FOREST PLANTING IN THE LAKE STATES 
69 
APPENDIX 
The stumpage values after representative periods of years in which 
Norway and northern white pine, white spruce and jack pine may 
be expected to grow to merchantable size, with different combinations 
of cost of planting plus land value, yields, compound interest rates, 
and taxes are presented in Tables 11 to 18. 
The following example from Table 18 will illustrate the method 
of calculation of the values in these tables : 
Cost of planting jack pine, $5.50 an acre carried at 6 per cent com- 
pound interest for 40 years $56.57 (C) 
Land value at $2 an acre, carried at 6 per cent compound interest 
for 40 years 20.57 (8) 
Annual expense for taxes and fire protection, 15 cents an acre, capi- 
talized at 6 per cent represents a value of $2.50, and carried at 6 
per cent compound interest for 40 years 25. 71 (E) 
Total investment and expenses at 6 per cent for 40 years 102. 85 
Deduction for land value, $2, and capital value of annual expenses, 
$2.50, at end of 40 years 4. 50 
Cost of growing crop of jack pine 98.35 (G) 
Value of the crop if it is assumed that the yield of 30 cords an 
acre in 40 years has a total stumpage value which just pays the 
cost of growing the crop 98.35 (Y) 
The stumpage value per cord which will pay 6 per cent compound 
interest on investment and expenses ($98.35-^-30) 3.28 (y) 
The same calculation may be expressed algebraically, representing years by 
n, interest rate by p, yield per acre of wood products by &, as follows : 
G=(C + S+E)(l + p«)-(S+E) 
Y G 
but G—Y, and y~~f ) = T 
^ - (C + S+E)(l + p») -(S+E) 
therefore, y=- h — — 
Actually in computing the values in the tables, a value of $2 for land was 
used uniformly throughout, although the first columns in each table provide for 
different combinations of land value with planting cost. The use of a figure 
other than $2 for land value, provided land value plus planting cost remain the 
same, will make a difference of only a few cents in the stumpage values as 
compared with those given in the tables. In the example just given, if $1 is 
used as land value instead of $2, and the planting is taken as $6.50 instead of 
$5.50, the sum of the two remaining the same, the stumpage value per cord 
becomes $3.31 instead of $3.28, a difference of only 3 cents. 
Table 11. — Norway and northern white pine stumpage values per M board feet, 
50 years, good sites, 10,000 board feet to the acre 
TO EARN 3 PER CENT 
Cost of 
Stumpage values per M, classified according to 
planting 
annual taxes in cents per acre, plus 5-cent fire 
plus 
protection 
land 
value 
per acre 
15 cents 
20 cents 
30 cents 
45 cents 
75 cents 
$5.50 
$3.90 
$4.47 
$5.60 
$7.29 
$10. 67 
6.50 
4.34 
4.91 
6.03 
7.73 
11.11 
7.50 
4.78, 
5.34 
6.47 
8.16 
11.55 
8.50 
5.22 
5.78 
6.91 
8.60 
11.99 
18.00 
5.88 
6.44 
7.57 
9.26 
12.64 
12.00 
6.75 
7.32 
8.44 
10. 14 13. 52 
15.00 
20.00 
25,00 
8.07 
10.26 
8.63 
10.82 
9.76 
11.95 
14.14 
11.45 
13.64 
14. 84 
17. 03 
12.46 
13.02 
15. 84 
19.22 
