Engineering Economicsvdvdv Moodle

8/17/2019 Engineering Economicsvdvdv Moodle

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Engineering Economic Analysis

Arif S. Malik

Department of Electrical & ComputerEngineering

College of Engineering

Table of Contents

– Time Value of Money

– Interest Formulas

– Discount Rate

– Escalation and Inflation

– Depreciation

– Classification of Costs

– Measure of Price

– Criteria used for Project Evaluation


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3

Time Value of Money• Money of the same dollar amount in different time

periods have different values (purchasing power)

• Primary Reasons:

• (1) Inflation tends to erode the purchasing power

(value) of money, (2) Money can be invested for

intervals of time to earn a real return (i.e.

independent of inflation or deflation), (3) Money

available in a future period is less valuable because it is not available for use at the present.

Fundamental concept (return on

investment )

• The mathematical process by which differentmonetary amounts are moved either forward or

backward in time to a common point in time iscalled present value or present worth analysis.

• The process of converting monetary valuesforward in time to an equivalent amount is called

compounding.• The process of converting monetary values

backward in time to an equivalent amount is calleddiscounting


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Interest Formulas – Single Compound Amount Formula

– Single Present Worth Formula

– Uniform Sinking Fund Formula

– Uniform Series compound amount formula

– Uniform Series Present Worth Formula

– Uniform Capital Recovery Formula

The following notation is used in

developing the formulas:

• i is an interest or discount rate

• N is the number of interest or discounting periods

• P is a present sum of money

• F is a future sum of money at the end of N periods

• A is an end-of-period payment (or receipt) in auniform series of payments (or receipts) over

N periods at i interest or discount rate.


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Single Compound Amount

Formula

P dollars deposited in an account at a

specific rate i grow to P(1+i) by the end of

the first period and to P(1+i)(1+i) by the

end of the second period. In general at the

end of N periods

F=P(1+i) N (1)

Single Compound Amount Formula(Cont’d)

Example 1: Jack deposits $200 in a saving

account that has an interest rate of 8%, then in

4 years time he will have

F = $200*(1+0.08)4

= $200*1.36= $272

and the FVF is $272/$200 = 1.36


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Single Present Worth Formula

The present worth P of a sum N periods in

the future, F, is determined by rearranging

Eq.(1)

(2)


(Cont’d)

• 1/(1+i) N called the single payment present worth

factor or Present Value Factor (PVF)

• i is usually called the discount rate(the discount

rate may be significantly different from the

interest rate). This factor is used whenever a

monetary amount is moved backward in time, i.e.,it is used to determine the present value of money

N periods in the future


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(Cont’d) Example 2: An expenditure of $5000 will be required at the

end of 2005, and some money must be put aside at the start of

2001 to cover this future expense. If the interest rate is 12%

per year, the present value of that future expense at the start

of 2001 is

P = F/(1+i) N

= $5000/(1.12)5

= $5000/1.7623

= $2837PVF = P/F = $2837/$5000 = 0.5674

Uniform Sinking Fund Formula

– A fund established to accumulate a desiredfuture amount of money at the end of givenlength of time through collection of uniformseries of payments

– Each payment called an annuity A, made at theend of each of N interest periods

– The total amount F at the end of each of N interest periods is the sum of the compoundamounts of the individual payments.


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(Cont’d)F=A(1+i) N-1 + A(1+i) N-2+. . .+A (3)

Multiplying the above equation by (1+i) on both sides

F(1+i)=A(1+i) N+A(1+i) N-1+. . . +A(1+i) (4)

Subtracting (3) from (4), we get

Fi = A(1+i) N-A

or (5)

The expression i/[(1+i) N

-1] is called the sinking fund factor , SFF.


(Cont’d)

Example 3: Mortgage bonds with a face value of

$1000 must be saved in 20 years. How much

money should be put into a saving account at the

end of each year (annuity) to meet that bond

commitment if the saving accounts pays 7%? The

answer is

A = (0.02439) $1000 = $24.39


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Uniform Series Compound

Amount FormulaA future sum F equivalent to a uniform series of

end-of-period sums A can be determined by

rearranging Eq. (5)

(6)

Where the term in brackets is called the uniform

series Compound Amount Factor (CAF).

Uniform Series Compound

Amount Formula (Cont’d)

Example 4: A deposit of $100 is placed in a savings

account at the end of each years from 1990 to 1999.

This savings account earns 8% annual interest. The

future value of this account at the end of 1999 will be

F = $100*[(1.08)10

- 1]/0.08= $100 * 14.487

= $1,448.70


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Uniform Series Present Worth

FormulaThe present value of annuity ‘P’ of the future sum atthe start of year 1 to N , discounted at the rate ‘i’ is

(7)

P = A*PWF(N yr,i%) (8)

Where PWF is (uniform series) Present Worth Factor

Also, PWF = CAF*PVF

The present value of an above example 4 is $671.

Uniform Series Present Worth Formula (Cont’d) Example 5: Present Value of Delayed Annuity. Thisexamples deals with the present value at the start of 2000 ofan annuity of $1000 per year extending from the end of 2005until the year 2025, with 10% interest. Payments occur at theend of each year, including 2025. This would be a 21-yearannuity, with a present value at the start of 2005 of

P2005 = A * PWF(21 yr, 10%)

= $1000 * 8.649

= $8,649

The discounted value at the start of 2000 can be computednow by discounting P2005 by 5 more years

P2000 = P2005 * PVF(5 yr, 10%)

= $8,649 * 0.6209 = $5,370


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Uniform Capital Recovery Formula

The capital recovery factor is used to compute the uniformannual payment ‘A’ (i.e. the annuity) the annuity required atthe end of the each year for N years such that the totaldiscounted value at the start of Year 1, discounted at i%, willequal the present amount P. By rearranging Eq. (7) we get

(9)

or A = P * CRF(N yr, i%)

Note that capital recovery factor; (CRF) = 1/ (PWF)

The capital recovery factor is useful for converting an initialcapital cost into an equivalent levelized annual cost of capitalover the lifetime of the capital investment.

Uniform Capital Recovery Formula(Cont’d)

Example 6 : A plant of capital cost of $50,000 and an expectedlifetime of 20 years has an annuity at 10%

A = P*CRF(20 yrs, 10%)

A = $50,000 * 0.1175

= $5,837

If the present worth of this equivalent annuity is computed, itwill again equal the initial capital cost, as it should be.

P = A * PWF(20 yrs, 10%)

= $5,837 * 8.514

= $50,000


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Application Exercise

• Mr. Jones wishes to establish a fund for hisnewborn child’s education. The fund pays $60,000

on the child’s 18th, 19th, 20th, and 21st birthdays.

The fund will be set up by the deposit of a fixed

sum on the child’s 1st through 17th birthdays. The

fund earns 6 percent annual interest. What is the

required annual deposit.

• What would the annual payments be, if the tuition

fees in Example 6.2 are $60,000, $67,000,

$75,000 and $83,000, respectively, for the fouryears involved?

Escalation and Inflation – Inflation refers to a rise in price levels caused by a decline in

the purchasing power of a currency

– Escalation, also refers to a rise in prices, usually classified aseither real or apparent.

– Real escalation defined as price rise over and above thegeneral rate of inflation such as fuel prices and may resultfrom factors such as resource depletion, new regulations andincreased demand with limited supply.

– Apparent escalation rate defined as the total annual rate ofincrease in a cost including the effects of both inflation and

real escalation. – The relationship for apparent escalation is as follows:

(1+e) = (1+e/)(1+f)

Where e is the apparent escalation rate, e / is the realescalation rate, and f is the inflation rate.


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Escalation and Inflation (Cont’d) Example 7:

Suppose the price of the coal in 2000 is $1.00/10

9

J,and the annual inflation rate over the period 2000-2010 is 6%.Assume that the price of the coal will escalate over the periodat an average annual rate of 1.5%. The price of coal in the year2010, expressed in 2000 dollars, can then be

Coal price in year 2010 = (coal price in 2000)*(1+e/)10

(year 2000 dollars) = $1.00/109J x (1.015)10

= $1.16/109J.

If the effects of inflation are included, then the coal price in theyear 2010 dollars, can be determined:

Coal price in year 2010 = (coal price in 2000)*(1+e)10

(year 2010 dollars) = $1.00/109J x (1.015x1.06)10

= $2.08/109J

Escalation and Inflation (Cont’d)

• Long-range planning studies can be

performed by either including or excluding

inflationary effects. In both cases, however,

it is essential that all cost and economic

parameters used in a study (e.g. the discount

rate and escalation rates) be treatedconsistently.


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Concept of Opportunity Cost

• Opportunity cost is the cost of doing something asmeasured by the loss of the opportunity to dosomething else, with the same amount of time andresources.

Example 8: Suppose you are a lawyer whosesalary is $100 per hour. You spend 2 hours intyping and organizing material per day, which youcould have spent doing more law work. If you hirea secretary to do all the typing and organizing you

will have to pay the secretary $10 per hour, thenthe opportunity cost incurred by not hiring asecretary is $90 per hour.

Discount Rate

• Critical economic parameter

• Theoretically it reflects the opportunity cost of

money to a particular investor (or in broad terms,

in a particular country)

• Since the opportunity cost is linked to the

prevailing conditions within a given country, the

discount rate, like the inflation rate, tends to vary,often significantly, from country to country


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Effect of Discount Rate on project

selection

Project A Project B

Costs ($) Revenue($) Cost ($) Revenue ($)

15,000 0 10,000 0

5,000 0 0 5000

0 6000 0 4000

0 6000 0 3000

0 6000 0 2000

0 6000 0 1000

0 6000 0 0

Effect of Discount Rate

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

0% 5% 10% 15% 20%

N e t P r e s e n t V a l u e

Discount Rate

Project A

Project B


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Depreciation – Decrease in worth

– Cost accounting viewpoint (Annual charge

against revenues used to repay the original

amount of capital borrowed from investors)

– Expansion planning studies depreciation is used

for calculating salvage value for equipment that

have expected lifetimes extending beyond the

end of study period.

Depreciation (Cont’d)

Four commonly used depreciation methods are:

– Straight-line

– Sum-of-the-year digits

– Declining balance

– Sinking fund


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Comparison of depreciation methods

Time End of plant life

Double-

Declining

balanceStraight

line

A c c u m u l a t e d D e p r e c i a t i o n ( p e r u n i t )

1.0

Sinking Fund

Sum-of-the

year digits

Depreciation (Cont’d) – Sum-of-the-year digits and Declining balance

methods are designed to increase cash flow in theearly years of investment

– In straight-line depreciation method thedepreciation charged each year constant

– In sinking fund the depreciation is lowest at the beginning of life and increase with time

– Whatever the method used, however, the sum ofall annual depreciation charges over the life of thealternative must equal initial investment in thealternative less the salvage value


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Classification of Costs

Basic Cost Concept

• Cheap to build or buy (First cost)

• Produce goods and services at the lowest

possible cost

Two distinct merit of figures are therefore

1. Capital Investment Cost

2. Variable Cost

Capital Investment Costs

Capital outlay necessary to build a plant or purchasean equipment and bring it into operation. For example, hydroelectric, coal and nuclear power

plants, the fixed investment charges are the largestcontributor to power generation cost.

Total capital investment costs include constructionor ‘overnight’ costs of building the facility,commonly known as fore costs and costs related toescalation and inflation charges accrued during the

project.


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Fixed Costs

Fixed Costs:

Fixed Cost can be further subdivided:

i) Fixed Investment Charges

ii) Fixed O&M costs

iii) Taxes and Insurance

Fixed Cost (Cont’d)

i) Fixed Investment Charges: Fixed Investment

Charges are a function of Capital Investment costs

and include

Depreciation (i.e. the annual charge for recovering

the initial capital investment in equipment or asset).

Return on Investment (for private organizations for

example, this includes interest paid to bondholdersand return to stockholders.


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Fixed Cost (Cont’d)

ii) Fixed O&M Costs: Include staff salaries,

consumables supplies and equipment,

miscellaneous costs etc.

iii) Taxes and Insurance: These are also

kind of fixed costs.

Variable Cost

Variable Costs

Depends directly on the amount of units produced for example electricity generated (they are expressed in terms of a monetary amount per kWh of

production). The variable costs can be further subdivided:

i) Variable O&M costs: could be consumableitems which need to be replaced after certain number of hours of service.ii) Variable Fuel costs: The cost related tofuel actually spent and used in energy production.


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Sunk Costs

It is already incurred cost or committed cost.

Such treatment of costs may results in high

investment returns. For example, a dam has

already been built for a hydro-electric project.

Now if a generating unit is added, the dam

cost will be considered as sunk cost and an

additional unit cost will only be considered in

testing the economy.

Life Cycle Cost

LCC is :

Total Initial cost + the running costs associatedwith operating the system throughout its lifetime.

LCC include:

1. Initial cost of installing the project

2. Replacement of components when they wear out

3. Regular maintenance

4. System overhauls costs

5. Operating costs

6. Administrative and overhead costs


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Measure of PricePublic Versus Private Perspective

Objective: Both want to maximize the income level and

minimize the risk of losses.

Price distortion caused by taxes, duties or subsidies distorts

the consumption of various goods and services. When prices

become misleading they produce wastage and provide little or

no incentive for conservation. Because of price distortions, a

conservation measure may be highly desirable from the

national (social) point of view, but quite unattractive as seen by the private industrialist.

Shadow Pricing – Prices and costs in economic terms - measured from

public point of view.

– Adjustments to prices made to reflect more closely thetrue social cost or the opportunity cost to the society, thenew value assigned becomes the ‘shadow price’

– Four major categories where shadow adjustment must be estimated

1. Miscellaneous social-cost/private cost discrepanciesespecially in public provided services

2. Labour and wages3. Capital charges and discount rates

4. Fiscal distortions, including sales taxes, duties, and subsidies.


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Miscellaneous Social-

Cost/Private-Cost DiscrepanciesFor example, in terms of failure to account for

pollution or environmental degradation in thecalculation of a coal-fired power plant or the highsubsidies and/or cross subsides in residential sectorsof electricity tariff. Such examples represent verylarge deviations between public and private costs.Subsidies are transfer payments used bygovernments to redistribute income or achieve some

other social objective. They do not represent the useof resources and hence are not a cost to economy.

Labour and Wages

Prices of labour should reflect the opportunity cost of its use.

In developing countries the opportunity cost of labours is

normally less than what the governments have fixed because

of high unemployment rate.

Example: Suppose in a country X, the monthly salary of a

professor is the same as that of a janitor. The opportunitycost of both men to the economy is not the same, one should

apply a shadow wage rate to reflect the real opportunity cost

of labour in economic analysis.


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Capital Charge and Discount Rates

The opportunity cost of capital is defined as discountrate, which is equal to the rate of return earned bythe marginal project in an investment portfolio. Inthe case of national economic development, theinvestment portfolio would consist of all projects to

be carried out within the capital budget constraint asdetermined by the availability of the foreignexchange and local currency. Economic analyst

suggests that true value of discount rate for society touse.

Fiscal Distortions, including Salestaxes, duties and Subsidies

• Price distortions by governments do not represent aresource cost and thus should be omitted from thecalculation of both benefits and costs.

• Border prices represents the economic costs and gains in terms of foreign exchange. Therefore, CIF(cost, insurance, freight) price for imports and FOB(free on board) price for exports - paid directly in

foreign exchange should be used. A good exampleis petroleum. Duties must be removed fromdomestic prices, i.e., prices of goods on the localmarket, to determine the economic cost.


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Fiscal Distortions, including Sales

taxes, duties and Subsidies (Cont’d)

• The distortions can be removed by simple

conversion factor used in border pricing called

Standard Conversion Factor (SCF) which is an

estimate of the average distortions between border

and local prices as measured by the ratio of total

trade excluding all duties, taxes and subsidies to the

actual recorded value of trade.

Other Price Adjustments

Apart from the above mentioned categories for shadow adjustments, there is another categorycalled Shadow Exchange Rate. In some countriesgovernment artificially adjust their currency ratewith dollars. Getting foreign exchange legally thereis difficult because the value is set artificially.Whereas foreign exchange available in black

market is much higher in price. In such countriesfor foreign exchange component of the costs, theshadow exchange rate should be used.


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Current Vs Constant PricesIt is important that the analysts understand the origin of any

price figures used in analytical work. Price deflators(inflators) must be used to convert earlier cost estimates to present-day prices or current costs to future prices. A mostcommon indicator used is the Consumer price index.

Consumer Price Index: Measure changes in price of a given basket of market goods

Criteria for Evaluation of ProjectsThere are three commonly used criteria for evaluating projects:

1. Present Worth Values

2. Yield

3. Payback or Capital Recovery Time

In the discussion that follows:

R t – denotes revenues (or benefits) in year t.Ct – denotes costs in year t

N – expected project life N time periods


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Criteria Based on Present Worth

Values

Four present worth criteria

i. Maximum net present worth

ii. Minimum present worth of costs

iii. Minimum present worth of unit costs

iv. Benefit-to-cost ratio

Maximum net present worth

All present worth criteria involves ranking

alternatives according to their net discounted

profits according to the difference between the

present value of benefits and the present value

of costs.

1


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Minimum Present Worth of Costs

With appropriate assumptions or corrections

for equality of service expected from each

alternative considered, the criterion of

minimum present worth of costs can be used.

1

Minimum Present Worth of Unit

Costs

It is almost same as above but it does, however, automatically

corrects for inequalities such as differences of size and

estimated operating lives. The unit generating cost of a

station whose construction, fueling and operation involve a

cost stream Ct, and whose energy output over time is

expected to be Et, is defined as:


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Benefit-to-Cost RatioThis criterion sometime is used in large power and water

projects by the ratios of the present worth values of revenues

to the present worth values of costs.

This formulation gives a measure of the discounted benefits per dollar of discounted costs.

Criteria Based on Yield

Internal Rate of Return

It is defined as the rate of discount at which the net presentworth of the operation becomes zero. To distinguish theinternal rate of return from the conventional discount rate, thesymbol r is used in the formulation.

: 0

1

Its advantage is, it is not using any discount rate. The projectcan be considered economical if internal rate of return is morethan acceptable discount rate.


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Criteria Based on Payback or Capital

Recovery TimeCriteria based on payback time have often been applied to plant selection both in planned economies and in privateenterprise. In general, the payback time T/ is defined byequation:

0

Short payback is preferable over longer payback period.

Ranking based on this criterion ignore the benefits and costs

that extend beyond the payback period and are often criticized as being ‘nearsighted’.

Criteria Based on Payback or CapitalRecovery Time (Cont’d)

If the cost stream Ct is broken down into an investment (I)that is made at one point in time, and variable costs (Ft)covering, for instance fuel, O&M costs in the case of a power plant, the above equation can be written in the followingform.

In this form, time T/ clearly appears as the time required for net operational revenues to payback the capital investment.


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Discounted Payback period

Discounted payback :

Some firm employ the discounted payback period, rather than the simple

payback period.

Ex : Our initial investment is 200

Year Cash flow

1 100.00

2 100.00 np = 2 years

3 81.70

4 100.00

Discounted cash flow at a 20% discount rate are:

Year Cash flow

1 83.30

2 69.94

3 47.30 np = 3 years

4 48.20

Example 1Suppose a new restaurant that just opened up had incurred an initial cost of $5000 and is expected to stay open for thenext 3 years. The net benefit for the next 3 years is expected to be $3000 per year. What is the net present worth of theinvestment? Should the investment have to be invested?The discount rate is 9%.

Solution: Apply the equation for net present worth (NPV)

C0 = $ -5,000

R 1 = R 2 = R 3 = $3,000

then NPV=-5000+3000*(1/1.09)+3000*(1/1.09)2+3000*(1/1.09)3

NPV = $2593.88

Therefore, the project should be accepted, since NPV>0


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Example 2

Find the internal rate of return (IRR) for the aboveexample.

0 = -5,000 + 3000{1/(1+r%) + 1/(1+r%)2

+1/(1+r%)3}

Solving this equation gives an IRR of 36.31%which is much higher than the opportunity cost ofcapital (9% in this example).

Example 3

Project C0 R 1 IRR,% NPV@10%

A -100 +200 100 82

B -10,000 +15,000 50 3,636

Both are good project, but B has the higher NPV and is,therefore, better. However, the IRR rule seems to indicatethat if you have to choose, you should go for A since it has

the higher IRR. If you follow the IRR rule, you have thesatisfaction of earning a 100% rate of return; if you followthe NPV rule, you are 3,636 richer.


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Example 4

Cash Flow($) Projects

A B C

C0 -2000 -2000 -2000

R 1 +1000 0 +1000

R 2 +1000 +2000 +1000

R 3 +5000 +5000 +100,000

NPV@10% +3,492 +3,409 +74,867

Payback Period (yrs) 2 2 2

The payback rule says that they all are equally attractive.But according to NPV the project C is the best project.

Example 5

Project C0 R 1 NPV@10 B/C ratio

A -100 +220 100 2

B -10,000 +14,000 2,727 1.27

Both are acceptable projects, since the benefit-to-cost ratio

in both cases are greater than 1.0. Using the benefit-cost

ratio as tool of evaluation, we ought to choose project A.

However, project B has a much higher NPV.


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Conclusions

• In case where a discount rate is reasonablyestablished, present worth analysis is certainly themost comprehensive approach.

• When discount rate is unknown or fixed atartificial level, the rate of return provide moreuseful information.

• Payback criterion is useful for quick preliminaryassessments.

Example 6

Consider a hydroelectric project with a capacity of 120MW, average annual energy generation of 600GWh/yr, a total cost of $150 million a construction

period of 5 years with cost disbursements of 20%each year, and a useful economic lifetime of 50 yearsafter the start of operation. The annual operation and maintenance costs will be $1,500,000/yr and theinterest rate is 12%. There is no inflation. Find theaverage unit cost of energy.


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Example 6 (Cont’d)Solution: The future value of construction costs, which isequal to the construction cost plus accumulated Interest

During Construction, (IDC), called Capitalized cost is

calculated at the end of year 5, which is the project

commissioning date.

Construction

year

Construction

Cost

Future value

Factor @12%

Original Cost

and IDC

1 30,000,000 1.574 47,220,000

2 30,000,000 1.405 42,150,000

3 30,000,000 1.254 37,620,000

4 30,000,000 1.120 33,600,0005 30,000,000 1.000 30,000,000

Total 190,590,000

Example 6 (Cont’d)It is assumed that all construction costs are paid at the end of each year,and also that all O&M costs and annual benefits occur at the end of eachyear.

The levelized annual capital cost or annual fixed investment charge is

CRF(50 yr, 12%)*Capitalized Cost

12.04% * $190,590,000 = $22,947,000/yr

Add annual O&M costs = $ 1,500,000/yr

Total uniform annual cost = $24,447,000/yr

Now divide by annual benefits to calculate the average unit cost of energy.

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Engineering Economicsvdvdv Moodle