ABACUS, Vol. 56, No. 2, 2020
doi: 10.1111/abac.12198
MARTINA K. LINNENLUECKE, YUN SHEN, TOM SMITH, YUSHU ZHU,
AND ZINI LIANG
What Does the CAPM Say About
Operating Leverage?
We examine the issue of operating leverage and firm value. Johnstone
(2020), in this issue, questions existing results which indicate that higher
operating leverage results in lower firm value. We agree with Johnstone
(2020) that this result is to be questioned and present a number of
arguments which indicate that operating leverage is irrelevant to the
valuation of the firm in the context of the CAPM model.
Key words: CAPM; Operating leverage; Value irrelevance; Real options.
This paper examines the issue of operating leverage and how it relates to firm
value. Johnstone (2020), in this issue, questions the accepted view in the literature
that high operating leverage (high fixed costs relative to variable costs) leads to a
higher cost of capital and hence lower firm value (Brealey et al., 2017). We believe
that Johnstone (2020) is correct in questioning this result. The intuition behind
Johnstone’s (2020) argument is that higher fixed costs may lead to lower total cost
overall and hence could result in a higher, not lower, firm value.1
Whilst we agree that Johnstone (2020) is correct in questioning this accepted view,
we do not concur either with his conclusion or with that of the established literature.
We argue instead that operating leverage is irrelevant to the value of the firm. We
focus our arguments on a number of different lines. First, we revisit the nature of the
CAPM model itself and the assumptions that underline it. Specifically, the CAPM is
not a production model, but rather a partial equilibrium model of choice between a
constant opportunity set of risk and return alternative investment assets (capital
assets). Hence, a discussion of how production is organized and split up between
fixed and variable costs is not within the realm of the CAPM’s scope.
Second, we argue that in equilibrium with two identical firms their values will be
the same regardless of the split between fixed and variable cost. Here we apply
equilibrium conditions and echo a homemade leverage result that is well known in
the literature (Modigliani and Miller, 1958).
Finally we examine a situation where firms are presented with opportunities to
expand or contract in the second period of the two-period model and examine
MARTINA K. LINNENLUECKE, TOM SMITH (tom.smith@mq.edu.au), and YUN SHEN are at Macquarie
University, Sydney. YUSHU ZHU is at the University of Queensland, St Lucia, and ZINI LIANG is at the
Australian National University, Canberra.
1
Sarkar (2018a) considers the relationship between operating leverage and financial leverage.
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CAPM AND OPERATING LEVERAGE
whether this is consistent with the assumption of a constant opportunity set and
what it means for firm value.
THE CAPM MODEL
Bill Sharpe and Harry Markowitz both worked at the Rand Corporation in early
1960. Markowitz couldn’t be Sharpe’s supervisor but Markowitz knocked on his
door to talk about Markowitz’s mean variance frontier work (Markowitz, 1952).
Markowitz became Sharpe’s unofficial supervisor and the rest, as they say, is
history, with both receiving the Nobel Prize in 1990.
The CAPM is well studied in the literature and its demise and even ‘death’ has been
posited and defended by many researchers (Dempsey, 2013; Brown and Walter, 2013;
Partington, 2013; Smith and Walsh, 2013). However, the CAPM stands tall as the most
enduring model in financial economics and continues to be the model most used in
practice for cost of capital and valuation purposes (Truong et al., 2008). As Smith and
Walsh (2013) point out, the mathematics of the Markowitz frontier mean that the
vector of expected returns of assets is spanned by any two frontier portfolios. Hence,
factor models that involve a search for factors risk falling into the trap of this
mathematical tautology. The CAPM specifies in advance that the market is on the
frontier and hence it is the only model well specified theoretically ex ante.
Sharpe’s (1964) model assumes a constant opportunity set and that investors
choose capital assets to maximize expected return from a given variance. It is a
partial equilibrium that does not involve consumption or production. The model
results from an equilibrium of the supply and demand of risky assets.
For a model of production, we need to go to Cox et al. (1985) but even this model,
which assumes constant returns to scale for production, does not model fixed costs versus
variable costs and so it too is silent on the operating leverage issue. Sarkar (2018b)
considers a model with production and investment flexibility. Essentially, this flexibility
puts us in a real options framework and we will have more to say on this later.
IRRELEVANCE ARGUMENT
We consider a situation with two identical firms. Firm A and Firm B each choose
a particular combination of fixed costs and variable costs. We assume that Firm A
has higher fixed costs and lower variable costs. The fixed costs could represent
investment in a factory, equipment, or even a dedicated full-time labour force
when rigid and inflexible labour laws are present.
Denote the optimal level of Operating Leverage (OL) of Firm A as
OLA = f(FA, VA)
where FA and VA are Firm A’s fixed and variable costs respectively.
Firm A chooses this level of Operating Leverage because
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ABACUS
OLA = f ðF A , V A Þ ≥ OLB = f ðF B ,V B Þ
where FB and VB are Firm B’s fixed and variable costs respectively.
However, Firm B chooses its optimal level of Operating Leverage OLB = f(FB, VB)
because
OLB = f ðF B , V B Þ ≥ OLA = f ðF A , V A Þ
In equilibrium these optimal levels of Operating Leverage must give the same
advantage to the firm so that
f ðF A , V A Þ = f ðF B , V B Þ
This result echoes that of Modigliani and Miller (1958) in their exposition of the
irrelevance of capital structure to the value of the firm. As in Modigliani and
Miller (1958), an argument can be made that operating leverage can interact with
financial leverage and change the risks of bankruptcy (Chen et al., 2019) but again
that takes us outside the CAPM model assumptions.
REAL OPTIONS
When there are opportunities to expand, contract, or abandon activities in the
second period of the two-period CAPM model, a combination of lower fixed costs
and higher variable costs might mean that a firm can react more effectively to
these opportunities. However, when we examine this further we see that elements
of flexibility in real options theory are not compatible with the CAPM model. For
example, the success or failure of the discovery phase in research and
development does not depend upon market conditions and hence has zero
systematic risk. This ability to abandon on failure of discovery and the ability to
carry on to the approval phase adds considerable value to the firm but this is not
recognized in the CAPM model as it provides no return for zero market risk. It
follows that the same applies for the approval process as it is not dependant on
market conditions but rather on the results of clinical trials or the equivalent. The
ability to be able to abandon if approval is not forthcoming and the ability to go
on to commercialization if approval is successful adds considerable value to the
firm but is not rewarded in the CAPM as there is zero market risk.2
2
However, real option theory does have something to say about fixed and variable costs as
investment in fixed assets prove to be more difficult to scale down than they are to expand. Hence
high operating leverage firms that have high expenditure in fixed assets tend to do poorly in down
markets because of the difficulty of scaling back (Zhang, 2005).
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CONCLUSION
This paper has considered the issue of operating leverage and firm value within
the CAPM framework. Johnstone (2020) argues that existing beliefs that high
operating leverage reduces firm value are open to question and suggests that high
fixed costs might lead to lower total costs and hence increased firm value. We
argue that Johnstone (2020) is correct to question the existing literature and we
demonstrate that in fact operating leverage is irrelevant to the value of the firm in
a CAPM setting.
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