# Discounting

Figure 1: J. Wellington Wimpy,[1] a cartoon character (and a friend of Popeye the sailor) from the 1930s famously said "I would gladly pay you Tuesday for a hamburger today!"[2] This illustrates discounting because money a few days from now isn't as valuable as money now.

The process of discounting is used to determine the present discounted value of a payment or revenue flow made in the future. This is how much something in the future would be worth in the present.[3]

Using the time value of money to compare the present and future value, the rate of the discount can either be fixed for the whole period or can vary annually. It is difficult to predict how markets and interest rates will change in the future, using a constant discount rate can protect against large and unexpected changes in the market.[4]

Discounting allows entities to compare the value of projects or financial assets over a number of time periods. Discounting standardizes the conditions surrounding the projects so they can be evaluated fairly and properly.[5]

With regards to energy projects, the discount rate is one factor used to determine the levelized cost of energy. The future production from energy projects acts as the future value in the discount rate equation.

### Social Discounting

There is a social aspect to discounting as well, it centres around ethical issues and current perspectives on the interests of future society and the generations that will be affected by the choices made in the present.[6] Continuing to use carbon and other emission intensive energy sources has much less value in the future due to the large social cost it imposes through externalities on both local and global society.

## Discount Rate and LCOE of Energy Projects

The potential of renewable energy projects are commonly assessed using discount rates of 3, 7 and 10%. Generally the lower the discount rate the smaller the range of levelized cost in the future. The higher the discount rate, the larger the range of LCOE in the future. Generally, the lower the discount rate, the lower median LCOE in the future as well.[7]

This table compares nuclear, coal and natural gas as baseload sources for renewable sources:

Coal[8] Nuclear[9] Natural Gas[10]
Discount
Rate
Median
($/MWH) Range ($/MWH)
Median
($/MWH) Range ($/MWH)
Median
($/MWH) Range ($/MWH)
3% 75 65.31-94.81 55 25.59-64.38 98 60.84-133.21
7% 82 75.53-107.42 82 37.23-100.75 103 65.95-138.42
10% 95 81.57-119.25 115 48.83-135.72 108 70.62-143.07
Note: These numbers are generated including a carbon price of USD $30 per tonne.[11] Nuclear is the cheapest form (of the three) at a 3% rate. Due to the high capital costs of building nuclear plants, the cost rises significantly as the discount rate increases. The higher discount rate makes a nuclear plant significantly more expensive in the future. Seeing how quickly the LCOE can change as the discount rate increases shows why renewable projects with high capital costs such as nuclear plants can be less attractive to firms. Despite these concerns, nuclear has a life-cycle of 60 years whereas coal and natural gas have life-cycles of 40 and 30 years respectively. As the systems progress through their life, renewables such as nuclear experience a lower LCOE compared with coal and natural gas. Renewables also have a lower LCOE in the long-run due to low (or no) fuel costs and emission costs.[12] ## The Role of New and Improved Technologies Capital costs can be reduced through the improvement of existing technology and the development of new technology. When comparing the LCOE of solar PV technologies from 2010 to 2015 the LCOE improved dramatically: Solar[13] Coal.[8] 2010 2015 2010 2015 Discount Rate Median ($/MWH)
Range
($/MWH) Median ($/MWH)
Range
($/MWH) Median ($/MWH)
Range
($/MWH) Median ($/MWH)
Range
($/MWH) 10% 616.55 186.54-934.63 115 87.98-373.65 80.05 33.2-152.27 95 81.57-119.25 Note: The only common discount rate for 2010 and 2015 was 10%. The minimum of the range for 2010 coal (from China, non-OECD members did not have a carbon price instituted) did not include a carbon price, the 2015 minimum (also from China) had a carbon price of$28.88 USD/MWh. The 2010 average carbon price for OECD countries was \$22.87 USD/MWh.

The table shows how the effect of technology can greatly affect the LCOE of energy systems. Solar PV technology has greatly improved, leading to much lower costs across all discount rates. Coal on the other hand, has experienced very little technological improvement and has experienced a rise is the LCOE. To some degree this is due to the price placed on carbon and other emissions from coal and other fossil fuel plants. The lower capital costs from improved technologies means that firms will be more attracted to renewable energy systems as they have a lower LOCE at all discount rates.

## References

1. Image found: https://www.flickr.com/photos/abeckstrom/5504735515 (Accessed September 3rd, 2016).
2. Yale book of quotations by Fred Shapiro, pg 677 (accessed online on September 3rd, 2016): https://books.google.ca/books?id=w5-GR-qtgXsC&pg=PA677&redir_esc=y&hl=en#v=onepage&q&f=false
3. R. A. Brealey et al. Fundamentals of Corporate Finance. Toronto: McGraw-Hill Ryerson, 2012, pp. 85.
4. J. Adejuwon et al. Climate Change 2001: Impacts, Adaptation and Vulnerability: Third Assessment Report of the IPCC. Cambridge: Cambridge University Press, 2001, pp. 97-98.
5. 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.
6. 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.
7. International Energy Agency. Projected Costs of Generating Electricity: 2015 Edition. Paris: OECD, 2015, pp. 4.
8. Various forms of coal fuel compared, ultra-supercritical, hard coal, lignite, pulverized (PC 800/ PC1000) and supercritical pulverized
9. Various reactors compared, the majority being ALWR, one LWR and one Generation III reactor.
10. CCGT plants compared.
11. IEA. Projected Costs of Generating Electricity: 2015 Edition, pp. 4.
12. IEA. Projected Costs of Generating Electricity: 2015 Edition, pp. 122.
13. Comparison among Residential rooftop systems, commercial rooftop systems and large-scale commercial systems.
14. The National Renewable Energy Lab (NREL): LCOE Calculator, [[Online], Available: http://www.nrel.gov/analysis/tech_lcoe.html

## Authors and Editors

Lyndon G., Jordan Hanania, Jason Donev
Last updated: September 17, 2016
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