## Building Blocks of Evaluation

Beyond the formula for the basic evaluation methods and risk assessment techniques, the practitioner needs to know some of the "nuts-and-bolts" of carrying out an economic analysis. He or she needs to know how to structure the evaluation process; how to choose a method of evaluation; how to estimate dollar costs and benefits; how to perform discounting operations; how to select an analysis period; how to choose a discount rate; how to adjust for inflation; how to take into account taxes and financing; how to treat residual values; and how to reflect assumptions and constraints, among other things. This section provides brief guidelines for these topics.

3.5.1 Structuring the Evaluation Process and Selecting a Method of Evaluation

A good starting point for the evaluation process is to define the problem and the objective. Identify any constraints to the solution and possible alternatives. Consider if the best solution is obvious, or if economic analysis and risk assessment are needed to help make the decision. Select an appropriate method of evaluation and a risk assessment technique. Compile the necessary data and determine what assumptions are to be made. Apply the appropriate formula(s) to compute a measure of economic performance under risk. Compare alternatives and make the decision, taking into account any incommensurable effects that are not included in the dollar benefits and costs. Take into account the risk attitude of the decision maker, if it is relevant.

Although the six evaluation methods given earlier are similar, they are also sufficiently different in that they are not always equally suitable for evaluating all types of energy investment decisions. For some types of decisions, the choice of method is more critical than for others. Figure 3.8 categorizes different investment types and the most suitable evaluation methods for each. If only a single investment is being considered, the "accept-reject" decision can often be made by any one of several techniques, provided the correct criterion is used.

The accept/reject criteria are as follows:

• LCC technique: LCC must be lower as a result of the energy efficiency or renewable energy investment than without it.

• NPV (NB) technique: NPV must be positive as a result of the investment.

FIGURE 3.8 Investment decisions and evaluation methods.

• B/C (SIR) technique: B/C (SIR) must be greater than one.

• IRR technique: the IRR must be greater than the investor's minimum acceptable rate of return.

• DPB technique: the number of years to achieve DPB must be less than the project life or the investor's time horizon, and there are no cash flows after payback is achieved that would reverse payback.

If multiple investment opportunities are available, but only one investment can be made (i.e., they are mutually exclusive), any of the methods (except DPB) will usually work, provided they are used correctly. However, the NPV method is usually recommended for this purpose, because it is less likely to be misapplied. The NPV of each investment is calculated and the investment with the highest present value is the most economic. This is true even if the investments require significantly different initial investments, have significantly different times at which the returns occur, or have different useful lifetimes. Examples of mutually exclusive investments include different system sizes (e.g., three different photovoltaic array sizes are being considered for a single rooftop), different system configurations (e.g., different turbines are being considered for the same wind farm), and so forth.

If the investments are not mutually exclusive, then (as shown in Figure 3.8), one must consider whether there is an overall budget limitation that would restrict the number of economic investments that might be undertaken. If there is no budget (i.e., no limitation on the investment funds available), than there is really no comparison to be performed and the investor simply makes an accept-reject decision for each investment individually as described above.

If funds are not available to undertake all of the investments (i.e., there is a budget), then the easiest approach is to rank the alternatives, with the best having the highest BCR or rate of return. (The investment with the highest NPV will not necessarily be the one with the highest rank, because present value does not show return per unit investment). Once ranked, those investments at the top of the priority list are selected until the budget is exhausted.

In the case where a fast turnaround on investment funds is required, DPB is recommended. The other methods, although more comprehensive and accurate for measuring an investment's lifetime profitability, do not indicate the time required for recouping the investment funds.

### 3.5.2 Discounting

Some or all investment costs in energy efficiency or renewable energy systems are incurred near the beginning of the project and are treated as "first costs." The benefits, on the other hand, typically accrue over the life span of the project in the form of yearly energy saved or produced. To compare benefits and costs that accrue at different points in time, it is necessary to put all cash flows on a time-equivalent basis. The method for converting cash flows to a time-equivalent basis is often called discounting.

The value of money is time-dependent for two reasons: First, inflation or deflation can change the buying power of the dollar. Second, money can be invested over time to yield a return over and above inflation. For these two reasons, a given dollar amount today will be worth more than that same dollar amount a year later. For example, suppose a person were able to earn a maximum of 10% interest per annum risk-free. He or she would require \$1.10 a year from now to be willing to forego having \$1 today. If the person were indifferent between \$1 today and \$1.10 a year from now, then the 10% rate of interest would indicate that person's time preference for money. The higher the time preference, the higher the rate of interest required to make future cash flows equal to a given value today. The rate of interest for which an investor feels adequately compensated for trading money now for money in the future is the appropriate rate to use for converting present sums to future equivalent sums and future sums to present equivalent sums (i.e., the rate for discounting cash flows for that particular investor). This rate is often called the discount rate.

To evaluate correctly the economic efficiency of an energy efficiency or renewable energy investment, it is necessary to convert the various expenditures and savings that accrue over time to a lump-sum, time-equivalent value in some base year (usually the present), or to annual values. The remainder of this section illustrates how to discount various types of cash flows.

Discounting is illustrated by Figure 3.9 in a problem of installing, maintaining, and operating a heat pump, as compared to an alternative heating/cooling system. The LCC calculations are shown for two reference times. The first is the present, and it is therefore called a present value. The second is based on a yearly time scale and is called an annual value. These two reference points are the most common in economic-evaluations of investments. When the evaluation methods are derived properly, each time basis will give the same relative ranking of investment priorities.

The assumptions for the heat pump problem—which are given only for the sake of illustration and not to suggest actual prices—are as follows:

1. The residential heat pump (not including the ducting) costs \$1,500 to purchase and install.

2. The heat pump has a useful life of 15 years.

3. The system has annual maintenance costs of \$50 every year during its useful life, fixed by contractual agreement.

4. A compressor replacement is required in the eighth year at a cost of \$400.

5. The yearly electricity cost for heating and cooling is \$425, evaluated at the outset, and increased at a rate of 7% per annum due to rising electricity prices.

6. The discount rate (a nominal rate that includes an inflation adjustment) is 10%.

7. No salvage value is expected at the end of 15 years.

The LCCs in the sample problem are derived only for the heat pump and not for alternative heating/cooling systems. Hence, no attempt is made to compare alternative systems in this discounting example. To do so would require similar calculations of LCCs for other types of heating/cooling systems. Total costs of a heat pump system include costs of purchase and installation, maintenance, replacements, and electricity for operation. Using the present as the base-time reference point, one needs to convert each of these costs to the present before summing them. Assuming that the purchase and installation costs occur at the base reference point (the present), the \$1,500 is already in present value terms.

Figure 3.9 illustrates how to convert the other cash flows to present values. The first task is to convert the stream of annual maintenance costs to present value. The maintenance costs, as shown in the cash flow diagram of Figure 3.9, are \$50 per year, measured in current dollars (i.e., dollars of the years in which

Task description3 (Find P, given A) Find the present value (Pm) of the \$50 annual maintenance cost (Am) over 15 yr

(Find P, given F) Find the present value (Pc) of the \$400 future cost of replacing compressor (Fc) at end of 8 yr a

Cash flow diagram \$50 \$50 \$50

Time in years

\$400

Time in years

Discounting operationb Pm = Am + UPW Pm = \$50 (UPW, 10%, 15 yr) Pm = \$50 (7.606) = \$380

(Find P, given A with escalation) Find the present value (Pc) of the annual electricity costs (Ae) over 15 yr, beginning with a first year's cost of \$425 and electricity cost escalation of 7%/yr

Time in years

Find the total present value of the Ph = purchase and installation heat pump (Ph) cost + Pm + Pc + Pe

Note: a P Present value, A = Annual value, F = Future value. Ph = \$7213

b UPW = Uniform present worth factor, SPW = Single present worth factor, UPW+= Uniform present worth factor with energy escalation. Purchase and installation costs are \$1,500 incurred initially.

FIGURE 3.9 Discounting for present value: a heat pump example. (From Marshall, H. E. and Ruegg, R. T., in Simplified Energy Design Economics, F. Wilson, ed., National Bureau of Standards, Washington, DC, 1980.)

TABLE 3.4 Discount Formulas

Standard Nomenclature Use When Standard Notation Algebraic Form

TABLE 3.4 Discount Formulas

Standard Nomenclature Use When Standard Notation Algebraic Form

 Single compound amount Given P; to find F (SCA, d%, N) F =P (1+ d )N Single present worth Given F; to find P (SPW, d%, N) ( 1+if Uniform compound amount Given A; to find F (UCA, d%, N) d Uniform sinking fund Given F; to find A (USF, d %, N) A _ p d ( 1+if -1 Uniform capital recovery Given P; to find A (UCR, d%, N) A _ p d( 1+if ( 1+i ) " -1 Uniform present worth Given A; to find P (UPW, d%, N) d( Uniform present worth Given A escalating at a rate e; (UPW*, d%, e, N) A (d-e

modified to find P

P, a present sum of money; F, a future sum of money, equivalent to P at the end of N periods of time at a discount rate of d; N, number of interest periods; A, an end-of-period payment (or receipt) in a uniform series of payments (or receipts) over N periods at discount rate d, usually annually; e, a rate of escalation in A in each of N periods.

modified to find P

P, a present sum of money; F, a future sum of money, equivalent to P at the end of N periods of time at a discount rate of d; N, number of interest periods; A, an end-of-period payment (or receipt) in a uniform series of payments (or receipts) over N periods at discount rate d, usually annually; e, a rate of escalation in A in each of N periods.

they occur). The triangle indicates the value to be found. The practice of compounding interest at the end of each year is followed here. The present refers to the beginning of year one.

The discounting operation for calculating the present value of maintenance costs (last column of Figure 3.9) is to multiply the annual maintenance costs times the uniform present worth (UPW) factor. The UPW is a multiplicative factor computed from the formula given in Table 3.4, or taken from a lookup table of factors that have been published in many economics textbooks. UPW factors make it easy to calculate the present values of a uniform series of annual values. For a discount rate of 10% and a time period of 15 years, the UPW factor is 7.606. Multiplying this factor by \$50 gives a present value maintenance cost equal to \$380. Note that the \$380 present value of \$50 per year incurred in each of 15 years is much less than simply adding \$50 for 15 years (i.e., \$750). Discounting is required to achieve correct statements of costs and benefits over time.

The second step is to convert the one-time future cost of compressor replacement, \$400, to its present value. The operation for calculating the present value of compressor replacement is to multiply the future value of the compressor replacement times the single-payment present worth factor (SPW) that can be calculated from the formula in Table 3.4, or taken from a discount factor look-up table. For a discount rate of 10% and a time period of 15 years, the SPW factor is 0.4665. Multiplying this factor by \$400 gives a present-value cost of the compressor replacement of \$187, as shown in the last column of Figure 3.9. Again, note that discounting makes a significant difference in the measure of costs. Failing to discount the \$400 would result in an overestimate of cost in this case of \$213.

The third step is to convert the annual electricity costs for heating and cooling to present value. A year's electricity costs, evaluated at the time of installation of the heat pump, are assumed to be \$425. Electricity prices, for purposes of illustration, are assumed to increase at a rate of 7% per annum. This is reflected in Table 3.4 by multiplying \$425 times (1.07)f where t =1,2,.. .,15. The electricity cost at the end of the fourth year, for example, is \$425(1.07)4 = \$557.

The discounting operation for finding the present value of all electricity costs (shown in Figure 3.9) is to multiply the initial, yearly electricity costs times the appropriate UPW* factor. (An asterisk following UPW denotes that a term for price escalation is included.) The UPW or UPW* discount formulas in Table 3.4 can also be used to obtain present values from annual costs or multiplicative discount factors from look-up tables can be used. For a period of 15 years, a discount rate of l0%, and an escalation rate of 7%, the UPW* factor is 12.1092. Multiplying the factor by \$425 gives a present value of electricity costs of \$5,146. Note, once again, that failing to discount (i.e., simply adding annual electricity expenses in current prices) would overestimate costs by \$1,229 (\$6,376 — \$5,146). Discounting with a UPW factor that does not incorporate energy price escalation would underestimate costs by \$1,913 (\$5,146 — \$3,233).

The final operation described in Figure 3.9 is to sum purchase and installation cost and the present values of maintenance, compressor replacement, and electricity costs. Total LCCs of the heat pump in present value terms are \$7,213. This is one of the amounts that a designer would need for comparing the cost-effectiveness of heat pumps to alternative heating/cooling systems.

Only one discounting operation is required for converting the present- value costs of the heat pump to annual value terms. The total present-value amount is converted to the total annual value simply by multiplying it by the uniform capital recovery factor (UCR)—in this case the UCR for 10% and 15 years. The UCR factor, calculated with the UCR formula found in Table 3.4, is 0.13147. Multiplying this factor by the total present value of \$7,213 gives the cost of the heat pump as \$948 in annual value terms. The two figures—\$7,213 and \$948 per year—are time-equivalent values, made consistent through the discounting.

Figure 3.9 provides a model for the designer who must calculate present values from all kinds of benefit or cost streams. Most distributions of values occurring in future years can be handled with the SPW, the UPW, or the UPW* factors.

### 3.5.3 Discount Rate

Of the various factors affecting the NB of energy efficiency and renewable energy investments, the discount rate is one of the most dramatic. A project that appears economic at one discount rate will often appear uneconomic at another rate. For example, a project that yields net savings at a 6% discount rate might yield net losses if evaluated with a 7% rate.

As the discount rate is increased, the present value of any future stream of costs or benefits is going to become smaller. High discount rates tend to favor projects with quick payoffs over projects with benefits deferred further in the future.

The discount rate should be set equal to the rate of return available on the next-best investment opportunity of similar risk to the project in question, i.e., it should indicate the opportunity cost of the investor.

The discount rate may be formulated as a "real rate" exclusive of general price inflation or as a "nominal rate" inclusive of inflation. The former should be used to discount cash flows that are stated in constant dollars. The latter should be used to discount cash flows stated in current dollars.

### 3.5.4 Inflation

Inflation is a rise in the general price level. Because future price changes are unknown, it is frequently assumed that prices will increase at the rate of inflation. Under this assumption, it is generally easier to conduct all economic-evaluations in constant dollars and to discount those values using "real" discount rates. For example, converting the constant dollar annual maintenance costs in Figure 3.9 to a present value can be easily done by multiplying by a uniform present-worth factor because the maintenance costs do not change over time. However some cash flows are more easily expressed in current dollars, e.g., equal loan payments, tax depreciation. These can be converted to present values using a nominal discount rate.

### 3.5.5 Analysis Period

The analysis period is the length of time over which costs and benefits are considered in an economic-evaluation. The analysis period need not be the same as either the "useful life" or the "economic life," two common concepts of investment life. The useful life is the period over which the investment has some value; i.e., the investment continues to conserve or provide energy during this period. Economic life is the period during which the investment in question is the least-cost way of meeting the requirement. Often economic life is shorter than useful life.

The selection of an analysis period will depend on the objectives and perspective of the decision maker. A speculative investor who plans to develop a project for immediate sale, for example, may view the relevant time horizon as that short period of ownership from planning and acquisition of property to the first sale of the project. Although the useful life of a solar domestic hot water heating system, for example, might be 20 years, a speculative home builder might operate on the basis of a two-year time horizon, if the property is expected to change hands within that period. Only if the speculator expects to gain the benefit of those energy savings through a higher selling price for the building will the higher first cost of the solar energy investment likely be economic.

If an analyst is performing an economic analysis for a particular client, that client's time horizon should serve as the analysis period. If an analyst is performing an analysis in support of public investment or a policy decision, the life of the system or building is typically the appropriate analysis period.

When considering multiple investment options, it is best with some evaluation methods (such as LCC, IRR, and ORR) to use the same analysis period. With others like NPV and BCR, different analysis periods can be used. If an investment's useful life is shorter than the analysis period, it may be necessary to consider reinvesting in that option at the end its useful life. If an investment's useful life is longer than the analysis period, a salvage value may need to be estimated.

### 3.5.6 Taxes and Subsidies

Taxes and subsidies should be taken into account in economic-evaluations because they may affect the economic viability of an investment, the return to the investor, and the optimal size of the investment. Taxes, which may have positive and negative effects, include—but are not limited to—income taxes, sales taxes, property taxes, excise takes, capital gain taxes, depreciation recapture taxes, tax deductions, and tax credits.

Subsidies are inducements for a particular type of behavior or action. They include grants—cash subsidies of specified amounts; government cost sharing; loan-interest reductions, and tax-related subsidies. Income tax credits for efficiency or renewable energy expenditures provide a subsidy by allowing specific deductions from the investor's tax liability. Property tax exemptions eliminate the property taxes that would otherwise add to annual costs. Income tax deductions for energy efficiency or renewable energy expenses reduce annual tax costs. The imposition of higher taxes on nonrenewable energy sources raises their prices and encourages efficiency and renewable energy investments.

It is important to distinguish between a before-tax cash flow and an after-tax cash flow. For example, fuel costs are a before-tax cash flow (they can be expensed), whereas a production tax credit for electricity from wind is an after-tax cash flow.

### 3.5.7 Financing

Financing of an energy investment can alter the economic viability of that investment. This is especially true for energy efficiency and renewable energy investments that generally have large initial investment costs with returns spread out over time. Ignoring financing costs when comparing these investments against conventional sources of energy can bias the evaluation against the energy efficiency and renewable energy investments.

Financing is generally described in terms of the amount financed, the loan period, and the interest rate. Unless specified otherwise, a uniform payment schedule is usually assumed. Generally, financing improves the economic effectiveness of an investment if the after-tax nominal interest rate is less than the investor's nominal discount rate.

Financing essentially reduces the initial outlay in favor of additional future outlays over time—usually equal payments for a fixed number of years. These cash flows can be treated like any other: The equity portion of the capital cost occurs at the start of the first year, and the loan payments occur monthly or annually. The only other major consideration is the tax deductibility of the interest portion of the loan payments.

### 3.5.8 Residual Values

Residual values may arise from salvage (net of disposal costs) at the end of the life of systems and components, from reuse values when the purpose is changed, and from remaining value when assets are sold prior to the end of their lives. The present value of residuals can generally be expected to decrease, other things equal, as (1) the discount rate rises, (2) the equipment or building deteriorates, and (3) the time horizon lengthens.

To estimate the residual value of energy efficiency or renewable energy systems and components, it is helpful to consider the amount that can be added to the selling price of a project or building because of those systems. It might be assumed that a building buyer will be willing to pay an additional amount equal to the capitalized value of energy savings over the remaining life of the efficiency or renewable investment. If the analysis period is the same as the useful life, there will be no residual value.

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