# Net present value

#### 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.

The net present value 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 is the discount repeat factor for an eternal series and is calculated as

#### 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.