What is the Faustmann formula?

The Faustmann formula calculates the land expectation value: the present value of an infinite series of identical timber rotations on bare land. It discounts the net revenue of one rotation and then accounts for repeating it forever, which is the correct way to value timberland because the land keeps producing crops after each harvest.

Why is land expectation value higher than single-rotation NPV?

Single-rotation NPV values just one crop and ignores that the land grows another stand afterward. Land expectation value captures the perpetual series by dividing the single-rotation present value by one minus the discount factor over the rotation, which raises the figure because future rotations have value today.

How does the discount rate change the optimal rotation?

A higher discount rate makes distant harvest revenue worth less today, pushing the economically optimal rotation to a shorter age — you cut sooner to capture cash and reinvest. A lower discount rate lets stands grow longer because waiting costs less. The tool scans ages to show this shift.

What costs should I include?

Include establishment cost at planting (site prep, seedlings, planting) as a cost at year zero, and annual management cost (taxes, administration, protection) as a recurring outflow over the rotation. Stumpage revenue is the value of standing timber sold at harvest, net of logging if you quote delivered prices.

What is the Tree Farm Rotation & NPV Calculator?

Use Faustmann land-expectation-value logic to compute the present value of a timber stand across alternative rotation lengths, discounting stumpage revenue against establishment and annual management cost. Helps forestry consultants and timberland investors find the economically optimal cutting age. It runs free in your browser on Gera Tools, with nothing uploaded.

Tree Farm Rotation & NPV Calculator

Name: Tree Farm Rotation & NPV Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

The hardest economic question in forestry is when to cut. This calculator applies Faustmann land-expectation-value logic to discount stumpage revenue against establishment and management cost, giving both single-rotation NPV and the perpetual-series value, and it scans rotation ages to find the optimum.

How it works

For a rotation of length T years, discount rate i, harvest stumpage R, establishment cost C0 at planting, and annual management cost a:

PV of one rotation (at year 0) =
   R / (1 + i)^T  -  C0  -  a × [ 1 - (1 + i)^-T ] / i

Land Expectation Value (perpetual series) =
   PV_one_rotation / ( 1 - (1 + i)^-T )

The single-rotation present value discounts the harvest back to planting, subtracts the up-front establishment cost, and subtracts the present value of the annual management cost (an annuity over the rotation). The Faustmann land expectation value then scales that to an infinite series of identical rotations, which is the correct valuation for productive forest land.

Optimal rotation age — volume vs. value

The economically optimal rotation maximizes land expectation value, not timber volume. These are not the same thing, and the distinction matters in practice.

The biological maximum rotation (the age at which the stand grows the most volume per year, measured as the age of maximum mean annual increment) is almost always longer than the economic optimum. This is because holding the stand past the LEV-maximizing age means the revenue from the still-growing trees is growing slower than the foregone interest you could have earned by cutting and reinvesting the stumpage proceeds.

A higher discount rate accelerates this crossover — it makes future revenue worth less today, so the economic case for cutting sooner is stronger. A lower discount rate (or a very high expected stumpage price appreciation) extends the optimal rotation, sometimes close to the biological maximum.

The tool scans ages around your entered rotation to report the LEV at each, so you can see where the optimum sits and how sensitive it is to a year or two of difference.

Worked example

Suppose you plant a stand with the following parameters:

Establishment cost at planting: $800 per acre
Annual management cost: $15 per acre per year
Expected stumpage revenue at harvest: $4,200 per acre (at year 30)
Discount rate: 5% real

For a 30-year rotation:

PV of harvest revenue = $4,200 ÷ (1.05)^30 ≈ $972
PV of annual management (annuity) = $15 × [(1 − 1.05^-30) / 0.05] ≈ $231
PV of one rotation = $972 − $800 − $231 ≈ −$59

The Land Expectation Value divides −$59 by (1 − 1.05^-30) ≈ 0.768, giving roughly −$77 per acre. This negative LEV tells you that at these figures and a 5% discount rate, a 30-year rotation does not pay. Extending the rotation to 40 years with higher stumpage revenue, or accepting a lower discount rate, can flip it positive. The scanner shows where the crossover occurs.

What the discount rate really means here

In timber valuation, the discount rate represents your cost of capital or opportunity cost — what you could earn by investing the land and money elsewhere. For private landowners using debt to finance the plantation, it is close to the borrowing rate. For institutional timberland investors, it is often a blended return target. A real (inflation-adjusted) rate of 4–7% is typical for timberland analysis.

Notes

This is a screening tool with constant or simply-growing revenue per rotation. A bankable appraisal models full growth-and-yield curves, thinning revenues, price trends over the rotation horizon, risk of fire, pest, and disease, and tax treatment of stumpage income. Use this to compare rotation ages and discount rate sensitivity quickly before commissioning detailed analysis.