LUISS – ENERGY ECONOMICS 2024/2025
LECTURE 7:
Economic Assessment and LCOE
Levelized Cost Of Energy
Prof. Carlo Andrea Bollino
University G Marconi, University of Perugia, University Luiss
KAPSARC, Saudi Arabia
Content of the Lecture
NPV
LCOE
NPV LCOE Net present value and Levelized cost of energy
Q
PE Q
= Cap * v * 8760
= PE ( Cap * v * 8760 )
Cap = capacity in MW
v = capacity factor (percentage of full load operation)
PE = average expected price of energy
NPV LCOE Net present value and Levelized cost of energy
NPV= -Inv0 +∑t=1,T (PE,t –cvar,t) Qt / (1+i)t
Assume annual cash flow constant: (PE–cvar)
NPV= -Inv0 + Q (PE–cvar) ∑t=1,T 1 / (1+i)t
NPV LCOE Net present value and Levelized cost of energy
NPV= -Inv0 +∑t=1,T (PE,t –cvar,t) Qt / (1+i)t
Assume annual cash flow constant: (PE,–cvar)
NPV= -Inv0 + Q (PE,–cvar) ∑t=1,T 1 / (1+i)t
Define present value factor:
PVFi,T = ∑t=1,T 1 / (1+i)t
which can be rewritten as:
PVFi,T = 1/i - 1/ [i (1+i)T]
LCOE with constant cash flow
NPV = -Inv0 + Q (PE–cvar) ∑t=1,T 1 / (1+i)t
NPV = -Inv0 + Q (PE–cvar) PVFi,T
Set NPV= 0
We can solve this equation for different variables:
- Solve for i
defines the IRR – internal rate of return
- Solve for T
defines the break-even payback time T*
- Solve for PE
defines the LCOE
LCOE with constant cash flow
NPV = -Inv0 + Q (PE–cvar) PVFi,T
- Solve for i defines the IRR – internal rate of return
The return rate that defines the equality between future stream of profit and
initial investment.
Keynes compares it with the market interest rate (Rm) to define the macro
economic investment function
If IRR > Rm
 it is convenient to invest
If IRR < Rm
 it is not convenient to invest
Conclusion: if monetary policy reduces Rm entrepreneur increase investment
LCOE with constant cash flow
NPV = -Inv0 + Q (PE–cvar) PVFi,T
- Solve for T defines the break-even payback time T*
Define AN = (PE–cvar) Q
Inv0 = AN ∑t=1,T 1 / (1+i)t
Inv0 = AN {1/i - 1/ [i (1+i)t] } = AN/i -AN / [i (1+i)t]
Multiply by i/AN
Inv0 i/AN = 1 - 1/ (1+i)t
1/ (1+i)t = 1 - Inv0 i/AN
taking logs:
T* = -1 / ln (1+i) ln (1 - Inv0 i/(PE–cvar) Q
LCOE with constant cash flow
NPV = -Inv0 + Q (PE–cvar) PVFi,T
- Solve for PE defines the LCOE
PE =Inv0 /[ Q ∑t=1,T 1 / (1+i)t ] + cvar
PE =Inv0 / [ Q PVFi,T ] + cvar
The concept of LCOE
Measures lifetime costs divided by energy production
Calculates present value of the total cost of building and operating a
power plant over an assumed lifetime.
Allows the comparison of different technologies (e.g., wind, solar,
natural gas) of unequal life spans, project size, different capital cost,
risk, return, and capacities
The concept of LCOE
Cost of energy production is crucial to assess whether an energy technology can
reach commercialization.
LCOE is a long term cost concept which accounts for all the resources and
physical assets required to yield a stream of electricity output.
LCOE represents a "break-even" value of an investment in a particular energy
project
Define:
I=investment (net of scrap value); D=depreciation; C=operating costs; E=energy
production.
LCOE
=
Total Life Cycle Cost
______________
Total Lifetime Energy
Production
=
I -D+C
_________________
E
The concept of LCOE – case of electricity generation
LCOE – case of electricity generation
LCOE – case of electricity generation
LCOE – case of electricity generation
LCOE – case of electricity generation
The Intended Nationally Determined Contributions (INDC)
LCOE
17
eni corporate university