Stochastic Equipment Capital Budgeting with Technological Progress

Published date01 November 2014
AuthorRoger Adkins,Dean Paxson
Date01 November 2014
European Financial Management, Vol. 20, No. 5, 2014, 1031–1049
doi: 10.1111/eufm.12000
Stochastic Equipment Capital
Budgeting with Technological Progress
Roger Adkins
Bradford University Schoolof Management, Emm Lane, Bradford BD9 4JL, UK
Dean Paxson
Manchester Business School, University of Manchester, Booth Street West, Manchester,
M15 6PB, UK
We provide multi-factor real option models (and quasi-analytical solutions) for
equipment capital budgeting under uncertainty, when there is either unexpected,
or anticipated, or uncertain (volatile) technological progress. We calculate the
threshold level of revenuesand operating costs using the incumbent equipment that
would justify replacement. Replacement is deferred for lower revenue thresholds.
If progressis anticipated or highly uncertain, alert financial managers should wait
longer before replacingequipment. Replacement deferral increases with decreases
in the expected correlationbetween revenue and operating costs, and with increases
in the revenue and/or operating cost volatility. Uncertain technological progress
increases the real option value of waiting. The best approach for equipment
suppliers is to reduce the expected revenueand/or cost volatility, and/or reduce the
expected uncertainty of technological innovations,since then an incentive exists for
the early replacement of old equipment when a technologically advanced version
is launched.
Keywords: EquipmentReplacement ,Capital Budgeting,Quasi-analytical Solution,
Real Replacement Option Value,Uncertain Technological Progress
JEL Classifications: D81, G31
1. Introduction
When a replaceable asset is installed, financial managers could assess its anticipated
lifetime from a standard net present value (NPV) analysis for an infinite replacement
We thank Nelson Areal, Alcino Azevedo, Michael Brennan, Chen Chao-Chun, Geoffrey
Evatt, Michael Flanagan, Nicos Koussis, Spiros Martzoukos, Ser-Huang Poon, Artur
Rodrigues, Mark Shackleton, Azfal Siddique, Richard Stapleton, an anonymous referee,
and participants at the EFMA 2011 Conference at the University of Minho, Braga, for their
valuable comments on earlier versions.
2013 Blackwell Publishing Ltd
© 2013 John Wiley & Sons Ltd
Roger Adkins and Dean Paxson
© 2013 John Wiley & Sons Ltd
chain, as in Lutz and Lutz (1951). This solution, though, is only strictly applicable
for like-for-like replacements, but there are many assets with embedded technological
progress that violate this assumption, including vehicles and aircraft with higher future
fuel efficiency, robotic machine tools with greater functionality, mobile phones and
computer-based products with faster and novel facilities. The presence of technological
progress means that the evaluated ex-ante lifetime may not coincide with its ex-post
Thus, the real economic lifetime for capital equipment depends not only on its physical
deterioration rate, but also on the technological progress embedded in the succeeding
equipment as the incumbent suffers implied obsolescence. Since the ex-post lifetime
is likely to be variable in the presence of technological progress, an evaluation using
the traditional NPV method for multiple (infinite) replacements may be misleading
due to its in-built assumption of an equal cycle time. Consequently, in this paper,
we adopt a dynamic programming formulation for determining the optimal conditions
signaling equipment replacement because that avoids a cycle time framework. This
approach is applied to replaceable equipment that is subject to both revenueand operating
cost deterioration and uncertainty, with technological progress that is unexpected, or
anticipated or uncertain.
In the absence of uncertainty, the effect of unforeseen technological progress on the
replacement policy is originally analyzed by Caplan (1940), whofocuses on “premature
abandonment” of old machines that “become old-fashioned” due to obsolescence, rather
than just physical decline. Building on the economic lifetime models of Hotelling
(1925) and Preinreich (1939), Caplan shows analytically that the consequence of
unanticipated technological progress is to shorten the active life of the incumbent. When
there is an unforeseen performance improvement in the succeeding asset or a more
technologically advanced asset becomes available sooner than expected, the incumbent
becomes prematurely obsolete. If the increase in profit potential from replacing the
incumbent more than compensates the loss in recovering the original investment, then
the incumbent is replaced before its ex-ante lifetime has expired. Caplan (1940) notes
that real depreciation should be the first derivative of the equipment real value with
respect to time as in Hotelling (1925), but that uncertainty and the degree of competition
should also be considered.
Eilon, King and Hutchinson (1966) is an early example of capital equipment
replacement in continuous time, with a closed-form solution for an optimal policy.
Stapleton, Hemmings and Scholefield (1972) apply numerical simulation to show that
if technological progress is foreseen, the optimal time between successive replacements
is lengthened. Although these authors adopt a dynamic programming formulation to
avoid the equal life assumption, Elton and Gruber (1976) show that an equal life policy
is optimum for assets with technological improvements. However, these analyses focus
on either anticipated or unanticipated technological progress, and do not provide simple
operational rules for deciding the optimal conditions for replacing the incumbent.
Several authors havestudied the adoption of technological innovations in a real options
context, sometimes in a duopoly. Huisman and Kort (2003) assume that a new technology
has a greater “efficiency” than the existing technology, and firms determine outcomes
in a strategic context. Huisman and Kort (2004) use a similar approach, except that the
new technology becomes available for adoption at some unknown time in the future.
Tsekrekos, Shackleton and Wojakowski (2010) provide capital budgeting rules for multi-
factor models of commodity prices. Armada, Kryzanowski and Pereira (2011) show
the im
lications for investment when there ma
be hidden rivals. Adkins and Paxson

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