# Payback

When evaluating the viability of a new project, a firm will determine what the payback period of the project is, this is determined by comparing the cost of the initial investment with the annual returns from the project. By comparing these figures, a firm can determine how long it will take for an investment to yield the initial amount used to produce it.[1] The shorter the payback period, the more desirable the project is as the return of investment allows for further expansion.

For example, if a firm builds a plant at a cost of $60m and has a annual revenue flow of$11m then:

= years

The payback period for an investment can apply to a firm with larger operations but it can also apply to individuals and the investments they make in their houses. For example, the while the cost for a ground source heat pump (GSHP) is initially more expensive, costing approximately 9-12% of construction cost of a house (compared to 5-6% with a conventional forced air system) it is estimated that the system has a payback period of 3-5 years.[2]

In the case of a GSHP there is no revenue generated so instead, the cost would be divided by the annual savings from not having to pay for residential heating. If a household saves \$1,300 per year with the GSHP then the payback period is:

= years

## Energy Payback Time

The Energy Payback Time or EPBT is the amount of time it takes for an energy system to generate the amount of energy equivalent to the amount that took to produce the system.[3]

For example, an 11 kW solar plant that produces 22.8MWh per year with a lifetime total of 570MWh, uses is 48.83 MWh to do so. To find the EPBT:[4]

= years

It will take 2.14 years for the solar power system to produce the same amount of energy that was used to assemble it.

## Energy Return on Investment

The energy return on investment (EROI) is the amount of energy that a system produces divided by the amount of energy it took to produce that output:[5]

EROI=

EROI is expressed as a ratio. For example, If a project has an EROI of 10:1 it produces 10 joules of energy for every 1 joule put into the production.

Different types of renewable energy systems yield different EROIs. For example, hydroelectric projects have an EROI of more than 100:1 whereas photovoltaic cells have an EROI of 6.8:1 and wind turbines have an EROI of 18:1.[6]

## References

1. Verbruggen, A., W. Moomaw, J. Nyboer, 2011: Annex I: Glossary, Acronyms, Chemical Symbols and Preﬁxes. In IPCC Special Report on Renewable Energy Sources and Climate Change Mitigation [O. Edenhofer, R. Pichs- Madruga, Y. Sokona, K. Seyboth, P. Matschoss, S. Kadner, T. Zwickel, P. Eickemeier, G. Hansen, S. Schlömer, C. von Stechow (eds)], Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.
2. L. Kowalczyk and J. Piotrowski. Energy Costs, International Developments and New Directions. New York: Nova Science Publishers Inc., 2009, pp. 151-152.
3. A. Sayigh. Comprehensive Renewable Energy. Amsterdam: Elsevier Ltd., 2012, pp. 38.
4. C. Marimuthu, V. KirUubakarana and R. Rajasekaran. "Energy Payback Period and Carbon Payback Period For Solar Photovoltaic Power Plant" International Journal of Chemical Sciences, 12, pp. 302.
5. "EROI of different fuels and the implications for society" by Hall, Lambert and Balogh. Energy Policy Volume 64, January 2014. Online: http://www.sciencedirect.com/science/article/pii/S0301421513003856 Accessed August 17th, 2017.
6. D. Murphy and C. Hall. "Year in review—EROI or energy return on (energy) invested." [Online], Available: http://onlinelibrary.wiley.com/doi/10.1111/j.1749-6632.2009.05282.x/full, Jan 29, 2010 [Sep 1, 2016]/

## Authors and Editors

Lyndon G., Jason Donev
Last updated: August 29, 2017
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