# 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

* I - investment*

* E - produced or saved energy per year (kWh/year)*

* c - energy cost per kWh (kWh ^{-1})*

### 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

*I - investment *

* y - investment lifetime (years) *

* C - average annual running costs () *

* E - energy produced or saved per year (kWh/year)*

### 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.