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1Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texa A&! "ni#erity.

Co$yri%ht The !'(ra)*+ill Com$anie, n'. -ermiion required or re$rodu'tion or di$lay.

CHAPTER VI

Annual Worth Analysis

McGra

wHill

ENGINEERING ECONOMY Fifth Edition

Blank an

Tar!uin



2Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. D


Ch" #$ %&arnin' O()&cti*&s$ To+ics

AW o*&r on& +ro)&ct li,& cycl&

AW calculations Ca+ital R&co*&ry analysis Two a++roach&s

-&l&ctin' Alt&rnati*&s (yAnnual Worth

AW analysis ,or a +&r.an&ntin*&st.&nt



%Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. D


#"/ A*anta'&s an 0s&s o, AnnualWorth

Po+ular Analysis T&chni!u&

Easily un&rstoo 1 r&sults ar&r&+ort& in 23ti.& +&rio

Eli.inat&s th& %CM +ro(l&.associat& with th& +r&s&ntworth .&tho Only ha*& to &*aluat& on& li,&

cycl& o, a +ro)&ct



Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. D


#"/ AW Calculations

G&n&ral in natur& such that$ AW 4 PW5A3P6i76n8

AW 4 9W5A396i76n8

Con*&rt all cash :ows to th&ir&n; o,;+&rio &!ui*al&nta.ounts





#"/ E!ui*al&nt Annual Cost

Cash;9low analysis a++roach wh&r& th&cash :ows ar& con*&rt& to th&irr&s+&cti*& &!ual6 &n;o,;+&rioa.ounts"

Th& r&sult is r&+ort& in t&r.s o,23+&rio

Variant o, th& +r&s&nt worth a++roach

Po+ular with so.& .ana'&rs who t&n

to think in t&r.s o, <23y&ar6 23.onths6&tc"





#"/ AW an R&+&ata(ility Assu.+tion

I, two or .or& alt&rnati*&s+oss&ss un&!ual li*&s6 th&non& n&& only &*aluat& th& AW,or any 'i*&n cycl&

Th& annual worth o, on& cycl&is th& sa.& as th& annual

worth o, th& oth&r cycl&s 5(yassu.+tion8



'Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. D


#"/ R&+&ata(ility Assu.+tion

Gi*&n alt&rnati*&s withun&!ual li*&s

Th& assu.+tions ar&:/" Th& s&r*ic&s so +ro*i& ar& n&&&,or&*&r

=" Th& >rst cycl& o, cash :ows is r&+&at&

,or succ&ssi*& cycl&s?" All cash :ows will ha*& th& sa.&

&sti.at& *alu&s in &*&ry li,& cycl&



(Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. D


#" /" On& or Mor& Cycl&s

Cycl&/

Cycl&=

Cycl&@

Annuali& any on& o, th& cycl&s

AW assu.&s r&+&ata(ility o,C9s

9in th& annualworth o, any'i*&n cycl&523+&rio8



)Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. D


#"/ #;y&ar D;y&ar Pro(l&. 5E"#"/8

See Example 6.1

Present Worth would mandate a18-year study period 3 Cycles o the 6-year pro!ect " cycles o the #-year pro!ect

6 year Pro!ect

# year Pro!ect



*Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. D


#"/ #;y&ar D;y&ar Pro(l&. 5E"#"/8

$eed an 18-year study period or %oth

Present Worth would mandate a 18-year study period 3 Cycles o the 6-year pro!ect " cycles o the #-year pro!ect

&eans a lot o calculation time'

6-year Pro!ect 6-year Pro!ect 6-year Pro!ect

D;y&ar Pro)&ct D;y&ar Pro)&ct





#"/ Ea.+l& #"/ 1 Continu&

I, on& assu.&s th& cash :ow+att&rns r&.ain th& sa.& ,orth& #; an D;y&ar +ro)&cts6

th&n all on& has to o is$6-year Pro!ect

D;y&ar Pro)&ct

9in th& AW o, any # 1 y&arcycl&

9in th& annual worth

o, any D;y&ar cycl&

An th&n co.+ar& th& AW# yr to AWD yr"





#"/ Ea.+l&

Consi&r a +ro)&ct with 2?6FFFannual o+&ratin' cost an a 26FFFin*&st.&nt r&!uir& &ach y&ars" i

4 /F7

9or on& cycl&

E(C ) 3*+++ , *+++ (/P* 1+0* )2*31#4yr

26FFF

F / = ?

A /; 4

2?6FFF

C i ht Th ! ( +ill C i - i i i d d ti di l





#"/ Multi+l& cycl&""sa.& r&sult

5or two cycles

E(C ) 3+++ , +++ 1,P/5* .1+* (/P* .1+* 1+

) 3+++ , 131# ) 231#4yr

F / = ?

# J K D/F

26FFF

26FFF

A /;/F 4 2?6FFF






#"/ A*anta'&s o, AW

A++lica(l& to a *ari&ty o,&n'in&&rin' &cono.y stui&s Ass&t R&+lac&.&nt

Br&ak&*&n Analysis

Mak& or Buy L&cisions

-tui&s &alin' with .,'" Costs

Econo.ic Valu& A& analysis5EVA8






#"/ AW R&!uir&.&nts

-i.ilar to th& Pr&s&nt WorthM&tho6 AW analysis r&!uir&s$ A iscount rat& (&,or& th&

analysis is start& Esti.at&s o, th& ,utur& cash

:ows

Esti.at& o, th& ti.& +&rio5s8in*ol*&

Co$yri%ht The !'(ra) +ill Com$anie n' -ermiion required or re$rodu'tion or di$lay





#"= Ca+ital R&co*&ry an AW Valu&s

Assu.& th& +ot&ntial +urchas&o, any +roucti*& ass&t

On& n&&s to know or &sti.at&$ Initial In*&st.&nt ; P Esti.at& 9utur& -al*a'& Valu& ; - Esti.at& li,& o, th& ass&t ; N Esti.at& o+&ratin' costs an

ti.in' O+&rati*& int&r&st rat& 1 i7






#"= Ca+ital R&co*&ry Cost

Thus6 .ana'&.&nt is conc&rn&a(out th& &!ui*al&nt annual cost o,owin' a +roucti*& ass&t"

This cost is t&r.& <Ca+ital R&co*&ryCost

CR is a ,unction o, P6 -6 i76 an

<n






#"= Ca+ital R&co*&ry Cost 5CR8

CR 4 th& &!ui*al&nt annual worth o,th& ass&t 'i*&n$

Ca+ital R&co*&ry 5CR8 is th& annuali&

&!ui*al&nt o, th& initial in*&st.&nt PF an

th& annuali& a.ount o, th& ,utur&

sal*a'& *alu& 9n

777.

PF

9N

F / = ? N;/N

-

Co$yri%ht The !'(ra)*+ill Com$anie n' -ermiion required or re$rodu'tion or di$lay





#"= Ca+ital R&co*&ry Cost 1 CR

Gi*&n$

Con*&rt to$

777. F / = ? N;/

N

PF

9N

$A per year(CRC)

PF

9N

F / = ? N;/N

777.

-





Co$yri%ht The !'(ra) +ill Com$anie, n'. -ermiion required or re$rodu'tion or di$lay.


COMP0TING CR 9OR INVE-TMENT-WITH -A%VAGE VA%0E-$

E(C ) P(/P* i* n - S(/5* i* n

Cost 4 < an -V 4 <; (y

con*&ntion

P

7.. 7

7.

In*&st P F 2

N

-al*a'& ,or 9N 2 at t 4 N

-







C&P9;$< CR 5= ;$>ES&E$SW;? S(@>(<E >(@9ES:

&ethod ; - compute E(C o the oriAinalcost and su%tract the E(C o thesalBaAe Balue

E(C ) P(/P* i* n - S(/5* i* n






#"= Mor& Traitional CR A++roach

&ethod ;; Su%tract the salBaAe Baluerom the oriAinal cost and compute theannual cost o the diDerence. (dd to

that the interest that the salBaAe Baluewould return each year* S> i.

C=i0) P - S (/P* i* n , Si






#"= CR 1 E+lain&

C=i0 ) P - S> (/P* i* n , S>i

CR is the annual cost associated withowning a productive asset over N time

periods at interest rate “i! per period





$y % $ , q $ $ y

#"= CR ; E+lain&

( rm inBests the ownersF moneyin productiBe assets.

$ot the rmFs money %elonAs tothe owners o the rm.

he owners expect a return ontheir unds %einA inBested.





$y % $ , q $ $ y

#"= CR ; E+lain&

; the rm inBests in a productiBeasset* then the annual cost o theinBestment at time t ) + and7

he estimated uture salBaAe BalueGnH time periods hence7

&ust %e eBaluated usinA an

appropriate discount rate%ecause7.





y % y

#"= CR ; E+lain&

he ownerFs unds are tied up inthe inBestment cost at time t ) +and could haBe %een inBested

elsewhere.

hus* the annualiIed cost o thetime t ) + inBestment must %e

determined to reJect thecommitment o unds to the asset.





#"= CR 1 -i'n Con*&ntions

Two a++roach&s ,or si'ns %&t <P carry a n&'ati*& si'n

5in*&st.&nt8

%&t <- carry a +ositi*& si'n 5i, a +ositi*&

sal*a'& *alu&8 Th&n CR will carry a n&'ati*& si'n

%&t <P carry a +ositi*& si'n an <-a n&'ati*& si'n Tr&ats <costs as +ositi*& *alu&s an any

+ositi*& sal*a'& as a n&'ati*& *alu&





#"? Alt&rnati*&s (y Annual Worth

Gi*&n a iscount rat& 5in a*anc&8

AW is +&rha+s th& &asi&st .&thoto a++ly ,or analysis o, alt&rnati*&s

Mutually Eclusi*& Analysis -&l&ct th& on& (&st alt&rnati*&

-in'l& Alt&rnati*& Acc&+t i, AW +ositi*&6 &ls& r&)&ct





#"? AW 1 Mutually Eclusi*&

Gi*&n a s&t o, two or .or&alt&rnati*&s6 &t&r.in& th& AW 5i786 th&n

-&l&ct th& alt&rnati*& with th& low&stannual cost or th& hi'h&st annual n&tcash :ow

I, +ur& cost situation 1 s&l&ct .in" costalt&rnati*&

I, .i& costs an r&*&nu&s 1 s&l&ctth& .a" AW 5i78 alt&rnati*&





#"? Ea.+l& #"?

Cash 9low Lia'ra. is$

/ = ?

P4;=?6FFF

- 4 2/6FF

;2#F

;2JFF ;2JF

;2KFF

;2KF

A 4 2/6=FF3yr





#"? Ea.+l& #"?

Th& Ca+ital R&co*&ry co.+on&ntis$

/ = ?

P4;=?6FFF

- 4 2/6FF

CR5/F78 4 ;=?6FFF5A3P6/F768

/6FF5A396/F768 4 ;26K==





#"? Ea.+l& #"?

R&*&nu& 1 O+ Costs ar&$

/ = ?

A 4 2/6=FF3yr

2#F

2JFF2JF

2KFF

2KF





#"? Ea.+l& #"?

Cost R&*&nu& co.+on&nt is s&&n to&!ual 5costs tr&at& as +ositi*&*alu&s8$

4F 1 F5A3G6/F768

4 F 1 DF"F

4 2D"F

/"K/F/





#"? Ea.+l& #"?

Total Annual worth 5CR Cost3R&*8 CR5/F78 4 ;26K==

R&*&nu&3Cost Annual a.ount$ 2D"F

AW5/F78 4 ;26K==2D"F AW5/F78 4 26?#="F

"his amount would #e reuired to recover theinvestment and operating costs at the %&rate on a per'year #asis





#" AW o, a P&r+&tual In*&st.&nt

E(C o a perpetual inBestment

; an inBestment has no nite cycle* it is

called a perpetual inBestment. ; GPH isthe present worth o the cost o thatinBestment* then E(C is P times i* theinterest P would haBe earned each year.

E(C)( ) PQ iR&.&.(&r$ P 4 A3i

9ro. th& +r&*iouscha+t&r





#" Ea.+l&$ P&r+&tual In*&st.&nt

EK(&P@E

wo alternatiBes are considered orcoBerinA a oot%all eld.

he rst is to plant natural Arass andthe second is to install (strour.;nterest rate is 1+04year.

(ssume the eld is to last a GlonA timeH.





#" Ea.+l& 1 Continu&

(lternatiBe (:

$atural <rass =eplantinA will %e

reLuired each 1+ years at a cost o21+*+++. (nnual cost or maintenanceis 2*+++. ELuipment must %epurchased or 2+*+++* which will %e

replaced ater years with a salBaAeBalue o 2*+++





#" 1 Ea.+l&$ Natural Grass

(lternatiBe (:

F / = ? # J K D/F

2/F6FFF

A 4 26FFF

9 4 26FFF

-inc& cost is +r&o.inat&6 l&t 584 cost an 5;8 4 sal*a'& *alu&s

P 4 2F6FFF2/F6FFF

9 4 26FFF

942F6FFF





#" Ea.+l&$ Natural Grass 1 Analysis

, 26+*+++ (4P*1+0*1+

, 2*+++ already an annual cost

, 2+*+++ P45*1+0*(4P*1+0*1+

- 2*+++ P45*1+0*(4P*1+0*1+, 21+*+++ (45*1+0*1+

- 2*+++ (45*1+0*1+

) 2 1#*+64year


# Ea.+l&$ Arti>cial Car+&t




#" Ea.+l&$ Arti>cial Car+&t5-ur,ac&8

( ) Pi or a perpetual lie pro!ect

(nnual Cost o ;nstallation:

)21+*+++ .1+ ) 21*+++4 year

(nnual &aintenance ) 2*+++4year

otal: 21*+++ , 2*+++ ) 2"+*+++4Mr

Choose (* cost less per year'





Chapter 6: Summary77.

(nnual Worth is popular7

5airly simple to understand7

>ariant o the Present worth approach7

Eliminates lowest common multiples oliBes when alternatiBes possess uneLualliBes

9nderstood %y decision maNersConsistent with present worth




En o, Cha+t&r # %&ctur& -&t

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