A Mathematical Model of Investment Incentives
An investment timing problem which takes into account both taxation (including tax exemptions) and financing by credit is considered. This problem is reduced to the optimal stopping of a two-dimensional diffusion process. We give the solution to the inves
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Abstract An investment timing problem which takes into account both taxation (including tax exemptions) and financing by credit is considered. This problem is reduced to the optimal stopping of a two-dimensional diffusion process. We give the solution to the investment timing problem as a function of parameters of the model, in particular, of the tax holiday duration and interest rate for borrowing. We study the question whether the higher interest rate for borrowing can be compensated by tax holidays. Keywords Investment timing problem • Credit • Real options • Optimal stopping • Tax holidays • Compensation of interest rate Mathematics Subject Classification (2010): 60G40, 91B38, 91B70
1 Introduction There is an important problem how to attract investments to the real sector of the economy when credit risks are high. Our work is devoted to the analysis of related tax mechanisms for such attraction. In economies with increased risks (political, credit etc.) and other unfavorable factors the following question arises: can tax benefits provide investor with the same conditions for investment as he would have in a “standard” economy without any risks and unfavorable factors. In other words, can tax benefits compensate unfavorable factors?
V. Arkin () A. Slastnikov Central Economics and Mathematics Institute, Nakhimovskii pr. 47, Moscow, Russia e-mail: [email protected]; [email protected] A.N. Shiryaev et al. (eds.), Prokhorov and Contemporary Probability Theory, Springer Proceedings in Mathematics & Statistics 33, DOI 10.1007/978-3-642-33549-5 2, © Springer-Verlag Berlin Heidelberg 2013
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V. Arkin and A. Slastnikov
In order to compensate risks and other unfavorable factors the following tax benefits are often used to attract investment: tax holidays, i.e. exemption from tax during a certain period, a reduction in tax rate, and accelerated depreciation. It is worth noting that increased credit risks imply increasing interest rates on credit. In practice, tax holidays are considered as a mechanism which can compensate all arising risks. Such a compensation problem was formulated and studied in [3, 4], where the risk is modelled by an additive term to the discount rate (a “risk premium”). Tax holidays, depreciation policy and a reduction in profit tax rate were considered as compensating mechanisms. In the paper, we study a possibility of applying the tax holidays mechanism (on the corporate profit tax) for the compensation of high-level interest rates. Various problems related to the influence of tax holidays on investment decisions, especially under risk and uncertainty, were studied in a number of papers (see, e.g. [5, 8, 10]). Potential possibilities of tax holidays as a mechanism for maximization of the expected discounted tax payments from the created firm were explored in [4]. This paper is organized as follows. Section 2 describes the behavior of an investor under uncertainty and in a fiscal environment, who is interested in investing into the project aimed at creating a new firm and faces the inv
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