INEN 2273v2

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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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Documents

INEN 2273v2