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

2. 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.

3. 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?

4. 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

5. 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).

6. 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.

7. 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

8. 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:

9. 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

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

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

12. 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
100.00
975.61
1000 2
12/1/18
51.22
0.00
151.22

13. 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”

14. 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!

15. 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:

16. 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)

17. 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

18. 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.

19. 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.

20. 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

21. Economic Analysis Life-Cycle Cost For our calculation, let’s use:
d = 3%; iINF = 5%
Therefore

22. 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

23. Economic Analysis Life-Cycle Cost
Here is a webpage that shows the US inflation rate in the recent past:
And for discount rates:

24. 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

25. 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:

26. LCOE
Rearranging these equations

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

28. 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

29. 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

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