Solving optimal timing problems elegantly

Few textbooks in mathematical economics cover optimal timing problems. Those which cover them do it scantly or in a rather clumsy way, making it hard for students to understand and apply the concept of optimal time in new contexts. Discussing the plentiful illustrations of optimal timing problems, we present an elegant and simple method of solving them. Whether the present value function is exponential or logarithmic, a convenient way to solve it is to convert the base to the exponential number e, thus making it easy to differentiate the new objective function with respect to time t. This convenient method of base conversion allows to find a second-order derivative and to use the second-order condition as a proof of optimum.