ECONOMIC ANALYSIS

3.4.1 CAPITAL INVESTMENT CHARACTERISTICS

Investments can be broadly categorized into capital costs and operating costs. Capi-tal investments are generally more strategic and have long-term effects. Decisions regarding capital investments are usually made at higher management levels within a company with the consideration of additional tax consequences as compared to the operating costs. Capital investments have four unique characteristics

Large initial costs

•

Long recovery period for the investment

•

Irreversible procedure

•

Signifi cant tax implications depending on the choice of fi nancing methods

•

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A capital investment usually requires a relatively large amount of money. Some-times, the funds available for the capital investment of an energy conservation project in a company are limited. That is, the initial capital costs exceed the total available funds. This creates a situation known as capital rationing. A capital investment is recovered over a period of years. The period between the initial installation and the last future cash fl ow is the life cycle or the life of the invest-ment. Since the benefi ts of the investment must be realized over the time when the energy conservation project is implemented, it is necessary to consider the time values of money to properly evaluate the feasibility of the investment. Further-more, once the capital investment is made, it is very hard to retract. Therefore, careful attention should be paid to the economic analysis of a potential energy conservation project.

Capital investment is usually a function of the capacity or the scale of the project.

The relationship between a capital cost and plant size is usually estimated by two methods: economic estimation using actual survey data and direct calculation from synthetic engineering data. The power function is the standard estimation function to determine capital investment at different scales. The main advantage of the power function is that estimates can be provided where no operating process exists (Gal-lagher et al., 2005). The power function is convenient for use in estimation because plant construction costs, K, can increase more or less proportionately with plant capacity, Q (Henderson and Quandt, 1980):

K=AQn (3.10)

The power function is often referred to as the “0.6 factor rule,” which says that a 1%

expansion in processing capacity yields a little less than 0.6% increase in capital costs (Ladd, 1998). In the chemical processing industry, the factor ranges from 0.4 to 0.9 (Peters and Timmerhaus, 1991). In the dry mill ethanol plant, the estimated power factor is 0.836 and the capital costs of a dry mill ethanol plant, therefore, increase more rapidly than the average for all processing plants with an average power factor of 0.6 (Gallagher et al., 2005).

3.4.2 TIME VALUEOF MONEY

Interest and infl ation are two primary factors associated with the time value of money. Interest is the ability to earn a return on money if it is loaned rather than consumed. There are two kinds of interest: simple interest and compound interest.

Under simple interest, interest is earned only on the original amount loaned. Under compound interest, interest is earned on the original amount loaned and any interest accumulated from the previous periods.

The formulas used to calculate future value from present value based on simple interest and compound interest are given by, respectively,

(1 )

Fn =P +ni (3.11)

(1 )ⁿ

Fn =P +i (3.12)

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where

Fn is the future amount of money at the end of the nth year P is the present amount of money

i is the interest

n is the number of years between P and Fn

Compound interest is more commonly used in practice than simple interest. The factor (1 + i)ⁿ is known as the single sum, future worth factor or the single payment, compound amount factor. Table 3.2 summarizes the time value of money factors.

Example 3.4

Determine the balance that will accumulate at the end of year 30 in an account that pays a 6%/year compound interest if a monthly deposit of $675 is made today.

Solution 3.4

This is a uniform series cash fl ow problem. From Table 3.2, we have

(

^{F A i n| , ,}

)

⁼⁽¹⁺ⁱ_i⁾ⁿ⁻¹

where

n = 30 years × 12 month/year = 360 month i = 6%/12 = 0.5%

TABLE 3.2

Summary of Discrete Compounding Time Value of Money Factors

To Find Given Factor Symbol Name

P F (1 + i)⁻ⁿ (P|F,i,n) Single payment, present worth factor

F P (1 + i)ⁿ (F|P,i,n) Single payment, compound amount

factor

P A (1 ) 1

(1 )

n n

i i i

+ −

+

(P|A,i,n) Uniform series, present worth factor

A P (1 )

(1 ) 1

n n

i i i +

+ −

(A|P,i,n) Uniform series, capital recovery factor

F A (1 i)ⁿ 1

i

+ − (F|A,i,n) Uniform series, compound amount factor

A F

(1 )ⁿ 1 i +i −

(A|F,i,n) Uniform series, sinking fund factor

P G

2

1 (1 ni)(1 i)ⁿ i

− + + − (P|G,i,n) Gradient series, present worth factor

A G (1 ) (1 )

[(1 ) 1]

n n

i ni

i i

−

−

+ − +

+ −

(A|G,i,n) Gradient series, uniform series factor

Source: Reprinted from Pratt, D. Energy Management Handbook (6th ed.), The Fairmont Press Inc., Georgia, 2006. With permission.

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( )

^{+ −}

= × = ×(1 0.005)³⁶⁰ 1=

| , , 675 0.678 millions dollars

0.005 F A F A i n

Example 3.5

Determine the equal monthly withdrawals that can be made for 30 years from an account with 0.678 million dollars available at the end of year 30 given in Example 3.4. The account continues to be paid at a compound interest of 6%/year. The fi rst withdrawal is to be made 1 month after the end of year 30.

Solution 3.5

From Table 3.2, we have

(

^{A P i n| , ,}

)

⁼₍₁ⁱ₊⁽¹⁺i₎nⁱ⁾₋ⁿ₁ where

n = 30 [years] × 12 [month/year] = 360 month i = 6%/12 = 0.5%

P = $678,000

( )

⁺

= × = × =

+ −

360 360

0.005(1 0.005)

| , , 678,000 $4,065

(1 0.005) 1 A P A P i n

Example 3.6

Determine the equal monthly payment for a 15 year mortgage loan of $170,000 at an annual fi xed interest of 5.25%.

Solution 3.6

From Table 3.2, we have

(

^{| , ,}

)

⁼₍₁₊⁽¹⁺₎n⁾₋ⁿ₁

i i A P i n

i

where

n = 15 [years] × 12 [month/year] = 180 month i = 5.25%/12 = 0.4375%

( )

⁺

= × = × =

+ −

180 180

0.004375(1 0.004375)

| , , 170,000 $1,366.6

(1 0.004375) 1 A P A P i n

Infl ation is a complex subject. Infl ation is a rise in the general price level. It can be described as a decrease in the purchasing power of money in general. An infl ation rate is published by the government based on the Consumer Price Index (CPI).

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Taking into account the infl ation effect, the current cash value can be converted to constant cash value by

Constant $=(current $)/(1+ f)ⁿ (3.13) The constant cash value can also be converted to current cash value by

Current $=(constant $)(1+ f)ⁿ (3.14) Example 3.7

Determine the constant cash value for $5000 at the end of 30 years from now if the infl ation rate is 3%.

Solution 3.7

Using Equation 3.13, Constant $ = (current $)/(1 + f)ⁿ = 5000/(1 + 0.03)³⁰ = $2060

3.4.3 DEPRECIATIONAND TAXES

Depreciation is a recognition that most assets decrease in value over time. The U.S.

federal income tax law permits deductions from taxable income to allow for this value loss of assets. These deductions are called depreciation allowances. A depreciable asset must be held by the business for producing income, wear out, or be consumed in its use and have a life longer than a year. Many methods of depreciation including straight line, sum-of-the-years digits, declining balance, and the accelerated cost recovery system have been allowed under the U.S. tax law over the years. The method currently used for calculating the depreciation of assets placed in service after 1986 is the Modifi ed Accelerated Cost Recovery System (MACRS). The allowable MACRS depreciation deduction for an asset is a function of the property class, the basis value, and the recovery period of the asset. Table 3.3 gives the MACRS property classes and

TABLE 3.3

MACRS Property Classes and Percentages by Recovery Year

Property

Class 3 year 5 year 7 year 10 year 15 year

Example assets

Special handling devices for food Special tools for motor vehicle manufacturing

Computers and offi ce machines General

purpose trucks

Offi ce furniture Manufacturing machine tools

Assets used in manufacturing of certain food products, Tugs and water

transport equipment Petroleum

refi ning assets

Fencing and landscaping Cement

manufacturing assets Telephone

distribution equipment

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percentages by recovery year. The basis of an asset is the cost of placing the asset in service. In most cases, the basis includes the purchase cost of the asset plus the costs, such as installation costs, necessary to place the asset in service.

Taxes are primarily designed to generate revenues for governmental entities.

Cash fl ows used for economic analysis should always be adjusted for the combined impact of all relevant taxes. Tax laws and regulations are too complex and intricate to be discussed in detail in this book. The amount of taxes is usually determined based on the tax rate multiplied by the taxable income. In the United States, depend-ing on income ranges, the marginal tax rates vary from 15% to 39% of taxable income as shown in Table 3.4.

Taxable income is calculated by subtracting allowable deduction from gross income. Gross income is generated when a company sells products or services.

Allowable deductions include salaries and wages, materials, interest payments, depreciation, and other costs associated with the business as listed in tax regulations.

Given the availability of the above information and the Before Tax Cash Flows (BTCF), the procedure to determine the After Tax Cash Flow (ATCF) on a year-by-year basis is given below:

Taxable income BTCF loan and bond interest d eprecation other allowable deductions

_ _

=_ (3.15)

TABLE 3.3 (continued)

MACRS Property Classes and Percentages by Recovery Year

Recovery Year

1 33.33% 20.00% 14.29% 10.00% 5.00%

2 44.45% 32.00% 24.49% 18.00% 9.50%

3 14.81% 19.20% 17.49% 14.40% 8.55%

4 7.41% 11.52% 12.49% 11.52% 7.70%

5 11.52% 8.93% 9.22% 6.93%

6 5.76% 8.92% 7.37% 6.23%

7 8.93% 6.55% 5.90%

8 4.46% 6.55% 5.90%

9 6.56% 5.91%

10 6.55% 5.90%

11 3.28% 5.91%

12 5.90%

13 5.91%

14 5.90%

15 5.91%

16 2.95%

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Taxes=Taxable incomes×Tax rate (3.16)

ATCF=BTCF−total loan and bond payments−taxes (3.17) It worth noting that depreciation reduces taxable income and thus taxes but does not directly enter into the calculation of cash fl ows. Depreciation is an accounting con-cept to stimulate business by reducing taxes over the life of an asset and it does not involve any cash changes.

3.4.4 CASH FLOW DIAGRAMS

For a quantitative analysis of an investment project, the project is usually separated into several elements including

Initial investment

•

Returns on investment

•

Economic life

•

Salvage value

•

The initial investment includes the price of equipment and materials and the ancil-lary costs of the fi nished project such as transportation, installation, and licensing fees. After an initial investment is made, returns will be achieved over the lifetime of the project. Taxes, operating costs, and maintenance costs must be subtracted from the gross project income. Returns are typically credited at discrete times on a monthly or yearly basis rather than on a continuous day-to-day basis. The economic return on an investment will not last indefi nitely. Equipment used for energy conservation and conversion has a physical lifetime. An estimate of the expected economical life is required. Economic life used in economic analysis of an investment project is usu-ally the best estimate of the length of time that equipment can be economicusu-ally used.

The physical lifetime for equipment may be used as the economic life of the equipment.

TABLE 3.4

Federal Tax Rates based on the Omnibus Reconciliation Act of 1993

Taxable Income, X($) Marginal Tax Rate Taxes Due

0–50,000 0.15 0.15X

50,000–75,000 0.25 7,500 + 0.25(X − 50,000)

75,000–100,000 0.34 13,750 + 0.34(X − 75,000)

100,000–335,000 0.39 22,250 + 0.39(X − 100,000)

335,000–10,000,000 0.34 113,900 + 0.34(X − 335,000)

10,000,000–15,000,000 0.35 3,400,000 + 0.35(X − 10,000,000) 15,000,000–18,333,333 0.38 5,150,000 + 0.38(X − 15,000,000)

>18,333,333 0.35 6,416,667 + 0.35(X − 18,333,333)

Source: Adapted from Pratt, D. Energy Management Handbook (6th ed.), The Fairmont Press Inc., Georgia, 2006. With permission.

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Economic life may be arbitrarily agreed on by contract. The Internal Revenue Ser-vice in the United States gives some guidelines for the economic life of assets as shown in Table 3.3. The economic value of the equipment at the end of its economic life must be included in the returns on investment.

The bottom line of an energy conservation project is that the revenues or savings generated by the investment must be greater than the costs involved. The number of years over which the revenues accumulate, the future revenues, the initial and future costs, and the future money value relative to present money value are important fac-tors in making an investment decision for an energy conservation project. A conve-nient way to display the revenues (or savings) and costs associated with an investment is a cash fl ow diagram. A cash fl ow diagram, as shown in Figure 3.2, is to show all cash infl ows and outfl ows plotted along a horizontal time line.

A graphic projection of the details of an investment project or a cash fl ow diagram can be used to represent the initial investment and the returns on the investment along with the economic life. Although cash fl ow diagrams are simply graphical representa-tions of revenues and costs, good cash fl ow diagrams are complete, accurate, and legible. It is usually advantageous to fi rst determine the time frame over which the cash fl ows occur. The lifetime of the investment is divided into periods, which are frequently, but not always, years. Individual revenues and costs are indicated by drawing vertical lines appropriately placed along the time scale. Upward directed lines indi-cate cash infl ow of revenues or savings while downward directed lines indiindi-cate cash outfl ow of costs. The relative magnitudes of cash infl ow and outfl ow are indicated by the height of the vertical lines.

3.4.5 ECONOMIC EVALUATION METHODS

There are a number of methods for evaluating economic performance. These methods include the simple payback period, life cycle cost method, net benefi t or net savings

0 1 2

$10,000

$2000

$500

3

$2000

$500 4

$2000

$500

10

$2000

$500

$500

$2000

$500

FIGURE 3.2 Cash fl ow diagram for uniform and discrete returns with a salvage value.

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method, benefi t/cost ratio method, internal rate of return method, overall rate of return method, and discounted payback method (Singh, 1986; Kreith and West, 1997; Mull, 2001). Usually, several methods are used to provide better understanding of an invest-ment’s worth. The simple payback period is commonly used by businesses. However, the primary criterion mandated for assessing the effectiveness of energy conservation investments in federal facilities and many state government facilities is the minimiza-tion of life cycle costs. Therefore, it is important to understand the life cycle cost analysis for federal and state facility projects.

3.4.5.1 Simple Payback Period

Simple payback period analysis is also called payback period analysis. It determines the number of years required to recover an initial investment through project returns.

The advantages of the simple payback period analysis are that it is simple and easily understood. However, it does not consider the time value of money, costs, or benefi ts of the investment following the payback period. It is assumed that the lifetime of the project is longer than the simple payback period.

Example 3.8

A heat pump has an initial cost of $10,000, energy savings of $25,000 per year, and a maintenance cost of $500 per year. Determine its simple payback period.

Solution 3.8

The heat pump’s simple payback period is

= =

−

$10,000

SPP 5 years

$2,500 $500 3.4.5.2 Discounted Payback Method

The discounted payback evaluation method measures the elapsed time between the point of an initial investment and the point at which accumulated savings and net of other accu-mulated costs are suffi cient to offset the initial investment. The shorter the length of time until the investment pays off, the more desirable the investment is. However, a shorter payback time does not always mean a more economically effi cient investment. Discounted payback method is often used as a supplementary measure when the project life is uncer-tain. It is used to identify feasible projects when the investor’s time horizon is constrained.

It is not a reliable guide for most complex investment decisions where the objective is to choose the most profi table investment alternatives. To determine the discounted payback period, fi nd the minimum solution value of N_min in the following equation:

( )

( )

min

0

1 1

N

n n

n n

B C

I d

=

− =

∑

+ ^(3.18)

where

Bn is the benefi t in period n Cn is the cost in period n

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I0 is the initial investment cost of an alternative d is the discount rate

Nmin is the discounted payback period 3.4.5.3 Benefi t to Cost Ratio Method

The benefi t to cost ratio method divides the benefi ts by costs and thus this method gives the measure as a dimensionless number. The higher the ratio is the more dollar savings are realized for every dollar of investment. The ratio method can be used to determine whether or not to accept or reject a given investment on economic grounds.

A formula for calculating the ratio of savings to investment costs is given by

0

SCR (1 )

N

n n

n n

S C

= d

=

∑

+ ^(3.19)

where

SCR is the savings to cost ratio Sn is the cost saving in year n Cn is the cost in year n d is the discount rate

3.4.5.4 Net Benefi ts or Savings Method

The net benefi ts or savings method is used to determine the excess of benefi ts or sav-ings over costs. The time values of all amounts are used. The net benefi ts method is particularly suitable for decisions made on the basis of long-run profi tability. A for-mula for determining the net benefi ts from an investment is given by

( )

0

( )

NB

1

N

n n

n n

B C

d

=

= −

∑

+ ^(3.20)

where

NB is the net benefi t B_n is the benefi t in year n C_n is the cost in year n d is the discount rate

3.4.5.5 Internal Rate of Return Method

The internal rate of return method solves for the interest rate for which dollar sav-ings are just equal to dollar costs over the relevant period. It is the rate for which net savings are zero. Unlike other methods, the internal rate of return method does not require a prespecifi ed discount rate in the computation but solves for a rate. It is a widely used method. The shortcomings include the possibility of no solution or multiple solution values.

The rate of return is typically calculated by a process of trial and error, by which various compound rates of interest are used to discount cash fl ows until a rate is found for which the net value of the investment is zero. For determining the internal rate of return, a trial interest rate is substituted for the discount rate, d, in Equation

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3.20. A positive NB means the rate of return is less than the trial interest while a negative NB means the rate of return is larger than the trial interest. Based on the information, try another rate until you fi nd the rate at which NB approaches zero.

3.4.5.6 Life Cycle Cost Method

A life cycle cost analysis is to quantify costs over the entire life cycle of the project investment. The life cycle cost method sums the costs of acquisition, maintenance, repair, replacement, energy, and other costs such as salvage value that are affected by the investment decision. All amounts are usually measured either in a present value or in an annual value. The time value of money must be taken into account for all amounts over the relevant period. Two important parameters for a life cycle cost analysis are the lifetimes of equipment and the interest rate. Different pieces of equipment may have different lifetimes. The lifetime is usually either found through vendors or estimated based on experience. A common life period must be chosen so that all alternatives are considered over the same time line. If the shortest life is used, a salvage value must be estimated for the longer-lived alternatives. If the longest life is used, shorter-lived alternatives are assumed to be repeatable (Capehart et al., 2006). The interest rate is the value that a company or organization uses for evaluat-ing its investments. This interest is often known as the minimum attractive rate of return (MARR). The value is company or organization specifi c and should be supplied by the company or organization.

The life cycle cost method is particularly useful for decisions that are made primarily on the basis of cost effectiveness to determine whether a given conserva-tion or renewable energy investment will lower total cost. However, it cannot be used to fi nd the best investment in general. Numerous alternatives may be compared. The alternative with the lowest life cycle cost that meets the investor’s objectives and constraints is the preferred investment. A formula for calculating the life cycle costs of each alternative is given by

LCC_n = +I_n E_n+M_n+ − (3.21)R_n S_n where

LCC_n is the life cycle cost of alternative n

I_n is the present value of investment costs of alternative n

E_n is the present value of energy costs associated with alternative n

M_n is the present value of nonfuel operating and maintenance cost of alternative n R_n is the present value of repairing and replacement costs of alternative n S_n is the present value of resale or salvage value associated with alternative n Example 3.9

An energy effi cient air compressor is proposed by a vendor. The compressor and installation will cost $30,000. It will require $1000 worth of maintenance each year for its life of 10 years. Energy costs will be $6000 per year. A standard air compres-sor will cost $25,000 and will require $500 worth of maintenance each year. Its energy costs will be $10,000 per year. Suppose the MARR is 10%, would you invest in the energy effi cient air compressor based on a life cycle cost analysis?

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