che 425 engineering economics and design...

Prof. Adnan AlamerChemical Engineering Dept., KFUPM.

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CHE 425 CHE 425

Engineering Economics and Engineering Economics and Design PrinciplesDesign Principles


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CHAPTER 7CHAPTER 7


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The The goal goal of any manufacturing of any manufacturing company is to make company is to make money money

Chemical Chemical ProcessingProcessingCompanyCompany

LowLow--ValueValueRaw Raw

MaterialsMaterials

HighHigh--Value Value ChemicalsChemicals

INTRODUCTION


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INTRODUCTION (Cont.)INTRODUCTION (Cont.)Purpose of Chapter

To discuss theTo discuss the principles of economic principles of economic analysisanalysis

ImportanceImportanceThis chapter covers all of the major This chapter covers all of the major topics required for completion of the topics required for completion of the Fundamentals of Engineering (FE) Fundamentals of Engineering (FE) examination.examination.


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TIME VALUE OF MONEY

PersonalIncome

Living Mainenance(Food, Clothing,

Housing, etc.)

DiscretionaryMoney

Consume as received Retain for futureconsumption

Simple saving Investment


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DefinitionsPP –– Principal or Present Value (of an investment) Principal or Present Value (of an investment)

FFnn –– Future Value (of an investment) Future Value (of an investment)

nn –– Years ( or other time unit) between Years ( or other time unit) between PP and and F F

ii –– Interest Rate (based on time interval for Interest Rate (based on time interval for nn) per ) per anumanum

Basis premise: Money when invested earns money. Basis premise: Money when invested earns money.

$1 today is worth more than $1 in the Future.$1 today is worth more than $1 in the Future.


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Money when invested earns money.Money when invested earns money.

$1 today is worth more than $1 $1 today is worth more than $1 in the future.in the future.


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DEFINION OF INVESTMENT


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SR100 today is worth SR100 today is worth more than more than

SR100 in the future.SR100 in the future.

TIME VALUE OF MONEY


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InterestInterestSimple Interest Simple Interest –– Annual Basis Annual Basis

Interest paid in any year = Interest paid in any year = PiPiss

PiPiss –– Fraction of investment paid as Fraction of investment paid as interest per year interest per year

After After nn years total interest paid =years total interest paid = PiPissnnTotal investment is worth = Total investment is worth = PP + + PiPissnnCould earn interest on earned interest Could earn interest on earned interest


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InterestCompound Interest Compound Interest

At time 0 we have P At time 0 we have P At the end of Year 1, we have At the end of Year 1, we have FF11 = = PP (1 + (1 + ii) ) At the end of Year 2, we have At the end of Year 2, we have FF22 = = PP (1 + (1 + ii))2 2

At the end of Year n, we have At the end of Year n, we have FFnn = = PP (1 + (1 + ii))nn

or or PP = = FFnn / (1 + / (1 + ii))nn


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Interest

SIMPLE INTEREST

COMPOUND INTEREST


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ExampleHow much would i need to invest at 8 % How much would i need to invest at 8 % p.a. to yield $5000 in 10 years p.a. to yield $5000 in 10 years

( )97.2315$

08.015000

500010

08.0

10

10

=+

=

===

P

Fni


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Example


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Example (cont.)


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What if Interest Rate Changes with Time?What if Interest Rate Changes with Time?


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Different Time Basis for Interest CalculationsRelates to statement Relates to statement ““Your loan is 6 % p.a. Your loan is 6 % p.a. compounded monthlycompounded monthly””

Define actual interest rate per compounding Define actual interest rate per compounding period as period as rr

iinomnom = Nominal annual interest rate= Nominal annual interest rate

mm = Number of compounding periods = Number of compounding periods per year (12)per year (12)


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Different Time Basis for Interest Calculations (cont.)

iieffeff = Effective annual interest rate= Effective annual interest rate

Look at condition after 1 yearLook at condition after 1 year

mir nom=

( )1 1 effF P i= +

11 −⎟⎠⎞

⎜⎝⎛ +=

mnom

eff mii


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ExampleExampleInvest $1000 at 10 % p.a. compounded Invest $1000 at 10 % p.a. compounded monthly. How much do I have in 1 year, 10 monthly. How much do I have in 1 year, 10 years?years?

( ) 04.2707$1

1047.011210.01

71.1104$1210.0110001

1010

12

12

1

=+=

=−⎟⎠⎞

⎜⎝⎛ +=

=⎟⎠⎞

⎜⎝⎛ +=⎟

⎠⎞

⎜⎝⎛ +=

eff

eff

mnom

iPF

i

miPF


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Example (cont.)Example (cont.)

As m decreases As m decreases iieffeff increases increases Is there a limit as Is there a limit as mm goes to infinity goes to infinity

Yes Yes –– continuously compounded interest continuously compounded interest Derivation Derivation –– pp. 229pp. 229--230 230 iieffeff (continuous) = (continuous) = eeiinomnom –– 11


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IN COMPARING ALTERNATIVES, THE EFFECTIVE ANNUAL RATE

AND NOT THE NOMINAL ANNUALRATE OF INTEREST MUST BE USED


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Cash Flow Diagrams (CFD)Cash Flow Diagrams (CFD)Represent timings and approximate Represent timings and approximate magnitude of investment on a CFD magnitude of investment on a CFD

xx--axis is time and axis is time and yy--axis is magnitude axis is magnitude both positive and negative investments both positive and negative investments are possible. are possible.

In order to determine direction (sign) of In order to determine direction (sign) of cash flows, we must define what system is cash flows, we must define what system is being considered. being considered.


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TYPES OF CFDs

CASH FLOW DIAGRAMS

(CFD)

DISCRETECFD

CUMULATIVECFD


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Discrete CFDDiscrete CFD


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Cumulative CFDCumulative CFD

Cumulative CFD


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Cumulative CFD (cont.)Cumulative CFD (cont.)


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Calculations from CFDCalculations from CFD


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Calculations from CFDCalculations from CFD


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Calculations with Cash Flow DiagramsCalculations with Cash Flow Diagrams

Invest 5K, 1K, 2K at End of Years 0, 1, 3, Invest 5K, 1K, 2K at End of Years 0, 1, 3, and take 3K at End of Year 4and take 3K at End of Year 4

0

$3000

$2000$1000

$5000

374

1


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Example 1Example 1How much in account at end of Year 7 if i How much in account at end of Year 7 if i = 8% p.a. = 8% p.a.

What would investment at Year 0 be to get What would investment at Year 0 be to get this amount at Year 7 this amount at Year 7

( ) ( ) ( )( )

84.9097$08.013000

08.01200008.01100008.01000,5

7

3

4677

=+−

+++++=

F

F

( )50.5308

08.184.9097

7 ==P


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Example 2Example 2What should my annual monthly car What should my annual monthly car payment be if interest rate is 8% p.a. payment be if interest rate is 8% p.a. compounded monthly?compounded monthly?

$20,000

A


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Example 2 cont.Example 2 cont.Compare at Compare at nn = 60 = 60

53.405$090.2979647.73

90.2979612

08.01000,20

47.73

1208.0

112

08.01

60

60

60

60

==−

−=⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +−=

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡−⎟

⎠⎞

⎜⎝⎛ +

=

AA

F

AAF


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AnnuitiesAnnuities

1 2 3 n

Uniform series of equally spaced – equal value cash flows


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AnnuitiesAnnuitiesWhat is future value What is future value FFnn = ? = ?

Geometric progressionGeometric progression

( ) ( ) AiAiAF nnn .....11 21 ++++= −−

( )⎥⎦

⎤⎢⎣

⎡ −+==

iiASF

n

nn11


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Discount FactorsDiscount Factors

Just a shorthand symbol for a formula in Just a shorthand symbol for a formula in iiand and nn

( ) ( )

( )( )( )n

n

n

nn

iiini

FPPA

iFni

FPFP

ini

FP

iFP

+−+

=⎟⎠⎞

⎜⎝⎛⇒→⇒

⎟⎟⎠

⎞⎜⎜⎝

⎛

+=⎟

⎠⎞

⎜⎝⎛=⇒

+=⎟

⎠⎞

⎜⎝⎛⇒

+=

111,,

11,,

11,,

1

Table 7.1


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Example 7.14Example 7.14


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DepreciationDepreciationTotal Capital Investment = Fixed Capital Total Capital Investment = Fixed Capital + Working Capital + Working Capital

Fixed Capital Fixed Capital –– All costs associated All costs associated with new construction, but with new construction, but LandLand cannot cannot be depreciated be depreciated Working Capital Working Capital –– Float of money to Float of money to start operationsstart operations

WCLandFCITCI L ++=


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DefinitionsDefinitionsSalvage Value Salvage Value

Value of Value of FCIFCILL at end of project at end of project Often = 0 Often = 0

Life of Equipment Life of Equipment nn –– Set by IRS Set by IRS

Not related to actual equipment life Not related to actual equipment life Total Capital for Depreciation Total Capital for Depreciation

FCIFCILL -- SS


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3 Basic Methods for Depreciation3 Basic Methods for Depreciation

Straight Line Straight Line Sum of Years Digits (SOYD) Sum of Years Digits (SOYD) Double Double DeruningDeruning Balance (DDB)Balance (DDB)


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Straight LineStraight Line

⎟⎠⎞

⎜⎝⎛ −

=n

SFCId LSL

k

n = # of years


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Sum of Years Digits (SOYD)Sum of Years Digits (SOYD)

( )( )[ ]( )1

21

1

+

−−+=

nn

SFCIknd LSOYDk

SOYD


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Double Declining Balance (DDB)Double Declining Balance (DDB)

⎥⎦

⎤⎢⎣

⎡−= ∑

−

=

1

0

2 k

jjL

DDBk dFCI

nd


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Example 7.21Example 7.21

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101501

71010$

10150$6

6

=−

=

=×=

×=

SL

st

L

d

Year

nS

FCI

Same for Years 1-7


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Example 7.21 (contExample 7.21 (cont’’d)d)

( )( )( )

[ ] [ ]

( )( )( )

[ ] [ ]

( )

( ) 6.309.4215072

9.4215072

301015028610150

8721

217

351015028710150

8721

117

2

1

2

1

=−=

==

=−=−−+

=

=−=−−+

=

DDB

DDB

SOYD

SOYD

d

d

d

d


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Taxation, Cash Flow, and ProfitTaxation, Cash Flow, and Profit

Tables 7.3 Tables 7.3 –– 7.4 7.4 Expenses = Expenses = COMCOMdd + + ddkk

Income Tax = (Income Tax = (RR –– COMCOMdd -- ddkk))ttAfter Tax (After Tax (net)Profitnet)Profit = = ((RR –– COMCOMdd ––ddkk)(1 )(1 –– tt) ) After Tax Cash Flow = After Tax Cash Flow = ((RR –– COMCOMdd –– ddkk)(1 )(1 –– tt) + ) + ddkk


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InflationInflation

$ Now Net Worth vs. $ Next Year $ Now Net Worth vs. $ Next Year

ff = Average inflation rate between Years = Average inflation rate between Years jjand and nn

( ) ( ) ( )jCEPCIfnjCEPCI n+=+ 1

fififii

+−

=−≅'

che 425 engineering economics and design...

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