Net present value

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Net present value

In PlanWise and StandWise, Heureka calcuates the net present value (NPV) for each treatment unit and management schedule generated. It is the sum of discounted revenues minus costs, for an approximately infinite time horizon, and with the real discount rate set by the user. For even-aged management, Heureka approximates an infinite time horizon by assuming that the third forest rotation management regime will be repeated in perpetuity. For uneven-aged management, the last cutting is assumed to be repeated in perpetuity with a cutting time interval equal to the time elapsed between the last two cuttings projected.

Note that RegWise does not calculate net present value in a satisfactory manner, since it only include values until the last period and ignores the value of the ending inventory. RegWise is thus not suitable for economic analysis and valuation purposes.

For each even-aged program generated in PlanWise (and the NPV-tool in StandWise), Heureka generates up to three unique rotations. The reason for not just repeating the second management regime is to allow for the possible change of growth conditions over time. The climate model, if activated in a simulation, affects site fertility so that a certain rotation will have a different growth potential than the previous one, and consequently the management regime should be adapted to that. The growth of plantations will also be affected by the planting year, since breeding effects is assumed to increase over time. For example, trees planted in twenty years will give higher yields that trees planted today.

Even-aged management

The net present value for even-aged management is calculated as

where
S = Final felling year for the rotation preceeding the last rotation simulated, and
Net revenue in year t, with t = 0 marking year 0 of the planning horizon, and
r = Real discount rate, and
discount factor for year t, and
SEV = Soil expectation value as given below

Soil expectation value

The soil expectation value (SEV) is by definition the net present value for an infinite time horizon when starting from bare land. In Heureka, the soil expecation value refers to the net present value of the last rotation simulated (assumed repeated in perpetuity). If you want to calculate the SEV with Heureka starting from today (year 0), you should use bare land as initial state.

The SEV is calculated as:

where
where T = Rotation length for the last forest generation,

α_SEV = "discount repeat factor" derived from a geometric series. A geometric series is the sum of an infinite number of terms that have a constant ratio (q_SEV) between successive terms. If ||q_SEV|| < 0, then

where


Note that if the discount rate r is 0, then q_SEV will be 1 and the sum will be infinitely large.

Uneven-aged management (CCF)

When calculating the net present value for an uneven-aged stand management program, some estimation of the terminal value at the end of the planning horizon must be included. One way is to assume that a steady state is reached at some point in the future. In analogy to even-aged management where a series of identical rotation regimes is assumed to be repeated in perpetuity, we can assume that a series of selection fellings is repeated with a certain cutting cycle after the end of the planning horizon. In the forest economic literature on stand-level management and valuation, one solution for this is called the equilibrium endpoint problem (Haight & Getz 1987, used by for example Wikström 2000, p. 454). A steady state here implies that the number of stems in each diameter class after harvest is the same in two subsequent periods, separated by a certain time interval. Another approach is to use a very long time horizon, such as 150 years, in which the discounted terminal value can be practically negligible of the discount rate is large enough. For example, with a 3 percent discount rate the discount factor for outcomes in 150 years is 1.1 percent. In Heureka a simplified approach is used combining the two approaches, with both a time horizon of at least 100 years (unless explicitly changed by the user), and assuming that the last harvest is repeated with a time interval equal to that passed between the last two harvests during the planning horizon. If there are less than two harvest periods during the planning horizon, Heureka searches up to 50 years beyond the last period. If there are still less than two harvest periods found, Heureka generates an unmanaged program instead. However, Heureka is not currently able to enforce any equilibrium constraints for the tree diameter distribution as described above. Instead, it is assumed that the minimum volume constraint (SVL10, “virkesförrådskurvan”) and the thinning algorithm, which has the same parameters in all periods, both should lead to a steady state after 100 years, at least from an economic perspective.

The net present value for uneven-aged management is calculated as follows. Note that the first summation is done up to the period before the last cutting period T, since the revenue in period T is already included in the so called Managed Forest Value (MFV). MFV is mathematically analogues to SEV but the value refers to an establied steady state forest, instead of bare land

with the same notations as above, and
U = Last cutting period
MFV = So called managed forest value, and similarily to SEV corresponds to an infinite geometric series. The difference to that SEV is calculated as a series of one-rotation net present values, while MFV is ca calculated as a series of identical harvests that takes place every n:th year.

The MFV is calculated as

where
R_U = Net revenue in last period U simulated by Heureka (internally by the program or reported). This is the revenue that is assumned to be repeated on perpetuity, and
Note that the ratio _CCF is equivalent to that for SEV, but with the rotation length T replaced by the cutting interval n.

Terminal value

Heurekas also calculates a result variable called Terminal Value, which has an associated Terminal Value Year. The Terminal Value Year is usually the same as the year after the last planning period. The terminal value represents the part of the net present value that remains after the last planning period. The terminal value is calculated by subtracting the sum of discounted net revenues (that occurs until the last planning period) from the net present value, and the prolonging that value to the last year.

For mer info on terminal value calculation, see Berakning_terminala_varden.pdf

References

• Haight, R.G., Getz, W.M. 1987. Fixed and equilibrium endpoint problems in uneven-aged management. Forest Science 33:908-931.
  
• Haight, R.G. 1987. Evaluating the efficiency of even-aged and uneven-aged stand management. Forest Science 33(1):116-134.
  
• Wiktröm, P. 2000. A solution method for uneven-aged management applied to Norway spuce. Forest Science 46(3):452-463