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INEN 2273 EngineeringEconomics
Dr. Alberto Marquez
Lamar University
[email protected] Engineering Department
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Introduction
Time value of Money
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Time value of money Opportunity cost
Not the same as inflation
Section 2.1
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Cash flow A cash flow represents the
money that will come out of or
into the investor as aconsequence of the developmentof the project.
Section 2.1
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Financial Science FS is the application of scientific tools
to investments
There is an art to the investment aswell.
Section 2.1
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Some relevant terms Capital
Interest
Present value
Future Value
Annuity
Internal rate of return
Minimum acceptable
rate of return
Simple interest
CompoundedInterest
Inflation
Taxes
Depreciation
Bonds
Section 2.1
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Cash flow series A series is a chain of flows that can
be represented by a diagram.
They could be periodic or not. Cash flow diagrams
Section 2.2
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Main formulae
Present value, future value,annuities, equivalences
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Compound interest
nirrn
n
nn
,,)1(
)1(1
!!
!
Section 2.4
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Single Amount:
Factor Notation and Formula:
!
!
n
n
i
ni
ini
1
1,,
1,,
Section 2.4
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Sample Cash Flow Diagram:
Single Amount
t=1 t=2 t=3 t=4 t=5 t=6 t=7 t=8 t=9
Section 2.4
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Series of cash flows
!!
!!
!!
!!
n
t
t
n
t
tn
t
n
t
t
n
t
t
t
tniPFAiAF
tiFPAiAP
11
11
,,)1(
,,)1(
Section 2.5
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Uniform Series:
Factor Notation and Formula:
-
!
-
!
1)1(
)1(,,|
)1(1)1(,,|
n
n
n
n
i
iiPniPAP
iiiAniAPA
Present
Worth
CapitalRecovery
Section 2.5.1
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Sample Cash Flow Diagram:
Uniform Flows
t=1 t=2 t=3 t=4 t=5 t=6 t=7 t=8 t=9
Section 2.5.1
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Uniform Series:
Factor Notation and Formula
1)1(
1)1(
!
!
n
n
i
ii
i
Section 2.5.1
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Internal rate of return=IRR
!
!
!
!
n
0t
*jt
n
0t
*
jt
i1A0
i1A0
t
tn
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Equivalence Two cash flow
series areequivalent at some
specified interestrate k% if theirpresent worth areequal using an
interest rate of k%
Example at 10%
$1,000 today
$1,100 in one year
$1,210 in two years
$576.1905 in eachyear, end of years 1and 2.
402.1 in each year,end of years 1through 3
Section 2.8
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Mathematical relationships
niFA
niFA
niAPniPA
niFPniPF
,,
1,,
,,
1,,
,,
1,,
!
!
!
!
!
!
!
!
n
t
n
t
nini
tini
inini
1
1
,,
1
,,
1
,,,,
,,,,
Section 3.6
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Mathematical relationships
mn
niFPmiFPnmiFP
miFP
niFPmniFP
miFPniFPmniFP
,,,,,,
,,
,,,,
,,,,,,
!!v
!
v!
Section 3.6
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Multiple compounding periods Nominal interests
Effective interest
Actual (real) interest Ex.: anticipated paid interest
Section 2.6
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Effective interest rate
11 nominaleffective
!
m
m
ri
Section 2.6
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Solutions using MS Excel Present value: PV(i%,n,A,F)
Present value: NPV( i%, Range)
Future Value: FV(i%,n,A,P) Annuity (A): PMT(i%,n,P,F)
Periods (n): NPER(i%,A,P,F)
Internal rate of return based on parameters
(irr): RATE(n,A,P,F) Internal rate of return based on flows (i):
IRR(Range)Section 2.9
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Building a spreadsheet
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Applications
Loan payment, Bonds, Projectcomparison, Measuring the worth ofinvestments
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Loan payments
Principal amount
Interest amount
Section 3.4
? A
1,,
1,,1
),,(1
,,
,,
1
!
!
!
!
!
!!
!
tniAPAEIAE
tniAPAI
iUI
tniAPAPayoff
tniAPAAUAPayoff
tniAPAU
t
tt
t
tt
t
tt
t
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Amortization scheduleP=100K, i=5%, n=5
Section 3.4
Period BeginningBalance
Interest PrincipalPayment
Totalpayment
New Balance
1 $100,000. $5,000.00 $18,097.48 $23,097.48 $81,902.52
2 $81,902.52 $4,095.12 $19,002.35 $23,097.48 $62,900.17
3 $62,900.17 $3,145.00 $19,952.47 $23,097.48 $42,947.69
4 $42,947.69 $2,147.38 $20,950.10 $23,097.48 $21,997.60
5 $21,997.60 $1,099.88 $21,997.60 $23,097.48 $0.00
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Bond Problems
Section 3.5
niFPFniAPVrPbond
,,,, !
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Measuring the Worth ofInvestments
PW,AW, FW, IRR, ERR,SIR,PBP,CW
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Alternative Evaluation Criteria Net present value
Future Value
Annuity Internal rate of return
Section 2.9
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NPV comparisonSame project life time.One alternative
1. Calculate the NPV with MARR.
2. Si NPV>0 then MARR is achievedand the project is accepted
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NPV comparisonSame project lifetime. Multiple alternatives
1. Calculate the NPV of each alternative
with MARR2. Select the alternative with the
highest NPV
3. If selecting more than one, select allthose where NPV>0.
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NPV for projects with differentlifetimes
To compare using NPV, the same projectlifetime should be used across all thealternatives A) Use the same period using a minimum
common multiple of the alternative periods
B) Use a period ofn years that will notnecessarily be the equivalent of the lifetime ofall the alternatives. This method is know as
planning horizon.
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Present Worth - PW
!
!
n
t
t
jtj iAiPW 0 )1(
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Annual Worth - AW
niiWiW
niniiW
jj
n
t
jtj
,,
,,,,0
!
-
!
!
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Future Worth - FW
!
!
n
t
tn
jtj iiW0
)1(
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Internal rate of return
IRR is the rate that turns the value ofthe project to cero.
It is called internal because it doesnot depend of other rates/
In the practical mathematical solutionthere could be more than one real
positive IRR.
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Internal rate of return - IRR
!
!
n
t
tn
jjt i0
*
)1(0
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MARR vs. TIR
costapital"u MARRIRR
Zero risk investment return
MARR
IRR current pro ects
IRR future pro ects
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External rate of return
ERR, similar as IRR, is the rate thatturns the value of the project to cero.
Alternative when there could is morethan one real positive IRR.
Separates positive cash flows (R forrevenue) from negative cash flows (C
for costs)
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External rate of return - ERR
!
!
!
!
!
n
t
tn
jtjt
n
t
tn
jt
n
t
tn
tjt
iCR
iCrR
0
00
*
)'1)((0
)'1()1(
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Savings/investment ratio - SIR
!
!
!n
t
tn
jt
n
t
tn
jt
j
iC
iR
iSIR
0
0
)1(
)1(
)(
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Payback period - PBP
0
0
!
!
u jtm
t
jt CRj
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Capitalized worth - CW
i
AP!
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Capital Recovery Formula
niniCR ,,,, !
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Further MathematicalDevelopments
Gradient, continuous compounding
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Arithmetic Gradient
!
!
1)1(
1)1(
1)1(2
n
n
n
i
n
iGA
ii
iniGP
Section 2.5.2
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Geometric Gradient:Factor Notation and Formula
!
{
-
!
ig1
1
11
1
1
in
iggi
i
gn
g
Section 2.5.2
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Continuous compounding
Section 2.7/2.71
1
),,(
1
eff
lim
!
!
!
!
g
gp
r
rn
rn
mn
m
ei
nr
eF
e
m
r
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Rule of 70%
Used to calculate the required period toduplicate capital
Approximated formula:
in
70!r
0.7n !
Section 2.7
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Reality issues
Changing interest ratesInflationTaxes
Depreciation
Section 3.1
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Changing interest rates
Section 3.2
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Inflation
i=combinedinterest rate
d=desired return
j=inflation rate
djjdi
jdi
!
! 111
Section 3.3
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Corporation Theoryand Costs Concepts
Cost terminology
Break-even point
Estimation
Section 8.1/8.2/8.3
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Cost terminology
Life cycle costs
Past and sunk costs
Future and opportunity costs Direct, indirect and overhead costs
Fixed and variable costs
Average and marginal costs
Section 8.1
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Cost terminologyLife cycle costs
First cost
Working capital
Operating and maintenance costs Disposal costs
Market or trade-in value
Salvage value
Book value
Scrap value
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Cost structurefor manufacturing
Direct material
Direct labor
Indirect material
Indirect labor
Fixed and miscellaneous
General and Administrative
Selling
Profit
Primecosts
FactoryOverhead
costs
Cost of goodsmanufactured
Cost ofgoodssold
Conversioncosts
Sellingprice
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Break-even point
Section 8.2
Fixed costs
Variable costs
Fixed + Variablecosts
RevenueBreaking even
Break even point
Profit
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Estimation
Section 8.3
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General Accounting principles
Balance sheet
Income statement
Ratio analysis
Section 8.4
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ASSETS
LIABILITIESNET WORTH
+
+
-
+--
SUPPLIERSCUSTOMERS
Everything should be recorded twice: once on the right, once on the left
A=L+NW
General Accounting Principles
Section 8.4
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Sample balance sheetJ a x t o o l a n d E n g i n e e r i n g C o m p a n y
B a l a n c e S h e e t a s o f d a t e
A s s e t s
C u r r e n t a s s e t s
C a s h 2 5 , 0 0 0$
A c c o u n t s r e c e i v a b l e 1 1 5 , 0 0 0$
R a w m a t e r i a l s 8 , 5 0 0$
W o r k i n p r o c e s s 7 , 0 0 0$
F i n i s h e d g o o d s i n v e n t o r y 3 , 0 0 0$
S m a l l t o o l i n v e n t o r y 1 2 , 5 0 0$
T o t a l c u r r e n t a s s e t s 1 7 1 , 0 0 0$
F i x e d a s s e t s
L a n d 3 0 , 0 0 0$
B u i l d i n g 2 0 0 , 0 0 0$
L e s s D e p re c i a t i o n r e s e r v e 5 0 , 0 0 0$ 1 5 0 , 0 0 0$
E q u i p m e n t 7 5 0 , 0 0 0$
L e s s D e p r e c i a t i o n r e s e rv e 1 5 0 , 0 0 0$ 6 0 0 , 0 0 0$
O f f i c e e q u i p m e n t 1 0 , 0 0 0$
T o t a l f i x e d a s s e t s 7 9 0 , 0 0 0$
T o t a l a s s e t 9 6 1 , 0 0 0$
L i a b i l i t i e s a n d N e t W o r t h
C u r r e n t l ia b i li t ie s
A c c o u n t s p a y a b l e 3 2 , 0 0 0 . 0 0$
T a x p a y a b l e 1 5 , 0 0 0 . 0 0$
T o t a l c u r r e n t l i a b i l i t i e s 4 7 , 0 0 0 . 0 0$
F i x e d l i a b i li t i e sM o r t g a g e l o a n p a y a b l e 1 3 0 , 0 0 0 . 0 0$
E q u i p m e n t l o a n p a y a b l e 3 5 0 , 0 0 0 . 0 0$
T o t a l f i x e d l i a b i l i t i e s 4 8 0 , 0 0 0 . 0 0$
T o t a l L i a b i l i t i e s 5 2 7 , 0 0 0 . 0 0$
N e t w o r t h
C o m m o n s t o c k 3 2 5 , 0 0 0 . 0 0$
R e t a i n e d e a r n i n g s 8 0 , 0 0 0 . 0 0$
E a r n e d s u r p l u s 2 9 , 0 0 0 . 0 0$
T o t a l e q u i t y 4 3 4 , 0 0 0 . 0 0$
T o t a l l i a b i l i t i e s a n d e q u i t y 9 6 1 , 0 0 0 . 0 0$Section 8.4
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Sample Income StatementCommercial
Jax Tool and Engineering company inc
Income statement period from date1 to date 2
Sales 1,200,000$
Less cost of good soldInitial Inventory 26,000$
Plus purchases 432,000$
Final Inventory 44,000$ 414,000$
Gross profit 786,000$
Less expenses
Direct labor 420,000$
Depreciation building 10,000$Depreciation equipment 30,000$
Repars and maintenance 41,500$
Indirect labor 218,000$
Utilities 9,800$Supplies Tooling 1,700$ 731,000$
Net profit before taxes 55,000$
Less income taxes 26,000$
Net profit (posted to earned surplus) 29,000$
Section 8.4
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Ratio Analysis
AssetsTotal
IncomeOperatingNet
ChargesInterest
interestandtaxesincomebeforeIncomerNet
WorthCapitalTotal
sLiabilitieTotal
inventoryAverage
soldgoodsofCost
ReceivableAccountAverage
salesNet
sliabilitiecurrent
securitiesemarkeatablterm-shortsreceivablecash
sliabilitieCurrent
assetsCurrent
EquitysOwner'Average
incomeNet
AssetsAverageTotal
incomeNet
!
!
!
!
!
!
!
!
!
OIT
TI R
DER
IT
RT
TR
CR
ROE
ROA
Section 8.4
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Ratio AnalysisOkie
anufacturing Okie Manufacturing
Co
parative Balance Sheets Co
parative inco
e State
ents 19X6 19X5
ASSETS Net s
les 1,625,450$ 1,450,000$
Current assets 19X6 19X5 Cost of goodss
ldCash 61,750$ 83,520$ Beginning In entory 50,000$ 40,000$
Acc
untsRecei
le 195,000$ 130,500$ Direct M
teri
ls 406,000$ 350,000$
In entory 65,000$ 50,000$ Direct Labor 801,500$ 700,000$Prepaid Expenses
,750$ 31,900$ F
ctory O erhead 94,603$ 90,000$T talcurrent assets 344,500$ 295,920$ T tal 1,352,103$ 1,180,000$
Fixed assets Less ending in entory 65,000$ 50,000$M
chienry
08,000$ 187,830$ Cost of goodss
ld 1,287,103$ 1,130,000$
Furniture 74,750$ 72,500$ Gr
ss pr
fit 338,347$ 320,000$Other
,750$ 23,750$ Otheroper ting expensesT
talFixed Assets 305,500$ 284,080$ Selling expenses 43,980$ 37,200$
T
tal assets 650,000$ 580,000$ Gener
l and Ad
inistr
ti e 180,606$ 174,370$
T tal OtherOper ting Expenses
4,586$ 211,570$
LIABILITIES & CAPITAL Net Oper
ting Inc
e 113,761$ 108,430$Current li
ilities Less Interest Expenses
1,600$ 18,000$
N tes pay
le 92,950$ 87,000$ Net inc e before taxes 92,161$ 90,430$
Acc unts pay
le 147,212$ 109,653$ Less Inc e T xes 40,188$ 39,400$T
xes pay
le 69,438$ 64,920$ Net Inc
e 51,973$ 51,030$
T talcurrent li
ilities 309,600$ 261,573$
Fixed li
ilities
Loans 100,000$ 90,000$
T
tal fixed li
ilities 100,000$ 90,000$T talli
ilities 409,600$ 351,573$
Capital
Stock 100,000$ 100,000$ Return on assets 8.45%Retained earnings 88,427$ 77,397$ Return on Owners Equity
.17%
Earned surplus 51,973$ 51,030$ Current R
ti
1.1127
T
talc
pital
40,400$ 228,427$ Acit Test R
ti
0.8293T talli
ilities and c pital 650,000$ 580,000$ Acc untsrecei
le turno er 9.987
In entoryTurno er
.3844
Debto to equityr ti 1.7038
Ti esinterest earned r ti 5.2667Oper
ting inc
e to T
talAssets 0.17502Section 8.4
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Comparison of Alternatives
Investment alternatives, planning horizon,cash flow profiles, specifying MARR, Cost ofcapital, comparing methods, replacement
analysis
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Developing investment alternatives
Section 5.2
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Defining the planning horizon
Section 5.3
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Developing cash flow profiles
Section 5.4
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The cost of capital
Section 5.5.1
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Comparing investment alternatives
Ranking approach
Incremental approach
Section 5.6
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Replacement analysis
Section 5.11
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Optimum replacement interval
Section 5.11.3
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Income Taxes andDepreciation
Depreciation, Income taxes, Effectsof interest on borrowed money
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Depreciation
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Taxes
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