Investments in Renewable Energy
Calculate investments in renewable energy.
Renewable energy  like the sun or wind  are available for free, but the equipment required to use the energy is not.
The economy in a renewable energy project can be calculated with alternative methods  the most common are
 payback time
 simple annual method
 discounted cash flow
Payback Time
Payback time  the time it takes to save or earn an amount equal to the investment  can be calculated as
t = I / A
= I / (E c) (1)
where
t = payback time (years)
I = investment
A = annual net income  or savings  from the investment
E = energy produced or saved per year (kWh/year)
c = cost or savings per energy unit (1/kWh)
Example  An Investment in a Windmill Generator
An amount of 100000 is invested in a windmill generator. The windmill is assumed to produce 8000 kWh/year . The cost to buy this energy from the local grid is 1 per kWh .
The savings on produced energy can be calculated as
A = (8000 kWh/year) (1 1/kWh)
= 8000
The payback time can be calculated to
t = 100000 / 8000
= 12.5 year
Renewable Energy  Payback Time Calculator
Simple Annual Method
The economy alternatively be evaluated by calculating the cost of the energy produced or saved. The cost of energy can be calculated as
c = (I / y + C) / E (2)
where
c = cost or savings per energy unit (1/kWh)
I = investment
y = investment lifetime (years)
C = average annual running costs (1/year)
E = energy produced or saved per year (kWh/year)
Example  An Investment in Solar Panels
An amount of 50000 is invested in a solar panel system with estimated annual energy production of 4000 kWh/year. The lifespan for the system is estimated to 25 year . The average annual cost to operate the system is assumed to be 1200 per year .
The cost of the produced energy can be calculated as
c = ((50000) / (25 years) + (1200 1/year)) / (4000 kWh/year)
= 0.8 1/kWh
Renewable Energy  Simple Annual Method Calculator
Discounted Cash Flow
Since money earned or spend in the future is not worth the same as money earned or spend today  it is common to discount the future cash flow back to a present value. The present value of the cash flows in a renewable project can be calculated as
P = F_{0} / (1 + i) ^{ 0 } + F_{1} / (1 + i) ^{ 1 } + F_{2}/ (1 + i)^{2}+ .... + F _{ n } / (1 + i) ^{ n } (3)
where
P = present value
F = cash flow
i = real interest rate
A renewable energy project typically start with a huge investment in the beginning continuing with smaller income and running costs. The cash flow for a typical year can be expressed as
F _{ n } = E _{ n } c _{ n }  C _{ n } (3a)
where
F _{ n } = cash flow per year (1/year)
E _{ n } = energy produced or saved per year (kWh/year)
c _{ n } = costs or savings per energy unit (1/kWh)
C _{ n } = running costs (1/year)
The real interest can be calculated as
i _{ n } = (1 + i _{ m n } )/ (1 + i _{ i n } )  1 (3b)
where
i _{ n } = nominal interest rate
i _{ m n } = real monetary interest rate
i _{ i n } = rate of inflation
Example  Investment in Renewable Energy and Discounted Cash Flow
An investment of 100000 saves 15000 kWh/year in energy. The energy cost is 1 per kWh , running costs to operate the system is 1000 , inflation rate is 0.02 (2%) and the monetary interest rate is 0.05 (5%) .
A discounted present value for the project over 10 years can be calculated to 23305 as indicated in the Google spreadsheet below.
You can download a copy of the spreadsheet as an excel file to your computer or to your Google Drive. You are free to modify and use the copy as you want.
Related Topics

Economics
Engineering economics  cash flow diagrams, present value, discount rates, internal rates of return  IRR, income taxes, inflation.
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