Economic assessment

Part of the Assessment module.

How much does a management strategy earn? ForestStudio values every harvest it simulates, per species, management unit and year, and can also count the costs of establishing and tending young stands.

The approach follows the wood from the forest to the balance sheet. Each section below starts with the general idea and then explains how ForestStudio does it.

Harvested trees

Every tree removed, with its species, diameter and volume.

Summary per management unit

Volume and mean tree size per species, plus the share of conifers.

Timber revenue per m³

From the species and the mean tree size. You can set your own prices.

Harvest cost per m³

From the harvesting method you choose, the species mix and the mean tree size.

Net revenue

Volume × (timber revenue − harvest cost), minus pre-commercial thinning costs per hectare, per management unit and year.

From harvested trees to management units

The starting point is the list of trees removed in a simulated year, each with its diameter (DBH), species, harvested volume, management unit and the harvesting method of that unit. ForestStudio estimates each tree’s stem volume from its diameter and height, with height derived from diameter.

These trees are then summarised per species and management unit (and per year):

  • the total harvested volume (m³), the sum over all trees of that species in the unit;
  • the quadratic mean diameter (QMD), the diameter of the tree with the average basal area. It describes the typical size of the harvested trees, and it is what timber revenues and harvest costs depend on;
  • the conifer share, the harvested conifer volume divided by the total harvested volume in the unit. Together with the harvesting method, it sets which harvest cost curve applies.

Basal area of each harvested tree, with DBH in cm:

\[BA = \frac{\pi}{4} \cdot DBH^2\]

Quadratic mean diameter of the harvested trees of one species in one management unit:

\[QMD = \sqrt{\frac{4}{\pi} \cdot \overline{BA}}\]

Harvesting method. Each management unit uses one of two harvesting systems, each combining a felling and an extraction process: harvester felling with forwarder extraction, or motor-manual felling (chainsaw) with skidder extraction. You choose the system for each management unit in the management scenario, with harvest_manual (the Manual Harvest column in the app): true for motor-manual felling with a skidder, false (the default) for harvester and forwarder. The choice changes the harvest costs, not which trees are removed.

Timber revenue

Some background. Harvested roundwood is sold as stem wood (sawlogs for sawmills), pulpwood (for pulp, paper and board) or energy wood. Stem wood is further sorted into assortments by length, diameter and quality, and a wood price matrix gives the price of each assortment. Thicker logs and better qualities fetch more per cubic metre. In Switzerland there are no fixed timber prices: they are set between forest enterprises, traders and sawmills, and the Federal Statistical Office tracks them in a producer price index for raw timber.

Classes follow the Swiss trading customs for raw timber (Schweizerische Handelsgebräuche für Rohholz), here for conifer stem wood. Logs are measured under bark; length is the log length, diameter the mid-diameter.

Length class Log length Diameter class Mid-diameter
L0 under 3 m 1a / 1b 10–14 / 15–19 cm
L1 3.0–6.0 m 2a / 2b 20–24 / 25–29 cm
L2 6.5–14.5 m 3a / 3b 30–34 / 35–39 cm
L3 15.0–22.0 m 4 / 5 / 6 40–44 / 45–49 / 50–59 cm

Quality is judged from defects such as branches, curvature, cracks, twist and pith, into four classes: A (no defects), B (good to medium), C (medium to below average) and D (low).

In ForestStudio, the model does not cut each tree into logs. Instead, it uses the mean size of the harvested trees as a proxy: the thicker the trees, the larger the share of valuable sawlogs. The timber revenue of the harvested wood, in CHF per m³, therefore follows a species-specific S-shaped curve of the QMD. Small trees yield mostly energy wood, worth about 50 CHF/m³. As trees get thicker, more of the stem can be sold as sawlogs and the timber revenue rises, until it levels off for large trees. How steep the rise is and where it levels off differs strongly between species: oak, maple and larch gain the most from size.

Ten S-shaped curves starting near 50 CHF per cubic metre for small trees. Oak, maple and larch rise to between about 240 and 280 CHF; spruce, beech, fir, pine, ash and other conifers level off between about 110 and 135 CHF; other broadleaves stay below 90 CHF.
Figure 1: Timber revenue per m³ of harvested wood as a function of the quadratic mean diameter of the harvested trees, by species group (Entlebuch parameters).

\[g(QMD) = P_{energy} + A \exp\left[-\exp\left(\frac{z}{A}\, e\,(s - QMD)\right)\right]\]

with \(P_{energy}\) = 50 CHF/m³. \(A\) is how much the timber revenue can rise above the energy-wood price, \(z\) how steeply it rises, and \(s\) the diameter around which it rises.

Species group Species A z s
Ash European ash 84.89 1.472 43.55
Beech European beech 65.00 2.169 20.47
Fir Silver fir 73.33 1.431 23.50
Larch European larch 192.94 4.536 35.05
Maple Field, Norway and sycamore maple 205.08 2.809 42.52
Oak Oaks 230.76 3.953 37.11
Other broadleaf Alders, birch, hornbeam, hazel, cherry, willows, whitebeam, rowan, lime, elm 39.22 1.559 23.82
Other conifer Yew 64.43 1.745 26.07
Pine Mountain and Scots pine 83.67 1.339 34.82
Spruce Norway spruce 60.70 1.913 17.66

The parameters were estimated for the Entlebuch case study region. For beech, \(A\) was fixed at 65 to better match the observed data.

Set your own prices

Per species · one value

Adapt the timber revenue curves to today’s market

The curves above are calibrated on reference prices from WSL’s SorSim tool. For each species, you can replace them with your own market price by entering a single value: the price you get for that species’ reference sawlog (quality B, length class L1, diameter class 4 for broadleaves and 2b for conifers).

ForestStudio then rescales the whole curve of that species to match: energy wood keeps its price, and the curve is stretched or compressed in between, so that the timber revenue differences between small and large trees keep the same proportions as in the original curve. Species you leave untouched keep their default curve.

Three S-shaped curves for spruce starting at 50 CHF per cubic metre. The default curve levels off near 110 CHF; the curve for a user price of 190 levels off higher, near 140 CHF, and the one for 110 lower, near 90 CHF.
Figure 2: Example for Norway spruce: the default timber revenue curve (reference sawlog price 150 CHF/m³) and the same curve rescaled to a user-defined reference price of 110 or 190 CHF/m³.

\[Revenue_{user}(QMD) = \frac{P_{ref,user} - P_{energy, user}}{P_{ref,model} - P_{energy,model}} \left[g(QMD) - P_{energy, model}\right] + P_{energy,user}\]

\(P_{ref,user}\) is the value you enter, \(P_{ref,model}\) the default reference price below, \(g(QMD)\) the default timber revenue curve and \(P_{energy}\) = 50 CHF/m³ the energy-wood price.

Species group Default reference sawlog price (CHF/m³) Reference assortment
Ash 130 L1, class 4, quality B
Beech 80 L1, class 4, quality B
Fir 126 L1, class 2b, quality B
Larch 340 L1, class 2b, quality B
Maple 250 L1, class 4, quality B
Oak 300 L1, class 4, quality B
Other broadleaf 110 L1, class 4, quality B
Other conifer 150 L1, class 2b, quality B
Pine 140 L1, class 2b, quality B
Spruce 150 L1, class 2b, quality B

Harvest costs

Some background. Harvest costs combine harvesting (felling the tree and preparing the logs) and extraction (bringing the logs to the forest road). The harvest cost per cubic metre falls when more volume is taken in one intervention and when the trees are larger (the Stückvolumengesetz), because fixed costs are spread over more wood. It also depends on the harvesting method, which slope, skid trails and soil sensitivity allow, and on the species mix.

In ForestStudio, timber revenues depend on the species and the wood, while harvest costs depend on productivity, which is set by the harvesting system and by the species mix. ForestStudio therefore uses one harvest cost curve per combination of harvesting method, which you choose per management unit, and conifer share of the harvest, grouped into the four classes of the Swiss National Forest Inventory (0–10%, 11–50%, 51–90% and 91–100%). Harvester and forwarder curves exist only for harvests with at least 51% conifers. If you choose a harvester in a broadleaf-dominated unit, the motor-manual curve for that conifer class is used instead.

All curves fall as trees get bigger: harvesting small trees is expensive per m³, and the harvest cost levels off for large ones. Harvester and forwarder become clearly cheaper than motor-manual felling once trees are of a reasonable size.

Six falling curves. Harvest costs start above 100 CHF per cubic metre for trees under 5 cm and fall to between about 20 and 35 CHF for large trees. Harvester and forwarder curves fall faster and end lower than motor-manual and skidder curves.
Figure 3: Harvest cost per m³ as a function of the quadratic mean diameter of the harvested trees, by harvesting method and conifer share (Swiss Plateau parameters).

\[HarvestCost(QMD) = intercept - A \exp\left[-\exp\left(\frac{z}{A}\, e\,(s - QMD)\right)\right]\]

The intercept is the case-specific minimum cost from WSL’s HeProMo model, in CHF/m³.

Harvesting method Conifer share Intercept A z s
Motor-manual + skidder 0–10% 280 247.99 7.215 −5.020
Motor-manual + skidder 11–50% 280 247.15 7.020 −5.035
Motor-manual + skidder 51–90% 280 253.58 5.268 −6.937
Motor-manual + skidder 91–100% 280 251.16 4.290 −10.887
Harvester + forwarder 51–90% 300 277.89 9.892 −2.389
Harvester + forwarder 91–100% 300 279.12 8.974 −4.903

The parameters apply to the Swiss Plateau region.

Your own harvest costs. Machine and personnel costs cannot be reliably separated, so harvest costs are adjusted as a whole, with a scaling factor per harvesting method. The factor follows the method you chose for the unit. A factor of 1.2, for example, makes harvester and forwarder operations 20% more expensive.

Net revenue

Each harvest gets the timber revenue curve of its species and the harvest cost curve of its harvesting method and conifer-share class. The net revenue is then:

Net revenue (CHF) = harvested volume × (timber revenue per m³ − harvest cost per m³) − pre-commercial thinning cost

The harvest part is calculated per m³. Pre-commercial thinning is calculated per hectare: it removes young trees that cannot be sold, so it brings no timber revenue and its cost does not depend on the volume removed. It applies to young stages only, with the cost of the stage the stand is in: thicket (QMD 0–10 cm) or pole wood (QMD 10–20 cm), see Before the first harvest.

For example, a harvest of 120 m³ of Norway spruce with a QMD of 35 cm, in a unit with more than 90% conifers harvested with harvester and forwarder, gives a timber revenue of about 98 CHF/m³ and a harvest cost of about 29 CHF/m³, leaving a net revenue of about 8’293 CHF. The same volume of beech in a pure beech stand, felled motor-manually, would bring a lower timber revenue per m³ and a higher harvest cost.

Before the first harvest

A young stand costs money long before it earns any. Establishing it means paying for plants, planting and, where deer are a problem, browsing protection, which can be a large share of the total. Tending and pre-commercial thinning then shape the species mix and select the future crop trees before any wood can be sold: they bring in little or nothing but are an investment in the future stand.

Planting

A fixed 400 CHF per planting operation (procurement, transport and means of transport), plus 0.80 CHF per plant for planting and tending, plus the price of the plant, which depends on the species (about 2 to 4 CHF). The only input needed is the number of plants.

Browsing protection

  • None: no cost.
  • Single plants: a biodegradable tree tube per plant, 23.05 CHF per plant including installation, maintenance and removal, plus 200 CHF of transport.
  • Fencing: deer-proof fencing in enclosures of at most 2 ha, 64.20 CHF per metre of fence plus 200 CHF of transport. The only input is the area to protect.

Pre-commercial thinning

Assuming 100 crop trees per hectare and no revenue:

  • Thicket (QMD below 10 cm), only in planted stands, 15 years after planting: five competitors removed per crop tree, 537.61 CHF/ha.
  • Pole wood 1 (QMD 10–20 cm), in all stands: three competitors removed per crop tree, 477.21 CHF/ha.

Commercial thinning starts at a QMD of 20 cm. These per-hectare costs are subtracted from the net revenue.

Planting

\[Cost = 400 + N_{plants} \cdot (P_{plant} + 0.8)\]

Single-plant protection

\[Cost = 200 + N_{plants} \cdot 23.05\]

Fencing. The protected area is split into square enclosures of at most 2 ha:

\[N_{enclosures} = \left\lceil \frac{Area\ [ha]}{2} \right\rceil \qquad FenceLength\ [m] = 4 \cdot N_{enclosures} \cdot \sqrt{\frac{Area\ [ha]}{N_{enclosures}} \cdot 10\,000}\]

\[Cost = 200 + FenceLength \cdot 64.20\]

Pre-commercial thinning

\[Cost = Area\ [ha] \cdot Cost_{stage}\ [CHF/ha]\]

with \(Cost_{stage}\) = 537.61 CHF/ha in the thicket stage (QMD 0–10 cm) and 477.21 CHF/ha in the pole-wood stage (QMD 10–20 cm).

The transport costs assume a 10-year maintenance period, four visits a year, a 5 km journey and 1 CHF/km on forest roads. Thinning costs assume a slope of 0–24%, mild winter conditions in an unfoliated stand, no weeds, existing skid trails, minimal cutting of removed trees and no pruning.

Price per plant (CHF), for orders of more than 500 plants from Forstbaumschule H.U. Ingold AG. Where no price was available, that of a similar species was used.

Species Price Species Price
Silver fir 2.35 Norway spruce 2.00
Maples 2.75 Mountain and Scots pine 2.15
Black and grey alder, birches, willows 2.05 Wild cherry 2.45
Hornbeam, hazel 2.75 Oaks 2.60
European beech 2.60 Whitebeam 4.20
European ash, wych elm 2.75 Rowan 2.75
European larch 2.15 English yew 3.90
Small-leaved lime 2.60 Douglas fir 2.15