# The Value of Capacity Sizing Under Risk Aversion and Operational Flexibility

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The Value of Capacity Sizing Under Risk Aversion

and Operational Flexibility

Michail Chronopoulos, Bert De Reyck, and Afzal Siddiqui

Abstract—Risk aversion typically erodes the value of an investment opportunity, often increasing the incentive to delay investment. Although this may be true when the decision maker has discretion only over the timing of investment, any additional discretion over the capacity of a project may lead to different results. In this paper, we extend the traditional real options approach by allowing for discretion over capacity while incorporating risk aversion and operational ﬂexibility in the form of suspension and resumption options. In contrast to a project without scalable capacity, we ﬁnd that increased risk aversion may actually facilitate investment because it decreases the optimal capacity of the project. Finally, we illustrate how the relative loss in the value of the investment opportunity due to an incorrect capacity choice may become less pronounced with increasing risk aversion and uncertainty.

Index Terms—Capacity sizing, energy sector, real options, risk aversion.

I. INTRODUCTION

PART from discretion over the timing of investments, a

ﬁrm typically also has the freedom to determine the scale

of a project, i.e., in the form of installed capacity. By adopting a high capacity, the ﬁrm may be unable to cover the investment cost in the case of an unexpected downturn, whereas if the ﬁrm installs a low capacity, then it may end up forgoing revenues if market conditions suddenly become favourable. Consequently,

choosing the correct capacity is crucial particularly when the expansion or contraction of an investment project after its initial installation is too costly, which may be the case in the electric power sector. For example, the investment cost of a run-of-river hydropower plant is convex in the capacity size, which implies diseconomies of scale [1]. Similarly, the cost of expanding offshore wind farms is twice that of a coal or a gas power plant [25]. Since such renewable energy technologies are expected

to contribute signiﬁcantly to the zero-carbon energy produc-

A

tion, it is imperative to estimate accurately the capacity that will be required in order to avoid the problem of either insufﬁcient investment or overbuilding.

In addition to sizing, accounting for a ﬁrm’s risk aversion is important in situations where markets are incomplete or technical risk exists. These features are likely to arise either in newly deregulated sectors, i.e., electric power in general, or in R&Dintensive projects, renewable energy technologies in particular. Also, ﬂexibility in the form of suspension and resumption options is embedded in many capital projects and can affect their proﬁtability and downside risk [9]. Although the traditional real options approach addresses the value of ﬂexibility and capacity sizing in capital budgeting decisions, the interaction between an investor’s risk tolerance and the optimal capacity to be installed remains an open question with resonance for an electric power sector that requires investment in renewable energy technologies on an unprecedented scale in order to meet future climate change targets.

In this paper, we analyze the impact of uncertainty, risk aversion, and operational ﬂexibility on investment timing and capacity decisions of a ﬁrm in order to assess the degree to which an inaccurate capacity choice impacts the value of the option to invest. Thus, the contribution of this paper is threefold. First, we develop a theoretical framework for investment with capacity sizing under uncertainty with risk aversion and operational ﬂexibility, and we derive closed-form expressions for the optimal investment and operational thresholds as well as the...

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