S U M M E R 2 0 1 0 7
By Ben Rashford
Thinking about diversifying your home or farm energy portfolio?
In addition to the big three – coal, oil, and natural gas – Wyoming also has abun-
dant renewable energy resources, such as wind and solar power. When does invest-
ing in renewable energy (RE) make sense, and when will it break the bank? This is
not easy to answer, but there are
several financial calculations that
can help.
This article describes three
calculations: simple payback, net
present value, and levelized cost
of energy. Each provides a differ-
ent way of determining whether
RE makes economic sense.
Simple Payback
Simple payback, or payback
period, is the number of years
it takes for the energy savings
to offset the initial investment
– payback can also account for
operation and maintenance costs
(O&M). The common assump-
tion is the shorter the payback
period, the more economical the
investment.
Simple payback is attractive
because it is easy to calculate
and understand. In reality, simple
payback can be simply mislead-
ing. Payback ignores several
important investment character-
istics, including: 1) time value of
money (see “Financial and renew-
able energy terms” at right), 2)
cost and savings after payback,
3) increases in energy prices and
4) gains on alternative investment
options you might have pursued
How to determine if that
RENEWABLE ENERGY
project makes economic sense
Financial and renewable energy terms
Annual energy output (or production) – Total
energy generated by a renewable energy (RE)
system in one year (typically measured in kilowatt
hours).
Annual energy savings – The amount of money
you save with a RE system – what would have been
spent buying electricity minus operating costs.
Time value of money – Money today is worth
more than the same amount of money in the
future because of inflation, the lost opportunity to
earn interest, and risk.
Present value – Dollar amounts from different
years cannot be added together without account-
ing for the time value of money. The present val-
ue is an estimate of today’s dollar value of future
dollar amounts.
Discount rate – The interest rate a person uses to
discount money in the future to money in the pres-
ent period. For RE investments, use the interest
rate on a similarly risky investment (e.g., govern-
ment bonds [2-4 percent] for low risk investments),
or, if you borrow money to finance the project, use
the interest rate the bank is charging.
Present Value Annuity Factor (PVAF) – A number
used to calculate the present value of a series of
equally sized payments spread over future time
periods.
instead of the RE project. Without these characteristics,
simple payback generally underestimates the payback pe-
riod making RE investments appear to be better deals than
they really are.
Net Present Value
A more flexible – and meaningful – calculation for evalu-
ating RE projects is net present value (NPV). NPV provides
today’s dollar value of a potential investment by taking all
costs and savings for the lifetime of the project and con-
verting them to present value and accounting for the time
value of money. NPV can also accommodate energy price
increases over time and can be used to directly compare
alternative projects.
NPV includes more information than simple payback
and is harder to calculate. For example, use a computer
program (e.g., Excel) or online calculator to account for
energy price calculation. Alternatively, a simplified NPV can
be calculated by assuming no price escalation. In this case,
the future stream of energy savings is called an annuity – a
series of equal cash flows. Then, the present value annuity
factor (PVAF; see table) can be used to calculate the NPV of
any project using only a calculator (see example next page).
Present Value Annuity Discount Factors
Discount Rate
(sidebar 1)
Useful Life (years)
10 15 20 25 30
2% 8.98 12.85 16.35 19.52 22.40
3% 8.53 11.94 14.88 17.41 19.60
4% 8.11 11.12 13.59 15.62 17.29
5% 7.72 10.38 12.46 14.09 15.37
6% 7.36 9.71 11.47 12.78 13.76
7% 7.02 9.11 10.59 11.65 12.41
Ben Rashford is an assistant professor in the Department of Agricultural and Applied Economics in the College of Agriculture
and Natural Resources at the University of Wyoming. He can be contacted at (307) 766-6474 or brashfor@uwyo.edu.
How big should the NPV be? That depends on the
other alternatives available for producing energy or invest-
ing your money. As a general rule, a project makes econom-
ic sense if the NPV is positive and greater than the NPV of
other alternatives. When comparing two alternatives, such
as a wind turbine vs. solar panels, the one with the larger
NPV makes the most economic sense.
Levelized Cost of Energy
For RE projects that directly generate electricity, such
as wind turbines and solar panels, levelized cost of energy
(LCOE) is another useful calculation. LCOE is the implied
price ($/kilowatt hour) of energy generated by the RE
system. Put differently, it is the minimum price needed to
break-even.
LCOE can be directly compared to the price the local
utility charges. If the RE system generates electricity for
less than the utility price, then the project is economically
feasible. LCOE, however, does not account for energy price
escalation. So, even if a RE project cannot beat the current
electricity price, it may be cost competitive if and when util-
ity rates rise.
Take Out the Guesswork
Determining the economic feasibility of RE projects
may not be easy but running the numbers and considering
several calculations will help ensure homeowners make an
educated decision. Of course, economic feasibility is not
all that matters. You may still want to invest in RE even if it
doesn’t pencil out because you value energy independence,
you think energy prices will increase significantly, or you
think the environmental benefits are worth the extra costs.
More Information
Milt Geiger is the University of Wyoming Cooperative
Extension Service energy coordinator. He has a wealth of
information about the economics of renewable energy to
share. He can be reached at (307) 766-3002 or at mgei-
[email protected]. For more information, go to http://www.
uwyo.edu/renew-energy
8 B A R N Y A R D S & B A C K Y A R D S
Calculating simple payback, net present value, and levelized cost of energy for a small wind turbine
To perform any financial calculation, first collect basic information about costs and expected production of the
proposed project. All the items listed below are needed for a small wind turbine. Our example uses values con-
sistent with a typical household wind turbine (rated at 2.4 kW) on a site with 12 mph average wind speeds.
Installed cost – $12,000
Rebates/incentives
[1]
– $4,000
Annual energy output– 5,280 kWh/year
Annual operation and maintenance– $120/yr
Given the basic information, calculate the net annual energy savings for the wind turbine by multiplying the
expected annual energy output (AEO) by the current electricity price then subtracting annual O&M:
A) Calculating simple payback
Calculate simple payback by plugging the necessary values into the following formula:
B) Calculating net present value (NPV)
First, calculate the present value of net annual energy savings by selecting the present value annuity factor (PVAF)
that is consistent with your discount rate and the expected life of the project (see PVAF table page 8). For this exam-
ple, the PVAF for a 2 percent discount rate over 20 years is 16.35. The discounted net annual energy savings is:
Discounted Net Annual Savings ($) = Net Annual Energy Savings × PVAF = $460. 80 × 16.35 = $7,534.74
This means that the $460.80 net benefit the wind turbine produces every year for the next 20 years is worth
$7,534.74 today. Note that this is less than $9,216 because it accounts for the time value of money.
Next, subtract the total initial costs from the discounted net annual savings to get the NPV:
NPV ($) = $7,534.74 – $8,000 = –$465.26
C) Calculating levelized cost of energy
Calculate levelized cost of energy by plugging the necessary values into the following formula:
This example demonstrates the importance of using multiple calculations. The simple payback period is a
little long (17.4 years) but shorter than the useful life (20 years). This suggests the wind turbine will pay for itself
before it stops working. The NPV, however, is negative suggesting that, accounting for the time value of money,
you will lose money on this project. On the other hand, the LCOE implies that the turbine will generate electricity
over the next 20 years at a cost of 11.5 cents per kWh. This is more than the current utility rate of 11 cents, but,
if energy prices rise in the near future, this wind turbine will be cost competitive.
[1]
Information on federal and state rebates/incentives for renewable energy is available on the Web at www.dsireusa.org
Useful life – 20 years
Retail electricity price – $0.11/kWh
Discount rate – 2%
Installed Cost ($) – Rebates ($)
$12,000 – $4,000
Net Annual Energy Savings ($/year)
$460.80
= 17.4 years
Payback (years) =
Initial Cost ($) + [O&M ($/year) × PVAF]
8,000 + [120 × 16.35]
Annual Energy Output (kWh/year) × PVAF
5,280 × 16.35
= $0.115/kWh
LCOE ($/kWh) =
LCOE ($/kWh) =
Payback (years) =
Net Energy Savings ($/year) = [AEO (kWh/year) × Price ($/kWh)] – O&M ($/year)
= [5,280 × 0.11] – 120 = $460.80
S U M M E R 2 0 1 0 9
