Net present value - Revision history

Jonare: Removed ||''q_SEV''|| > 0 from the explanation of SEV.

2025-05-15T08:08:05Z

Removed ||''q<sub>SEV</sub>''|| > 0 from the explanation of SEV.

Jonare at 12:49, 30 September 2024

2024-09-30T12:49:03Z

LarsSangstuvall at 06:53, 31 August 2022

2022-08-31T06:53:18Z

LarsSangstuvall at 20:37, 21 April 2022

2022-04-21T20:37:23Z

LarsSangstuvall at 07:12, 20 April 2022

2022-04-20T07:12:26Z

LarsSangstuvall at 13:32, 13 April 2022

2022-04-13T13:32:53Z

JeanetteEggers at 10:10, 4 August 2021

2021-08-04T10:10:57Z

Peder: /* Uneven-aged management (CCF) */

2021-07-26T14:24:46Z

Uneven-aged management (CCF)

Peder: /* Uneven-aged management (CCF) */

2021-07-26T14:21:50Z

Uneven-aged management (CCF)

Peder: /* Uneven-aged management (CCF) */

2021-07-26T14:16:47Z

Uneven-aged management (CCF)

@@ Line 26: / Line 26: @@
 The SEV is calculated as: <br>
-<math>SEV = \displaystyle \alpha_{SEV}\sum_{t=0}^{T} \delta_t R_t </math>
+<math>SEV = \displaystyle \alpha_{SEV}\sum_{t=0}^{T} \delta_t R_t ,</math>
-where <br>
+<br>
-where ''T'' = Rotation length for the last forest generation, <br>
+where ''T'' = Rotation length for the last forest generation and
-''&alpha;<sub>SEV</sub>'' = "discount repeat factor" derived from a [https://en.wikipedia.org/wiki/Geometric_series geometric series]. A geometric series is the sum of an infinite number of terms that have a constant ratio (q<sub>SEV</sub>) between successive terms. If ||''q<sub>SEV</sub>''|| < 0, then
+''&alpha;<sub>SEV</sub>'' = "discount repeat factor". ''&alpha;<sub>SEV</sub>'' is derived from a [https://en.wikipedia.org/wiki/Geometric_series geometric series]. A geometric series is the sum of an infinite number of terms that have a constant ratio (q<sub>SEV</sub>) between successive terms. ''&alpha;<sub>SEV</sub>'' is calculated as
-<math>\alpha_{SEV} = \displaystyle \frac{1}{1-q_{SEV}}</math>
+<math>\alpha_{SEV} = \displaystyle \frac{1}{1-q_{SEV}} ,</math>
-where <br>
+where
-<math>q_{SEV} = \displaystyle {(1+r)}^{-T}</math> <br>
+<br>
 <br>Note that if the discount rate r is 0, then ''q<sub>SEV</sub>'' will be 1 and the sum will be infinitely large.

@@ Line 1: / Line 1: @@
 <noinclude>
-{{Languages}}</noinclude>
+{{Languages|Net present value}}
 ===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.

@@ Line 19: / Line 19: @@
 <math>\delta_t = \displaystyle (1+r)^{-t}=</math>discount factor for year t, and <br>
 ''SEV'' = Soil expectation value as given below
 ====Soil expectation value====

@@ Line 11: / Line 11: @@
 The net present value for even-aged management is calculated as <br>
-<math>\NPV_{evenaged} = \displaystyle \sum_{t=0}^{S} \delta_t R_t + \delta_{S}\cdot SEV</math>
+<math>NPV_{evenaged} = \displaystyle \sum_{t=0}^{S} \delta_t R_t + \delta_{S}\cdot SEV</math>
 where <br>

@@ Line 9: / Line 9: @@
 ====Even-aged management====
-The net present value for even-aged management is calculated as
+The net present value for even-aged management is calculated as <br>
-NPV_{evenaged} = \displaystyle \sum_{t=0}^{S} \delta_t R_t + \delta_{S}\cdot SEV
+<math>\NPV_{evenaged} = \displaystyle \sum_{t=0}^{S} \delta_t R_t + \delta_{S}\cdot SEV</math>
 where <br>

@@ Line 4: / Line 4: @@
 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.
+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. However, users can choose to prolong the time period for which net present value is calculated using the 'additional periods' setting in the simulation window.
 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.

@@ Line 51: / Line 51: @@
 <br>where
 <br>R<sub>U</sub> = 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
-<math>q_{CCF} = \displaystyle {(1+r)}^{-n}</math>
+<br><math>q_{CCF} = \displaystyle {(1+r)}^{-n}</math>
 Note that the ratio <sub>CCF</sub> is equivalent to that for SEV, but with the rotation length T replaced by the cutting interval n.
 <br>

@@ Line 45: / Line 45: @@
 with the same notations as above, and <br>
 ''U'' = Last cutting period<br>
-''MFV'' = So called managed forest value, which similarly to SEV corresponds to an infinite [https://en.wikipedia.org/wiki/Geometric_series geometric series], with a constant yield every n:th year, where n is the (assumed) fixed cutting cycle.
+''MFV'' = So called managed forest value, and similarily to SEV corresponds to an infinite [https://en.wikipedia.org/wiki/Geometric_series 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 <br>
 <math>MFV = \displaystyle \frac{R_U}{1-q_{CCF}} </math>
 <br>where
-<br>R<sub>U</sub> = Net revenue in last period U simulated by Heureka (internally by the program or reported), and
+<br>R<sub>U</sub> = 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
 <math>q_{CCF} = \displaystyle {(1+r)}^{-n}</math>
-Note that the ratio <sub>CCF</sub> is equivalent to that for SEV, but with the rotation length T replace by the cutting interval n.
+Note that the ratio <sub>CCF</sub> is equivalent to that for SEV, but with the rotation length T replaced by the cutting interval n.
 <br>

Net present value - Revision history

Jonare: Removed ||''qSEV''|| > 0 from the explanation of SEV.

Jonare at 12:49, 30 September 2024

LarsSangstuvall at 06:53, 31 August 2022

LarsSangstuvall at 20:37, 21 April 2022

LarsSangstuvall at 07:12, 20 April 2022

LarsSangstuvall at 13:32, 13 April 2022

JeanetteEggers at 10:10, 4 August 2021

Peder: /* Uneven-aged management (CCF) */

Peder: /* Uneven-aged management (CCF) */

Peder: /* Uneven-aged management (CCF) */

Jonare: Removed ||''q_SEV''|| > 0 from the explanation of SEV.