Net present value

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Net present value

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.

For each alternative generated in even-aged management, Heureka generates up to three unique rotations. The reason for not just repeating the second management regime is to allow for the possible chang in 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 at which time planting is done, 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

$NPV_{evenaged} = \displaystyle \sum_{t=0}^{S} \delta_t R_t + \delta_{S}\cdot SEV$
where
S = Final felling year for the rotation preceeding the last rotation simulated, and
$R_t =$ Net revenue in year t, with t = 0 marking year 0 of the planning horizon, and
r = Real discount rate, and
$\delta_t = \displaystyle (1+r)^{-t}=$ 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:

$SEV = \displaystyle \alpha\sum_{t=0}^{T} \delta_t R_t$ where
where T = Rotation length for the last forest generation,

α is the discount repeat factor for an eternal series and is calculated as

$\alpha = \displaystyle \frac{1}{1-({1+r})^{-T}}$

Uneven-aged management

The net present value for continuous cover forestry (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

$NPV_{CCF} = \displaystyle \sum_{t=0}^{T-1} \delta_t R_t + \delta_{T}\cdot MFV$
where
T = Last cutting period
$R_t =$ Net revenue in year t, with t = 0 marking year 0 of the planning horizon, and
r = Real discount rate, and
$\delta_t = \displaystyle (1+r)^{-t}=$ discount factor for year t, and
MFV = So called managed forest value, which is simply a geometric series, with a constant yield every n_th year, where n is the (assumed) fixed cutting cycle after

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

Net present value

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