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