Introduction to Economic AnalysisPart 2

February 12, 2014

Learning Outcomes

•An understanding of essential economic considerations including:

o Life Cycle Costingo Levelized Cost of Electricity (LCOE)

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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.

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Class Components

• Economic Analysiso Life-Cycle Costo Unit Electrical Cost

• Payback Analysis

• LCOE

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Resources

• Photovoltaic Systems Engineering, Messenger & Ventre (3rd 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

Economic Analysis

• Present Worth

oThe Present Worth Factor, FPW, is given by:

oAnd 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 iINF)

Economic Analysis

• Present Worth

oNote: If there is no inflation, or if the impact of inflation is not included, then the Present Worth Factor at the nth year becomes:

oAnd the annual PW factor is then:

oThis is sometimes called the discount factor

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.

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.

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

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%; iINF = 1.5%

• Therefore

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 01 Refrigerator 02

First Year PW First Year PW

Purchase price

$600 $600 $800 $800

Electricity cost

$126 $1342 $84 $895

LCC $1942 $1695

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

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:

LCOE• Rearranging these equations

LCOE factors

• Costso Initial investment or capitol

costo O&M and operating costso Financing costso Insurance costso Taxes (County, State and

Federal)o Return on Investmento Decommissioning

• Incentiveso Tax credits (State and

Federal)o Depreciation (MACRS)o Incentive revenue

• Energyo Estimated year one

productiono Annual degradationo System availability

LCOEExpanding the previous equation

where:o I = Initial capital costo D = Depreciationo T = Tax rateo O = Annual operating cost (O&M, loan payments, insurance, etc.)o R = Incentive revenueo S = Salvage valueo Q1 = Year one energy production o Degradation rate