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Analytic solutions for the value of the option to (dis)invest

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It is well known that costly reversibility complicates capital investment analysis to the point where closed form expressions for the value of a firm’s investment opportunities seldom exist. In such circumstances numerical evaluation is normally taken as the most practical (and often, the only) way of determining investment value. However, we demonstrate that power series expansions can often be used to obtain analytic expressions for the value of a firm’s investment opportunities. We use them in a research and development (R&D) setting to determine investment value when cash flows are generated by two well known stochastic processes. The first is based on the Cox, Ingersoll and Ross (1985) ‘square root’ process; the second on the Uhlenbeck and Ornstein (1930) mean reverting random walk. The criteria which lead to optimal investment decisions when the option to abandon or take up investment opportunities have the non‐trivial values implied by these processes, are also briefly examined.

Document Type: Original Article


Affiliations: 1: Africa Centre for Investment Analysis, University of Stellenbosch, South Africa, 2: Accounting and Finance Group, Warwick Business School, 3: Department of Accounting and Finance, School of Business and Economics, University of Exeter, UK

Publication date: April 1, 2001


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