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Title: Multi-Factor Analytical Models of Re-Investment Under Uncertainty
Author: Adkins, Roger
Awarding Body: The University of Manchester
Current Institution: University of Manchester
Date of Award: 2010
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In this thesis, we formulate a quasi-analytical solution method for determining the timing boundary for multi-factor real option models, and apply it to economic problems of re-investment having a fixed re-investment cost. In the absence of an eligible dimension reducing transformation, numerical solution methods are normally used to evaluate the timing boundary, but analytical methods are elegant and less onerous. We develop a quasi-analytical method for determining the timing boundary for models whose factors are described by geometric or arithmetic Brownian motion processes, which, because it is expressed as a solution to a set of simultaneous equations, is implicit. Fixed cost re-investment problems, with two or more factors, are a particularly appropriate vehicle for demonstrating the appeal of the quasi-analytical method, because of the complete absence of a dimension reducing transformation. We find that the standard finding for one-factor models on the viability condition for investing in an opportunity is extendable to the multi-factor models by showing that the net incremental value rendered by the re-investment has to significantly exceed the net re-investment cost for it to be economically justified. Although the various models are founded on an infinite re-investment chain, we observe only finite chains for many industrial and commercial assets, so a recurring theme of our studies is abandonment and the inclusion of a suitable mechanism in the formulation for terminating the infinite process. Three distinct classes of re-investment are considered. In Chapter 3, we study the two-factor renewal model, with deteriorating stochastic revenue and operating cost. We find that the correlation between the two factors exerts considerable control over the shape of the timing boundary, which shows that focusing exclusively on one-factor models and ignoring additional factors can produce misleading results. Further, the timing boundary is more greatly influenced by the revenue reversionary level than by the .operating cost reversionary level and the re-investment cost. We also consider the magnitude of the reversionary revenue required to terminate the chain. In Chapter 4, we study a replacement model with stochastic escalating cost and tax allowances due to the depreciation charge, based on declining balance, straight line and sum of year's digits schedules. Replacement depends on asset age, with younger assets being replaced at lower operating cost thresholds. Further, asset age is critical in deciding the preferred depreciation lifetime, tax rate and depreciation schedule. In Chapter 5, we study the impact of salvage value on replacement. The presence of this additional factor not only . lowers the operating cost threshold, but also permits the abandonment decision to be modelled. In Chapter 6, we study a two-factor model for renovating a property, with building quality deteriorating stochastically and a market-based rental price, which expresses both renovation and abandonment opportunities. We show that the three decisions of continuance, renovation and abandonment comprise an exhaustive decision space. 12
Supervisor: Not available Sponsor: Not available
Qualification Name: Faculty of Humanities Qualification Level: Doctoral
EThOS ID:  DOI: Not available