  We consider an optimal stopping time problem related with many models found
in real options problems. The main goal of this work is to bring for the field
of real options, different and more realistic pay-off functions, and negative
interest rates. Thus, we present analytical solutions for a wide class of
pay-off functions, considering quite general assumptions over the model. Also,
an extensive and general sensitivity analysis to the solutions, and an economic
example which highlight the mathematical difficulties in the standard
approaches, are provided.
