Introduction to Economic Analysis Part 1 February 10, 2014

Learning Outcomes An understanding of essential economic considerations including: o Life Cycle Costing o Cash Flow Analysis o Payback Analysis 2

Value to participants 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

Class Components Economic Analysis o Time Value of Money o Present Worth Factors o Life-Cycle Cost o Unit Electrical Cost Borrowing Money Payback Analysis Externalities o Subsidies 4

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

Introduction PV systems produce electric power in a world in which other well-developed and widely-used electric power technologies exist. So how can PV systems compete with these other electricity sources? In many respects, the answer to this question depends upon the economic viability of the PV system

Introduction As Whisnant et al. point out, the choice to design and build a PV system will also depend upon many factors, such as financial risk, environmental, political, and humanitarian concerns!

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

Economic Analysis Issues to tackle: o 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). o 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.

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

Economic Analysis Elementary Example – Simple Interest o Borrow money (C o ) for a term (T) in years with simple annual interest (i s ) o The amount to be paid back will be: o Numerically, for 5% interest and 1.5 years:

Economic Analysis But realistically, interest is added to the remaining balance, and an amortization schedule is produced: o Borrow money (C o ) for a term of n years with annual interest (i) YearPayment on Principle Interest Payment Total PaymentBalance 1A1A1 iC o A 1 + iC o C o -A 1 2A2A2 i(C o -A 1 )A 2 + i(C o -A 1 )C o -A 1 -A 2 3A3A3 i(C o -A 1 -A 2 )A 3 + i(C o -A 1 -A 2 )C o -A 1 -A 2 -A 3 nAnAn i(C o -…-A n-1 )A n-1 + i(C o -…-A n-1 )C o -A 1 -…-A n

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

Economic Analysis Continuing the amortization schedule calculation: o Solve this previous equation for A 1 and calculate the annual payment from PMT = A 1 + iC o o Note: Most borrowed money is paid back on monthly basis, not annual basis. o CLASS EXERCISE – how does this formula change for monthly payment, and annual interest of i?

Economic Analysis Time Value of Money o 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. o Put money (N 0 ) in a savings account that pays an annual interest rate of d. (In Econ101 this is called the “discount rate”): o Albert Einstein is reputed to have said: “ The most powerful force in the universe is compound interest”

Economic Analysis Time Value of Money o Now consider the initial price of an item (C 0 ) in an economy subject to an annual inflation rate of i INF. Inflation reflects an annual devaluation of purchasing power (i.e., annual increase in item price) o 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 o Now consider the case when C 0 equals N 0. Then the following factor emerges: o The quantity F PV is the Present Worth Factor, and of course, can be used to calculate this quantity: o 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 )

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. 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:

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: o And for discount rates: o For our calculation, let’s use: d = 0.1%; i INF = 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 * Refrigerator 01Refrigerator 02 First YearPWFirst YearPW Purchase price $600 $800 Electricity cost $126$1342$84$895 LCC$1942$1695