292 NPV PROBABILITY DISTRIBUTION OF RISKY INVESTMENTSTable 15.6 Calculated Chi-square table double exponential distribution
ε ̃t=ρ ̃εt− 1 +u ̃t
kc|rho 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.00 11.7 19.2(∗) 3.1 12.8 13.2 4.9 5.5 11.7 20.4(∗) 17.9
0.05 10.7 11.5 12.0 11.8 18.4 16.5 9.9 15.3 22.3(∗) 29.1(∗)
0.10 23.7(∗) 5.1 19.8(∗) 13.9 9.5 11.1 13.7 11.9 19.9(∗) 20.0(∗)
0.15 9.3 10.5 16.8 10.5 7.2 14.4 18.5(∗) 15.4 9.5 10.7
0.20 25.2(∗) 16.1 17.9 28.7(∗) 21.1(∗) 47.4(∗) 17.0 35.1(∗) 27.4(∗) 35.0(∗)
0.25 24.9(∗) 18.6(∗) 25.1(∗) 17.2 17.1 37.0(∗) 28.2(∗) 15.7 21.7(∗) 29.1(∗)
0.30 36.4(∗) 26.4(∗) 31.8(∗) 30.3(∗) 30.0(∗) 21.2(∗) 35.5(∗) 30.6(∗) 44.1(∗) 37.8(∗)
0.35 40.0(∗) 35.1(∗) 33.9(∗) 24.5(∗) 30.6(∗) 37.8(∗) 20.2(∗) 26.8(∗) 43.1(∗) 39.4(∗)
0.40 51.1(∗) 34.6(∗) 45.6(∗) 28.6(∗) 42.0(∗) 58.1(∗) 49.8(∗) 45.3(∗) 61.8(∗) 47.8(∗)
n= 10 NS=5,000 χ^27 (α= 0. 01 )= 18. 48 χ^27 (α= 0. 05 )= 14. 07
Table 15.7 Calculated Chi-square table double exponential distribution
ε ̃t=ρ ̃εt− 1 +u ̃t
kc|rho 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.00 2.9 10.7 9.3 5.3 9.0 5.2 10.9 7.9 10.0 6.8
0.05 19.3(∗) 8.1 2.5 3.5 9.3 10.3 3.8 4.7 9.4 5.7
0.10 9.9 10.8 16.8 6.4 13.9 15.5 6.6 12.2 6.1 7.8
0.15 13.8 10.4 13.2 13.1 12.9 13.7 15.9 14.2 11.0 11.5
0.20 19.4(∗) 15.5 17.9 8.2 6.6 6.2 18.6(∗) 32.9(∗) 18.8(∗) 10.
0.25 42.3(∗) 29.2(∗) 28.0(∗) 30.2(∗) 34.0(∗) 29.1(∗) 28.6(∗) 27.6(∗) 38.2(∗) 33.5(∗)
0.30 31.4(∗) 46.5(∗) 33.3(∗) 34.5(∗) 40.7(∗) 31.9(∗) 15.9 27.6(∗) 52.2(∗) 17.4
0.35 17.9 52.4(∗) 39.2(∗) 42.1(∗) 60.4(∗) 33.7(∗) 39.1(∗) 62.0(∗) 23.2(∗) 31.9(∗)
0.40 42.6(∗) 42.9(∗) 31.4(∗) 48.1(∗) 48.0(∗) 43.0(∗) 27.9(∗) 55.3(∗) 40.8(∗) 39.6(∗)
n= 10 NS=5,000 χ^27 (α= 0. 01 )= 18. 48 χ^27 (α= 0. 05 )= 14. 07
rate, the null hypothesis is rejected systematically as cash flows obeying a
double exponential probability distribution do not conform to the CLT.
The simulation results, however, differ drastically from the uniform dis-
tribution when the discount rate is increased. We observe that as soon as the
discount rate crosses the 20% line, then the CLT ceases to ensure convergence
of the NPV probability distribution towards a normal distribution.
We therefore come to the conclusion that, up to a certain point, a thick-
tailed distribution like the double exponential would limit the effectiveness
of the CLT in ensuring the normality of the NPV distribution. In such a case,