7-Engineering Economics 2014

7/25/2019 7-Engineering Economics 2014

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ME395: Introduction to Mechanical Design

MECHANICAL ENGINEERING


Engineering Economics

Based on

White, J.A (1990) Engineering Economics,

Chapter 15 in Eshbach's andboo! o"

Engineering #$ndamenta%s (&th Edition), John

Wi%e ons(a*ai%ab%e on+%ine thro$gh the W -ibraries)

Joyce Cooper

esign "or En*ironment -ab

ni*ersit o" Washington

cooper/s$.ashington.ed$

UWME DFE Lab:

http233"ac$%t.ashington.ed$3cooper/s3

4%an,

decompose, benchmar!

#orm$%ate ana%e

Comm$nicate /$sti"


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Solid Fuels Processing Technologies


Engineering economics

6n essence, design decisions are economic decisions.

7er "e sit$ations e8ist in hich there are not a%ternati*e materia%s,processes, and phsica% designs a*ai%ab%e to the engineer and each

a%ternati*e has di""erent costs associated ith it.

:he economics o" engineering decisions m$st be *ieed "rom

a broad perspecti*e. :he %i"e+cc%e cost o" a prod$ct is the tota% cost o" design, prod$ction,

maintenance, s$bse;$ent rep%acements o*er the %i"e o" the prod$ct

and retirement of the product.

esign choices dictate a broad set o" costs (e.g., scres *s. snap "itsimpact assemb%, maintenance, and recc%ing costs).


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:pica% economic decisions con"ronting engineers are ne

prod$ct or process introd$ction, %ease *ers$s b$, ma!e

*ers$s b$, rep%acement o" machiner and e;$ipment,

process modi"ication, and capacit e8pansion.

6n per"orming economic comparisons o" engineeringa%ternati*es, it is recommended that a cash "%o approach be

ta!en.

ere, an end+o"+period cash "%o con*ention is $sed. peci"ica%%,

hen the period is e;$a% to a ear, an receipts or disb$rsementsocc$rring d$ring a ear i%% be shon as occ$rring at the end o" the

ear and the present is considered to be the end o" ear zero.

We $se this con*ention in ma!ing cash "%o diagrams.


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Cash "%o diagrams Cash "%o diagrams are $sed to depict the timing and

magnit$des o" the cash "%o amo$nts in the present "$t$re.

4$rchase costs ann$a% e8pendit$res "or maintenance, energ, and%abor charges and sa%*age *a%$es occ$r in a cash "%o series.

Cash "%o diagrams Begin at ear 0 (no) and end at the end o" the pro/ect (ear n++ represents pro/ect horion)

Cash "%os each ear can be a combination o" receipts and paments & 5 ?


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:pes o" cash "%os

Single payment cash flow+ can occ$r at the beginning o" a time %ine

(t@0), at the end o" the time %ine (t@n), or an time in beteen.

Uniform series cash flow+ consists o" a series o" e;$a% transactions

starting at t@1 and ending at t@n. A is tpica%% $sed to represent

the magnit$de o" each "%o.

Uniform gradient cash flow+ starts ith a cash "%o (denoted as ) at t@=

and increases b each ear thro$gh t@n, at hich time the cash "%o is(n+1)

t=2

G

t=n

2G

3G

(n-1)G

t=1

A each

t=n

e.g., 6ncreasing

maintenance costs ith

aging e;$ipment

e.g., re*en$e (an $p arro) or

materia% costs (a don

arro)

e.g., e;$ipment costs

P

t=0


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Cash "%o diagrams

#or e8amp%e, a mechanica% de*ice i%% cost =0,000 hen p$rchased.

aintenance i%% cost 1,000 per ear. :he de*ice i%% generate re*en$eso" 5,000 each ear "or 5 ears, a"ter hich the sa%*age *a%$e is e8pected

to be D,000.

#rom #E


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:he time *a%$e o" mone

6n genera%,


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Simple nterest 6" 6 borro a present s$m o" mone or a principal P at a simple

interest rate i, the ann$a% cost o" interest is 6@4i. 6" 6 repa the %oan in a lump sum at the end o" n ears, the amo$nt oed

is2

Amo$nt oed @ 4 H n6 @ 4(1Hni)

#or e8amp%e, 6" 6 borro 1,000 "or ? ears at a simp%e interest rate o" 10I, at the end

o" the ? ears 6 oe2Amo$nt oed @4(1Hni)@1,0001H?(0.1)K@1,?00

here2

4@ princip%e or present orth

6@ ann$a% cost o" interest

i@ ann$a% interest rate

n@ n$mber o" ears


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Compo!nd nterest 6n compo$nd interest, the interest d$e at the end o" a period is not

paid o$t b$t is instead added to the principa%. :h$s, d$ring the ne8t

period, interest is paid on the tota% s$m.#irst period2 amo$nt oed1@4(1Hi)

econd period2 amo$nt oed=@ 4(1Hi)Hi4(1Hi)@ 4(1Hi)=

nth period2 amo$nt oedn@ 4(1Hi)n

imp%e *s. compo$nd interest #or 1,000 %oaned "or ? periods at 10I simp%e or compo$nd interest

Simple vs. Compound Interest

$0

$500

$1,000

$1,500

$2,000

0 1 2 3 4 5 6

End of Interest Period

Am

ountOwed

Simple Interest

Compound Interest

Simple Interest

period

(1) amount

ow ed at the

beginning of the

period

(2)=1,000 x 10%

interest amount

for period

(3)=(1)+(2)

amount

ow ed at the

end of the

period

1 $1,000 $100 $1,100 =1,000(1+.1)

2 $1,100 $100 $1,200 =1,000(1+.2)

3 $1,200 $100 $1,300 =1,000(1+.3)

4 $1,300 $100 $1,400 =1,000(1+.4)

5 $1,400 $100 $1,500 =1,000(1+.5)

6 $1,500 $100 $1,600 =1,000(1+.6)

Compound Interest

period

(4) amount

ow ed at the

beginning of

the period

(5)=(4)x10

% interest

amount for

period

(6)=(4)+(5)

amount ow ed

at the end of

the period

1 $1,000 $100 $1,100 =1,000(1.1)

2 $1,100 $110 $1,210 =1,000(1.1)^2

3 $1,210 $121 $1,331 =1,000(1.1)^3

4 $1,331 $133 $1,464 =1,000(1.1)^4

5 $1,464 $146 $1,611 =1,000(1.1)^5

6 $1,611 $161 $1,772 =1,000(1.1)^6

6n the reading, a%%

interest ca%c$%ationsare based on

compo$nd interest

rather than simp%e

interest.


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:ime *a%$e o" mone

:he interest rate $sed in ca%c$%ations is !non

as the e""ecti*e interest rate.

#or compo$nd interest2

6" compo$nding is once a ear, the interest rate isca%%ed an e""ecti*e ann$a% interest rate.

E""ecti*e ;$arter%, month%, or dai% interest rates are

a%so $sed.


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:he time *a%$e o" mone nemonic con*ention

:he amo$nt oed in the nth period is ca%%ed the "$t$re orth or "$t$re

*a%$e (#) ith "o%%oing mnemonic con*ention $sed2

# @ 4(1Hi)n

denoted as # @ 4(#L4 iI,n)

here (#L4 iI, n) can be stated as

#ind #, gi*en 4, $sing an interest rate o" iI o*er n ears.F

:he ;$antit (1 H i)n is re"erred to as the sing%e s$m, "$t$re orth

"actor and is genera%% ca%%ed a discounting factor DSC"U#$#% F&C$"'S ("or "$t$re and other timed "%os) are tab$%ated

in the appendi8 o" the reading.

WhMN beca$se sometimes e8ams do not a%%o o$ to bring a ca%c$%ator or $se E8ce%O.

here2

F ( the f!t!re )al!e or f!t!re worth

4@ princip%e or present orth

i@ ann$a% interest rate

n@ n$mber o" ears


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:ime *a%$e o" mone

6 p$t 1,000 in a ban! acco$nt that earns &I per ear. o m$ch

i%% 6 ha*e in 10 earsM :he 1,000 is re"erred to as the present *a%$e o" the in*estment. 6 am tring to

ca%c$%ate the "$t$re *a%$e o" the in*estment a"ter 10 ears.

# @ 4(#L4 iI,n) @ 4(1Hi)n

# @ 1000(1H0.0&)10 @ 1,&P0

We%% that is /$st not eno$gh, 6 ant G


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isco$nt "actors "or discrete compo$nding

#rom Engineering Economic Ana%sis, EIT Reference Manual,

4ro"essiona% 4$b%ications 6nc.

Factor Name Converts Symbol FormulaSingle payment compoundamount

P to F (F/P, i%, n) niPF )1( +=

Single payment present worth F to P (P/F, i%, n)n

iFP

+= )1( Uniform series sinking fund F to A (A/F, i%, n)

1)1( +=

ni

iFA

Capital recovery P to A (A/P, i%, n)

11

1

+

+=

n

n

)i(

)i(iPA

Uniform series compoundamount

A to F (F/A, i%, n)

iiAF

n

1)1( +

=

Uniform series present worth A to P (P/A, i%, n)n

n

)i(i

)i(AP

+

+=

1

11

Uniform gradient present worth G to P (P/G, i%, n)

+

+

+=

nn

n

)i(i

n

)i(i

)i(GP

11

112

Uniform gradient future worth G to F (F/G, i%, n)

+=

i

n

i

iGF

n

2

1)1(

Uniform gradient uniformseries

G to A (A/G, i%, n)

+

=

11

1n)i(

n

iGA

e.g., 4eriodic contrib$tion to 6


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sing disco$nt "actors2 consider the nationa% debt

#rom http233.bri%%ig.com3debtQc%oc!3 at ?21D this morning

#rom http233.treas$rdirect.go*3R43debt3c$rrent

And according to the :reas$rO


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sing disco$nt "actors

Concerning the nationa% debtO :he nationa% debt is S1D.9 tri%%ion. What is the re;$ired

pament per ear to comp%ete% pa o"" the debt in =0 ears,

ass$ming an interest rate o" ?IM

time0 1 = OO. =0

1D.9 tri%%ion

A A A

sing the capita% reco*erdisco$nt "actor ("or %oan repament)

A @ 4(AL4,?I,=0)

@ (1D.9 tri%%ion)T0.0PD=@ 1.5? tri%%ion per ear (hmm)

1)06.01(

)06.01(06.09.17$

20

20

+

+= trillionA

#rom http233.treas$rdirect.go*3R43debt3c$rrent


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sing disco$nt "actors ith cash "%o diagrams

4resent orth e;$i*a%ent #or an interest rate o" iI, the present worth e*!i)alent o" the cash "%o series is2

4 @ +=0,000(4L# iI,0) H &000(4L# iI,1) H &000(4L# iI,=) H &000(4L# iI,>) H &000(4L# iI,&)

H 11,000(4L# iI,5)

G

methods2 :he present orth (4W) or the ann$a% orth (AW)

Estimate the present orth "or a%% a%ternati*es G< estimate the ann$a%orth "or a%% a%ternati*es, and compare them.

6nterna% rate o" ret$rn (6


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endof

year(n cashflow

present

worthfactor

-134+2. 56

present

worth

e*!i)alent(@cash"%o

8

present

orth

"actor)

0 0 1 01 =,000 0.P>>> 1,??D

= =,000 0.?9&& 1,>P9

> =,000 0.5DPD 1,15D

& =,000 0.&P=> 9?5

5 =,000 0.&019 P0&

S!m(thepresentworthe*!i)alent 76,>


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Comparing a%ternati*es2

compare the incrementa% 6


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:he impact o" ta8es and depreciation

6n considering the impact o" ta8es on the economic per"ormance o"

a%ternati*es, it is necessar to consider depreciation. epreciation charges are considered beca$se

nder ta8 %a, depreciation charges are an a%%oab%e corporate ded$ction indetermining the income ta8 %iabi%it "or a "irm.

income ta8es are cash "%os and depreciation charges a""ect the sie o"the income ta8 paid

epreciation is an arti"icia% e8pense that spreads the p$rchase price

o" an asset or other propert o*er time.

:he inc%$sion o" depreciation increases the a"ter+ta8 present orth(pro"itabi%it) o" an asset.


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epreciation methods

4rior to the ear% 19P0s, a n$mber o" di""erent depreciationmethods ere $sed in the to determine ta8ab%e income.

Common% $se methods ere2

straight+%ine depreciation ass$mes a constant depreciation value

dec%ining ba%ance ass$mes a constant depreciation rate per ear.

acce%erated depreciation methods do$b%e dec%ining ba%ance

the dec%ining ba%ance depends on acc$m$%ated depreciation

s$m+o"+the+earXs+digits

depreciation is determined b m$%tip%ing the depreciab%e cost b a scheduleof fractions

n

SCD n

=

here

@ depreciation charge "or ear

C @ the p$rchase price and

n @ the e8pected sa%*age *a%$e


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epreciation methods

A"ter 19P1, the acce%erated cost reco*er sstem (AC


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:he depreciation o" st$""2AC+ear c%ass (A< midpoint o" U@& ears) s$ch as specia% too%s and de*ices $sed in theman$"act$re o" r$bber prod$cts, specia% hand%ing de*ices s$ch as ret$rnab%e pa%%ets, and

o*er+the+road tractors. :he 5+ear c%ass (A< midpoint o" &+10 ears) s$ch as comp$ters and periphera%s,

a$tomobi%es, b$sses, genera% carpets, and e%ectronic components.

:he D+ear c%ass (A< midpoint o" 10+1? ears) s$ch as o""ice "$rnit$re, rai%road cars and%ocomoti*es, and most prod$ction e;$ipment $sed to man$"act$re ood prod$cts, sporting

goods, /ee%r, m$sica% instr$ments, "i%ms, and tapes, among others. :he 10+ear c%ass (A< midpoint o" 1?+=0 ears) s$ch as assets $sed to man$"act$re tobacco

and certain "ood prod$cts, as e%% as that $sed in petro%e$m re"ining.

:he 15+ear c%ass (A< midpoint o" =0+=5 ears) s$ch as te%ephone distrib$tion e;$ipment,seage treatment p%ants, and assets $sed to prod$ce e%ectricit "or sa%e.

:he =0+ear c%ass (A< midpoint o" =5H ears rea% propert) s$ch as seer pipe, "armb$i%dings, rai%road steam or e%ectric generating e;$ipment, and te%ephone distrib$tion p%ants.

:he rea% propert c%ass is di*ided into residentia% and nonresidentia% residentia% propert isreco*ered o*er =D.5 ears and nonresidentia% propert is reco*ered o*er >1.5 ears.

A< @ assets depreciation range


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AC


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AC


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AC+ear reco*er propert. :he AC>>)@ ?,??? B1@=0,000+?,???@ 1>,>>&

=

@

=0,000(0.&&&&)

@

P,PPP B=

@

1>,>>&

+

P,PPP

@

&,&&?

>

@

=0,000(0.1&P=)

@

=,9?& B>

@

&,&&?

+

=,9?&

@

1,&P=

&@=0,000(0.0D&1)@ 1,&P= B&@1,&P=+1,&P=@ 0

For /(724,444Dt = dtP

So in 85years the boo? )al!e is @ero+ f yo!r

cash flow diagram had a hori@on of less than8 years, yo! wo!ld ha)e a sal)age )al!e+




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:a8es

:pes

4ropert ta8es+ based on the *a%$e o" the propert oned and do not*ar ith pro"its,

a%es ta8es+ imposed on the sa%e o" prod$cts, $s$a%% paid b thep$rchaser

E8cise ta8es+ imposed on the man$"act$re o" certain prod$cts %i!etobacco and a%coho%, these are $s$a%% passed on to the cons$mer

6ncome ta8es+ imposed on corporate pro"its or persona% income, gainsres$%ting "rom the sa%e o" capita% propert are s$b/ect

Beca$se state ta8es are ded$ctib%e "rom "edera% ta8es, thee""ecti*e ta8 rate is2

e""ecti*e ta8 rate@state rate H(1+state rate)("edera% rate)




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:a8 E8amp%e

A corporation that pas 5>I o" its pro"its in income ta8es. 6t in*ests

10,000 in an asset that i%% prod$ce >,000 ann$a% re*en$e "or eightears. 6" the ann$a% e8penses are D00, the sa%*age *a%$e at the end

o" P ears is 500, and an 9I interest is $sed, hat is the a"ter+ta8

present orth disregarding depreciationM

4 @ +10,000 H (>000)(4LA,9I,P)(1+.05>) N (D00)(4LA,9I,P)(1+.05>) H (500)(4L#,9I,P)

@ +10,000 H (>000)(5.5>5P)(1+.05>) N (D00)(5.5>5P)(1+.05>) H (500)(0.5019)

@ +>,D??

#rom #E


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6ncome ta8es

What does depreciation do to income ta8esM

6t red$ces the a"ter ta8 cash "%os2

A:C#t @ B:C#t(1+rt)+rtt

here t @ depreciation charge "or ear t

A:C#t @ a"ter+ta8 cash "%o "or ear t

B:C#t @ be"ore+ta8 cash "%o "or ear t

rt @ income ta8 rate "or ear to depreciation itse%" is not a

cash "%oN b$t it has a ro%e in the

"ina% estimation o" cash "%os.




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6n"%ation

6n"%ation is a meas$re o" the b$ing poer o"

mone. When sharp increases occ$r in the amo$nt o"

c$rrenc in circ$%ation, s$dden decreases can

occ$r in the p$rchasing poer o" mone d$e to

rising prices.

enera%%, the in"%ation rate "or a co$ntr is

determined $sing a mar!et bas!etF

approach2

6n"%ation is represented as the a*erage rate o"

increase in prices "or a ide range o" goods and

ser*ices. :he Cons$mer 4rice 6nde8 (C46) is one

common% $sed meas$re o" in"%ation in the .




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6n"%ation

Economic st$dies m$st be per"ormed in terms o" constant+

*a%$e do%%ars. :here are se*era% methods to accomp%ish this hen in"%ation is

present. Gne is to rep%ace the e""ecti*e ann$a% interest rate i

ith a *a%$e ad/$sted "or in"%ation. :he ad/$sted *a%$e is

ca%%ed the combined disco!nt rate2

icombined @ i H / H i/

here / is the in"%ation rate per ear and is $sed to comp$te the

present orth *a%$es.

#rom #E


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Concepts


Cash "%os

isco$nt "actors

Comparing a%ternati*es

epreciation, ta8es, and in"%ation



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Z$estionsM

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