1. Introduction to Economic Analysis Part 2 February 12, 2014

2. Learning Outcomes An understanding of essential economic considerations including: o Life Cycle Costing o Levelized Cost of Electricity (LCOE) 2

3. Value to participants The Levelized Cost of Electricity (LCOE) is extensively employed in the energy industry, as it is used to compare costs among energy sources, or to compare the cost of energy from variations in the same technology. It also has some limitations in its application. It is essential for PV designers to know how to calculate and to apply the LCOE in any PV project. 3

4. Class Components Economic Analysis o Life-Cycle Cost o Unit Electrical Cost Payback Analysis LCOE 4

5. Resources Photovoltaic Systems Engineering, Messenger & Ventre (3 rd Edition), Ch.8 Economic Analysis and Environmental Aspects of Photovoltaic Systems, R.A.Whisnant, S.A.Johnston, & J.H.Hutchby, in Handbook of Photovoltaic Science and Engineering, Luque et al., Ch 21 “Levelized Cost of Electricity,” T.Yates & B.Hibberd, in SolarPro, V5N3, April/May 2012 Notes from S.Trimble

6. Economic Analysis Present Worth o The Present Worth Factor, F PW, is given by: o And the Present Worth (PW) is the amount of money needed at the present time (invested at d) in order to purchase an object at a future time (with inflation rate of i INF )

7. Economic Analysis Present Worth o Note: If there is no inflation, or if the impact of inflation is not included, then the Present Worth Factor at the n th year becomes: o And the annual PW factor is then: o This is sometimes called the discount factor

8. Economic Analysis Present Worth o This analysis can be extended to consider the case of recurring costs (fuel, maintenance & operation, etc.). One can sum up the PW of each separate expense.

9. Economic Analysis Present Worth o This calculation assumes the recurring cost starts at the beginning of each year; if the cost occurs at the end of each year, the factor changes to: o Furthermore, the Present Worth calculation can be amended to include variations in annual discount rate and inflation rate. This is important as it is almost foolhardy to assume that either of these rates will remain constant from year to year.

10. Economic Analysis Life-Cycle Cost o As stated in Messenger and Ventre, “Once the PW is known for all cost categories related to the purchase, maintenance, and operation of an item, the life-cycle cost (LCC) is defined as the sum of the PWs of all the components.” o This simple example shows the power of LCC analysis: Refrigerator 01 costs $600 and uses 150kWh of electricity per month; refrigerator 02 costs $800 and uses 100kWh of electricity per month. Assume that neither refrigerator will require any maintenance or repair for 10 years. Also assume that electricity costs $0.07/kWh and will remain this cost for the same 10 year period. Choose a sensible discount rate and inflation rate, and perform a life-cycle cost analysis for a ten year period to determine which refrigerator is a more frugal purchase

11. Economic Analysis Life-Cycle Cost o Here is a webpage that shows the US inflation rate in the recent past: http://www.usinflationcalculator.com/inflation/current-inflation-rates/ o And for discount rates: http://www.newyorkfed.org/markets/statistics/dlyrates/fedrate.html o For our calculation, let’s use: d = 0.1%; i INF = 1.5% Therefore

12. Economic Analysis Life-Cycle Cost o For our calculation FY electricity cost = 12*(0.07)*(150 or 100) PW electricity cost = FY electricity cost * 10.65 Refrigerator 01Refrigerator 02 First YearPWFirst YearPW Purchase price $600 $800 Electricity cost $126$1342$84$895 LCC$1942$1695

13. Levelized Cost of Electricity LCOE is defined as an energy source’s total lifetime cost of operation divided by the total lifetime energy production: Its main function is to provide a way to compare the relative cost of energy produced by different energy- generating sources regardless of project scale or operating time frame Note: LCOE is a metric with units $/kWh

14. LCOE Rewriting the previous equation Both sides of the equation have the units of $ - the left side is the value of the energy generated and the right side is the total LCC – so both must be present worth calculations:

15. LCOE Rearranging these equations

16. LCOE factors Costs o Initial investment or capitol cost o O&M and operating costs o Financing costs o Insurance costs o Taxes (County, State and Federal) o Return on Investment o Decommissioning Incentives o Tax credits (State and Federal) o Depreciation (MACRS) o Incentive revenue Energy o Estimated year one production o Annual degradation o System availability

17. LCOE Expanding the previous equation where: o I = Initial capital cost o D = Depreciation o T = Tax rate o O = Annual operating cost (O&M, loan payments, insurance, etc.) o R = Incentive revenue o S = Salvage value o Q 1 = Year one energy production o   Degradation rate