically significant at 0.99, 0.90, 0.95, and 0.95, in the order indicated. These poor correlation results cast doubt on the efficacy of these measures as reliable indicators of operating and financial leverage. Determinants of Leverage In this section, we examine whether the measures of leverage are determined by firm‐specific characteristics. 1
O’Brien and Vanderheiden mentioned two other proxies: the ratio of depreciation to sales and the ratio of depreciation to total assets. These are not considered here for lack of data. 2
The ratio of total debt to total assets is used because Philippine firms rely less on long term debt to finance even their long‐tern needs. The 2008 long term debt to total fixed capital (long term debt plus equity) is only 7% on the average. 6
Both DOL1 and DOL2 are regressed against FA/TA, GR/TA, and dummy variables representing whether the firm is listed and whether they belong to the manufacturing, trade, real estate, or other industries. In addition, Both DFL1 and DFL2 are regressed against FA/TA, GR/TA, DRATIO, and dummy variable representing whether the firm is listed and the industry dummy variables. The resulting regression coefficients, except for the intercepts, are all statistically insignificant. Concluding Remarks The results of the empirical study are not very encouraging. This cast doubts on the usefulness of DOL and DFL as external measures of operating and financial leverage. The poor results could very well be due to the weaknesses of the methods used because of their underlying assumptions or to the accuracy of the financial data employed. For whatever reason, it appears that the DOL and DFL have little usefulness at present in evaluating the inherent riskiness of individual business firms. Further research is indicated in the direction of improving the estimation methods and in applying these to more accurate financial data. The influence of DOL and DFL on capital structure can also be looked into within the framework of competing capital structure theories. 7
Acknowledgement The author thanks Prof. Erwin Raya for the use of his base data for 1997‐2006 and the UPCBA Librarian and her staff for their help is sourcing some references and the materials needed to complete the financial data.
8
REFERENCES Bingham, E.F. and Houston,, J.F. (1996). Fundamentals of Financial Management: The Concise Edition, Forth Worth: The Dryden Press. Business World (1998‐2009), Top 1000 Corporations in the Philippines (Vols 12‐23), Quezon City: Business World Publishing Corporation. Dugan, M. T. and Shriver, K. A. (1992), An empirical comparison of alternative methods for the estimation of the degree of operating leverage, Financial Review, 24, 309‐321. Gujarati, D. N. (1995), Basic Econometrics, 3rd ed. New York: McGraw‐Hill. Lord, R.A. (1998), Properties of time‐series estimates of degree of leverage measures, The Financial Review, 33, 69‐84. Mandelker, G. N. and Rhee, S. G. (1984), The impact of the degrees of operating and financial leverage on systematic risk of common stock, Journal of Financial and Quantitative Analysis, 24, 309‐391. Mansfield, E. (1966). Managerial Economics and Operations Research: Techniques, Applications, Cases, 3rd ed., New York: W. W. Norton & Co. O’Brien, T. J. and Vanderheiden, P. A. (1987), Empirical measurement of operating leverage for growing firms, Financial Management, 16, 45‐53. Poblador, N. S. (1998), The Economics of the Firm: Managerial Applications, rev. ed., Quezon City: AFA Publications, Inc. 9
‐
Revenues TR TC F BEP Quantity Chart 1 ‐ Break‐even Chart: Linearity Assumption 10
Revenues TC TR F BEP Optimum Quantityy Chart 2 ‐ Break‐even Chart Based on Economic Theory 11
10
DOL - OV Method
5
0
-5
-10
-4
-2
0
2
4
6
DOL - MR Method
Chart 3 – Degrees of Operating Leverage 12
6
DFL - OV Method
4
2
0
-2
-4
-4
-2
0
2
4
6
DFL - Method
Chart 4 – Degrees of Financial Leverage 13
Table 1 Empirical Comparison of DOL1 and DOL2 Estimates No.
Public Listing
Listed
Non-listed
Total
Growth Rate
Less than 0%
0-5%
5-10%
10-15%
15-20%
Over 20%
Industry
Manufacturing
Trade
Real Estate
Others
DOL1
Mean
S.D.
DOL2
Mean
S.D.
Paired
Observations
t-statistics
17
126
143
0.658
0.785
0.770
0.813
0.933
0.920
0.319
1.045
0.962
1.387
2.041
1.988
-0.992
1.390
1.112
14
30
47
22
15
15
1.512
0.629
0.563
0.681
0.943
0.964
0.873
0.988
0.989
0.881
0.473
0.660
1.403
0.910
1.151
0.443
0.812
1.026
1.656
2.173
2.000
2.861
0.631
1.098
-0.272
0.646
2.004
-0.376
-0.585
0.214
74
34
10
25
0.644
0.881
1.051
0.881
0.955
0.881
0.773
0.912
0.883
1.326
0.878
0.736
2.066
1.432
1.355
2.572
0.963
1.499
-0.480
-0.285
14