Analytic solutions for the value of the option to dis)invest Nicholas Biekpe, 1 Paul Klumpes 2 and Mark Tippett 3 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, Streatham Court, Rennes Drive, Exeter, EX4 4PU, UK M.J.Tippett@exeter.ac.uk 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. 1. Introduction O neofthemostsignificantdevelopmentsincapital investment analysis since the seminal works of Irving Fisher 1907,1930) has come with the realiza- tion that some of the central tenets of neoclassical investmenttheorydonotholdupinpractice.Itisnow generally conceded, for example, that irreversibility and the possibility of delay are critical characteristics of any investment decision. This means that firms are viewed as having the right but not the obligation to incur future capital investment expenditures. However, when firms do elect to exercise these options and thus take irreversible investment decisions, they give up the possibility of waiting for new information, and this could affect the desirability and=or timing of the investment expenditures they actually end up making. Furthermore, this lost option value is an opportunity cost, which must be included in the assessment of a capital project's viability. In other words, the irrever- sibility of investment decisions means that firms ought to invest to the point where the expected present value of project cash flows just exceeds the purchase and installation costs by an amount equal to the value of keeping the investment option alive Dixit and Pindyck, 1994; Trigeorgis, 1996). The accumulated weight of both the empirical and analytical evidence is that the inclusion of these formerly ignored) option values can lead to significantly different investment evaluation criteria to those based on the simple net present value rules of traditional neoclassical theory Burgstahler and Dichev, 1997). One of the difficulties with these more realistic investment appraisal techniques, however, is that they invariably lead to intractable expressions for the value of the firm's investment opportunities. In such cases custom dictates that numerical evaluation is the most practical and often, the only) way of determining optimal investment expenditures Trigeorgis, 1996, chapter 10). However, we demonstrate that under fairly mild regularity conditions, power series expan- sions can often be used to obtain analytic expressions R&D Management 31, 2, 2001. # Blackwell Publishers Ltd, 2001. Published by Blackwell Publishers Ltd, 149 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA.