Grade Value Increase Rates for Northeastern Timber Species (DRAFT)

(This paper was written in January, 1998 but never submitted for publication.  I'll probably get around to it eventually after I've found time to update the stumpage prices.)

Abstract.  Existing research and market value data are synthesized to develop grade value increase rates for the full range of timber species, diameters and grades found throughout the Northeast.  Grade value increase rates are determined by grade increase probabilities, relative tree values by grade and diameter, and by current market values.  These rates may be used in computer growth simulators to more accurately project and analyze tree value growth.  Management can significantly influence grade value increase rates by discriminating against trees with little potential for tree grade increase, and favoring trees with good potential for tree grade increase.  Good information on grade value increase rates substantiates the value of management for grade production.  Grade value increase rates are typically equal to or greater than volume and market value increase rates.     

Background

Tree value increase rates are the sum of volume, grade value and market value increase rates (Davies 1991, 1996).  There are substantial, high quality data on volume increase rates for all species of trees grown in the Northeast region (McCay and DeBald 1972, Arner et al 1990) and the North Central region (Buongiorno and Hseu 1993, Strong et al 1995, Niese et al 1995, Hseu and Buongiorno 1997, Reed and Mroz 1997).  There are some good quality data on timber market value increase rates for these same species (Dennis 1987, Sendak 1994, Nolley 1994, Luppold and Baumgrass 1995). 

There is little quality data on grade value increase rates, even though there is good quality data on the three components of grade value increase: a) relative tree values by species, grade, diameter and height (Mendel et al 1975); b) probabilities for increase in tree grade by species, grade and diameter (Yaussey 1993); current market values for timber of different species and grades (Doolan 1997). 

This paper describes a method for combining these three data sets to calculate grade value increase rates for timber species in the Northeast.  Grade value increase rates may be used in computer growth simulation models for more accurate projections of future stand values and for financial analyses of alternative treatment options.  Better financial analyses will improve the effectiveness of forest management and will help promote better forest management on private and public lands.

Factors in Grade Value Increase Rates

Some trees increase in grade value as they grow into higher grade categories by virtue of a) simply increasing their size if they are free of defects, or b) eliminating defects by growing clear wood over them.  Other trees do not grow into higher tree grades, but they nonetheless increase in grade value because larger trees have proportionately more high quality lumber in them than smaller trees of the same grade.  In order to calculate grade value increase rates, the proportions of trees that do and do not increase in tree grade must be calculated, and the increases in grade value for each category must be calculated (McCay and DeBald 1972).

Most studies of changes in tree grades and values have used a period of 10 years (Trimble and Mendel 1969, Grisez and Mendel 1972, Godman and Mendel 1978).  This time interval is convenient because it is within the planning horizons of most landowners and because most managed hardwood timber trees will grow 2 inches in diameter per 10 years. If tree grades are based on 2-inch diameter classes (and numbers of defects), trees can potentially increase one grade every 10 years.

The US Forest Service hardwood tree grading system (Hanks 1976) is somewhat difficult to apply in these conditions because tree grades are based on 3-inch diameter classes (and numbers of defects). This system (hereafter referred to as the FS system) has additional handicaps in the difficulty of application by field foresters, the lack of grade categories for large, high quality trees over 16" DBH, and in its incompatibility with commonly used sawmill log grading systems. 

Therefore a different tree grading system (hereafter referred to as the KD system) based on sawmill log grading systems is used in this paper (Davies 1996, Appendix A).  This system includes specifications for hardwood and softwood tree grades.  Use of this tree grading system also facilitates the calculation of up-to-date tree grade values from current sawmill log price data (Davies 1998).

Tree Grade Increase Probabilities

Yaussey (1993) developed equations for the NE-TWIGS (Teck 1990) growth simulator program that would allow the program to calculate the probabilities of trees reaching different US Forest Service (USFS) tree grades at 16" DBH.  These equations were based on extensive forest inventory data in which foresters estimated future tree grades at 16" DBH.  Other studies allow the inference of tree grade increase probabilities from tree grade distribution tables for different species and diameters (Trimble 1965, Ernst and Marquis 1979, Dale and Brisbin 1985, Myers et al 1986). 

Tree grade increase probabilities (Table 1) were derived from the Yaussey equations by first creating a spreadsheet program that calculated the probabilities for all species and grades from the equations, and then by calculating the percentages of trees that had higher grade potentials for each grade and species category.  See Appendix B for all grade increase probabilities and calculations.

Table 1.  Probabilities for tree grade (KD) increases by species and tree grade path--after Yaussey (1993).
Species	Grade 5 to 4	Grade 4 to 3	Grade 3 to 2	Grade 2 to 1
Ash	.86	.48	.35	.35
Basswood	.95	.87	.02	.02
Beech	.31	.22	.45	.45
Black Birch	.53	.21	.13	.13
Black Cherry	.80	.42	.35	.35
Black Oak	.84	.71	.08	.08
Chestnut Oak	.79	.38	.22	.22
Hemlock	.60	.60	.60	.60
Hickory	.73	.38	.25	.25
Red Maple	.53	.24	.15	.15
Red Oak	.79	.44	.33	.33
Red Pine	.81	.49	.36	.36
Spruce	.81	.49	.36	.36
Sugar Maple	.66	.28	.21	.21
White Birch	.53	.21	.13	.13
White Oak	.73	.41	.31	.31
White Pine	.81	.49	.36	.36
Yellow Birch	.53	.21	.13	.13
Yellow Poplar	.63	.51	.40	.40
Averages	.70	.42	.27	.27

Note: Yaussey's paper did not include data for red pine and spruce.  The probabilities for
white pine are substituted for these species in Table 1. 

It should be noted that the grade increase probabilities derived from Yaussey's equations are significantly lower than the probabilities that may be inferred from some of the other papers on tree grade distributions.  For example, it may be inferred from Ernst and Marquis (1979) that grade increase probabilities for Allegheny black cherries 10-16" DBH are nearly 80%.  Yaussey's lower probabilities (roughly 40%) for the same species and sizes are likely due to poorer average growing stock in Yaussey's regional data (for Kentucky, Maryland, Pennsylvania and West Virginia) than in the Allegheny State Forest data. 

Grade Value Increases Without Tree Grade Increases

Tree value conversion standards (TVCS's) were developed by the Northeast Forest Experiment Station in order to help foresters and landowners calculate financial maturity for various hardwood timber species (Mendel et al 1975).  These standards were based on the amount of factory grade lumber that could be sawn from trees of various species, grades, diameters and merchantable heights. 

The standards were expressed in 1968 market values, but the 1968 price relatives for lumber grades are quite close to current price relatives (Lemsky 1968, Parker 1997).  Therefore, although absolute lumber prices have changed considerably, the current relative tree values by diameters and tree grades should be essentially unchanged since 1968.

Table 2 shows rates of grade value increase alone from 10 year increases in tree values for different species, grades and diameters--assuming 2 inches of diameter growth in this time period, but without increase in tree grade or tree height.  The rates were calculated by subtracting the rates of volume increase from the total rates of value increase for the 2 inch per 10-year intervals.  See Appendix C for more detail.

Table 2.  Annual grade value increase rates without tree grade changes per 10 years of growth at 10 RPI--after Mendel et al (1975).
	12" DBH	14" DBH	16" DBH	18" DBH
Species	1 Log, Gd 3	1.5 Logs, Gd 2	2 Logs, Gd 1	2.5 Logs, Gd 1
Ash	.06	.02	.02	.02
Basswood	.06	.02	.02	.02
Beech	.04	.04	.03	.02
Black Birch	.11	.03	.02	.02
Black Cherry	.18	.02	.02	.02
Black Oak	.04	.03	.02	.02
Chestnut Oak	.04	.04	.02	.02
Hemlock	.04	.03	.02	.02
Hickory	.04	.09	.04	.03
Red Maple	.04	.01	.02	.02
Red Oak	.05	.02	.02	.02
Red Pine	.04	.03	.02	.02
Spruce	.04	.03	.02	.02
Sugar Maple	.11	.03	.02	.02
White Birch	.04	.01	.02	.02
White Oak	.04	.09	.03	.02
White Pine	.04	.03	.02	.02
Yellow Birch	.11	.03	.02	.02
Yellow Poplar	.07	.02	.02	.02
Averages	.06	.03	.02	.02

Note: Mendel et al's paper did not include data for red pine and spruce.  The rates for white pine are substituted for these species in Table 2.

Tree Grade Values

The Sawlog Bulletin has been publishing log prices and grade specifications from sawmills throughout New England and New York State since 1989 (Doolan 1997).  While specifications vary, a majority of mills use the same specifications for prime, select, grade 1 and grade 2 logs (Appendix D).  A spreadsheet program was developed to calculate the average prices for logs at these mills.  Stumpage prices for tree grades were derived by taking a percentage (75%) of the butt log value and subtracting logging and trucking costs (Davies 1998).  Table 3 shows November 1997 values for all species reported on, including estimated grade 5 (wood, pulp) values expressed as values per Mbf.

Table 3.  Stumpage prices by species and tree grade (KD) derived from Sawlog Bulletin average prices--November, 1997
Species	Grade 5 $/Mbf	Grade 4 $/Mbf	Grade 3 $/Mbf	Grade 2 $/Mbf	Grade 1 $/Mbf
Ash	20	49	142	256	415
Basswood	5	5	14	96	164
Beech	5	5	7	51	86
Black Birch	10	53	90	175	396
Black Cherry	15	95	253	444	675
Black Oak	5	11	100	218	265
Chestnut Oak	5	5	40	59	78
Hemlock	5	5	24	48	70
Hickory	5	5	7	51	86
Red Maple	5	5	55	127	188
Red Pine	5	5	91	175	231
Spruce	5	77	93	171	246
Sugar Maple	15	106	261	464	715
Red Oak	25	119	254	369	562
White Birch	5	15	48	89	110
White Oak	5	5	79	175	235
White Pine	5	30	62	143	249
Yellow Birch	10	63	107	211	373
Yellow Poplar	5	10	15	84	109
Averages	8	35	92	179	276

While these grade specifications differ from the FS tree grade specifications used in the Mendel et al (1975) study, the relative values of lumber sawn from trees of different grades and diameters should be sufficiently comparable for the purposes of this paper.  The probabilities of grade increases in the two systems should also be sufficiently comparable.  USFS tree grades 3 to 1 are very similar to KD tree grades 4 to 2.   

The spreadsheet program actually calculated negative stumpage values for grade 4 white oak, chestnut oak, red maple, beech, basswood and yellow poplar; grade 3 stumpage values for basswood and yellow poplar were also negative.  Table 2 shows positive values for these categories because such trees would still have positive cordwood values, and to facilitate the calculations of grade value increase.

Synthesizing the Data

Another spreadsheet program was developed to calculate grade value increase rates from the data in Tables 1, 2 and 3.  The results are shown in Table 4.  The program first calculated the 10 year rate of value increase from one grade to the next for each grade in Table 3 and multiplied it by the percentage of trees capable of making that increase according to the probabilities in Table 1.  Next, the program calculated the percentage of trees not capable of making the grade increase and multiplied it by the rate of value increase for that same tree grade in Table 2.  Finally, the program added these two rates. 

Table 4.  Annual grade value increase rates per 10 years: Composite rates by species and grade for trees that do and do not increase in tree grade.
	Grade 4	Grade 3	Grade 2	Grade 1
Species	12"	14"	16"	18"
Ash	.09	.10	.04	.03
Basswood	.00	.10	.19	.02
Beech	.03	.04	.07	.04
Black Birch	.15	.04	.03	.03
Black Cherry	.20	.09	.03	.03
Black Oak	.08	.21	.06	.02
Chestnut Oak	.01	.19	.02	.02
Hemlock	.02	.11	.05	.03
Hickory	.01	.05	.11	.04
Red Maple	.02	.15	.04	.02
Red Oak	.14	.07	.03	.03
Red Pine	.01	.28	.04	.02
Spruce	.26	.02	.04	.03
Sugar Maple	.18	.07	.03	.03
White Birch	.08	.07	.03	.02
White Oak	.01	.26	.05	.03
White Pine	.17	.07	.05	.03
Yellow Birch	.16	.04	.03	.03
Yellow Poplar	.05	.03	.11	.02
Averages	.09	.10	.06	.03

Probabilities of increasing to KD tree grade 1 were estimated by using the same probabilities for increasing to KD tree grade 2 (FS tree grade 1).  Trend analysis would indicate that these probabilities should be lower.  The higher probabilities were chosen to partially compensate for the inability of the program to include trees which go from a grade 2 to a veneer butt log tree instead of a prime butt log tree.  Examination of the data in Table 3 indicates that such trees would in most cases triple in grade value instead of double in grade value over the 10-year period.

In order to make the spreadsheet program work for 12" KD grade 4 trees, cordwood/pulp prices from recent Southern New England stumpage prices reports were translated into Mbf prices.  Where cordwood/pulp values would have been negative or 0--as in the case of soft hardwoods or softwoods--they were still given minimal positive values in order for the spreadsheet program to perform its calculations.

Discussion

Relative Abilities of Species to Overcome Grade Specification Limitations

Grade value increase rates are determined by the presence or absence of "grade stoppers" (limbs, knots, seams, decay, sweep, crook (Ernst and Marquis 1979).  Presence or absence of grade-stopping defects is a function of how tree species shed limbs, plus site characteristics, disturbance history and past management (Trimble 1965). 

Species such as beech and black/yellow birch shed limbs late and are slow to grow over the stubs.  Conversely, species such as black cherry and yellow poplar shed limbs early and grow over stubs relatively fast.  Other species are intermediate in their abilities to overcome defects.  Red oak often produces dormant buds after shedding young limbs; these buds are considered defects and are overgrown slowly (Trimble 1965).  Trees on poor sites grow over defects more slowly and are more susceptible to stress related defects. 

Contributions of Management

Management oriented towards increasing tree grade values will first remove trees that are below grade (Trimble 1965).  These are trees that will never qualify for the minimum tree grade (grade 3 in the FS system, grade 4 in the KD system).  Management will secondly remove some of the trees that will not meet the grade requirements at threshold DBH.  For example, a 14" DBH KD grade 3 black birch tree that cannot make grade 2 might be removed, but a 14" DBH red oak tree with the same grade limitations might be left because of its relatively higher value.

This type of management will significantly increase tree grade increase probabilities.  The Allegheny hardwood stands studied by Ernst and Marquis (1979) were all second growth on state forest lands, and were either uncut or had been thinned once.  Therefore part of the higher-grade increase probabilities for these stands (twice those in the Yaussey study) is a function of silvicultural treatments; another part is a function of preventing high-grade harvests.

The probability of tree grade increases could theoretically approach 100% if thinnings were to begin early in a stand's life.  Research into tree grade improvement in stands that had been thinned every 10 years for 40 years (Strong et al 1995) indicates that this was indeed the case in stands that had been moderately thinned (77 sq ft residual basal area).  Average FS tree grades improved 110% on trees that grew 3.4" in 20 years (3" FS tree grades).  Tree grade increases were 80% for light (88 sq ft residual basal area) and heavy (62 sq ft residual basal area) thinnings with 3.2" and 3.6"  diameter increases, respectively.      

Other Factors

Although Yaussey (1993) found site index to be a significant factor in determining the probability of tree grade increase, other researchers found it to be an insignificant factor in butt log grade distributions (Dale and Brisbin 1985, Myers et al 1986).  The difference between grade increase probabilities on site index 60 and 70 land using Yaussey's coefficients is only a matter of a few percent for all species.

Changes in tree value due to increases in merchantable height or increases in grade of upper logs were not considered in this paper.  McCay and DeBald (1972) found little difference in tree value change due to these factors over 10 year periods, but they hypothesized that these factors could be more significant over longer management periods.  Examination of the tree value conversion standards in Mendel et al (1975) indicates that this factor could be significant for 12" and 14" DBH trees that are more likely to increase in log height.

Rates of Grade Value Increase 

Some species show extremely high rates of grade value increase at certain diameters.  For example, black and white oak show very high rates at 14" DBH; basswood and hickory show high rates at 16" DBH.  These high rates are the product of high probabilities for grade increases and large difference in grade values at those grade and diameter thresholds. 

Most species show declining rates of grade value increase with larger diameters.  This is to be expected as the differences between grade values diminish with diameter and grade, and as probabilities for grade increases also diminish.  However, the grade value increase rates for grades 2 and 1 could be deceptively low because there is no provision in the KD tree grading system--or in the probabilities for grade increases--for the extremely high value of veneer logs of some species. 

Black cherry and sugar maple veneer logs, for instance, can be worth up to $3,000 per Mbf--as compared with around $1700 per Mbf for the next lowest grade (prime) logs--and they have the same minimum tip diameters as prime logs at many mills.  Since the specifications for veneer logs vary considerably, it is not possible to define a majority standard for them.  Nevertheless, it would be possible for a cherry or maple tree to go from a KD grade 2 to a veneer grade in 10 years, and doubling or tripling in grade value instead of increasing by 50-60% as it would do if it were to go to a grade 1 tree.

Applications

With the exceptions of the INFORM (Hepp 1992) and NE-TWIGS (Teck 1990) programs, computer tree growth simulators leave out grade value increases in projections of tree value growth.  However, most simulators do allow for estimates of market value increase (inflation) in growth projections.  The grade value increase rates in Table 4 may be added to these estimated rates. 

Difficulties arise where there is a wide range of grades and sizes for a given species in an inventory.  If the program allows for calculations of average diameters and grades by species, the grade value increase rates associated with those diameters and grades may be added to the rate of market value increase/inflation. 

INFORM setup data forms require user input of tree grade values and grade increase probabilities by species and grade.  Users can use the data in Table 5 to estimate probabilities if they know the grade value multipliers between grades.  Grade value multipliers may be determined by simply dividing tree grade values: 4/3, 3/2, 2/1.    

Table 5.  Grade increase probability factors for use with INFORM.
2X Multiplier (.07 Per Year)		2.5X Multiplier (.10 Per Year)		3X Multiplier (.12 Per Year)
Probability	GVI Rate	Probability	GVI Rate	Probability	GVI Rate
1.00	0.07	1.00	0.10	1.00	0.12
0.90	0.06	0.90	0.09	0.90	0.11
0.80	0.06	0.80	0.08	0.80	0.10
0.70	0.05	0.70	0.07	0.70	0.08
0.60	0.04	0.60	0.06	0.60	0.07
0.50	0.04	0.50	0.05	0.50	0.06
0.40	0.03	0.40	0.04	0.40	0.05
0.30	0.02	0.30	0.03	0.30	0.04
0.20	0.01	0.20	0.02	0.20	0.02

Conclusions

Grade value increase rates for different northern timber species and grades may be calculated from existing data on tree grade increase probabilities, relative tree grade values (TVCS's), and current market values.  Use of these data in computer tree growth simulators will increase the accuracy of value growth projections and financial analyses.  This information will reveal the true value of investments in grade timber management.      

While it is difficult to calculate the exact value contribution of management for grade production from the existing data, it appears to be in the range of 60-100% above total value growth rates in unmanaged stands (volume plus grade value).  Most of the contribution of management is in increasing grade value increase rates (Godman and Mendel 1978,  Strong et al 1995).  These increased rates result from foresters eliminating below grade trees and other trees that are unlikely to increase in grade value.  They also result from foresters increasing rates of volume growth on residual stands and preventing high-grade cutting operations.

If thinnings, improvements harvests and selection harvests can nearly double the probability of tree grade increases (Ernst and Marquis 1979, Yaussey 1993), and if grade value increase rates in unmanaged stands are roughly 3% per year (Table 4), then well-managed timber stands should grow at roughly 5-6% per year in grade value--in addition to the 3-4% per year they grow in volume and the 3-4% per year they grow in market value (Davies 1991, 1996). 

When discounted to the present, the increase in future returns due to good management is significant.  The net present value of good management for young northern hardwoo