This material is optional, and is provided for those interested in a detailed example of how to calculate the net present value of timber in carbon dioxide sequestration services.

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For this example, let's compare three different options:

OPTION 1: Faustmann forest, no carbon sequestration

This option was considered previously in the web unit.  The net present value of forests in timber alone is shown as the red line in Figure 7.

OPTION 2: Optimal Carbon Only Rotation

We assume that each board foot of timber sequesters an additional 2.31 Kg of carbon from the atmosphere. The price of each ton of carbon dioxide taken out of the atmosphere and stored in trees is $10 per 1000 Kg of CO₂. For our purposes, we assume that this price is paid as carbon dioxide is sequestered, and it is a one-time payment for each ton removed.

Over a timber rotation, the benefits of sequestering carbon are calculated as:

 

Thus, each additional board foot of timber is provides benefits of P_C. These must be discounted back to the beginning of the rotation. The integral accounts for the discounting and additional growth of timber.

Forests provide carbon sequestration while they are growing, but if they are harvested, carbon is lost. This loss of carbon must be counted in this equation. We assume that 60% of the harvest of timber is placed in long lived timber products, but that the remaining 40% is emitted to the atmosphere. Thus, the following term must be subtracted from the value of the timber rotation to account for the fact that timber harvests emit carbon into the atmosphere: 

 

Since we are still trying to maximize net present value of timber rotations over all time, we determine optimal rotations by using these two components in the Faustmann formula. The net present value of carbon sequestration is: 

 

 

This formula can be used to calculate the blue line in Figure 7.

OPTION 3: Optimal Timber and Carbon Rotation

We also can add this together with the regular Faustmann formula to determine what would be the optimal harvest age if we are trying to maximize timber yield and carbon sequestration at the same time. This leads to the following formula for the net present value:

 

 

The net present value of the optimal timber and carbon forest is shown in green in Figure 7.

The following table provides the values for our species above for our timber only model, our carbon only model, and our joint model.

From this table, you can see that the optimal age of harvesting trees for carbon sequestration alone is in excess of 150 years, for timber alone it is 30 years, and for both it is between 30 and 40 years. The carbon component increases the optimal age for harvesting trees.