Appendix E – Methods and Assumptions
Used in Chapter 5
This appendix provides further detail on the
methods employed and assumptions made in the
analysis of Chapter 5.
Rearranging the formula gives an
explicit definition:
25
THE LEVELIZED COST OF ELECTRICITY
The levelized cost of electricity (LCOE) is
defined as the charge per kilowatt-hour (kWh)
that equates the discounted present value of
revenues to the discounted present value of costs,
including the initial capital investment and
annual operating costs as well as any future
replacement capital costs incurred over the life
of a facility. These costs include taxes paid. For
example, for a solar project running for 25 years
with installation over the year prior, let
t=0,1,2…25. Write the annual capital investment
as Kt , the annual operating and maintenance
expenditures as Ot , the annual taxes paid as Vt ,
all denominated in $/year, and the annual output
schedule as Qt , denominated in megawatts per
year (MW/year). Then the LCOE is defined
implicitly by this formula:
25
⌺
t=0
LCOE Qt
________
=
(1 + R)t
25
⌺
t=0
Kt + Ot + Vt
__________
,
(1 + R)t
where R is the cost of capital, which is discussed
in more detail below.i
Kt + Ot + Vt
__________
⌺
(1 + R)
t=0
t
LCOE = ________________ .
25
Qt
_______
⌺
t=0
(1 + R)t
The LCOE may be reported as either a real LCOE
or a nominal LCOE. In calculating a real LCOE,
the values of all of the cash flow inputs — Kt , Ot ,
and Vt — must be real, i.e., with any inflation
factor removed. Since tax calculations, such as
depreciation charges, are inherently nominal,
care must be taken to be sure that the tax cash
flows have been correctly adjusted to remove the
inflation factor properly. The cost of capital must
also be a real cost of capital. The U.S. Energy
Information Administration (EIA) reports real
LCOEs in its Annual Energy Outlook.3 In calculating a nominal LCOE, the values of all cash flow
inputs must be nominal — i.e., with inflation
included. The cost of capital must also be a
nominal cost of capital. The U.S. Department
of Energy’s National Renewable Energy Lab
(NREL) reports both real and nominal LCOEs
as an output of its System Advisor Model (SAM).1
In general, with positive inflation, a nominal
LCOE will be higher than a real LCOE.
i See, for example, NREL1 and Short, Packey, and Holt.2
Appendix E – Methods and Assumptions Used in Chapter 5
313
The traditional LCOE, whether real or nominal,
is fixed throughout the life of the project —
as indicated by the term “levelized.” However,
in calculating a nominal LCOE, all other costs
are understood to be increasing with inflation.
An alternative definition of the nominal LCOE
recognizes that the charge may be escalated at
the inflation rate, I, and reports the first year’s
charge. This is comparable to reporting the
first-year price of a power purchase agreement
that includes a clause increasing the annual
price for the rate of inflation, as NREL’s SAM
does. This LCOE is defined implicitly by
the formula:
25
t
LCOE1 (1 + I) Qt
25
Kt + Ot + Vt
______________ =
__________ .
⌺
⌺
(1 + R)
(1 + R)
t=0
t=0
t
t
Rearranging the formula gives an explicit
definition:
25
Kt + Ot + Vt
__________
(1 + R)t
t=0
________________
.
LCOE1 =
25
t
(1 + I) Qt
________
⌺
⌺
t=0
(1 + R)t
Although this calculation is executed in nominal dollars, it is comparable to a real LCOE
because the charge escalates with inflation from
the base value. This is the LCOE we report in
Chapter 5.
314
MIT STUDY ON THE FUTURE OF SOLAR ENERGY
COST OF CAPITAL
A key input in calculating the levelized cost
of electricity is the discount rate applied to cash
flows in different years. For our central case we
employ a weighted average cost of capital
(WACC) that is calculated using a 7.5% cost
of debt, a 10% cost of equity, and a 60% debt
ratio. We assume a marginal federal corporate
income tax rate of 35% and, for California, a
marginal state corporate tax rate of 8.84%. This
yields a combined state and federal corporate
tax rate of 40.75%, which gives us a WACC
of 6.67%:
D
E
WACC = ___ RD (1ⳮ␶C )Ⳮ___ RE =
V
V
60%⳯7.50⳯59.25%Ⳮ40%⳯10% = 6.67%.
For Massachusetts, we assume a corporate
income tax rate of 8% so that the WACC is
6.69%. These are all nominal discount rates, to
be applied to cash flows that reflect anticipated
inflation. We assume the corresponding inflation rate is 2.5%, which is the rate we apply
to the various cash flows in our calculation.
The WACC should be applied to the solar
project’s unlevered net cash flow after taxes,
i.e., not taking into account the project’s
interest tax shields. This is because the benefits
of the interest tax shield show up through the
use of an after-tax cost of debt in the formula.
Applying the WACC to cash flows that already
reflect interest tax shields double counts the
tax benefits of debt. All tax shields other than
interest tax shields — such as depreciation tax
shields — are included in the cash flows to
which the WACC is applied.ii
This cost of capital is appropriate for a power
generator operating in a competitive wholesale
market without any assured rate of return —
i.e., a “merchant model.” Many solar projects
are financed using a power purchase agreement
(PPA) sold to a utility, whether regulated or
operating in competitive wholesale markets.
The PPA shifts price risk from the power
generator to the power purchaser. This would
then mean that the project’s revenue is less
risky and should be discounted by a lower rate.
Of course, the price negotiated as part of a
PPA will reflect the cost of shifting this risk,
so that the net value of the stream of revenue
should remain roughly the same. In any case,
the PPA does not affect the cost of producing
the power — hence we do not reflect the lower
risk of PPAs in our calculation of LCOE.
We also use this cost of capital for the residential PV system, which would be appropriate for
the third-party ownership model in which the
tax and financial position of the corporate
owner is like that of the corporate owner of a
utility-scale PV system.
iiAn alternative would be to employ the cash flows after tax, including the interest tax shields along with all
others. In this case, it is appropriate to use a weighted average with the before-tax cost of debt, which gives us
a cost of capital of 8.50%:
D
E
RA = ___ RDⳭ___ RE = 60%⳯7.50Ⳮ40%⳯10% = 8.50% .
V
V
Appendix E – Methods and Assumptions Used in Chapter 5
315
REFERENCES
1
NREL System Advisor Model (SAM): Levelized Cost
of Energy (LCOE). National Renewable Energy
Laboratory. https://www.nrel.gov/analysis/sam/
help/html-php/index.html?mtf_lcoe.htm
2
Short, W., D. J. Packey, and T. Holt. Manual for the
Economic Evaluation of Energy Efficiency and
Renewable Energy Technologies. National Renewable
Energy Laboratory. NREL/TP-462-517. (March 1995).
http://www.nrel.gov/docs/legosti/old/5173.pdf
3
Levelized Cost of New Generation Resources in the
Annual Energy Outlook 2013. U.S. Energy
Information Administration. (January 2013).
http://www.eia.gov/forecasts/aeo/er/pdf/electricity_
generation.pdf
The hyperlinks in this document were active as of April 2015.
316
MIT STUDY ON THE FUTURE OF SOLAR ENERGY
Appendix F – Background Material
for Chapter 8
The simulations discussed in Chapter 8 of this
report, concerning the integration of solar
electricity generation with wholesale electricity
markets, focused on a particular year (2030) and
used a single set of assumptions for projected
electricity demand, fuel costs, and installed
generation mix (for a medium-term time frame).
This appendix briefly summarizes the data used.
ASSUMPTIONS FOR THE
ERCOT-LIKE SYSTEM
the profile to the year 2030, we assumed
a constant rate of growth in demand of 1%
per year.
• Wind and solar profiles likewise use 2012
data from the ERCOT website1 (Planning
and Operations Information). The profiles
were scaled in proportion to the installed
solar capacity being simulated. Installed wind
capacity in 2030 was assumed to total 15 GW.
• Assumptions concerning the already installed
generation mix for both the medium- and
long-term scenarios are shown in the figure
below, which uses data published by the U.S.
Energy Information Administration (EIA).2
• For hourly load in 2030, we assumed the
reference annual profile based on hourly
demand in 2011 and 2012. The profile was
downloaded from the Electric Reliability
Council of Texas (ERCOT) website.1 To scale
Figure F.1 Installed Capacity for the ERCOT-Like System2
Long-Term Analysis
Medium-Term Analysis
(Mix is optimally complemented)
(Fixed thermal mix)
Mix Composition (28.5 GW thermal)
Mix Composition (62.3 GW thermal)
Wind
18%
Coal
32%
Cogeneration
19%
CCGT
44%
Wind
11%
Cogeneration
31%
CCGT
8%
Nuclear
9%
Nuclear
6%
Coal
20%
Gas Turbine
2%
• We assume that cogeneration capacity remains unchanged at 17 GW.
• Key assumptions for thermal generators (e.g., investment cost, fuel cost, heat rate, etc.)
are summarized in Table F.1.
Sources: SunShot Vision Study (February 2012)3
“Cost and performance data for power generation technologies” by Black and Veatch4
ERCOT’s Long-Term Transmission Analysis 2010–2030 (for start-up costs)1
Appendix F – Background Material for Chapter 8
317
Table F.1 Assumptions for Thermal Generators in the ERCOT-Like System4
Energy
Fuel Cost
Variable
O&M
Total
Variable
Overnight
Capital Cost
Economic
Life
[$/MWh]
[$/MWh]
[$/MWh]
[k$/MW]
56
5
61
1,200
8
80
30
110
9
2
18
4
10
1
10
0
Heat Rate
Fuel Cost
[Mbtu/MWh]
[$/Mbtu]
CCGT
7
8
CGT
10
Technology
Coal
Nuclear
ASSUMPTIONS FOR THE
CALIFORNIA-LIKE SYSTEM
• For hourly load in 2030, we assumed the
reference annual profile based on hourly
demand in 2011. The profile was taken from
the California Independent System Operator
(ISO) Open Access Same-time Information
System (OASIS).5 To scale the profile to the
year 2030, we assumed a constant rate of
growth in demand of 1% per year.
• Wind and solar production profiles were
obtained from the daily California ISO
Renewables Watch.6
Rate of
Return
Annualized
Capital Cost
[years]
[%]
[k$/MW]
20
10,2
142,88
660
20
10,2
78,58
22
2,900
20
10,2
345,29
10
6,200
20
10,2
738,21
• For hydro units, we used historical production data profiles to estimate relevant input
parameters such as maximum output,
run-of-the-river capacity, and maximum
energy available in each period.6
• For thermal generators, we assumed the same
characteristics as in our simulations for the
ERCOT-like system (see Table F1).
• In the long-term scenario, the already
installed generation mix is assumed to
include 10 GW of wind, 8.5 GW of cogeneration, and 7.95 GW of thermal capacity
(Figure F2).
Figure F.2 Installed Capacity for the California-Like System (Long-Term Analysis)2
Combustion Turbines
4%
CCGT
9%
Wind
38%
Nuclear
17%
Cogeneration
32%
318
MIT STUDY ON THE FUTURE OF SOLAR ENERGY
REFERENCES
1
Electric Reliability Council of Texas (ERCOT).
www.ercot.com
2
Form EIA-860 Detailed Data: Year 2012. U.S. Energy
Information Administration. http://www.eia.gov/
electricity/data/eia860/
3
Margolis, R., C. Coggeshall, and J. Zuboy. SunShot
Vision Study. U.S. Department of Energy. NREL
Report No. BK-5200-47927; DOE/GO-1020123037. (Feb 2012). http://www1.eere.energy.gov/
solar/pdfs/47927.pdf
4
Cost and Performance Data for Power Generation
Technologies. Prepared by Black and Veatch for the
National Renewable Energy Laboratory (Feb 2012).
http://bv.com/docs/reports-studies/nrel-costreport.pdf
5
Open Access Same-time Information System
(OASIS). California ISO. http://oasis.caiso.com/
mrioasis
6
Renewables Watch. California ISO. http://www.
caiso.com/green/renewableswatch.html
The hyperlinks in this document were active as of April 2015.
Appendix F – Background Material for Chapter 8
319