# 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.

## Related Documents

### Net Present Worth (NPW) of a Cash Stream

The value of a stream of payments is called the Net Present Worth (NPW).