Much of the work on investment under uncertainty assumes that the project's value follows Geometric Brownian Motion (GBM) with constant volatility. I use a more general assumption for the project-value process. I use the so-called Constant-Elasticity-of-Variance (CEV) diffusion model where the volatility is a non-increasing function of the project's value. I show that, if the CEV volatility structure holds, the firm that uses the standard GBM assumption is exposed to significant errors when making the optimal investment decision. In particular, the GBM assumption often yields suboptimal postponement of investment and undervalues the option of waiting to invest under deteriorated business conditions.
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