We consider an optimal investment problem in which the cost of the investment decreases over time. This decrease is modelled using the negative of a non-decreasing Levy process. The decreasing cost is a way of modelling that innovations drive down the cost of the investment. We present general results on how to compute both the value of the investment, as well as the optimal time at which the investment should be done. Several explicit examples of how different Levy processes influence the value of the investment are given as illustrations of the general results. The main tools used are fluctuation theory for Levy processes and inversion of Laplace transforms. When the inversion can be done analytically, we can present analytical solutions where in some cases only numerical solution has previously been known.