Description
This paper aims to identify the more accurate method of estimating a firm’s degree of
operating leverage (DOL) between two popular DOL estimation techniques: that proposed by
Mandelker and Rhee (M&R), and that proposed by O’Brien and Vanderheiden (O&V).
Journal of Financial Economic Policy
An additional analysis on operating leverage estimation methods
Steven Stelk Sang Hyun Park Michael T Dugan
Article information:
To cite this document:
Steven Stelk Sang Hyun Park Michael T Dugan , (2015),"An additional analysis on operating leverage
estimation methods", J ournal of Financial Economic Policy, Vol. 7 Iss 2 pp. 180 - 188
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Santi Gopal Maji, Utpal Kumar De, (2015),"Regulatory capital and risk of Indian banks: a
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http://dx.doi.org/10.1108/J FEP-06-2014-0038
Kristoffer J . Glover, Gerhard Hambusch, (2014),"The trade-off theory revisited: on the effect of
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An additional analysis on
operating leverage estimation
methods
Steven Stelk
Department of Finance, Real Estate and Business Law,
The University of Southern Mississippi, Hattiesburg, Mississippi, USA, and
Sang Hyun Park and Michael T. Dugan
Knox School of Accountancy, Hull College of Business, Augusta, Georgia, USA
Abstract
Purpose – This paper aims to identify the more accurate method of estimating a frm’s degree of
operating leverage (DOL) between two popular DOL estimation techniques: that proposed by
Mandelker and Rhee (M&R), and that proposed by O’Brien and Vanderheiden (O&V).
Design/methodology/approach – O’Brien and Vanderheiden argue that M&R measure growth in
operating earnings relative to the growth in sales rather than DOL. The authors estimate the relative
growth estimate, RGE, fromthe O&Vtechnique (operating earnings growth rate/sales growth rate) and
compare this with the DOL estimates from the M&R technique to see if they are similar.
Findings – The authors fnd that the DOLestimates fromthe M&Rmethod are indistinguishable from
the relative growth estimates from the O&V method, providing the frst direct evidence that O&V’s
critique is correct. The M&R DOL estimates primarily measure the growth in operating earnings
relative to the growth in sales, not DOL.
Originality/value – A frm’s DOL is a determinant of its common stock’s systematic risk, which
determines a frm’s equity cost of capital. The equity cost of capital is a fundamental part of capital
budgeting, capital structure and stock price analysis. Accurately estimating a frm’s DOL is important
to researchers and corporate fnancial managers. Existing diversity in DOL estimation techniques
raises questions about the validity of various techniques and limits comparability of existing studies.
This paper demonstrates why the O&V technique should be used in place of the M&R method.
Keywords Estimation, Financial risk and risk management, Corporate fnance and governance,
Capital budgeting
Paper type Research paper
1. Introduction
A large body of theoretical and empirical research has identifed a frm’s operating
leverage as one of the real determinants of a common stock’s systematic risk (Hamada,
1972; Rubinstein, 1973; Lev, 1991; Gahlon, 1981; Gahlon and Gentry, 1982; Mandelker
and Rhee, 1984; Griffn and Dugan, 2003, among others). Systematic risk is, in turn, a
determinant of a frm’s equity cost of capital. Given that a frm’s equity cost of capital is
a fundamental part of capital budgeting analysis, capital structure analysis and stock
price analysis, accurately estimating a frm’s degree of operating leverage (DOL) is
important to both researchers and corporate fnancial managers.
Diversity continues to exist in operating leverage estimation techniques, raising
questions about the validity of various techniques and limiting the comparability of
The current issue and full text archive of this journal is available on Emerald Insight at:
www.emeraldinsight.com/1757-6385.htm
JFEP
7,2
180
Received1 October 2014
Revised23 October 2014
Accepted23 October 2014
Journal of Financial Economic
Policy
Vol. 7 No. 2, 2015
pp. 180-188
©Emerald Group Publishing Limited
1757-6385
DOI 10.1108/JFEP-10-2014-0056
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existing studies. This paper compares two popular methods for estimating DOL and
identifes the more appropriate technique. We consider the method proposed by
Mandelker and Rhee (1984), (M&R hereafter) and the method proposed by O’Brien and
Vanderheiden (1987) (O&V hereafter). O&V argue that the M&R technique yields
downward-biased DOL estimates because it primarily measures the growth in
operating earnings relative to the growth in sales rather than DOL. O&V offer an
estimation technique with a trend component to control for this growth that potentially
gives better DOL estimates. Previous studies have shown that the O&Vmethod does, in
fact, give DOL estimates closer to what the classical model would predict when
compared to the M&R estimates, which tend to cluster at or below one (O’Brien and
Vanderheiden, 1987 and Dugan and Shriver, 1992). Researchers have also found that
each estimation technique gives signifcantly different results when the DOL estimates
are used to explain systematic risk (Dugan et al., 1994 and Li and Henderson, 1991).
Despite this evidence, the M&R technique remains a popular way for researchers to
estimate DOL (Poulsen et al., 2013; Chen et al., 2011; Guthrie, 2011; García-Feijóo and
Jorgensen, 2010). Perhaps, that is because the existing evidence is only suggestive, and
no research of which we are aware has empirically tested O&V’s critique. Using a novel
approach, we provide the frst direct empirical evidence that the M&R method does
primarily measure the growth in operating earnings relative to the growth in sales
rather than DOL, just as O&V argue. This shortcoming means that DOL estimates for
growing frms generated using the M&Rmethod tend to be biased downward, resulting
in downward-biased estimates of operating risk, systematic risk and hurdle rates if DOL
is used as an input. The O&V method does impose a small cost in terms of
computational effort compared to the M&R method, but the consequences of using a
downward-biased DOL estimate make the tradeoff worth considering. Taken with
existing evidence, the results in this paper suggest that the O&Vtechnique is preferable
to the M&R method for estimating DOL. Financial policy makers in growing frms who
set hurdle rates for projects, make capital budgeting decisions and make capital
structure decisions will beneft from the more accurate DOL estimates from the O&V
technique.
2. DOL estimation techniques
In general terms, operating leverage is the single period magnifcation of the uncertainty
of operating earnings relative to the uncertainty of sales. DOL is defned as the
percentage deviation in operating earnings from its expected value relative to the
percentage deviation in sales revenue from its expected value, or:
DOL ?
?
X
t
E
(
X
)
t
? 1
?
?
S
t
E
(
S
)
t
? 1
?
(1)
where,
DOL ?the degree of operating leverage;
X
t
?realized operating earnings in period t;
S
t
?realized sales volume in period t; and
E(.) ?the expected value of (.).
181
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Equation (1) is hereafter called the classical model. As direct measurement of expected
operating earnings and expected sales volume is not possible, researchers have
developed multiple proxies using historical accounting data. The existing diversity in
DOLestimation techniques makes comparison diffcult and raises the question of which
technique is the most appropriate. An accurate estimate of DOL is valuable to
researchers in developing and testing models of the fundamental determinants of risk
and the cost of capital, and to practitioners who are considering the impact of DOL in a
particular frm when setting hurdle rates for projects, making capital budgeting
decisions and making capital structure decisions. This paper contributes to the
literature by identifying the more appropriate method of estimating a frm’s DOL
between two popular techniques: that proposed by Mandelker and Rhee (M&R), and
that proposed by O’Brien and Vanderheiden (O&V). We summarize the two methods
below.
2.1 Mandelker and Rhee
Mandelker and Rhee (1984) offer the following time-series method for estimating DOL,
which recognizes that DOL is built on the concept of elasticity:
Ln EBIT
jt
? a
j
? c
j
Ln Sales
jt
? ?
jt
, (2)
where,
EBIT
jt
?operating earnings for frm j at time t;
Sales
jt
?is net sales for frm j at time t;
?
jt
?a disturbance term; and
c
j
?the DOL estimate for frm j
2.2 O’Brien and Vanderheiden
O’Brien and Vanderheiden (1987) note that M&R’s method, while straightforward to
estimate, fails to control for growth in operating earnings and sales. The authors argue
that M&R’s use of observed values for operating earnings and sales revenue effectively
substitutes one period’s operating earnings and sales for the next period’s expectations.
This substitution is problematic if sales and operating earnings tend to grow over time.
As there is no trend component in M&R’s time-series regression, the relative growth of
operating earnings to sales loads on c
j
, the DOL estimate. Thus, O&V argue that c
j
primarily measures the trend of operating earnings relative to the trend of sales. The
authors propose the following method to control for this trend:
Let EBIT
t
be E(EBIT
t
)exp(?
t
EBIT
) and Sales
t
be E(Sales
t
)exp(?
t
sales
). Thus, ?
t
EBIT
is the
continuous compound rate of change fromE(EBIT
t
) to EBIT
t
and ?
t
sales
is the continuous
compound rate of change from E(Sales
t
) to Sales
t
so that:
?
t
EBIT
?
?
EBIT
t
E
(
EBIT
)
t
? 1
?
and ?
t
sales
?
?
Sales
t
E
(
Sales
)
t
? 1
?
(3)
Let g
x
and g
s
be the growth rates in expected operating earnings and expected sales,
respectively. Then:
E(EBIT
t
) ? EBIT
0
exp(t · g
EBIT
) and E(Sales
t
) ? Sales
0
exp(t · g
sales
), (4)
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where, EBIT
0
and Sales
0
are the beginning levels of operating earnings and sales,
respectively.
Combining terms, we get:
EBIT
t
? EBIT
0
exp(t · g
EBIT
? ?
t
EBIT
) and Sales
t
? Sales
0
exp(t · g
sales
? ?
t
sales
). (5)
Converted to logarithms, the expressions become:
Ln EBIT
t
? Ln EBIT
0
? t · g
EBIT
??
t
EBIT
(6)
and
Ln Sales
t
? Ln Sales
0
? t · g
sales
??
t
sales
. (7)
After estimating equations (6) and (7) by least squares and obtaining the residuals, ?
t
EBIT
is regressed on ?
t
sales
to estimate the following equation:
?
t
EBIT
? DOL ?
t
sales
? ?
t
. (8)
Under this two-stage method, DOL measures the average sensitivity of the percentage
deviation of the operating earnings fromits trend relative to the percentage deviation of
sales from its trend.
3. Testing O&V’s theory
O&V offer M&R’s own results as evidence for the need of a trend component when
estimating DOL. If the growth rate in sales is roughly equal to the growth rate in
operating income, which should be true if DOL is stable over time, then M&R’s DOL
estimate would tend toward one. In point of fact, the construction of the estimation
technique assumes that DOL is constant over the sample period, and so one would
expect M&R’s DOL estimates to cluster around one. M&Restimate DOL for a sample of
255 manufacturing frms with annual data from1957 to 1976. Most of the DOLestimates
cluster around one, just as the O&V critique predicts (Table I).
Other researchers have presented similar evidence. Dugan and Shriver (1992) use
both methods to estimate DOL for a sample of manufacturing frms over two time
Table I.
DOL estimates from
Mandelker and Rhee
(1984)
SIC code (First two-digits) Industry description Sample size DOL
20 Food and kindred products 32 0.96
26 Paper and allied products 13 0.91
28 Chemical 36 0.91
29 Petro-Chemical 20 1.08
32 Glass and cement gypsum 10 0.91
33 Steel works, etc. 21 0.73
35 Machinery 40 1.01
36 Appliances 24 1.09
37 Auto 24 0.99
49 Utilities 35 0.85
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periods: 1976-1985 and 1971-1985. The authors fnd that the O&V technique provides
more DOL estimates above one than the M&R technique (see Table II below). As the
classical model restricts DOL to be one or greater, the method that provides more
estimates above one is likely to be the more valid estimation technique. More
importantly, the results suggest that the M&Rmethod produces downward-biased DOL
estimates compared to the O&V method, resulting in downward-biased estimates of
operating risk, systematic risk and hurdle rates if DOL is used as an input.
The M&R estimation technique remains a popular way for researchers to estimate
DOL, despite evidence that it may systematically underestimate DOL. This may be
because the existing evidence is only suggestive, and no paper, of which we are aware,
has empirically tested O&V’s critique. We close this gap in the literature. If the M&R
method is primarily measuring the growth in operating earnings relative to the growth
in sales, then the DOL estimates fromthe M&Rmethod should be roughly equivalent to
the relative growth estimates from the O&V method. Specifcally, we expect that:
c
j
?
g
EBIT
g
sales
, (9)
where, c
j
is the DOL estimate fromthe M&R estimation technique fromequation (2) and
g
EBIT
and g
sales
are the coeffcients on the trend components fromthe O&Vtechnique from
equations (6) and (7), respectively.
4. Data and methodology
We obtain data from the annual COMPUSTAT fle which consist of 16,289
manufacturing frms that were listed on NYSE, AMEX and NASDAQ over the years
1998-2012. The sample is then limited to frms that reported strictly positive operating
earnings over the 15 consecutive years, which reduces the total observations to 956
frms in 14 industry groups[1].
We begin by calculating the M&R DOL estimates for each frm [c
j
from equation (2)]
and label this DOL
MR
. We then perform the trend regressions as required in the frst
stage of the O&Vapproach and record the coeffcient of growth in EBITand coeffcient
of the growth in Sales [g
EBIT
and g
sales
from equations (6) and (7)]. We then take the ratio
of the growth in EBIT coeffcient to the growth in Sales coeffcient and label this as the
relative growth estimate, or RGE, where:
Table II.
Proportions of DOL
estimates above one
from Dugan and
Shriver (1992)
SIC code (First two-digits) Industry description Sample size M&R (%) O&V (%)
20 Food and kindred products 35 0 49
26 Paper and allied products 22 0 64
28 Chemical 56 0 57
29 Petro-Chemical 23 26 78
35 Machinery 26 0 81
36 Appliances 52 46 71
37 Auto 31 52 3
Overall composite 245 19 57
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RGE ?
g
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g
sales
(10)
Finally, we calculate the mean percentage error (MPE) for each industry (grouped by
two-digit sic code) between the M&R DOL estimates and the O&VRGEs and performa
t-test to determine whether any of the MPEs is signifcantly different from zero. We
calculate the MPEin two different ways for robustness. The frst MPEcalculation is the
difference between the M&R DOL estimate and the RGE divided by the RGE, or:
MPE
RGE
?
(c
j
? RGE)
RGE
(11)
The second MPE calculation is the difference between the M&R DOL estimate and the
RGE divided by the M&R DOL, or:
MPE
DOL
?
(RGE ? c
j
)
c
j
(12)
If O&V’s critique is correct, then equation (9) will hold, and the MPE estimates from
equations (11) and (12) will not be signifcantly different from zero.
5. Results
Table III reports the MPE results and t-statistics by the industry group. The MPE
RGE
metrics for only 2 of the 14 industries are signifcantly different from zero: food and
kindred products (SIC code 20) and control equipment (SIC code 38). None of the 12 other
industry groups has MPE
RGE
metrics that are signifcantly different from zero.
Likewise, the MPE
DOL
metrics for only 2 of the 14 industries are signifcantly different
fromzero: construction materials (SICcode 34) and steel works (SICcode 33). None of the
12 other industry groups has MPE
DOL
metrics that are signifcantly different fromzero.
The DOLestimates fromthe M&Rmethod are roughly equivalent to the relative growth
estimates from the O&V method. The results offer the frst direct, empirical evidence
that O&V’s critique is correct: the M&RDOLestimates primarily measure the growth in
operating earnings relative to the growth in sales, not DOL.
While we do not argue that either technique is perfectly accurate, this paper’s
purpose is to present evidence on the nature of the problemwith M&R’s method. By not
including an additional trend component in the time-series regression, M&R force the
trend of operating earnings relative to the trend of sales onto the DOL estimate. If this
trend effect dominates, then DOL estimates using this method will primarily measure
the growth in operating earnings relative to the growth in sales rather than DOL. The
aforementioned results offer strong evidence that this is indeed the case.
Most importantly for researchers and practitioners, the M&R method gives
downward-biased DOL estimates, at least in part, because it primarily measures the
growth in operating earnings relative to the growth in sales. As one might expect, the
growth rate in operating income for most frms tends to be roughly equal to or slightly
belowthe growth rate in sales, resulting in M&R DOL estimates that cluster at or below
one. Relying on downward-biased DOL estimates will result in downward-biased
estimates of operating risk, systematic risk and hurdle rates if DOL is used as an input.
185
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Table III.
Mean percentage
error (MPE) between
DOL
MR
and RGE
across industries
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6. Conclusion
An accurate DOL estimate is valuable to researchers in developing and testing models
of the fundamental determinants of risk and the cost of capital, and to practitioners who
are considering the impact of DOL in capital budgeting and capital structure decisions
for a particular frm. Diversity continues to exist in operating leverage estimation
techniques, raising questions about the validity of various techniques and limiting the
comparability of existing studies. We extend the literature by comparing two popular
methods for estimating DOL and identifying the more appropriate technique. We
consider the method proposed by Mandelker and Rhee (1984) and the method proposed
by O’Brien and Vanderheiden (1987). O’Brien and Vanderheiden argue that the M&R
technique gives downward-biased DOL estimates because it primarily measures the
growth in operating earnings relative to the growth in sales rather than DOL. Existing
studies fnd that the O&V method does, in fact, give higher DOL estimates that are
closer to what the classical model would predict when compared to the M&R estimates,
which tend to cluster at or below one. This shortcoming means that DOL estimates for
growing frms generated using the M&Rmethod tend to be biased downward, resulting
in downward-biased estimates of operating risk, systematic risk and hurdle rates if DOL
is used as an input. While the existing evidence is suggestive, it is indirect, and the M&R
technique remains popular to this day among researchers.
Using a novel approach, we fnd the frst direct empirical evidence that the M&R
method does primarily measure the growth in operating earnings relative to the growth
in sales rather than DOL. For a sample of 956 frms in 14 industry groups over the years
1998-2012, we fnd that the DOL estimates from the M&R method are substantially
equivalent to the relative growth of EBIT to sales revenue, just as the O&V critique
suggests. Taken with existing evidence, the results suggest that the O&V technique is
preferable to the M&R method for estimating DOL. Financial policy makers in growing
frms who set hurdle rates for projects, make capital budgeting decisions and make
capital structure decisions will beneft from the more accurate DOL estimates from the
O&V technique.
Note
1. We recognize that this restrictionlimits the sample size andmaycause a loss of generality, but
it prevents applying an ad hoc approach to address frms that report negative earnings.
References
Chen, H.J., Kacperczyk, M. and Ortiz-Molina, H. (2011), “Labor unions, operating fexibility, and
the cost of equity”, Journal of Financial and Quantitative Analysis, Vol. 46 No. 1, pp. 25-58.
Dugan, M.T., Minyard, D.H. and Shriver, K.A. (1994), “A re-examination of the operating
leverage-fnancial leverage tradeoff hypothesis”, The Quarterly Review of Economics and
Finance, Vol. 34 No. 3, pp. 327-334.
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, Vol. 27 No. 2, pp. 309-321.
Gahlon, J.M. (1981), “Operating leverage as a determinant of systematic risk”, Journal of Business
Research, Vol. 9 No. 3, pp. 297-308.
Gahlon, J.M. and Gentry, J.A. (1982), “On the relationship between systematic risk and the degrees
of operating and fnancial leverage”, Financial Management, Vol. 11 No. 2, pp. 15-23.
187
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leverage
estimation
methods
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García-Feijóo, L. and Jorgensen, R.D. (2010), “Can operating leverage be the cause of the value
premium?”, Financial Management, Vol. 39 No. 3, pp. 1127-1154.
Griffn, H.F. and Dugan, M.T. (2003), “Systematic risk and revenue volatility”, Journal of Financial
Research, Vol. 26 No. 2, pp. 179-189.
Guthrie, G. (2011), “A note on operating leverage and expected rates of return”, Finance Research
Letters, Vol. 8 No. 2, pp. 88-100.
Hamada, R.S. (1972), “The effect of the frm’s capital structure on the systematic risk of common
stocks”, The Journal of Finance, Vol. 27 No. 2, pp. 435-452.
Lev, B. (1991), “On the association between operating leverage and risk”, Journal of Financial and
Quantitative Analysis, Vol. 9 No. 4, pp. 627-641.
Li, R. and Henderson, G.V. Jr (1991), “Combined leverage and stock risk”, Quarterly Journal of
Business and Economics, Vol. 30 No. 1, pp. 18-39.
Mandelker, G.N. and Rhee, S.G. (1984), “The impact of the degrees of operating and fnancial
leverage on systematic risk of common stock”, Journal of Financial and Quantitative
Analysis, Vol. 19 No. 1, pp. 45-57.
O’Brien, T.J. and Vanderheiden, P.A. (1987), “Empirical measurement of operating leverage for
growing frms”, Financial Management, Vol. 16 No. 2, pp. 45-53.
Poulsen, M., Faff, R. and Gray, S. (2013), “Financial infexibility and the value premium”,
International Review of Finance, Vol. 13 No. 3, pp. 327-344.
Rubinstein, M.E. (1973), “Amean-variance synthesis of corporate fnancial theory”, The Journal of
Finance, Vol. 28 No. 1, pp. 167-181.
Corresponding author
Steven Stelk can be contacted at: [email protected]
For instructions on how to order reprints of this article, please visit our website:
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doc_878229466.pdf
This paper aims to identify the more accurate method of estimating a firm’s degree of
operating leverage (DOL) between two popular DOL estimation techniques: that proposed by
Mandelker and Rhee (M&R), and that proposed by O’Brien and Vanderheiden (O&V).
Journal of Financial Economic Policy
An additional analysis on operating leverage estimation methods
Steven Stelk Sang Hyun Park Michael T Dugan
Article information:
To cite this document:
Steven Stelk Sang Hyun Park Michael T Dugan , (2015),"An additional analysis on operating leverage
estimation methods", J ournal of Financial Economic Policy, Vol. 7 Iss 2 pp. 180 - 188
Permanent link to this document:
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Santi Gopal Maji, Utpal Kumar De, (2015),"Regulatory capital and risk of Indian banks: a
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http://dx.doi.org/10.1108/J FEP-06-2014-0038
Kristoffer J . Glover, Gerhard Hambusch, (2014),"The trade-off theory revisited: on the effect of
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An additional analysis on
operating leverage estimation
methods
Steven Stelk
Department of Finance, Real Estate and Business Law,
The University of Southern Mississippi, Hattiesburg, Mississippi, USA, and
Sang Hyun Park and Michael T. Dugan
Knox School of Accountancy, Hull College of Business, Augusta, Georgia, USA
Abstract
Purpose – This paper aims to identify the more accurate method of estimating a frm’s degree of
operating leverage (DOL) between two popular DOL estimation techniques: that proposed by
Mandelker and Rhee (M&R), and that proposed by O’Brien and Vanderheiden (O&V).
Design/methodology/approach – O’Brien and Vanderheiden argue that M&R measure growth in
operating earnings relative to the growth in sales rather than DOL. The authors estimate the relative
growth estimate, RGE, fromthe O&Vtechnique (operating earnings growth rate/sales growth rate) and
compare this with the DOL estimates from the M&R technique to see if they are similar.
Findings – The authors fnd that the DOLestimates fromthe M&Rmethod are indistinguishable from
the relative growth estimates from the O&V method, providing the frst direct evidence that O&V’s
critique is correct. The M&R DOL estimates primarily measure the growth in operating earnings
relative to the growth in sales, not DOL.
Originality/value – A frm’s DOL is a determinant of its common stock’s systematic risk, which
determines a frm’s equity cost of capital. The equity cost of capital is a fundamental part of capital
budgeting, capital structure and stock price analysis. Accurately estimating a frm’s DOL is important
to researchers and corporate fnancial managers. Existing diversity in DOL estimation techniques
raises questions about the validity of various techniques and limits comparability of existing studies.
This paper demonstrates why the O&V technique should be used in place of the M&R method.
Keywords Estimation, Financial risk and risk management, Corporate fnance and governance,
Capital budgeting
Paper type Research paper
1. Introduction
A large body of theoretical and empirical research has identifed a frm’s operating
leverage as one of the real determinants of a common stock’s systematic risk (Hamada,
1972; Rubinstein, 1973; Lev, 1991; Gahlon, 1981; Gahlon and Gentry, 1982; Mandelker
and Rhee, 1984; Griffn and Dugan, 2003, among others). Systematic risk is, in turn, a
determinant of a frm’s equity cost of capital. Given that a frm’s equity cost of capital is
a fundamental part of capital budgeting analysis, capital structure analysis and stock
price analysis, accurately estimating a frm’s degree of operating leverage (DOL) is
important to both researchers and corporate fnancial managers.
Diversity continues to exist in operating leverage estimation techniques, raising
questions about the validity of various techniques and limiting the comparability of
The current issue and full text archive of this journal is available on Emerald Insight at:
www.emeraldinsight.com/1757-6385.htm
JFEP
7,2
180
Received1 October 2014
Revised23 October 2014
Accepted23 October 2014
Journal of Financial Economic
Policy
Vol. 7 No. 2, 2015
pp. 180-188
©Emerald Group Publishing Limited
1757-6385
DOI 10.1108/JFEP-10-2014-0056
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existing studies. This paper compares two popular methods for estimating DOL and
identifes the more appropriate technique. We consider the method proposed by
Mandelker and Rhee (1984), (M&R hereafter) and the method proposed by O’Brien and
Vanderheiden (1987) (O&V hereafter). O&V argue that the M&R technique yields
downward-biased DOL estimates because it primarily measures the growth in
operating earnings relative to the growth in sales rather than DOL. O&V offer an
estimation technique with a trend component to control for this growth that potentially
gives better DOL estimates. Previous studies have shown that the O&Vmethod does, in
fact, give DOL estimates closer to what the classical model would predict when
compared to the M&R estimates, which tend to cluster at or below one (O’Brien and
Vanderheiden, 1987 and Dugan and Shriver, 1992). Researchers have also found that
each estimation technique gives signifcantly different results when the DOL estimates
are used to explain systematic risk (Dugan et al., 1994 and Li and Henderson, 1991).
Despite this evidence, the M&R technique remains a popular way for researchers to
estimate DOL (Poulsen et al., 2013; Chen et al., 2011; Guthrie, 2011; García-Feijóo and
Jorgensen, 2010). Perhaps, that is because the existing evidence is only suggestive, and
no research of which we are aware has empirically tested O&V’s critique. Using a novel
approach, we provide the frst direct empirical evidence that the M&R method does
primarily measure the growth in operating earnings relative to the growth in sales
rather than DOL, just as O&V argue. This shortcoming means that DOL estimates for
growing frms generated using the M&Rmethod tend to be biased downward, resulting
in downward-biased estimates of operating risk, systematic risk and hurdle rates if DOL
is used as an input. The O&V method does impose a small cost in terms of
computational effort compared to the M&R method, but the consequences of using a
downward-biased DOL estimate make the tradeoff worth considering. Taken with
existing evidence, the results in this paper suggest that the O&Vtechnique is preferable
to the M&R method for estimating DOL. Financial policy makers in growing frms who
set hurdle rates for projects, make capital budgeting decisions and make capital
structure decisions will beneft from the more accurate DOL estimates from the O&V
technique.
2. DOL estimation techniques
In general terms, operating leverage is the single period magnifcation of the uncertainty
of operating earnings relative to the uncertainty of sales. DOL is defned as the
percentage deviation in operating earnings from its expected value relative to the
percentage deviation in sales revenue from its expected value, or:
DOL ?
?
X
t
E
(
X
)
t
? 1
?
?
S
t
E
(
S
)
t
? 1
?
(1)
where,
DOL ?the degree of operating leverage;
X
t
?realized operating earnings in period t;
S
t
?realized sales volume in period t; and
E(.) ?the expected value of (.).
181
Operating
leverage
estimation
methods
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Equation (1) is hereafter called the classical model. As direct measurement of expected
operating earnings and expected sales volume is not possible, researchers have
developed multiple proxies using historical accounting data. The existing diversity in
DOLestimation techniques makes comparison diffcult and raises the question of which
technique is the most appropriate. An accurate estimate of DOL is valuable to
researchers in developing and testing models of the fundamental determinants of risk
and the cost of capital, and to practitioners who are considering the impact of DOL in a
particular frm when setting hurdle rates for projects, making capital budgeting
decisions and making capital structure decisions. This paper contributes to the
literature by identifying the more appropriate method of estimating a frm’s DOL
between two popular techniques: that proposed by Mandelker and Rhee (M&R), and
that proposed by O’Brien and Vanderheiden (O&V). We summarize the two methods
below.
2.1 Mandelker and Rhee
Mandelker and Rhee (1984) offer the following time-series method for estimating DOL,
which recognizes that DOL is built on the concept of elasticity:
Ln EBIT
jt
? a
j
? c
j
Ln Sales
jt
? ?
jt
, (2)
where,
EBIT
jt
?operating earnings for frm j at time t;
Sales
jt
?is net sales for frm j at time t;
?
jt
?a disturbance term; and
c
j
?the DOL estimate for frm j
2.2 O’Brien and Vanderheiden
O’Brien and Vanderheiden (1987) note that M&R’s method, while straightforward to
estimate, fails to control for growth in operating earnings and sales. The authors argue
that M&R’s use of observed values for operating earnings and sales revenue effectively
substitutes one period’s operating earnings and sales for the next period’s expectations.
This substitution is problematic if sales and operating earnings tend to grow over time.
As there is no trend component in M&R’s time-series regression, the relative growth of
operating earnings to sales loads on c
j
, the DOL estimate. Thus, O&V argue that c
j
primarily measures the trend of operating earnings relative to the trend of sales. The
authors propose the following method to control for this trend:
Let EBIT
t
be E(EBIT
t
)exp(?
t
EBIT
) and Sales
t
be E(Sales
t
)exp(?
t
sales
). Thus, ?
t
EBIT
is the
continuous compound rate of change fromE(EBIT
t
) to EBIT
t
and ?
t
sales
is the continuous
compound rate of change from E(Sales
t
) to Sales
t
so that:
?
t
EBIT
?
?
EBIT
t
E
(
EBIT
)
t
? 1
?
and ?
t
sales
?
?
Sales
t
E
(
Sales
)
t
? 1
?
(3)
Let g
x
and g
s
be the growth rates in expected operating earnings and expected sales,
respectively. Then:
E(EBIT
t
) ? EBIT
0
exp(t · g
EBIT
) and E(Sales
t
) ? Sales
0
exp(t · g
sales
), (4)
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where, EBIT
0
and Sales
0
are the beginning levels of operating earnings and sales,
respectively.
Combining terms, we get:
EBIT
t
? EBIT
0
exp(t · g
EBIT
? ?
t
EBIT
) and Sales
t
? Sales
0
exp(t · g
sales
? ?
t
sales
). (5)
Converted to logarithms, the expressions become:
Ln EBIT
t
? Ln EBIT
0
? t · g
EBIT
??
t
EBIT
(6)
and
Ln Sales
t
? Ln Sales
0
? t · g
sales
??
t
sales
. (7)
After estimating equations (6) and (7) by least squares and obtaining the residuals, ?
t
EBIT
is regressed on ?
t
sales
to estimate the following equation:
?
t
EBIT
? DOL ?
t
sales
? ?
t
. (8)
Under this two-stage method, DOL measures the average sensitivity of the percentage
deviation of the operating earnings fromits trend relative to the percentage deviation of
sales from its trend.
3. Testing O&V’s theory
O&V offer M&R’s own results as evidence for the need of a trend component when
estimating DOL. If the growth rate in sales is roughly equal to the growth rate in
operating income, which should be true if DOL is stable over time, then M&R’s DOL
estimate would tend toward one. In point of fact, the construction of the estimation
technique assumes that DOL is constant over the sample period, and so one would
expect M&R’s DOL estimates to cluster around one. M&Restimate DOL for a sample of
255 manufacturing frms with annual data from1957 to 1976. Most of the DOLestimates
cluster around one, just as the O&V critique predicts (Table I).
Other researchers have presented similar evidence. Dugan and Shriver (1992) use
both methods to estimate DOL for a sample of manufacturing frms over two time
Table I.
DOL estimates from
Mandelker and Rhee
(1984)
SIC code (First two-digits) Industry description Sample size DOL
20 Food and kindred products 32 0.96
26 Paper and allied products 13 0.91
28 Chemical 36 0.91
29 Petro-Chemical 20 1.08
32 Glass and cement gypsum 10 0.91
33 Steel works, etc. 21 0.73
35 Machinery 40 1.01
36 Appliances 24 1.09
37 Auto 24 0.99
49 Utilities 35 0.85
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periods: 1976-1985 and 1971-1985. The authors fnd that the O&V technique provides
more DOL estimates above one than the M&R technique (see Table II below). As the
classical model restricts DOL to be one or greater, the method that provides more
estimates above one is likely to be the more valid estimation technique. More
importantly, the results suggest that the M&Rmethod produces downward-biased DOL
estimates compared to the O&V method, resulting in downward-biased estimates of
operating risk, systematic risk and hurdle rates if DOL is used as an input.
The M&R estimation technique remains a popular way for researchers to estimate
DOL, despite evidence that it may systematically underestimate DOL. This may be
because the existing evidence is only suggestive, and no paper, of which we are aware,
has empirically tested O&V’s critique. We close this gap in the literature. If the M&R
method is primarily measuring the growth in operating earnings relative to the growth
in sales, then the DOL estimates fromthe M&Rmethod should be roughly equivalent to
the relative growth estimates from the O&V method. Specifcally, we expect that:
c
j
?
g
EBIT
g
sales
, (9)
where, c
j
is the DOL estimate fromthe M&R estimation technique fromequation (2) and
g
EBIT
and g
sales
are the coeffcients on the trend components fromthe O&Vtechnique from
equations (6) and (7), respectively.
4. Data and methodology
We obtain data from the annual COMPUSTAT fle which consist of 16,289
manufacturing frms that were listed on NYSE, AMEX and NASDAQ over the years
1998-2012. The sample is then limited to frms that reported strictly positive operating
earnings over the 15 consecutive years, which reduces the total observations to 956
frms in 14 industry groups[1].
We begin by calculating the M&R DOL estimates for each frm [c
j
from equation (2)]
and label this DOL
MR
. We then perform the trend regressions as required in the frst
stage of the O&Vapproach and record the coeffcient of growth in EBITand coeffcient
of the growth in Sales [g
EBIT
and g
sales
from equations (6) and (7)]. We then take the ratio
of the growth in EBIT coeffcient to the growth in Sales coeffcient and label this as the
relative growth estimate, or RGE, where:
Table II.
Proportions of DOL
estimates above one
from Dugan and
Shriver (1992)
SIC code (First two-digits) Industry description Sample size M&R (%) O&V (%)
20 Food and kindred products 35 0 49
26 Paper and allied products 22 0 64
28 Chemical 56 0 57
29 Petro-Chemical 23 26 78
35 Machinery 26 0 81
36 Appliances 52 46 71
37 Auto 31 52 3
Overall composite 245 19 57
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RGE ?
g
EBIT
g
sales
(10)
Finally, we calculate the mean percentage error (MPE) for each industry (grouped by
two-digit sic code) between the M&R DOL estimates and the O&VRGEs and performa
t-test to determine whether any of the MPEs is signifcantly different from zero. We
calculate the MPEin two different ways for robustness. The frst MPEcalculation is the
difference between the M&R DOL estimate and the RGE divided by the RGE, or:
MPE
RGE
?
(c
j
? RGE)
RGE
(11)
The second MPE calculation is the difference between the M&R DOL estimate and the
RGE divided by the M&R DOL, or:
MPE
DOL
?
(RGE ? c
j
)
c
j
(12)
If O&V’s critique is correct, then equation (9) will hold, and the MPE estimates from
equations (11) and (12) will not be signifcantly different from zero.
5. Results
Table III reports the MPE results and t-statistics by the industry group. The MPE
RGE
metrics for only 2 of the 14 industries are signifcantly different from zero: food and
kindred products (SIC code 20) and control equipment (SIC code 38). None of the 12 other
industry groups has MPE
RGE
metrics that are signifcantly different from zero.
Likewise, the MPE
DOL
metrics for only 2 of the 14 industries are signifcantly different
fromzero: construction materials (SICcode 34) and steel works (SICcode 33). None of the
12 other industry groups has MPE
DOL
metrics that are signifcantly different fromzero.
The DOLestimates fromthe M&Rmethod are roughly equivalent to the relative growth
estimates from the O&V method. The results offer the frst direct, empirical evidence
that O&V’s critique is correct: the M&RDOLestimates primarily measure the growth in
operating earnings relative to the growth in sales, not DOL.
While we do not argue that either technique is perfectly accurate, this paper’s
purpose is to present evidence on the nature of the problemwith M&R’s method. By not
including an additional trend component in the time-series regression, M&R force the
trend of operating earnings relative to the trend of sales onto the DOL estimate. If this
trend effect dominates, then DOL estimates using this method will primarily measure
the growth in operating earnings relative to the growth in sales rather than DOL. The
aforementioned results offer strong evidence that this is indeed the case.
Most importantly for researchers and practitioners, the M&R method gives
downward-biased DOL estimates, at least in part, because it primarily measures the
growth in operating earnings relative to the growth in sales. As one might expect, the
growth rate in operating income for most frms tends to be roughly equal to or slightly
belowthe growth rate in sales, resulting in M&R DOL estimates that cluster at or below
one. Relying on downward-biased DOL estimates will result in downward-biased
estimates of operating risk, systematic risk and hurdle rates if DOL is used as an input.
185
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Table III.
Mean percentage
error (MPE) between
DOL
MR
and RGE
across industries
S
I
C
C
o
d
e
(
F
i
r
s
t
t
w
o
-
d
i
g
i
t
s
)
I
n
d
u
s
t
r
y
d
e
s
c
r
i
p
t
i
o
n
S
a
m
p
l
e
s
i
z
e
M
P
E
R
G
E
?
(
D
O
L
M
R
-
R
G
E
)
/
R
G
E
M
P
E
D
O
L
?
(
R
G
E
-
D
O
L
M
R
)
/
D
O
L
M
R
M
e
a
n
(
t
-
s
t
a
t
i
s
t
i
c
s
)
M
e
a
n
(
t
-
s
t
a
t
i
s
t
i
c
s
)
2
8
C
h
e
m
i
c
a
l
s
8
9
?
0
.
1
9
6
2
(
?
0
.
6
5
)
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0
.
3
7
4
4
(
?
1
.
5
4
)
3
6
A
p
p
l
i
a
n
c
e
s
7
3
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0
.
9
3
5
8
(
?
0
.
8
0
)
1
.
0
6
1
(
0
.
4
8
)
3
5
M
a
c
h
i
n
e
r
y
6
6
9
.
8
7
7
8
(
1
.
0
8
)
6
.
2
9
9
4
(
0
.
9
1
)
2
0
F
o
o
d
a
n
d
k
i
n
d
r
e
d
p
r
o
d
u
c
t
s
6
3
?
0
.
1
6
2
7
*
(
?
2
.
1
2
)
0
.
7
3
5
1
(
1
.
2
2
)
4
8
C
o
m
m
u
n
i
c
a
t
i
o
n
6
2
0
.
3
4
8
4
(
0
.
6
1
)
?
0
.
1
1
0
8
(
?
0
.
6
9
)
3
8
M
e
a
s
u
r
i
n
g
a
n
d
c
o
n
t
r
o
l
e
q
u
i
p
m
e
n
t
5
0
?
0
.
2
7
4
5
*
*
(
?
2
.
7
2
)
0
.
5
9
9
8
(
0
.
9
2
)
3
7
A
u
t
o
3
8
0
.
0
1
3
2
(
0
.
0
1
)
?
0
.
3
3
9
7
(
?
1
.
1
8
)
1
3
P
e
t
r
o
l
e
u
m
a
n
d
n
a
t
u
r
a
l
g
a
s
3
0
0
.
1
9
3
3
(
1
.
6
9
)
0
.
0
8
7
(
0
.
6
9
)
2
7
P
r
i
n
t
i
n
g
a
n
d
p
u
b
l
i
s
h
i
n
g
2
5
?
0
.
6
6
0
7
(
?
0
.
6
9
)
2
2
.
3
8
9
9
(
1
.
0
5
)
3
4
C
o
n
s
t
r
u
c
t
i
o
n
m
a
t
e
r
i
a
l
s
2
4
0
.
3
5
7
4
(
0
.
3
8
)
?
0
.
3
1
7
6
*
*
(
?
3
.
0
6
)
2
6
P
a
p
e
r
a
n
d
a
l
l
i
e
d
p
r
o
d
u
c
t
s
2
0
?
0
.
5
0
2
2
(
?
2
.
6
5
)
4
.
6
3
8
5
(
1
.
2
3
)
2
9
P
e
t
r
o
c
h
e
m
i
c
a
l
1
9
?
0
.
1
5
2
2
(
?
2
.
6
1
)
0
.
7
0
1
(
1
.
3
2
)
3
3
S
t
e
e
l
w
o
r
k
s
,
e
t
c
.
1
5
1
.
0
8
5
(
1
.
7
5
)
?
0
.
5
3
4
5
*
*
(
?
3
.
1
4
)
2
3
O
t
h
e
r
s
c
u
r
t
a
i
n
s
,
h
o
m
e
f
u
r
n
i
s
h
i
n
g
s
/
a
p
p
a
r
e
l
a
n
d
o
t
h
e
r
f
n
i
s
h
e
d
p
r
o
d
u
c
t
s
/
t
e
x
t
i
l
e
b
a
g
s
,
c
a
n
v
a
s
p
r
o
d
u
c
t
s
/
m
i
s
c
t
e
x
t
i
l
e
p
r
o
d
u
c
t
s
/
a
u
t
o
t
r
i
m
)
1
7
?
1
.
4
8
4
9
(
?
1
.
4
8
)
0
.
5
0
3
3
(
1
.
3
5
)
N
o
t
e
:
*
a
n
d
*
*
d
e
n
o
t
e
s
i
g
n
i
f
c
a
n
c
e
a
t
t
h
e
5
a
n
d
1
%
l
e
v
e
l
s
,
r
e
s
p
e
c
t
i
v
e
l
y
(
t
w
o
-
t
a
i
l
e
d
t
e
s
t
)
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6. Conclusion
An accurate DOL estimate is valuable to researchers in developing and testing models
of the fundamental determinants of risk and the cost of capital, and to practitioners who
are considering the impact of DOL in capital budgeting and capital structure decisions
for a particular frm. Diversity continues to exist in operating leverage estimation
techniques, raising questions about the validity of various techniques and limiting the
comparability of existing studies. We extend the literature by comparing two popular
methods for estimating DOL and identifying the more appropriate technique. We
consider the method proposed by Mandelker and Rhee (1984) and the method proposed
by O’Brien and Vanderheiden (1987). O’Brien and Vanderheiden argue that the M&R
technique gives downward-biased DOL estimates because it primarily measures the
growth in operating earnings relative to the growth in sales rather than DOL. Existing
studies fnd that the O&V method does, in fact, give higher DOL estimates that are
closer to what the classical model would predict when compared to the M&R estimates,
which tend to cluster at or below one. This shortcoming means that DOL estimates for
growing frms generated using the M&Rmethod tend to be biased downward, resulting
in downward-biased estimates of operating risk, systematic risk and hurdle rates if DOL
is used as an input. While the existing evidence is suggestive, it is indirect, and the M&R
technique remains popular to this day among researchers.
Using a novel approach, we fnd the frst direct empirical evidence that the M&R
method does primarily measure the growth in operating earnings relative to the growth
in sales rather than DOL. For a sample of 956 frms in 14 industry groups over the years
1998-2012, we fnd that the DOL estimates from the M&R method are substantially
equivalent to the relative growth of EBIT to sales revenue, just as the O&V critique
suggests. Taken with existing evidence, the results suggest that the O&V technique is
preferable to the M&R method for estimating DOL. Financial policy makers in growing
frms who set hurdle rates for projects, make capital budgeting decisions and make
capital structure decisions will beneft from the more accurate DOL estimates from the
O&V technique.
Note
1. We recognize that this restrictionlimits the sample size andmaycause a loss of generality, but
it prevents applying an ad hoc approach to address frms that report negative earnings.
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Corresponding author
Steven Stelk can be contacted at: [email protected]
For instructions on how to order reprints of this article, please visit our website:
www.emeraldgrouppublishing.com/licensing/reprints.htm
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