Optimal timing for investment decisions

The net present value (NVP) is an important concept in investment decisions. As Ingersoll and Ross have pointed out, the future fluctuation of interest rates is expected to have significant effects on the present value (PV) of the project concerned. If interest rates are expected to fall off in the next year, deferring an investment for yet another year is likely to be more gainful even if its current NPV is positive. The effects of deferment can be valued from its corresponding American option value. Berk proposed a simple criterion for investment decisions which incorporate this American option value of investment. The simplicity of this model is obtained from the appropriate usage of a callable bond. It is admirable that this model does not postulate any assumptions on the behavior of interest rates. But this construction of the model has the pros and cons. It is easy to implement this model in business because the only adjustment required in this model is to replace the interest rate in NPV with the callable rate. On the other hand, the properties of this criterion have not been clarified. In this paper we analyze Berk's model under the assumption that interest rates follow the geometric Brownian motion (GBM). By assuming the movement of interest rates, we can derive an analytical solution for the optimal timing for the investments in terms of the parameters of the GBM. This enables us to perform comparative statics and simulation. These results extract some properties of Berk's model and help the decision makers in implementing Berk's model.