Overview

We are now completing the last part of a three-lesson arc in economics and solar project finance. By now, you should observe significant connectivity between the past two lessons. We have discussed the economic drivers in energy systems, the basics of clients as utility maximizers, and then addressed multiple ways in which we as designers/engineers on a team can access the goal of maximizing solar utility for our clients in a given locale.

In Lesson 7, we will discuss ways to deliver useful metrics to our clients from a finance perspective. We will approach SECS through Life Cycle Cost Analysis (LCCA), dealing with concepts of financial paybacks on investment, solar savings, time value of money for long periods of evaluation, and levelized costs of energy.

By the end of this lesson, you should be able to:

• define the time value of money;
• describe the concept of solar fraction;
• list economic figures of merit in solar project valuation;
• process simple and complicated financial spreadsheets for solar hot water projects;
• apply solar savings evaluation to the life cycle costing of small solar projects.

What is due for Lesson 7?

This lesson will take us one week to complete. Please refer to the Course Calendar in Canvas for specific time frames and due dates. Directions for the assignments below can be found within this lesson.

Questions?

If you have any questions, please post them to the Lesson 7 General Questions thread in Yellowdig. I will check the forum regularly to respond. While you are in a discussion, feel free to post your own responses if you, too, are able to help out a classmate.

Fundamentals

We will be considering cash flows - namely, revenues - expenses or savings - costs -  in a process called Life Cycle Cost Analysis (LCCA). As you have seen in the reading, cash flows can be developed for systems operations, for investment decisions, and for financing. We will be representing cash flows in a simple, discrete pattern called end-of-period cash flow, where the periodicity is 1 year, and the compounding or discounting uses an annual rate.

• Given: SECSs tend to have life-spans that are quite long, often well beyond the 25 years of the PV module warranties.
• Also given: A lot can happen financially in 30 years! The USA has had three recessions since 1988 (list of U.S. recessions) [3], and fluctuations in the rate of inflation between 2-6%.
• And finally: SECSs are still "fresh" to many consumers and will be "foreign" systems to most clients in the beginning of a project development.
• Result: energy systems that have a long horizon of life, a long financial period of evaluation to assess, and yet existing within a dynamic financial setting: increased uncertainty and risk (without better information available).

Did you see that last bit?

Clients will perceive increased uncertainty and risk without better information available. That's your job! To provide better information and transparent project evaluation, which demonstrates an understanding of both the solar resource and the financials associated with a proposed SECS. Chapter 10 of the textbook discusses how conveying the financial metrics within a project proposal is one way to provide useful information in a transparent manner.

Time Value of Money

In Life Cycle Cost Analysis, one of the important criteria is the period of analysis, or period of evaluation. The "period" conveys a time horizon for your LCCA. If we recall our microeconomic drivers affecting the elasticity of demand, we know that the time horizon is an important factor. In our case, SECS will tend to have long life-spans.

As such, we are dealing with the concept of "value" at various points in time.

• Present Value (PV, not photovoltaics this time!): specifies worth for assets like SECSs, for money, or for periodic cash flows, where the worth is in today’s dollars, provided the rate of return is specified (as "d"). The value is processed from year "n" back to "year zero" (meaning the present).

$$PV=\frac{FV}{{(1+d)}^n}$$

• Future Value (FV): specifies the worth of things as a dollar value in the future. We use FV for Fuel Costs (FC) and Fuel Savings (FS) in LCCA. Costs are represented as "C" and Savings as "S." The rate of inflation is specified here as "i."

$$FV=C\cdot {(1+i)}^{n-1}$$

• Present Worth in year n (PW_n): This is the ratio of the future costs with respect to the discount rate over time.

$$P{W}_n=\frac{C\cdot {(1+i)}^{n-1}}{{(1+d)}^n}$$

You will notice that the same topics are discussed in detail in the assigned reading of the Manual for Economic Evaluation by Short et al. (1995).

Discount Rates

There are two ways to represent discount rates, and you will observe both in the SAM simulation software or similar financial analysis tools. Using these rates, we can produce a discounted cash flow model (DFM) to compare projects.

• Real Discount Rate ($d_r$) indicates the actual return received by lender or investor on the project (excluding the effect of inflation).
• Nominal Discount Rate ($d_n$) refers to the total of the Real Discount Rate plus projected rate of inflation.
• Note: As such, Real Discount Rate is usually a lower value than the Nominal Discount Rate due to inflation.
• Caveat: If the inflation rate is negative (deflation) then the Real Discount Rate would actually be higher than the Nominal Rate.

$$(1+d_n)=(1+d_r)\cdot (1+i)$$ $$d_n=[(1+d_r)\cdot (1+i)]-1$$ $$d_r=\left[\frac{(1+d_n)}{(1+i)}\right]-1$$

The Short et al. article shows the Nominal Discount Rate loosely approximated as$d_r\approx d_n-i$. But will the fuel inflation rates be the same as labor inflation rates? Or insurance inflation rates? We will have an example in the discussion where we pull apart different inflation rates and use real discount rates in the analysis of a solar hot water system.

Taxes and Depreciation

We have already seen that the DSIRE website [4] for the states and federal government of the USA is a useful resource for incentives. Part of those incentives are tied in to tax credits, and there is a significant portion of your reading devoted to the concept of depreciation.

• Depreciation: the use of income tax deductions to recover the costs of property used in trade/business or for the production of income. Depreciation does not include land.
• MACRS: Modified Accelerated Cost Recovery System [5]. You should observe that the Wikipedia site and you're reading from Short et al. will be quite similar. MACRS is used in the SAM simulation software.

Net Salvage Value

One of the things that occurs in an LCCA at the end of the Period of Analysis is the question of how to finish the summation. This is like the Monty Python movie, The Holy Grail [6], where the old fellow says: "I'm not dead!" At the end of your 15-25 year evaluation for LCCA, you will no doubt still have a fully functional SECS! They don't just break down and fall apart, and in fact they will likely last for decades beyond your evaluation period. So how do we assess the value of the system at the end of the period?

We assume that the system has a net salvage value (a resale value) that is a fraction of its initial value, translated into present dollars. In our discussion, we will assume a 20-year-old solar hot water system still has 30% of its initial value, framed in present dollars for year 20.

In this case, if the total system cost is $16,000, its 30% salvage value will be 4,800.

Applying the Present Value formula (see above), with the market discount rate of 8%, we can find:

Salvage value = $4,800 / (1 + 0.08)²⁰ = $1,030

This will be monetary value of the system at the end of its 20-year service life.

Solar Savings

When I think about a SECS and the potential solar utility for a client in a given locale, I am familiar with the variable costs (VC) of fuel in a home or a commercial building. I am also familiar that SECSs have a relatively high fixed cost (FC) of the system's initial investment. So, I need a metric that can show me the annualized and cumulative flow of cash as costs and savings (in today's dollars) over the period of analysis.

We see in our reading that earlier solar engineers had developed strategic ways to apply the concepts of Life Cycle Costing Analysis (LCCA) for SECSs. Because solar technologies like PV (photovoltaics) and SHW (solar hot water) tend to substitute for fuels that need to be purchased, the authors recognized a value in specifying SECS financial potential in terms of avoided fuel costs (another FC), otherwise termed fuel savings (FS). The opposite of a "cost" is a "savings" in marginal analysis, right? But saving fuel is only one of at least seven parameters affecting the flows of cash for a system. Annualized cash flows are the sum of costs and savings in a year.

• The Solar Savings (SS) are the sum of avoided fuel costs (fuel savings) and incremental costs of operation for the SECS that we calculate for a system, typically on an annual basis, then put in today's dollars, and finally summed for a cumulative solar savings. Notice that (in the best scenarios) there are three savings parameters (+) and four cost parameters (-) assessed. Can you describe what each of these parameters is, and how they each function?

SS = FS - incremental mortgage/loan payment

- incremental maintenance/insurance

- incremental parasitic energy costs

- incremental property taxes

+ tax credit incentives

+ production credit incentives

• The Life Cycle Savings (LCS) are the cumulative solar savings for the period of analysis, framed in today's dollars.

Loads, Costs, and Fractions

We know that a local SECS like a Solar Hot Water system will have a certain quantity of demand from a residential family.

• Annual Loads (L) Example: In the Midwest of the USA, a residential family will consume 1.5-2 MWh of energy to heat water per year. That's an energetic load.
• Annual Costs (C) Example: In the USA, an average retail electricity cost is \$0.08/kWh, or \$80/MWh.
• Annual Solar Fraction (F): The fraction of energy provided by a SECS relative to the total energy demanded for the periodic step size (here, annual). In the solar field, we call the supplemental energy required beyond the SECS: "auxiliary" energy (even if it is a primary energy source in society).

We often design a domestic solar hot water (DSHW) system to provide an annual fraction F = 0.4-0.7 (40-70% of the total annual demand), sized for the summer loads, because the heat would be wasted/dumped in the summer. That would mean the client would be buying a bigger system that does not have utility in the summer. Better to have a less sufficient system for hot water in the winter, than for the client to pay for something they cannot use part of the year.

In our reading, we made the distinction between the annual solar fraction (uppercase F) and the monthly solar fraction (lowercase f). We can use the solar fraction as a factor in project finance to estimate an ideal array size for our client in his/her locale. Consider that a large solar fraction will entail more modules or panels, and will increase the cost for the client in the system investment (according to the unit cost). It will also increase the time to payback the investment. Our clients will no doubt have finite cash on hand to put a down payment into a SECS, and to acquire a loan for the rest of the investment. They may also require a fast payback that will influence the sizing of the system.

• An annual solar fraction of zero (F=0) is where the client opts for no installation of a new SECS.
  • $F=0$ will have the highest energy costs (fuel costs; $FC$ ) of any alternative SECS
• An annual solar fraction of one $\left(F=1\right)$ is where the client opts for a SECS that covers all energy loads for the entire year.
  • $F=1$ will have the highest solar investment costs ($C_S$), with the lowest associated annual energy costs
• We are to work with the client to find a strong solution between those two trivial extremes (a maximum return on investment), specifically a return with net positive in cumulative solar savings (Life Cycle Savings: LCS).

$$L\cdot F\cdot C_{fuel}=$$annual fuel savings (considered before discounting or fuel inflation rates)

Domestic Solar Hot Water Financial Analysis

We have covered methods to account for the costs and savings for a generic SECS in the previous pages. In those readings, we introduced the time value of money. So, let's think about the "time value of money" using a spreadsheet. The questions below are to be leading topics that will dig into the coupled meanings of Life Cycle Savings, Solar Savings, Fuel Savings, time value of money, systems payback, and paying back a loan. Some of the questions may be easier than others, but there are not necessarily clear answers to all of them. Also some people in class may have more experience with this type of analysis than others, so it would be beneficial to work together as a group through this discussion.

An example spreadsheet for solar hot water systems in a residential home (Domestic Solar Hot Water, or DSHW) is published as a shared Google spreadsheet. The direct link to access the file is in the middle of this page. This spreadsheet is set up in many columns: each column is representing a separate sequence of years for discrete financial analysis. There are accompanying graphs to link with the data, presenting loan payments and annualized Solar Savings increasing each year. Because the spreadsheet is dynamic, it would be better if you download a copy of the file and try changing things like the discount rate, fuel cost, loan size, and systems size (solar fraction) and see what the response will be.

There are two example systems analyzed in the spreadsheet. The first system has a solar fraction F = 0.65, costing \$16k with a 20% Down Payment and the remainder paid through a back loan at 7% interest. The second system has a solar fraction F = 0.85, costing \$26k with a 20% Down Payment, and the remainder paid through a back loan. Both systems have a potential resale value of 30% of initial investment ($16k), framed in Present Value (a different kind of "PV"). This is a detailed spreadsheet presenting you with an example of discrete financial analysis where we consider the time value of money over 20-year span. Half the battle in developing a useful spreadsheet is figuring out where everything is. Later, we will also dig into the financial output in SAM simulations.

NOTE: You must be logged into Google in order to view this spreadsheet.

Link to Google spreadsheet [7]

Study the spreadsheet and then discuss the following questions in the Yellowdig community.

1. Why is there Time "Zero?" What years do the two systems "pay back?" Why is there an additional financial increase for Year 20 at the end?
2. Look at columns $B$ through $I$ and identify the role that each of the columns serves leading up to Solar Savings and the Cumulative Solar Savings (framed in present worth).
3. Where does one find the market discount rates to estimate present values (seen in Column $Q$ and $R$ of the first sheet), and why is it that we need to consider future values in present worth when we are accounting for the project finance of SECS? What would the special meaning of the rate be if we raised that value from 8% in Column $R$, to a value high enough to drive the LCS to \$0?
4. In the red colored "loan" columns, do you see the connection to the reading regarding the rate of the loan and the annual loan payments? Why is the interest rate listed as a "discount rate"?
5. Which system would seem to be a reasonable investment for a middle-class family of 4 (two incomes, <\$100k annual gross income) living in Michigan, USA? Why?

• A comment: Columns $N$ , $O$ , and $P$ are tied to the use of fuel to heat water (annual loads: $L$ ), the annual Solar Fraction for the installed system (annual solar fraction: $F$ ), and the annual cost of the fuel ($C_F$ as electricity in \$/MWh, or \$0.8/kWh). We are initially guessing a system size, and that 65% of the annual energy will be covered by this array. In mid-continental USA, each person consumes ~8 MWh of energy to heat water per year. Here, we are estimating for a residential family of four.

Deadline

There is no hard deadline for this discussion activity, but it would be good to have some initial relfections posted in the middle of the study week (Sunday), and comments and replies will be due by the end of the point-earning period. 

Figures of Merit

What are the figures of merit to which our clients will respond?

• Net Present Value (NPV): in our case, deals with annualized costs and revenues that account for discount rates.
• Total Life-Cycle Cost (TLCC): used to assess marginal costs and the timing of costs when comparing alternative projects. Provides no frame of reference for acceptable/unacceptable costs, and doesn't address returns and benefits.
• Levelized Cost of Energy (LCOE): used to compare alternative technologies that often have different operational periods, different scales of operation and investment, or both. The common example is comparing a renewable technology like wind or solar electricity to a generation unit that requires geofuels. LCOE is often used to rank alternatives for effective budgeting of expenditures. As different investment sizes are not considered in a unit cost, LCOE is not recommended when choosing among systems that are "mutually exclusive." The LCOE represents the costs of the system throughout its lifetime spread evenly over the energy produced by the system, It is computed as the TLCC (discounted to the base year) divided by the lifetime energy production.
• Internal Rate of Return (IRR): the discount rate at which the NPV for the period of analysis is zero.
• Discounted Payback Period (DPB): contrasted with a simple payback, the discounted payback helps to compare risk between project options.

Summary

Good progress, class! We have now completed our three-lesson arc through Lesson 5: economic analysis, Lesson 6: solar utility for the client and locale, and finally Lesson 7: financial life cycle cost analysis.

In Lesson 7, we read about and discussed ways to deliver metrics to our clients that would be useful for financial assessment and project comparison. We called the overall process Life Cycle Cost Analysis (LCCA), dealing with concepts of financial paybacks on investment, solar savings, time value of money for long periods of evaluation, and levelized costs of energy. We introduced solar-specific terms such as the annual Solar Fraction (F), the Solar Savings (SS), and the Life Cycle Savings (LCS).

We discovered that financial analysis can be as direct as using a spreadsheet and some basic assumptions to assess financial cash flows and energy flows, or it can be a detailed simulation using meteorological data. We used discrete annualized methods of analysis common to project management in industry.

Coming up in the next three lessons, we will add to that strategy, and you will keep developing your arguments by building from sources found on the web (or from clients).

Design is pattern with a purpose.

Whereas art and science provide mechanisms to ultimately open windows into apparent patterns about us, design and engineering are purposeful approaches to establish systems that fit the revealed pattern. [Brownson, SECS, Ch. 16]