260 MISC. PUBLICATION 218, U. S. DEPT. OF AGRICULTURE 
that deferment of income might be involved, as explained later in 
discussing the effect of the property tax on the growing of timber. 
At this point, the discussion is confined to the choice between destruc- 
tive cutting and holding. 
It will be assumed that the timber owner will generally be guided by 
the desire to make the maximum profit or suffer the minimum loss. 
Under this assumption, decision whether to cut now or at some future 
time will depend on whether the value to be obtained at the future time 
is expected to be greater or less than the sum of the present realizable 
yield plus all carrying charges to the future date. Obviously, if the 
future yield is greater than the present realizable value plus carrying 
charges, the owner will find it advantageous to hold the forest for 
future cutting. If, on the other hand, it appears probable that the 
value to be obtained at the future date will not be so great as the 
present realizable value plus carrying charges, it will be advantageous 
to cut now. The principal carrying charges are interest, taxes, and 
protection costs, the first two being generally much creater than the 
third. For the purposes of this discussion, interest is the interest 
which might be earned on the present realizable value, regardless of 
whether the invested capital was owned or borrowed. 
It may be helpful to give the general principle stated above the 
precise form of mathematical terminology. 
An owner of old-growth timber, in deciding upon his cutting policy, 
must take into consideration the following factors: Present realizable 
value of stumpage (or realization through conversion into products), 
V,, and realizable value of stumpage 1 year hence Vj. 
It is assumed, as in other examples in this report, that interest at p 
rate, taxes at r rate, and other carrying charges, e, are due at the end 
of the year. ; 
V,— 
Ii—V,=V,(1+p+r)-+e, or if V; op trte, 
it is immaterial whether the timber be cut now or allowed to remain. 
This is the case of a marginal owner of timber. A change in any of the 
factors will definitely decide for him whether to hold his timber or 
cut it. 
It—Vi>Voll-+p+r) +e, or if UE pyr 4 
0 
it is profitable to hold the timber, and the owner will find it to his 
advantage to refrain from cutting under such conditions. This is 
the case of the speculative timber holder. 
Vi Vo aaah) er Ue gyi fa 
Vo Vo 
it is advantageous to cut the timber. This is the case of the active 
operator of old-growth timber. 
To take an example, assume: 
IBreSeMt pValue cas ae wee oko ks Ma ie 0 SANA ee $100. 00 
IntereSt soe eee Ee eh OE OD Ce Ee ee ee 3. 00 
oh CRED ee Sea LT ICR Ge ie Me ED ON Ma RRR IES fag) eho Fee TEST 75O 
Othericarryime chargesls. 2 vs 22 2. as fe a ee 50 
