che 425 engineering economics and design...
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Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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CHE 425 CHE 425
Engineering Economics and Engineering Economics and Design PrinciplesDesign Principles
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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.
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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.
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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.
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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What if Interest Rate Changes with Time?What if Interest Rate Changes with Time?
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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)
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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IN COMPARING ALTERNATIVES, THE EFFECTIVE ANNUAL RATE
AND NOT THE NOMINAL ANNUALRATE OF INTEREST MUST BE USED
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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.
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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TYPES OF CFDs
CASH FLOW DIAGRAMS
(CFD)
DISCRETECFD
CUMULATIVECFD
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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Cumulative CFD (cont.)Cumulative CFD (cont.)
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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Cumulative CFD (cont.)Cumulative CFD (cont.)
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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Cumulative CFD (cont.)Cumulative CFD (cont.)
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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AnnuitiesAnnuities
1 2 3 n
Uniform series of equally spaced – equal value cash flows
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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AnnuitiesAnnuitiesWhat is future value What is future value FFnn = ? = ?
Geometric progressionGeometric progression
( ) ( ) AiAiAF nnn .....11 21 ++++= −−
( )⎥⎦
⎤⎢⎣
⎡ −+==
iiASF
n
nn11
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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 ++=
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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)
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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Straight LineStraight Line
⎟⎠⎞
⎜⎝⎛ −
=n
SFCId LSL
k
n = # of years
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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Sum of Years Digits (SOYD)Sum of Years Digits (SOYD)
( )( )[ ]( )1
21
1
+
−−+=
nn
SFCIknd LSOYDk
SOYD
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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Double Declining Balance (DDB)Double Declining Balance (DDB)
⎥⎦
⎤⎢⎣
⎡−= ∑
−
=
1
0
2 k
jjL
DDBk dFCI
nd
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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Example 7.21Example 7.21
207
101501
71010$
10150$6
6
=−
=
=×=
×=
SL
st
L
d
Year
nS
FCI
Same for Years 1-7
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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
Prof. Adnan AlamerChemical Engineering Dept., KFUPM.
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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