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Net Present Value and LCOE Equations

This page documents the main equations used in the geothermal economics calculations, as implemented in EconomicsCalculator.compute_economics().

Net Present Value (NPV)

The Net Present Value (NPV) is the sum of all discounted net revenues over the project lifetime:

\[ \mathrm{NPV} = \sum_{t=0}^{N} \mathrm{DR}(t) = \sum_{t=0}^{N} \frac{\mathrm{NR}(t)}{(1 + r)^{t}} \]

where:

  • \(\mathrm{DR}(t)\) is the discounted revenue for each year \(t\)
  • \(\mathrm{NR}(t)\) is the net revenue in year \(t\)
  • \(r\) is the discount rate
  • \(t\) is the year index

Net Revenue

Net revenue is calculated as:

\[ \mathrm{NR}(t) = \mathrm{GR}(t) - \mathrm{T}(t) \]

where:

  • the gross revenue is calculated as \(\mathrm{GR}(t) = \mathrm{I}(t) - \mathrm{C}(t)\)
  • the tax is calculated as \(\mathrm{T}(t) = \max(\mathrm{TGR}(t), 0) \cdot \mathrm{T_r}\)
  • \(\mathrm{T_r}\) is the tax rate
  • and the taxable gross revenue is calculated as \(\mathrm{TGR}(t) = \mathrm{I}(t) - \mathrm{C_{tax}}(t)\)

Income

The income is based on the produced energy and the heat price (with possible subsidy):

\[ \mathrm{I}(t) = \mathrm{E_{p,w}}(t) \cdot \mathrm{HP}(t) \]

where:

  • \(\mathrm{E_{p,w}}(t)\) is the total effective energy contained in produced water
  • \(\mathrm{HP}(t)\) is either the feed-in price or the regular price, depending on the subsidy period

Costs

Total costs

Total costs are the sum of electricity cost, OPEX, loan payments, and equity:

\[ \mathrm{C}(t) = \mathrm{C_{elec}}(t) + \mathrm{C_{opex}}(t) + \mathrm{IP}(t) + \mathrm{PP}(t) + \mathrm{Eq} \]

where:

  • Electricity costs, \(\mathrm{C_{elec}}(t)\), are defined below
  • Operational costs, \(\mathrm{C_{opex}}(t)\), are defined below

and interest \(\mathrm{IP}(t)\) and principal \(\mathrm{PP}(t)\) payments are calculated using standard annuity formulas (based on the size of the loan \(L\), the loan rate \(L_{rate}\), and number of loan years \(L_{year}\)).

and equity is defined as

\[ \mathrm{Eq} = \mathrm{C_{capex,tot}} \cdot \mathrm{Eq}_{\text{share}} \]

where \(\mathrm{C_{capex,tot}}\) is the total CAPEX costs and \(\mathrm{Eq}_{\text{share}}\) is the equity share (%) and the loan is defined as

\[ \mathrm{L} = \mathrm{C_{capex,tot}} - \mathrm{Eq} \]

Taxable costs include depreciation:

\[ \mathrm{C_{tax}}(t) = \mathrm{C_{elec}}(t) + \mathrm{C_{opex}}(t) + \mathrm{IP}(t) + \mathrm{D}(t) \]

Capital Expenditure (CAPEX)

The CAPEX is calculated in steps:

\[ \mathrm{C_{capex,o}} = \mathrm{C_{capex,b}} + \mathrm{C_{capex,v}} \cdot \mathrm{P_{i}}(0) \]

where:

  • \(\mathrm{C_{capex,b}}\) is the base capital expenditure for the project,
  • \(\mathrm{C_{capex,v}}\) is the variable capital expenditure per installed kW,
  • \(\mathrm{P_{i}}(0)\) is the installed power capacity at the start of the project.

The total CAPEX including well costs, contingency, and pump costs is:

\[ \mathrm{C_{capex,tot}} = \left( \mathrm{C_{capex,o}} + \mathrm{C_{wells}} \right) \cdot (1 + \mathrm{C_{capex,c}}) + N_{\text{wi}} \cdot \mathrm{C_{pump}} \]

where:

  • \(\mathrm{C_{wells}}\) is the total cost of all wells,
  • \(\mathrm{C_{capex,c}}\) is the contingency fraction,
  • \(N_{\text{wi}}\) is the number of injection wells,
  • \(\mathrm{C_{pump}}\) is the cost per pump.

The CAPEX is assigned to the first year in the cashflow.

Electricity Cost

\[ \mathrm{C_{elec}}(t) = (\mathrm{E_{c,inj}}(t) + \mathrm{E_{c,prd}}(t)) \cdot \mathrm{EP} \cdot (1 + \mathrm{i_r})^{t} \]

where:

  • \(\mathrm{E_{c,inj}}(t)\) is the energy required to operate the injection pump per well [GJ]
  • \(\mathrm{E_{c,prd}}(t)\) is the energy required to operate the production pump per well [GJ]
  • \(\mathrm{i_r}\) is the inflation rate

Depreciation

Depreciation is linear over the depreciation period:

\[ \mathrm{D}(t) = \begin{cases} \frac{\mathrm{C_{capex,tot}}}{\mathrm{D_{years}}} & \text{if } t \leq \mathrm{D_{years}} \\ 0 & \text{otherwise} \end{cases} \]

Fully Expanded NPV Equation

\[ \mathrm{NPV} = \sum_{t=0}^{N} \frac{\mathrm{I}(t) - \mathrm{T}(t) - \mathrm{C}(t)}{(1+r)^{t}} = \sum_{t=0}^{N} \frac{\mathrm{I}(t) - \mathrm{T}(t) - \big(\mathrm{C_{elec}}(t) + \mathrm{C_{opex}}(t) + \mathrm{IP}(t) + \mathrm{PP}(t) + \mathrm{Eq} \big)}{(1+r)^{t}} \]

Levelized Cost of Energy (LCOE)

The LCOE is the ratio of discounted costs to discounted energy output:

\[ \mathrm{LCOE} = 100 \cdot \frac{ \sum_{t=0}^{N} \frac{\mathrm{C_{elec}}(t) + \mathrm{C_{opex}}(t) + \mathrm{IP}(t) + \mathrm{PP}(t) - \mathrm{C_{tax}}(t) \cdot \mathrm{T_r} + \mathrm{Eq}}{(1 + r)^{t}}} { \sum_{t=0}^{N} \frac{(\mathrm{E_{p,w}}(t) ) \cdot (1 - \mathrm{T_r})}{(1 + r)^{t}}} \]

For further details, see the EconomicsCalculator API documentation.