Model of R&D timing at an enterprise under uncertainty

The object of the study is an enterprise (in real sector) which has a possibility to carry out structural changes through the implementation of some innovative project. At some time the enterprise decides to carry R&D for the implementation of an innovative project. During R&D stage the company receives subsidies from the state, and expenses are deducted with the certain increasing coefficient. After the R&D stage, an innovative project starts implementation only with some probability. The enterprise operates under uncertainty, its profits flow is modeled by a stochastic process, and after the project implementation it changes to another stochastic process. We consider the problem of choosing such a moment for R&D start when the expected net discounted income of the enterprise would be maximal. It is proved that the optimal time to start R&D for the implementation of an innovative project coincides with the first time when the current profit of an enterprise exceeds certain threshold. We derive the explicit formula for the dependence of this threshold on the parameters in the model: the average growth rate and volatility of enterprise’s profits before and after the project implementation; the tax burden; the volume of subsidies provided; the amount of investments necessary for the project implementation; duration of the R&D stage; the probability of the project implementation; discount rates. The conditions under which the optimal time to start R&D will be finite (with a positive probability) are investigated. We study the dependence of this optimal time on the tax burden, the amount of subsidies, R&D costs and the probability of project implementation.