Academic journal article International Journal of Business

Corporate Investment Choice and Exchange Option between Production Functions

Academic journal article International Journal of Business

Corporate Investment Choice and Exchange Option between Production Functions

Article excerpt


The theory of real options can potentially provide fundamental tools to analyze the investment values, when dealing with research and development projects, natural-resource investments, technological innovations...Real options have several characteristics in common with usual financial options. For example, they can take account of other investment opportunities such as standard financial assets. Using a substitute asset, a risk-premium can be determined and analyzed.

We refer for instance to the seminal paper by Pindyck (1988) on real options and investment choice, Pindyck (1994), Dixit and Pyndick (1994), Trigeorgis (1993 a,b,c; 1996) or Schwartz and Trigeorgis (2001) for general properties about real option analysis. Other references are for example Brennan and Schwartz (1985) for valuation of natural resources investments, Paddock et al. (1988) for the case of offshore petroleum leases, McDonald and Siegel (1986) for the value of time to invest...

In this paper, we compare several production strategies of a firm that can decide either to invest only on one single production mode, either to switch between two production strategies. They can have different initial investment amounts, input costs, output levels and prices...Such investment choice is often encountered when the input costs increase significantly, as for example the energy and commodity prices. To analyze such decision problem, we introduce a general exchange option valuation when facing the choice between two investment projects.

We assume that, in a first step, the investor must invest a fixed amount before starting the production. In a second step, when the production begins, the manager must pay production costs. We study the different solutions of this valuation problem, in particular when the manager searches for the maximization of the expected return of his "Profit and Loss" (P&L). We determine the values of exchange options when we have to evaluate all the P&L depending on the different production models, to take account of potential switches between projects during the management period.

We provide a general valuation formula of the exchange options associated to these P&L by using a family of switching options. We assume that the project manager compares two different ways of production: Products can be identical or differ; the manager can choose either to allocate his whole endowment on only one production mode, or to switch from one production mode to the other one.

In that latter case, he must invest initially the required amount, which corresponds to the sum of both amounts necessary to initialize each of the production mode. We detail several particular cases, for example when output levels are equal.

This paper is organized as follows: Section II recalls main results about the valuation of the exchange options for Lognormal asset prices, first introduced by Margrabe (1978). Section III provides the general model and results about the valuation of exchange options between production functions. Finally, Section VI contains the concluding remarks. (1)


In what follows, we briefly recall the main result of Margrabe (1978) about the valuation of the exchange option between assets [X.sub.1] and [X.sub.2], in order to get Max([X.sub.1], [X.sub.2]). The idea of Margrabe (1978) is to use the Black and Scholes (1973) formula by considering asset [X.sub.2] as a numeraire (see also Stulz, 1982). Thus the price of [X.sub.1] corresponds to ([X.sub.1]/[X.sub.2]) units of asset [X.sub.2]. Therefore, the exchange option has strike 1 with underlying ([X.sub.1]/[X.sub.2]). Assume that both [X.sub.1] and [X.sub.2] are lognormal distributed:


where [W.sub.1] and [W.sub.2] are Gaussian random variables with variance 1 and linear correlation [rho]. Then, we get:


The volatility of underlying [sigma] ([X. …

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