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# -*- coding: utf-8 -*- |
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"""Module to collect useful functions for economic calculation. |
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This file is part of project oemof (github.com/oemof/oemof). It's copyrighted |
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by the contributors recorded in the version control history of the file, |
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available from its original location oemof/oemof/tools/economics.py |
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SPDX-License-Identifier: MIT |
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""" |
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def annuity(capex, n, wacc, u=None, cost_decrease=0): |
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r"""Calculates the annuity of an initial investment 'capex', considering |
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the cost of capital 'wacc' during a project horizon 'n' |
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In case of a single initial investment, the employed formula reads: |
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.. math:: |
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\text{annuity} = \text{capex} \cdot |
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\frac{(\text{wacc} \cdot (1+\text{wacc})^n)} |
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{((1 + \text{wacc})^n - 1)} |
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In case of repeated investments (due to replacements) at fixed intervals |
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'u', the formula yields: |
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.. math:: |
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\text{annuity} = \text{capex} \cdot |
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\frac{(\text{wacc} \cdot (1+\text{wacc})^n)} |
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{((1 + \text{wacc})^n - 1)} \cdot \left( |
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\frac{1 - \left( \frac{(1-\text{cost\_decrease})} |
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{(1+\text{wacc})} \right)^n} |
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{1 - \left(\frac{(1-\text{cost\_decrease})}{(1+\text{wacc})} |
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\right)^u} \right) |
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Parameters |
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---------- |
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capex : float |
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Capital expenditure for first investment. Net Present Value (NPV) or |
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Net Present Cost (NPC) of investment |
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n : int |
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Horizon of the analysis, or number of years the annuity wants to be |
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obtained for (n>=1) |
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wacc : float |
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Weighted average cost of capital (0<wacc<1) |
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u : int |
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Lifetime of the investigated investment. Might be smaller than the |
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analysis horizon, 'n', meaning it will have to be replaced. |
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Takes value 'n' if not specified otherwise (u>=1) |
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cost_decrease : float |
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Annual rate of cost decrease (due to, e.g., price experience curve). |
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This only influences the result for investments corresponding to |
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replacements, whenever u<n. |
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Takes value 0, if not specified otherwise (0<cost_decrease<1) |
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Returns |
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------- |
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float |
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annuity |
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""" |
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if u is None: |
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u = n |
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if ( |
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(n < 1) |
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or (wacc < 0 or wacc > 1) |
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or (u < 1) |
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or (cost_decrease < 0 or cost_decrease > 1) |
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): |
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raise ValueError("Input arguments for 'annuity' out of bounds!") |
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return ( |
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capex |
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* (wacc * (1 + wacc) ** n) |
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/ ((1 + wacc) ** n - 1) |
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* ( |
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(1 - ((1 - cost_decrease) / (1 + wacc)) ** n) |
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/ (1 - ((1 - cost_decrease) / (1 + wacc)) ** u) |
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) |
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) |
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oemof /
oemof-tools
