l6 FOREST VALUATION 



his money. The $10,000 is the income value of the farm at 5%, 

 and is equal to the net income capitalized at 5%. 



2. If the income is periodic, comes every fifteen years, as in 

 the case of the forest cut over every fifteen years, the foregoing is 

 modified as follows : 



present value = ^^^^J'^f ^^~L.^ 

 500 (i.03 " ") 



103''— I (1.03 

 500 



(1.03"— I) 



or in general : 



(i.op'-i) 



where A is the periodic rent or money income at each cut in the 

 above case. If in the above case the first cut comes in six years 

 instead of fifteen the owner is fifteen less six or nine years to the 

 good and this may be expressed as follows : value of property : 



.Soo 1.03 



-(1.03'^- I) 

 That is, the sum is prolonged at 3% for nine years, or in general, 



(i.op'-i) 



where x is the number of years before the first payment is due. 

 Note: Care must be taken to see that the sum A is really the 

 sum in every case. To illustrate : A forest of 100 acres can be cut 

 over every 20 years for $50 worth of timber (stumpage value) per 

 acre. The yearly expenses for the 20 years sum up to $15 per acre 

 so that the net income A is 50-15 or $35. If now the first cut may 

 be made at once the value of this property is : 



income value = $50 + ^j , and not-^— ^ ^^ — 



1.03"— I T.03-"— I 



because the first income is larger by 15 than the established future 

 incomes. 



