United States 

Department of 

Agriculture Rate of Value C 

Forest Service 

Nottheastern Forest in Pennsy Experiment Station 

Research 

Paper N E-547 

Owen W. Herrick 
Abstract 

Data from remeasured Pennsylvania forest inventory plots revealed that 

during a 13-year period the compound rate of value change in uncut hardwood 

forest stands averaged 4.7 percent, and ranged from -5.5 to 18.8 percent. No 

well-defined means for predicting a stand's rate of value change could be 

identified, However, some measures of initial stand condition can be IJS~~ to 

get a general indication of what to expect in stands with management potential. For example, stands with the highest rates of value change (averaging 7.5 

percent) have (1) Tree of average basal area less than 5 inches in diameter; 

(2) less than 10 percent of their basal area in large sawtimber-size trees; and 

(3) some yellow-poplar, northern red oak, andlor black oak. 

The Author 

Owen W. Herrick is a research forester in the Regional Forest Resource 

Economics Unit at the Northeastern Forest Experiment Station, Broomall, Pa. 

He is engaged in research that provides economic criteria and information for 

regional programs, policies, and decisions respecting forest-based activities 

in the Northeast. 

Manuscript received for 

publication 19 January 1984 
The Study 

Investigations into the rate at 

which timber increases in value generally have recognized the benefits 

of concentrating timber investment 

capital in well-stocked stands of poleand small sawtimber-size northern 

hardwoods. Additional guidelines that 

indicate what rates of value change 

to expect of various stands of timber 

would aid people who have to make 

decisions about managing forest 

land. 

An expectation index such as 

average rate of value change for forest 

stands could be useful in comparing 

timber stands and rating prospective 

stand management options. This paper reports results from analyses of 

statewide forest inventory measurements that quantify value change in 

hardwood timber stands, and provide 

further understanding of the link 

between timber stand characteristics 

and prospective value change. 

Background 

Given available markets for the 

species, tree value is influenced by 

diameter, merchantable height, and 

quality. The rate of change in tree 

value generally is based on estimates 

of prospective change in these attributes applied in the compound interest expression: 

where r is the compound interest rate 

of value change, n is the period of 

time considered (often 10 years), V, 

is the value of the tree n years hence, 

and V, is its current value. 

Generalized results from a series 

of studies (Leak et al. 1968; Mendel 

1969; Mendel and Trimble 1969; Trimble 

and Mendel 1969; Grisez and Mendel 

1972; Mendel et al. 1973) that have 

used the expression cited to evaluate 

projections of hardwood tree value 

can be summarized as follows: 

* Rate of value increase is inversely 

related to initial tree diameter 

(assuming initial diameter meets 

minimum merchantability specifications). 

* High-vigor trees (greatest diameter 

growth rate) have higher rates of 

value increase than trees of low 

vigor. 

Improvement in tree quality results 

in much higher rates of vaiue increase than increases due to growth 

alone. 

Trees that increase in merchantable 

height usually show greater rates 

of value increase than trees that 

add no merchantable height. 

The unique characteristics of a 

timber stand can be captured in rate 

of value change calculations by aggregating the value of individual trees 

and their potential development. Evaluations of silvicultural treatment 

possibilities for the stand often are 

handled similarly, making projections 

of the growth and value of trees in the 

future stand and focusing treatment 

results within a relatively short planning period. 

More than estimates of growth 

and value are needed to develop expectation indexes that can serve as 

benchmarks of average rate of value 

change for timber stands. The rate of 

value change over a time period is 

determined by initial stand value and 

the relationship between the values 

at the beginning and end of the time 

period. Accordingly, the foundation 

for an index or average rate of value 

change is a record of actual timber 

stand change registered over an 

interval between measurements. 

The USDA Forest Service updates 

statewide timber resource information 

approximately every 10 years. Part of 

the updating process includes remeasuring a network of permanent forest 

inventory plots in each state. Pennsylvania was remeasured during 1978 

(Considine and Powell 1980) and 331 

plots from that inventory are the 

basis for this analysis of rate of value 

change in hardwood forests between 

the 1965 and 1978 surveys. 

Tree merchantable height, diameter (d.b.h.), and tree grade (based on 

butt-log grade measures) were converted to board-foot and cubic-foot 

volumes (Scott 1979, 1981). The volumes were then translated into dollar 

values to express the rate of value 

change on each forest inventory plot 

between 1965 and 1978. The dollar 

values are based on tree-value conversion standards (Mendel et al. 1976; 

DeBald and Mendel 1976). These standards reflect a tree's net worth as 

414-inch lumber andlor pulpwood, 

allowing for the cost of conversion. 

The same (current) dollar-value standards were applied to both 1965 and 

1978 survey measurements to evaluate the stand's development and not 

allow valuation items that are irrelevant to biological change to get in the 

way. This use of constant value standards avoids effects of inflation and 

changes in timber prices that occurred 

during the period. 
Results 

Timber stand characteristics 

thought to correlate with the rate of 

value change were used as predictor 

variables to analyze rate of change. 

These variables are measures of: 

Site class 

Physiographic class 

Timber stand age 

Average tree diameter 

Tree species composition (O/O) 

Forest type 

Treeslacre 

Basal area (BA)lacre 

Diameter of tree of average BA 

Timber stocking (O/O) 

Timber volume: 

Board feetlacre 

Cubic feetlacre 

Timber quality: 

% Growing-stock trees 

O/O Sawtimber in each tree grade 

Timber stand-size composition: 

% Sapling-size trees 

O/O Pole-size trees 

O/O Small sawtimber trees 

% Large sawtimber trees 

(15 inches +) 

% 4-inch diameter-class trees 

O/O Softwood species 

Timber value: 

Average tree value 

Initial stand value 

O/O H ig h-value species ($80 +IM bf) 

% Medium-value species 

($50-$801M bf ) 

% Low-value species ($5OlM bf) 

The timber stand variables were 

screened as potential predictors of 

rate of value change using stagewise 

multivariate procedures including 

automatic interaction detection (AID). 

Between 1965 and 1978, inventory plots in the hardwood forests of 

Pennsylvania had a 3.7 percent average rate of value change. Tree cutting 

took place in one-fourth of these 

hardwood stands. When I include only 

the forest stands that had no timber 

cutting activity between surveys, the 

average rate of value change was 4.7 

percent. These rates of change ranged 

from -5.5 to 18.8 percent (Fig. 1). 

Despite the wide variety of potential predictors, analyses failed to 

identify associations between rates 

of value change and timber stand 

characteristics that would be useful 

in a predictive sense. Only loosely 

defined patterns of relationship 

showed up between characteristics 

representing initial timber stand 

conditions and the resulting rates of 

value change. 

COMPOUND RATE OF VALUE CHANGE (Percent) 

Figure 1 .-Compound rate of change in timber value for hardwood forests 

in Pennsylvania, 1965-78. 
Analyses were then concentrated 

on a subset of the data that included 

only plots from timber stands with 

adequate potential to achieve acceptable utilization of the site. That is, the 

initial stand condition was above the 

C-line that most stocking guides use 

to represent a position where 10 

years of growth will achieve the lowest 

limit of acceptable stocking (Gingrich 

1967). Stands below the C-line definitely are understocked and ordinarily would not be candidates for 

decisions requiring a rate of value 

change index. 

This subset of timber stands 

with "management potential" had 

rates of value change that ranged 

from -3.0 to 11.9 percent, and a 4.3 

percent average. Again, no useful 

predictive relationship was evident 

between initial timber stand characteristics and subsequent rates 

of value change. Results from AID 

analysis only loosely defined the 

structural pattern using initial stand 

condition measures of tree size, 

density, species composition, and 

quality (Fig. 2). For example, stands 

with the highest rates of value change 

in these hardwood forests have: 

Tree of average basal area less 

than 5 inches in diameter, 

Less than 10 percent of their basal 

area in large sawtimber size trees. 

Some yellow-poplar, northern red 

oak, andlor black oak. 

These conditions identify them 

as members of Group 9, where rates 

of value change average 7.5 percent. 

In addition to this highest rate group, 

five others (Groups 8, 13, 17, 18, and 

19) fell at or above the 4.3-percent 

statewide average rate of value change 

for these above C-level stands. 

oak and/or black oak 

Diameter of tree 

of average BA 

elm, 

yellow birch, 

aspen, 

chestnut oak, 

black locust 

Figure 2.-Guide for estimating rates of value change in hardwood forests, 

A timber stand is assigned to a value-change group on the basis of characteristics of the stand. The average rate of value change 1965 to 1978 is 

shown for each group. Decimal fractions on each leg show the portion of 

the Pennsylvania sample in that group. 
Conctusion 

It has been said before (Mendel 

et al. 1973) but it's worth repeating: 

dollar value increase reflects the 

change in value of trees resulting 

from increases in diameter, merchantable height, or improvement in 

quality. A rate of value increase, on 

the other hand, accounts for the 

initial investment in capital (the value 

of the trees at the beginning of the 

period) that must be made to attain 

the dollar-value increase (added 

value by the end of the period). The 

rate of return on the investment (rate 

of value change) over the period is 

determined by the initial value and 

the relationship between the values at 

the beginning and end of the time period. Consider the following example: 

From a financial standpoint, the 

responsibility for choosing a proper 

course of action for handling a particular stand of timber rests with the 

owner, too. Once financial objectives 

are sorted out-dollar-value increase 

or rate of return on investment-it 

remains to determine the value-growth 

status of the timber stand. I looked 

at recently remeasured forest inventory plots in Pennsylvania to determine rates of value change in 

hardwood forests. The plots indicate 

that uncut hardwood timber stands 

in Pennsylvania are increasing in 

Initial value Ending value Change in No. of Rate of 

(vd ( Kt) value years value change 

............................ Dollars --------- ------ ------- ------ Percent 

In both cases there was a $5.00 

change in value. But in the first case, 

its smaller investment in capital ($10 

versus $50) clearly has a greater impact on the resulting rate of value 

change over the 10 years. 

It is the timberland owner who 

determines the financial objectives of 

his or her ownership. On the basis of 

the definitions mentioned, will it be 

dollar-value increase regardless of 

the amount of capital investment? Or 

will it be a prescribed rate of return 

on the capital investment? 

value at a rate of 4.7 percent, on average. But wide variation was evident in 

the rates of change during the 13-year 

period between inventories-from 

-5.5 to 18.8 percent. These results 

are appropriate where gross change 

estimates are desired. However, the 

results are limited as a management 

tool for foresters and landowners. 

The comprehensive analyses of these 

data yielded no well-defined predictive relationships between site characteristics or initial timber stand 

conditions and subsequent rates of 

value change. 

A predictor or expectation index 

of rate of value change would be most 

useful. But only general notions seem 

possible when judging potential rate 

of value change in hardwood timber 

stands. Measures of tree size, stand 

density, species composition and 

quality can help. They represent key 

characteristics of initial timber stand 

conditions that can be used to pigeonhole stands with management potential into very loosely defined rate of 

value-change groups. These groups, 

with average rates of value change 

ranging from 1.6 to 7.5 percent, can 

serve as useful baselines for comparing timber stands and prospective 

stand management options. 
Literature Cited 

Considine, Thomas J., Powell, Douglas 

S. Forest statistics for Pennsylvania-19'78. Resour. Bull. NE-65. 

Broomall, PA: U.S. Department of 

Agriculture, Forest Service, Northeastern Forest Experiment Station; 

1980. 88 p. 

DeBald, Paul S.; Mendel, Joseph J. 

Composite volume and value tables 

for hardwood pulpwood. SETs: 

Stand Evaluation Tools 3. Res. Pap. 

NE-338. Upper Darby, PA: U.S. 

Department of Agriculture, Forest 

Service, Northeastern Forest Experiment Station; 1976. 43 p. 

Gingrich, Samuel F. Measuring and 

evaluating stocking and stand 

density in upland hardwood forests 

in the Central States. Forest Science 13:38-53; 1967. 

Grisez, Ted J.; Mendel, Joseph J. The 

rate of value increase for black 

cherry, red maple, and white ash. 

Res. Pap. NE-231. Upper Darby, 

PA: U.S. Department of Agriculture, 

Forest Service, Northeastern Forest Experiment Station; 1972. 26 p. 

Leak, William B.; Filip, Stanley M.; 

Solomon, Dale S. Rate of value 

increase for yellow birch in New 

England. Res. Pap. NE-120. Upper 

Darby, PA: U.S. Department of 

Agriculture, Forest Service, Northeastern Forest Experiment Station; 

1968. 11 p. 

Mendel, Joseph J. Financial maturity 

of paper birch. In: Birch symposium 

proceedings. 1969 August 19-21; 

Durham, NH. Upper Darby, PA: U.S. 

Department of Agriculture, Forest 

Service, Northeastern, Forest Experiment Station; 1969: 135-144. 

Mendel, Joseph, J.; Trirnble, George 

R., Jr. The rate of value increase for 

yellow-poplar and beech. Res. Pap. 

NE-140. Upper Darby, PA: U.S. Department of Agriculture, Forest 

Service, Northeastern Forest Experiment Station; 1969; 27 p. 

Mendel, Joseph J.; Grisez, Ted J.; 

Trimble, George R., Jr. The rate of 

value increase for sugar maple. Res. 

Pap. NE-250. Upper Darby, PA: U.S. 

Department of Agriculture, Forest 

Service, Northeastern Forest Experiment Station; 1973. 19 p. 

Mendel, Joseph J.; DeBald, Paul S.; 

Dale, Mart in E. Tree value conversion standards for hardwood sawtimber. SETs: Stand Evaluation 

Tools 2. Res. Pap. NE-337. Upper 

Darby, PA: U.S. Department of 

Agriculture, Forest Service, Northeastern Forest Experiment Station; 

1976. 74 p. 

Scott, Charles T. Northeastern forest 

survey board-foot volume equations. Res. Note NE-271. Broomall, 

PA: U.S. Department of Agriculture, 

Forest Service, Northeastern Forest Experiment Station; 1979. 3 p. 

Scott, Charles T. Northeastern forest 

survey revised cubiofoot volume 

equations. Res. Note NE-304. 

Broomall, PA: U.S. Department of 

Agriculture, Forest Service, Northeastern Forest Experiment Station; 

1981. 3 p. 

Trimble, George R., Jr.; Mendel, Joseph 

J. The rate of value increase for 

northern red oak, white oak, and 

chestnut oak. Res. Pap. NE-129. 

Upper Darby, PA: U.S. Department 

of Agriculture, Forest Service, 

Northeastern Forest Experiment 

Station; 1969. 29 p. 
Herrick, Owen W. Rate of value change in Pennsylvania timber 

stands. Res. Pap. NE-547. Broomall, PA: U.S. Department of 

Agriculture, Forest Service, Northeastern Forest Experiment 

Station; 1984. 5 p. 

Data from remeasured Pennsylvania forest inventory plots 

revealed that during a 13-year period the compound rate of value 

change in uncut hardwood forest stands was 4.7 percent, and 

ranged from -5.5 to 18.8 percent. No well-defined means for 

predicting a stand's rate of value change could be identified. 

However, some measures of initial stand condition can be used 

to get a general indication of what to expect in stands with management potential. For example, stands with the highest rates 

of value change (averaging 7.5 percent) have (1) Tree of average 

basal area less than 5 inches in diameter; (2) less than 10 percent 

of their basal area in large sawtimber-size trees; and (3) some 

yellow-poplar, northern red oak, andlor black oak. 

ODC 653:748 

Keywords: Compound interest; financial objectives; hardwood 

forests 

a U.S. GOVERNMENT PRINTING OFFICE: 1984-705-0291521 
Headquafters of the Nodheastern Forest Expwtriment Station are in 

Broomall, Pa. Field laboratories are maintained at: 

0 Amherst, Massachusetts, in cooperation with the University of 

Massachusetts. 

0 Berea, Kentucky, in cooperation with Berea College. 

0 Burlington, Vermont, in cooperation with the University of 

Vermont. 

0 Belaware, Ohio. 

0 Durhm, New Hampshire, in cooperation with the University of 

New HmpSra3. 

0 Hamden, Connectkut, in cooperation with Yale University. 

0 Morgantown, West Virginia, in cooperation with West Virginia 

University, Morgantown. 

0 Orono, Maine, in cooperation with the University of Maine, 

Orono. * Parsons, West Virginia. 

Princeton, West Virginia. * Syracuse, New York, in cooperation with the State University of 

New York College of Environmental Sciences and Forestry at 

Syracuse University, Syracuse. 

0 University Park, Pennsylvania, in cooperation with the 

Pennsylvania State University. * Warren, Pennsylvania.