JEAN-PAUL PAQUIN, ANNICK LAMBERT AND ALAIN CHARBONNEAU 293Table 15.8Calculated Chi-square table double exponential distribution
ε ̃t=ρε ̃t− 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 5.1 3.2 7.9 10.4 4.2 4.1 4.6 5.0 3.2 5.3
0.05 5.3 6.0 5.8 2.4 6.6 2.3 9.5 5.5 5.0 5.7
0.10 6.7 15.7 16.4 13.5 7.2 4.7 11.0 5.9 11.1 5.2
0.15 4.5 22.4(∗) 15.6 12.5 17.9 20.4(∗) 19.1(∗) 26.3(∗) 13.7 23.2(∗)
0.20 19.4(∗) 15.7 22.4(∗) 16.7 21.2(∗) 10.5 33.4(∗) 11.1 28.3(∗) 12.3
0.25 20.6(∗) 13.1 26.5(∗) 21.8(∗) 42.0(∗) 20.0(∗) 21.0(∗) 19.0(∗) 19.5(∗) 29.6(∗)
0.30 35.1(∗) 32.9(∗) 22.5(∗) 24.3(∗) 19.2(∗) 35.7(∗) 35.4(∗) 39.3(∗) 35.1(∗) 22.2(∗)
0.35 34.7(∗) 47.9(∗) 24.5(∗) 42.1(∗) 20.1(∗) 30.1(∗) 42.0(∗) 38.5(∗) 25.7(∗) 23.0(∗)
0.40 41.4(∗) 31.3(∗) 39.4(∗) 45.7(∗) 43.5(∗) 57.6(∗) 47.8(∗) 34.3(∗) 37.4(∗) 43.8(∗)n= 40 NS= 5000 χ^27 (α= 0. 01 )= 18. 48 χ^27 (α= 0. 05 )= 14. 07
a 20% discount rate would constitute an upper limit, which, incidentally, is
still pretty high. On the other hand, one has to ask oneself if such a thick-
tailed distribution provides a realistic description of investment decision
problems facing managers. One would suspect that such a distribution is
fairly rare considering that they imply highly probable extreme values. Now,
it is a well known fact that most investment decisions involve bounded
monetary consequences. Decision-makers always have the possibility of
opting out of an investment project in order to avoid the extremely negative
consequences.
Simulation trials have also been carried out for second-order autoregres-
sive processes. The results do not bring any noticeable difference from those
obtained with first-order autoregressive processes under the same three
probability distributions. The conclusion remains unchanged.
15.7 CONCLUSION
This chapter has dealt with the evaluation of risky capital investment
projects when cash flows are serially dependent and conform either to a
first-order or a second-order autoregressive stochastic stationary process.
The authors have demonstrated mathematically that the NPV probability
distribution does not strictly conform to the CLT asymptotic Normal distri-
bution properties. The only exception occurs when the discount rate is set
to zero. Under such conditions, it is also demonstrated that the CLT’s limit
property is not hampered when cash flows are serially dependant and obey
a first-order autoregressive process.