FOREST PROBLEMS. 211 



stock. The expense for taxes and the cost of protection 

 from fires, etc., is 5 cents per acre per annum; the value 

 of the stumpage is $1 per thousand feet, board measure. 

 Mr. S. thinks that the quality of the forest will be im- 

 proved gradually, and expects an increase in productive- 

 ness of 1 per cent, annually. He figures, besides, on rising 

 stumpage prices, the rise keeping step with the increase 

 in population (1^ per cent.). He has a chance to invest 

 money at 5 per cent, in an equally safe manner and wants 

 to sell the forest. 



Question: Below what price per acre is it not advisable 

 for Mr. S. to sell? 



Points: Mr. S. must figure at 5 per cent, interest, as 

 the equally safe investment promises him 5 per cent, 

 as well. 



2. If the productiveness of the forest increases by 1 per 

 cent, per annum, and the stumpage price at H per cent, 

 per annum, the receipts will grow at the rate of 1\ per cent. 

 per annum. In discounting these receipts backwards, 

 we have to figure at 5 per cent. 2-} per cent. = 2^ per 

 cent. 



3. The present value of all annual receipts is 



25,000 



0.050-0.025* 



4. The present value of all expenses (taxes and pro- 



.. , . 100,000X0.05 

 tection) is - -^ . 



25,000 100,000 + 0.05 



0050=0026 005~ = X - 



Result: $900,000 for the whole forest, or $9 per acre. 



