A SHORT LEAF PINE PROBLEM (ARK.) 



PREMISES: The S. & A. Lumber Co., of B., Arkansas, 

 owns 100,000 acres of forest stocked, per acre, with 6000 feet board 

 measure merchantable short leaf pine, and has a mill of thirty 

 million feet board measure annual capacity. The stumpage is worth 

 $1 per 1000 feet board measure. The land is unfit for agriculture. 

 Under conservative cutting the forest will continuously produce 200 

 feet board measure per acre per annum, after the "Virgin Surplus" 

 of the forest, consisting per acre of 4500 feet of hypermature and 

 mature trees, has been removed. Under conservative cutting, the 

 logging expenses are 10 cents higher per thousand feet board meas- 

 ure. Prices are expected to rise at i i-i per cent per annum. Fig- 

 ure at 6 per cent. Taxes are ict per acre per annum. Protection 

 from fire, under conservative lumbering, will cost sets per acre per 

 annum. 



QUESTION : Which pays better, conservative or exhaustive 

 lumbering ? 



POINTS: 



1. If prices rise at i 1-2 per cent., future yields must be dis- 

 counted back to the present moment at 6 per cent — i 1-2 per 

 cent equal to 4 1-2 per cent. 



2. Under exhaustive lumbering, the forest will yield 30,000,000 

 feet b. m. for 20 years, and nothing more. The land, being non- 

 agricultural, will be thrown away after 20 years. The value of all 

 yields expected from the forest, minus taxes for 20 years, is there- 

 fore : 



30000 (1.045'" — i) 1000 (i.og» — I) 



0.045 X 1.04520 0.06 X I.0ff» 



3. Under conservative lumbering, we withdraw as well annu- 

 ally 30 million feet from the forest, as long as the mature stock of 

 4500 X 100,000 equal to 450 million feet lasts, namely for 15 years. 



4. From the i6th year on, we cut only the annual production, 

 namely, 200 x 100,000 equal to 20 million feet per annum. 



5. As the extra logging expenses, in this case, are 10 cents 

 higher, the timber has a stumpage value of 90 cents only, instead of 

 $1 per 1000 feet board measure. 



6. Taxes and protection from fire will cost annually 0.04 x 

 100,000 equal to $4000. 



7. Thus, under conservative management, the present value 

 of all expected yields, minus expenses for taxes and protection is : 



27000 (1.045"— I) 18000 _ 4000 



0.045x1.045" ■*" 0.045x1.045" " ~^:^ 

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