Costs and Values in a Logging Operation. 685 



operation, which is in turn conditioned by the amount of timber 

 cut, and apparently should be apportioned on a quantity basis. 

 The smaller items may be distributed one way or the other with- 

 out affecting the results very much, but it is important that a 

 charge which constitutes a high proportion of the cost of logging, 

 such as the cost of constructing a railroad, be apportioned be- 

 tween the species on a proper basis. 



The same idea of apportionment on a value basis may be ap- 

 plied in the use of the Forest Service formula for obtaining 

 stumpage values. It seems that this formula applied directly to 

 each species and product exaggerates the differences in value be- 

 tween the low grade and high grade products by assuming that 

 the operator must make an equal percentage of profit on each. 

 What the operator is primarily interested in is the profit on the 

 entire operation. If there is enough high grade products to 

 yield a profit sufficient to warrant the operation, in all prob- 

 ability the operator will be willing to increase his total profit 

 by handling at the same time low grade products, even if he 

 cannot make nearly as large a percentage of profit on these as 

 on those of greater value. Therefore it is easy to see that the 

 unmodified Forest Service formula may show a negative stump- 

 age value for a product which would actually be handled with 

 profit both to the operator and to the stumpage owner. 



This difficulty has in some cases been corrected by assigning 

 arbitrary stumpage values to the low grade products and reduc- 

 ing the stumpage values on high grade products so as to give the 

 operator the same profit on the operation. A similar result can 

 be obtained by a logical mathematical process as long as the 

 products can really be handled without loss, that is, as long as 

 the f. o. b. mill value of the lowest grade product included is 

 more than the operating costs exclusive of railroad construction 

 (or other equally fixed charges) and of operator's profit. Of 

 course there must be enough high grade products to make the 

 operation profitable as a whole. The method is to distribute the 

 railroad construction costs on the value basis as already ex- 

 plained, and then to apportion the stumpage value of the aver- 

 age acre as a whole between the different products in proportion to 

 the gross profit on each. This has the effect of distributing the 

 operator's profit in the same proportion, since the gross profit is 

 divided between the operator and the stumpage owner. The 

 stumpage value for the average acre, X, may be obtained by the 



