Browsing by Subject "near-optimal stopping"

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  • Nordlund, Toni (2003)
    Venture capital is in general terms an outside investment to a start-up business that hasstrong gro~rth opportunities but no access to capital markets. We study the rationalvaluation of such investments by constructing a model where a venture project is in atraditional fashion implemented as a cooperation between two complementary parties. Theinvestor, or the venture capitalist, keeps the project running by supplying equity capital,while the entrepreneur collaborates by supplying unique human capital. The key factor in themodel is that the infusion of capital is staged, so that the venture capitalist in the capacity ofan inside investor exercises strategic discretion to periodically rescreen the current state ofthe project along with the future prospects. If the project turns out a failure, the venturecapitalist exits immediately with a zero scrap value. His primary objective is however to findthe optimal timing for an initial public offering (IPO), where the accumulated equity stake issold in the market. It follows that the rational valuation emerges as an optimal stoppingprob em, which is approached by means of real options. Drawing on the optimality principle of dynamic programming and the general stoppingtheory, the rational value and the optimal stopping rule are derived in detail. The concepts ofregularity and an excessive majorant are introduced as elemental building blocks in theanalysis. It is in fact shown that the rational value conforms to a specific smallest excessivemajorant that incorporates in a simple way the time-to-build element created by the stagingof capital infusion. As a novelty in the venture-financing literature, we also introduce theconcept of a near-optimal stopping rule in conjunction with the optimal rule. Near-optimalitysimply means that a rule may call for stopping even if the time-to-build element implicit in theventure project is larger in value than the gain obtainable by immediate stopping. Both theoptimal rule and near optimal rules are made use of to study some absorbing aspects ofventure financing. We for example establish the effect of entrepreneurial exit options on theoptimal stopping behaviour of the venture capitalist, and on the rational real-option value. Equipped with the optimal rule, the study lastly derives sufficient conditions under whichstopping, and an IPO in particular, is not optimal to the venture capitalist. The starting point for the study is provided by the following references.Shiryayev, A. N. (1978): Optimal Stopping Rules. Springer-Verlag. Harrison, J.M., and Kreps, D.M. (1979): Martingales and Arbitrage in Multip riod SecuritiesMarkets. Journal of Economic Theory, vol. 20, pp. 381-408. Trigeorgis, Lenos (1996): Real Options: Managerial Flexibility and Strategy in ResourceAllocation. The MIT Press.