Photovoltaic Systems Engineering SEC598F18 Photovoltaic Systems Engineering Session 20 PV Economic Analysis November 14, 2018

Value to class members A Solar Energy project is much more than an engineering design exercise. This engineering enterprise (like most others) is carried out in the business world, where economic issues and policy issues play an essential role. An understanding of the rudiments of economic analysis is critical.

Economic Analysis The following considerations form the basis of an economic analysis appropriate to PV commercialization: What is the initial cost of the system? What are the maintenance costs? What are the component replacement costs? What incentives are available? What will be the cost of electricity? Should the money to fund the project be borrowed?

Session Components Borrowing Money Economic Analysis Levelized Costs Simple interest Amortization Economic Analysis Time Value of Money Life Cycle Costs Present Worth Factors Levelized Costs LCOE LACE LCOS

Economic Analysis Issues to grasp: Time Value of Money This is a central concept in finance theory – it is the principle that a certain currency amount of money today has a different buying power (value) than the same currency amount of money in the future. Life Cycle Costing Apart from the initial construction cost, LCC analysis takes into account all the user costs and agency costs related to future activities, including future periodic maintenance and rehabilitation. All the costs are usually discounted and totaled to a present day value known as net present value (NPV).

Economic Analysis Additional issues to grasp: 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. Levelized Cost of Storage (LCOS) is a recently proposed adjunct to the LCOE to consider the costs and impacts of battery and other storage options in PV systems.

All this would be easy to evaluate if: Economic Analysis All this would be easy to evaluate if: Costs were constant Inflation did not exist Loans had no interest All of the above combine in a fascinating fashion – to be shown below

Borrowing money – Simple Interest Economic Analysis Borrowing money – Simple Interest Borrow money (Co) for a term (T) in years with simple annual interest (is) The amount to be paid back will be: Simple example, for 5% interest and 2 years:

Economic Analysis But a different approach is to add the interest to the remaining balance This produces an amortization schedule: Borrow money (Co) for a term of n years with annual interest (i) Year Payment on Principle Interest Payment Total Payment Balance 1 A1 iCo A1+ iCo Co-A1 2 A2 i(Co-A1) A2+ i(Co-A1) Co-A1-A2 3 A3 i(Co-A1-A2) A3+ i(Co-A1-A2) Co-A1-A2-A3 n An i(Co-…-An-1) An+ i(Co-…-An-1) Co-A1-…-An

Economic Analysis Continuing the amortization schedule calculation: Make all of the payments equal: The amount borrowed equals the sum of the payments:

Economic Analysis Continuing the amortization schedule calculation: The first payment toward the principle is: The annual payment would then be:

Economic Analysis Comparison Borrow $2000 for a term of 2 years with annual interest (5%); Calculate the payback schedule for simple interest, And with amortization process   Payment Beginning Ending Cumulative No. Date Balance Interest Principal 1 12/1/17 2,000.00 100.00 1,000.00 2 12/1/18 0.00 200.00   Payment Beginning Ending Cumulative No. Date Balance Interest Principal 1 12/1/17 2000.00 100.00 975.61 1024.39 1000 2 12/1/18 51.22 0.00 151.22

Economic Analysis Time Value of Money The value of money at a future point of time would take account of interest earned or inflation accrued over a given period of time. This notion exists both because there is an opportunity to earn interest on the money and because inflation will drive prices up, thus changing the "value" of the money. Put money (N0) in a savings account that pays an annual interest rate of d. In Economics 101 this is called the “discount rate”: Albert Einstein is reputed to have said: “The most powerful force in the universe is compound interest”

Economic Analysis Time Value of Money Now consider the initial price of an item (C0) in an economy subject to an annual inflation rate of iINF. Inflation reflects an annual devaluation of purchasing power (i.e., annual increase in item price) Interesting economic decision presents itself: if the cost of an item increases at a rate that exceeds the rate of saved money, maybe the item should purchased right away. But if the item cost decreases with time (deflation), should one delay the purchase? Maybe not – the use of the item is postponed until purchase!

Economic Analysis Present Worth Now consider the case when C0 equals N0. Then the following factor emerges: The quantity FPV is the Present Worth Factor, and of course, can be used to calculate this quantity:

Economic Analysis Present Worth The Present Worth Factor, FPW, is given by: 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 iINF)

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

Economic Analysis Present Worth 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 The previous 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: 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 As stated in Messenger and Abtahi, “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.” 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 For our calculation, let’s use: d = 3%; iINF = 5% Therefore

Economic Analysis Life-Cycle Cost For our calculation Refrigerator 01 FY electricity cost = 12*(0.07)*(150 or 100) PW electricity cost = FY electricity cost * 10.92 Refrigerator 01 Refrigerator 02 First Year PW Purchase price $600 $800 Electricity cost $126 $1376 $84 $917 LCC $1976 $1717

Economic Analysis Life-Cycle Cost Here is a webpage that shows the US inflation rate in the recent past: http://www.usinflationcalculator.com/inflation/current-inflation-rates/ And for discount rates: http://www.bankrate.com/rates/interest-rates/federal-discount-rate.aspx

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

One LCOE Resource “Levelized Cost of Electricity,” T.Yates & B.Hibberd, in SolarPro, V5N3, April/May 2012

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

LCOE Expanding the previous equation where: I = Initial capital cost D = Depreciation T = Tax rate O = Annual operating cost (O&M, loan payments, insurance, etc.) R = Incentive revenue S = Salvage value Q1 = Year one energy production d = Degradation rate

LCOE Effect of location Yates & Hibbard also analyze other factors, inside one technology: Effect of location