Part 1 - AL-Tax

appearance of future competitors attracted by extraordinary rents in the industry.Let us consider that assumption, and to model the pre-tax rate of return as a geometricBrownian motion with drift:dp αp dt σp dz (2.18)where dz is the increment of a Wiener process, α 1 is the drift parameter, andσ the variance parameter. Given that the project is expected to generate economicrents in the beginning, new similar projects will come and reduce the economicrent, a fact that is modeled with a negative trend.As an example of a geometric Brownian motion with negative drift, we presentin Figure 2.4 a sample path of equation (2.18) with a drift rate of 5% per year anda standard deviation of 25% per year. The graphic is built with monthly timeintervals.Now the expected NPV of the project is (see Dixit and Pindyck, 1994):and the expected NPVT:pE[ NPV* ] ⎡ E ptte( ρδπ )⎤0∫dt⎣⎢ 0⎦⎥ρδπ αChapter 2⎡ E[ NPVT ] E τ( ptt δ)e ( ρδπ )⎤∫dt A⎣⎢0⎦⎥τδπρδπ pA0 .ρδπα 0.140.120.100.080.060.040.020.0055 60 65 70 75 80 85 90 95 00Figure 2.4Geometric Brownian motion with negative drift25