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ENGR 3360U Winter 2014Unit 6-3

Alternate Choices using AW

Dr. J. Michael Bennett, P. Eng., PMP,UOIT,

Version 2014-I-01

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Unit 6 Annual Cash Flow

Change Recor

2014-!-01 !nitial Creation

2014-!-016-2 "r# $#%# &ennett' (#Eng#' (%( ENGR 3360U Eng Eco

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Course )utline

1# Engineering Econo*ics2# General Econo*ics

1# %icroecono*ics2# %acroecono*ics

3# %one+ an the &an, oCana a3# Engineering Esti*ation4# !nterest an E.ui/alence

# (resent Worth Anal+sis6# Annual Cash Flow

# Rate o Return Anal+sis# (ic,ing the &est Choice# )ther Choosing echni.ues

10# Uncertaint+ an Ris, 11# !nco*e an "e5reciation12# A ter-ta Cash Flows13# Re5lace*ent Anal+sis

14# !n lation1 # %ARR 7election16# (u8lic 7ector !ssues1 # What Engineering shoul ,now

a8out Accounting1 # (ersonal Econo*ics or the

Engineer

2014-!-01 "r# $#%# &ennett' (#Eng#' (%( ENGR 3360U Eng Eco6-3

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Unit 6 Roa %a5

6#1 )ne 9i e C+cle6#2 Ca5ital Reco/er+ an Annual Worth6#3 Alternati/e 7elections6#4 Annual Worth o (er*anent !n/est*ents6# 7al/age

6#6 %ortgages


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2014-!-01 "r# $#%# &ennett' (#Eng#' (%( ENGR 3360U Eng Eco6-

6#1 A /antages o Annual Cash Flow

(o5ular anal+sis techni.ue

Easil+ un erstoo -- results are re5orte in :

5er ti*e 5erio ' usuall+ : 5er +ear Eli*inates the 9C% 5ro8le* associatewith the 5resent worth *etho

)nl+ ha/e to e/aluate one li e c+cle

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; EUAC e.ui/alent uni or* annual cost; EUA& < = = = 8ene its; EUAW

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AW Calculation ro* (W or FW

Co*5utation ro* (W or FWAW < (W?A@(' i ' nB orAW < FW?A@F' i ' nB

AW con/erts all cash lows to their en o 5erio e.ui/alent a*ounts in : 5er +ear

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AW alue ro* Cash Flows

AW /alues can 8e calculate irectl+ ro*cash lows or onl+ one life cycle

Not necessar+ to consi er the 9C% o li/esas is in (W or FW anal+sis

For alternati/e co*5arison' select thealternati/e with the 8est AW /alue

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E a*5le 6#1

Darr+ 8u+s so*e urniture or :1'000# !t shoullast 10 +ears# At ' what is the AW

AW < 1000?A@(' ' 10B < 142#40


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AW an Re5eata8ilit+ Assu*5tion

! two or *ore alternati/es ha/e une.ual li eesti*ates' onl+ e/aluate the AW or one li ec+cle o each alternati/e

he annual worth o one c+cle is the sa*e asthe annual worth o all uture c+cles ? ro*re5eata8ilit+ assu*5tionB

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Re5eata8ilit+ Assu*5tion

Gi/en alternati/es with une.ual li/es' theassu*5tions are

1. The services provided are needed forever

2. The first cyc le of cash flows is repeated for all successivecycles in the same manner

3. All cash flows will have exactly the same estimated values in

every life cycle.Note: The third assumption may be unrealistic in many

problems encountered in industry

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)ne or %ore C+cles

Cycle1

Cycle2

Cyclek

Annualize any one of the cycles

AW assumes repeatability of cashows

Find the annualworth of any given

cycle !"period#

…

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6 ear H 12 ear Alternati/es For (W or FW anal+sis' nee an 12 +ear stu + 5erio

2 li e c+cles o the 6 +ear 5roIect1 li e c+cles o the 12 +ear 5roIect

%eans *ore calculation e ortJ

6 year Project 6 year Project

$ year %ro&ect

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E a*5le 6#2 -- Using AW Anal+sis! the cash low 5atterns are assu*e to re*ain thesa*e or the 6 an 12 +ear 5roIects or uturec+cles' then or AW *etho

%ro&ect A' ( years

%ro&ect )' 12 years

Find the AW of any (*yearcycle

Find the AW of any 12*year cycle

Compare AW A value for ( years with AW )

for 12 years to select the betteralternative

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E a*5le 6#2

wo 5u*5s are 8eing consi ere with theollowing s5ecs#

(u*5A (u*5& !nit cost '000 '000 7al/age 1' 00 1'000

Use ul 9i e 12 6


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Co*5are

AW?5u*5AB< - 000?A@(' ' 12BK1 00?A@F' ' 12B

< - 1#3K 3# < - AW ?5u*5&B

< - 000?A@(' ' 6B K 1000?A@F' ' 6B

< - 0


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A /antages@A55lications o AWA55lica8le to a /ariet+ o engineering econo*+

stu ies such asAsset re5lace*ent&rea,e/en anal+sis%a,e-or-&u+ ecisions7tu ies ealing with *anu acturing costs

Econo*ic /alue a e ?E AB anal+sis

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6#2 Calculating Ca5ital Reco/er+ an AW

An econo*ic alternati/e shoul ha/e the ollowingcash low esti*ates *a e

!nitial in/est*ent -- (

Esti*ate uture sal/age /alue -- 7 Esti*ate li e -- n !nterest rate -- i ?this is usuall+ the %ARRB Esti*ate annual o5erating costs L A)C

Capital Recovery (CR) is the annualized equivalent of

the initial investment P and the future salvagevalue S for n years at i%

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Ca5ital Reco/er+ Cost

!t is important to "no# the equivalent annualcost of o#ning an asset $his cost is called Capital Recovery& or CR

CR is determined using 'P S i and n

# # #

is initial purchase price at time !

"stimated salva#evalue at time n is $

! 1 2 …………………………. n%1 n

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Ca5ital Reco/er+ Cost

+iven'

Convert to'

, 1 2 - n*1n

An amount of A per year (CR)

%

, 1 2 - n*1n

***+

.

***+

l h l

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Co*5aring CA(! A9 REC) ER with AW

CR is a cost' so it carries a negati/e signCR is the annual e.ui/alent ?an A /alueB that re5resentsthe i*5lie Mcost o an asset or n +ears at i with a irst

cost o ( an a sal/age /alue o 7 in +ear n

CR oes N) inclu e annual o5erating costs' A)C

o o8tain AW once CR is eter*ine ' calculate

AW < - CR - A)C

where A)C itsel is an annual e.ui/alent a*ount ?sa*eeach +earB

U i 6 A l C h Fl

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Ca5ital Reco/er+ CalculationsC)%(U !NG CR F)R !N E7 %EN 7 W! D A 7A9 AGE A9UE

%etho 1 Co*5ute e.ui/alent annual cost o the in/est*ent (

an su8tract the e.ui/alent annual sa/ings o thesal/age /alue 7# his is

(?A@(' i ' nB - 7?A@F' i ' nB

"eter*ine CR as the negati/e ?costB o this relation

CR = -[P(A/P, i%,n) - S(A/F, i%, n)]

U i 6 A l C h Fl

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%ore Co**onl+ Use CR Calculation

%etho 27u8tract sal/age /alue 7 ro* original cost ( an

calculate the e.ui/alent annual cost o ?(-7B

A to that the interest which the sal/age /alue woulreturn each +ear' 7?iB

CR < -O?( - 7B?A@('i'nB K 7?iBPQ-O(?A @('i'nB-7?A@F'i'nBP an ?A@('!'nB

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CR A*ount What !t %eansCR is the annual cost associated with owning a productive asset over n time periods at interest rate i% per period

E.ui/alentl+' CR *a+ 8e inter5rete as the *ini*u* a*ount o *one+ an in/est*ent *ust earneach o n +ears to reco/er the initial cost at a return o i

Why? Remember, the purchase of assets to conduct

business involves a commitment of the owner's funds. As such, an investment is a commitment of the owner’s funds over n time periods. Thus, the owners expect areturn on that investment.

U it 6 A l C h Fl

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6#3 E/aluating Alternati/es Using AWFor *utuall+ e clusi/e alternati/es' select one

with lowest AW o costs?ser/iceB or highestAW o net inco*es ?re/enueB

his *eans' select the nu*ericall+ largest AWalternati/e

! AW S 0 at %ARR' the ?re/enueB alternati/e isnot econo*icall+ Iusti ia8le' since initial

in/est*ent ( is not reco/ere o/er n +ears atthe re.uire rate o %ARR < i 5er +ear

U it 6 A l C h Fl

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E a*5le 6#3

elesat s Ani,-1 was the worl s irst o*estic co**unicationssatellite when it was launche in 1 2' 8ringing li/e 8roa casts o

Hockey Night in Cana a to northern co**unities# Fourteenlaunches later in 2004' the Ani, F2 was the irst satellite toco**ercialiTe the = aV re.uenc+ 8an or cost-e icient' two-wa+ 8roa 8an ser/ices# elesat is intereste in a 5iece o Earth-

8ase trac,ing e.ui5*ent' which will re.uire an in/est*ent o :13*illion# Eight *illion ollars will 8e co**itte now an there*aining : *illion e 5en e at the en o +ear 1 o the 5roIect#Annual o5erating costs or the s+ste* are e 5ecte to start the irst+ear an continue at :0# *illion 5er +ear# he use ul li e o thetrac,er is +ears with a sal/age /alue o :0# *illion# Calculatethe AW /alue or the s+ste*' i the cor5orate %ARR is currentl+12 5er +ear#

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Cash Flow "iagra*s a an 8

, - . / 0 1 6 2 3

43+,

41+,4,+5

, - . / 0 1 6 2 3

7 8 49

a# b#


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CR < -QO #0 K #0?(@F' 12 ' 1BP?A@(' 12 ' B L 0# ?A@F' 12 ' BB < -QO12#46P?0#2013B L 0#040 < :-2#4

he correct inter5retation o this result is /er+ i*5ortant to elesat# !t *eans

that each an e/er+ +ear or +ears' the e.ui/alent total re/enue ro* thetrac,er *ust 8e at least :2'4 0'000 #$ t to "eco&e" the initial '"e ent o"thin&e t ent 'l$ the "e*$i"e "et$"n of + % 'e" yea" his oes not inclu ethe A)C o :0# *illion each +ear# 7ince this a*ount' CR < :2#4 *illion'is an e*$i&alent ann$al co t, as in icate 8+ the *inus sign' total AW is

oun AW < -2#4 - 0# < :-3#3 *illion 5er +ear

his is the AW or all uture li e c+cles o +ears' 5ro/i e the costs rise at thesa*e rate as in lation' an the sa*e costs an ser/ices are e 5ecte toa55l+ or each succee ing li e c+cle#


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E a*5le 6#4 L (iTTa&utt

(iTTa&utt' a 5o5ular )shawa 5iTTa Ioint' co*5etes well in the north en 'attracting *an+ "urha* an U)! stu ents# !t also has an on-line/irtual store an eli/ers on e*an ' which the uni/ersit+ ,i s reall+li,e# !t turns out that *ost stu ents or er the sa*e 5iTTa' 5e55eroni withancho/ies an shroo*s# he owner' who coinci entall+ is ta,ing ENGR3360' wants to re uce eli/er+ ti*es 8+ stoc,ing the cars with thisco**on 5iTTa' ai*ing at gra88ing *ar,et share 8+ routing the we8or ers through )n-7tar to the nearest 5iTTa car on the roa thus

eli/ering the 5iTTa in su5er- ast ti*es o e ect this' she 5ro5osesinstalling )n-7tar in all o her /ehicles# )n-7tar will also gi/e irectionsto an+ location in the cit+# ?)n-7tar is satellite wirelessB#Each s+ste* costs :4'600' has a -+ear li e c+cle an *a+ 8e sal/age

or :300# otal o5erating costs are :6 0 or the irst +ear' increasing 8+: 0 5er +ear therea ter# Assu*e that the %ARR is 10 # he increaseinco*e is assu*e to 8e :1200@+r or all #

What is the CR an AW nee e to reco/er this cost


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(iTTa&utt E a*5le

Cash Flow "iagra* is

1 2 - /0

% *2- ,,,

. 3!10,,

*!(0,

*!4,, *!40,*!5,,

*!50,

A 3!12,," yr


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(iTTa&utt E a*5le

he Ca5ital Reco/er+ co*5onent is

1 2 - /0

% *2- ,,,

. 3!10,,

CR(-,%) 8 :./ ,,,( ;P -,% 1) <

-1,,( ;= -,% 1) 8 :413..


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(iTTa&utt E a*5leCost@Re/enue co*5onent is seen to e.ual

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(iTTa&utt E a*5le?Re/enue L )5erating CostsB are

1 2 - /0

Annual Re/enue < A < K:1200@+r

*!(0,

*!4,,*!40,

*!5,,*!50,

An n u a l ) 5 e r a t i n g C o s t s


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(iTTa&utt Answer otal Annual worth ?CR K Cost@Re/B

CR?10 B < -: 22Re/enue@Cost Annual a*ount :4 # 0AW?10 B < -: 22K:4 # 0AW?10 B < -: '362# 0

This is a bad deal at 10% and/or an incomeof + $1200. Question: what would you haveto ma e in additional !ro"t for this to wor #


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75ecial Cases or AW Anal+sis

! cash low re5eata8ilit+ assu*5tion can t 8e *a e' s5eci + a stu + 5erio o n +earsan 5er or* anal+sis with this n in all

co*5utations ?E a*5le 6#4?8B i thisB

! 5roIects are in e5en ent ' select all withAW X 0 at i < %ARR' 5ro/i e no 8u getli*it is e ine #


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6#4 AW o a (er*anent !n/est*ent

! an in/est*ent has no inite c+cle ?or a /er+ longesti*ate li eB it is calle a 5er5etual or 5er*anentin/est*ent

! =(V is the 5resent worth o the cost o the in/est*ent'

then the AW /alue is ( ti*es i AW

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E a*5le 6#

A roa *ust get 5ast a *ountain# here are 2o5tions tunnel through the *ountain or 8uila roa aroun it su55orte 8+ concrete 5illars#

he cost or the tunnel is : # % an theuse ul li e is in inite# he roa woul cost: % 8ut onl+ last 0 +ears# Assu*e 6 #



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7olution

unnel A < (i# 7o A < # ?0#06B < :330 Roa A < ?A@('6 ' 0B < :31

7elect the roa #



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6# 7al/age alue

; When there is a sal/age /alue at the en othe li e o an asset' it is re5resente as aone-ti*e cash low 8ene it at the en o the

asset s li e# L E a*5le 7al/age /alue ?7B o asset with a4 +ear li e

, 1 2 - /

.



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7al/age alue' cont #

; When there is an initial cost ?(B ollowe 8+ a sal/age/alue ?7B the annual worth ?AWB can 8e co*5ute 8+

AW < (?A@(' i' nB L 7?A@F' i' nB

.RAW < ?( L 7B?A@F' i' nB K (i.RAW < ?( L 7B?A@(' i' nB K 7i



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6#6 %ortgages in Cana a

; he legal ocu*ent L 9ong ter* a*ortiTe loan that is use or 8u+ing 5ro5ert+ L ! 5a+*ents are not *a e' the len er can seiTe the 5ro5ert+

an sell it to reco/er the e8t

L 9egal ocu*ent outlines the ter*s an con itions orre5a+*ent o the loan ?a*ortiTation 5erio ' interest rate'

5enalties' etc#B

; A*ortiTation L 9ength o ti*e it ta,es to 5a+ o loan assu*ing

; ayments are made on time with no additional payments; &nterest rate doesn't chan#e



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%ortgages in Cana a

; A*ortiTation 5erio s are t+5icall+ 8etween L +ears to 3 +ears L he nor* is 20 or 2 +ears

; er*s L A *ortgage is o ten *a e u5 o s*aller 5erio s

calle Mter*s an a ter* is the 5erio in whichthe interest rate Mter* is i e #

L At the en o the ter*' the *ortgage can 8erenewe or a another ter* at the current interestrate#



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+5es o %ortgages

; MCon/entional L For or less o the a55raise /alue

; MDigh-ratio *ortgages L Digher than an usuall+ re.uire an outsi eagenc+ such as the C%DC ?Central %ortgage

an Dousing Cor5orationB to insure the *ortgage#

; 7o*e )thers L )5en' /aria8le rate' AR%' ca55e rate'

con/erti8le rate' secon ' re/erse' an CD!(#



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%ortgage E.uit+ an !nterest Rates

; E.uit+ L he /alue re*aining in a 5ro5ert+ a ter all *ortgage an

loans registere against the title are su8tracte ro* its/alue#

; !nterest Rate L !nterest rate is e 5resse as; ( compounded semi%annually) not in advance

L An old "n#lish term when led#ers were *ept by hand L Nominal rate mort#a#e at +( is actually 3( semi%annually



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7u**ar+

; Unli,e 5resent worth anal+sis' annual cashlow anal+sis oes N) re.uire a co**on

anal+sis 5erio 8etween the alternati/es#

; Dowe/er two assu*5tions are inclu e L hat the actual /alues o uture instances o a

ser/ice are the sa*e as the current instance L here is a co**on *ulti5le o use ul li/es

8etween the alternati/es; As the /alue o n increases the ca5ital reco/er+

actor a55roaches i



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7u**ar+' cont #

; %ortgages in Cana a are a*ortiTe o/er anu*8er o +ears#

; here are a nu*8er o t+5es o *ortgages#; E.uit+

L he a55raise 5ro5ert+ /alue L /alue o*ortgage owing

; !nterest rate is tra itionall+ state as L co*5oun e se*i-annuall+' not in a /ance


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Documents

3360 Unit 06.3 2014-I-01