The authors investigate a problem of giving recommendation to company in which of two projects it should invest if initially projects values are unknown but can be learned over time. They consider the problem of selecting the better project from two. More precisely, the paper solves a cash-flow maximization problem of a company which is defined as the expected value of a project gain under taking into account expected cumulative costs of learning. The authors consider the problem with infinite time horizon. The consecutive steps for solving this control problems are standard. At first, it is defined expected discounted cash flow, next the value function is defined by max of expected discounted cash flow, where the maximization is over all admissible policies and finally choosing the optimal policy as admissible policy realising the value function. The solution to this stochastic-control optimal-stopping problem is given. The optimal policy is obtained from the value function, which solves an Hamilton-Jacobi-Bellman quasi-variational inequality. To do this authors have to overcome different technical difficulties.