Table 6 Summary statistics for lumber price simulation
Ln P Price
Rent m
3
Error term 5.8875
Mean 375.39
− 0.00116
36.90 0.2856
108.23 0.2031
25.22 Standard deviation
4.7525 115.88
Minimum −
23.56 −
0.8364 7.0043
1101.32 0.7346
206.05 Maximum
2.2517 985.44
229.61 Range
1.5710
Under the depreciation approach, Fig. 1 shows that the time path of net income has fairly stable
confidence intervals over time compared to those generated when fire risk is simulated. The upper
and lower CIs are far apart about 500 million but appear to be equidistant from the mean. Table 7
reports that for the 20 years mean net income ranges from about 133 million to 374 million. The
difference in the time paths generated using the depreciation and the wealth approach is less
marked in this case. The shapes of the curves are similar; however, the wealth approach generates a
time path, which is less variable. Under the depre- ciation approach, mean net income ranges from 116
to 270 million and the 95 CI around the annual mean ranges from 6.9 to 381 million.
Fig. 2 shows that for a given year the distribution of net income values for the depreciation and the
wealth approach is very similar. Again, the depre- ciation approach results in a distribution with a
slightly larger range and the middle of the distribu- tion is higher.
10. Fire and price risk simulations
In reality, timber capital is subject to both fire and price risk. Therefore, simulating both types of
risk together may provide more realistic and appli- cable results. The final set of simulations uses the
fire risk and price risk parameters from the previous simulations to illustrate the combined effect of
these two types of risk on the value of net income.
11. Results
As with the previous simulations, the results of this combined simulation are summarized in a table
of descriptive statistics Table 8 and a series of figures Figs. 1 and 2. As with the price risk
simulation, a cumulative frequency diagram and histogram are only shown for year 10.
Fig. 1 shows that when the depreciation ap- proach is used the mean yearly net income values
produce a somewhat unstable path. The upper CI
Table 7 Price risk simulation summary statistics: net income, years 1–20
Lowest of annual Average of annual
Highest of annual Annual net income statistic
Depreciation approach 288 936 520
132 652 963 Mean
374 045 681 130 393 535
Lower 95 confidence interval 64 341 341
− 34 121 181
509 822 227 Upper 95 confidence interval
297 607 298 614 569 846
Wealth approach 269 709 346
116 018 452 212 688 904
Mean 47 157 086
Lower 95 confidence interval −
9 061 119 179 095 907
372 642 633 Upper 95 confidence interval
186 015 211 444 053 368
Table 8 Price and fire risk simulation summary statistics: net income, years 1–20
Annual net income statistic Lowest of annual
Average of annual Highest of annual
Depreciation approach 60 405 755
Mean 241 060 264
137 330 540 −
1 357 505 422 −
642 290 552 −
82 846 996 Lower 95 confidence interval
497 696 587 Upper 95 confidence interval
315 087 376 591 251 783
Wealth approach Mean
208 402 188 115 950 744
268 417 402 −
23 932 034 177 537 244
Lower 95 confidence interval 30 473 649
185 849 964 448 431 123
376 991 472 Upper 95 confidence interval
of this path is relatively stable in comparison to the lower confidence interval, which is highly spo-
radic across years. Table 8 confirms the variability in the yearly means, which range from about 60
million to 241 million. The influence of fire risk appears to dominate since the resulting figure
closely resembles the corresponding chart for fire risk.
Again, the time path of net income that results when the wealth approach is used is less stochastic
than the path generated when the depreciation approach is used. Yearly means are still somewhat
variable, ranging from 116 to 268 million; how- ever, the CIs around the means are much tighter
than the confidence intervals in the depreciation approach. In addition, the chart resembles the
price risk chart suggesting that price risk is the dominant influence on net income.
From Fig. 2, we can see, that again the depreci- ation approach generates a distribution of annual
values for year 10 with a greater spread. The tails of the distribution extend further and contain
more values than the corresponding chart for the values generated by the wealth approach. The
middle of the distribution also occurs at different points; the median of distribution generated by
the depreciation is between 50 and 100 million larger.
12. Discussion
