This document proposes a method for calculating compensation for the removal of a healthy tree based on the net present value of the tree's future leaf area over its remaining lifespan. The value is determined by the tree's size, growth rate, expected lifespan based on mortality curves, and discount rate. Tables can be used to look up the number of replacement trees owed based on the removed tree's diameter at breast height. The compensation provided would be either planting an equivalent number of replacement trees or a cash amount based on typical tree planting costs.

1. Compensating for the Loss of a Healthy Tree:
How Many Trees Do You Owe Me?
David J. Nowak
US Forest Service
Syracuse, NY

2. 2004

3. Google goes Public

4. Invest $10,000
Boris Badenov
**ONE HUNDRED EIGHTEEN**
**118**

5. Invest $10,000 – Offer: $12,800 (inflation)
Boris Badenov
**ONE HUNDRED EIGHTEEN**
**118**

6. Invest $10,000 – Current Value = $95,000
Boris Badenov
**ONE HUNDRED EIGHTEEN**
**118**

7. Tree Value?

8. Tree Value?

9. Fallacy of Tree Value
There is no NASDAQ for trees
We do not know the true value of trees
We may never know the true value of trees

10. Proposed Solution
Compensate on equal trees, not $
Calculate number small trees = removed tree
Size based methods:
Method No. 1” trees to replace 30” tree
DBH 30
Basal area 900
Leaf area ~70

11. Proposed Solution
Compensate based on leaf area
Many tree values associated with leaf area
Tends to increase through time (predictable)

12. Issue
Need to consider future values (lost or gained)
Net present value (NPV) of future leaves
NPV of 1” DBH large, long-lived tree = 34,000 ft2
Replace a 24” DBH large tree:
Years Remaining NPV leaves (3% rate) No. replacement trees
1 6,000 ft2 0.2
50 187,000 ft2 5.6

13. Calculating Tree Compensation
Tree size
Life span
Growth rate
Discount rate

14. Tree Size
Large: London
planetree
(Platanus hybrida)
Small: crapemyrtle
(Lagerostroemia
indica).
0.2 in/yr; 100 years to death

15. Life Span
Combined DBH mortality curve with average
DBH distribution

16. Life Span
Average population mortality = 1,2,3 or 4%

17. Life Span
Long-lived = 87 years Mod. Long-lived = 50 yrs Mod. Short-lived = 34 yrs Short-lived = 26 yrs

18. Calculating Tree Compensation
Tree size (large vs. small)
Life span (1-4% annual mortality rate)
Growth rate (0.2 inches/year)
Discount rate (2, 3, and 4%)

19. Compensation Rate by DBH (3%; Large Tree)
Replacing large tree with large tree

20. Maximum Compensation Values (3% rate)
Replacement tree : Large Small
Existing Tree L ML MS S L ML MS S
Large Long-lived (L) 6.6 12.2 20.9 31.5 13.6 19.5 29.9 41.1
Mod. Long-lived (ML) 4.4 8.1 14.0 21.1 9.1 13.0 20.0 27.5
Mod. Short-lived (MS) 3.4 6.2 10.7 16.2 7.0 10.0 15.3 21.1
Short-lived (S) 2.9 5.3 9.1 13.7 5.9 8.5 13.0 17.9
Small Long-lived (L) 0.9 1.6 2.8 4.1 1.8 2.6 3.9 5.4
Mod. Long-lived (ML) 0.7 1.3 2.3 3.4 1.5 2.1 3.3 4.5
Mod. Short-lived (MS) 0.6 1.1 1.9 2.9 1.3 1.8 2.8 3.8
Short-lived (S) 0.5 1.0 1.7 2.5 1.1 1.5 2.4 3.3

21. Look-up Tables
DBH (inch)
YRS TO
DEATH 1 2 3 4 5 6 7 8 9 10
80 0.9 1.1 1.3 1.6 1.8 2.0 2.3 2.5 2.8 3.1
81 1.0 1.1 1.3 1.6 1.8 2.0 2.3 2.5 2.8 3.1
82 1.0 1.2 1.4 1.6 1.8 2.1 2.3 2.6 2.8 3.1
83 1.0 1.2 1.4 1.6 1.8 2.1 2.3 2.6 2.8 3.1
84 1.0 1.2 1.4 1.6 1.8 2.1 2.3 2.6 2.9 3.1
85 1.0 1.2 1.4 1.6 1.9 2.1 2.4 2.6 2.9 3.2
86 1.0 1.2 1.4 1.6 1.9 2.1 2.4 2.6 2.9 3.2
87 1.0 1.2 1.4 1.6 1.9 2.1 2.4 2.6 2.9 3.2
88 1.0 1.2 1.4 1.7 1.9 2.1 2.4 2.7 2.9 3.2
89 1.0 1.2 1.4 1.7 1.9 2.2 2.4 2.7 2.9 3.2
90 1.0 1.2 1.5 1.7 1.9 2.2 2.4 2.7 3.0 3.2
Bold = large, long-lived tree
replaced with comparable tree

22. Replacement trees: Mod Short-lived Large Tree

23. Limitations
Likely minimum compensation
Does not include:
Social values (Grandpa planted tree; historical tree)
Punitive damages
Effect of multiple surrounding trees (forests)
Value of dead trees

24. Compensation
Determine number of trees based on size and
life span remaining (look-up tables or program)
Replant the trees, or
Compensation in dollars based on cost of
planting trees (not value of tree)
Example: owed 10 trees; cost of planting = $1,000
per tree (compensation = $10,000)

25. Summary
dnowak@fs.fed.us nrs.fs.fed.us/units/urban
Tree compensation:
Can be calculated based on NPV of leaf area
Varies with tree size and life span remaining
Can be converted to dollars based on cost of
planting new trees