8/19/2019 3360 Unit 07.2 2014-I-01

1/21

ENGR 3360U Winter 2014Unit 7.2

Internal Rate of Return Analysis

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

Version 2014-II-01

8/19/2019 3360 Unit 07.2 2014-I-01

2/21

Unit 7 Rate of Return

Chan e Re!or"

2014#I#01 Initial Creation

2014#I#017#2 $r. %. &ennett' (.En .' (%(

8/19/2019 3360 Unit 07.2 2014-I-01

3/21

Unit 7 Rate of Return

2014#I#01 $r. %. &ennett' (.En .' (%(7#3

7.3 Cautions When Usin IRR

When a))lie" !orre!tly' the IRR *etho" +ill al+ays result in aoo" "e!ision an" shoul" ,e !onsistent +ith (W' AW' or -W*etho"s.

o+e/er' for so*e ty)es of !ash flo+s the IRR *etho" !an ,e

!o*)utationally "iffi!ult an" or lea" to erroneous "e!isions Rein/est*ent assu*)tion is at i for IRR *etho" not the %ARR.If %ARR is far fro* i ' *ust use !o*)osite rate

o*e !ash flo+s +ill result in *ulti)le i /alues. Raisesuestions as to +hi!h' if any' i /alue is )ro)er /alue

8/19/2019 3360 Unit 07.2 2014-I-01

4/21

Unit 7 Rate of Return

2014#I#01 $r. %. &ennett' (.En .' (%(7#4

)e!ial IRR (ro!e"ure for %ulti)leAlternati/es

-or analysis of t+o or *ore alternati/es usinIRR' resort to a "ifferent analysis a))roa!h as

o))ose" to re ular (W or AW *etho"%ust a))ly an in!re*ental analysis a))roa!h to

uarantee a !orre!t "e!ision' i.e.' sa*e as (W

or AW

8/19/2019 3360 Unit 07.2 2014-I-01

5/21

Unit 7 Rate of Return

In!re*ental IRR # 5IRR

If the "e!ision has alrea"y ,een *a"e' *a ethe !al!ulation as seenIf +e ha/e 2 alternati/es' !o*)are thein!re*ental or "ifferen!es ,et+een the 2alternati/es

a e the hi her initial#!ost 8 lo+er#initial!ost.If 5IRR9%ARR !hoose hi her else lo+er

2014#I#01 $r. %. &ennett' (.En .' (%(0.1#:

8/19/2019 3360 Unit 07.2 2014-I-01

6/21

Unit 7 Rate of Return

E;a*)le 7#10

If an ele!tro*a net is installe" in a !oal )lant' it +ill re*o/e *etal fro* the fee"an" sa/e ease for 3 years at

8/19/2019 3360 Unit 07.2 2014-I-01

7/21

Unit 7 Rate of Return

olution

A 0 @ 200 #2'7@3 1000 #17@3 #17@3 #17@31 1000 1000 D26 @332 1000 1000 @:7 6D43 0 0 0 0

4 0 0 0 0: 0 0 0 0 N(W 217 0 #2:6

2014#I#01 $r. %. &ennett' (.En .' (%(7#7

(W

5IRR %ARR so sele!t A

8/19/2019 3360 Unit 07.2 2014-I-01

8/21

Unit 7 Rate of Return

2014#I#01 $r. %. &ennett' (.En .' (%(7#@

7.4 %ulti)le IRR olutions

A !lass of IRR )ro,le*s e;ist that +ill )ossess*ulti)le i /alues

Ca)a,ility to )re"i!t the )otential for *ulti)lei /alues

WE IGNFRE

8/19/2019 3360 Unit 07.2 2014-I-01

9/21

Unit 7 Rate of Return

2014#I#01 $r. %. &ennett' (.En .' (%(7#D

ests for %ulti)le i /alues

1. Cash -lo+ Rule of i nshe total nu*,er of real /alue i ?s is al+ays less than or

e ual to the nu*,er of si n !han es in the ori inal !ashflo+ series

2. Cu*ulati/e Cash -lo+ Rule of i ns

-or* the !u*ulati/e !ash flo+ of the in/est*ent an"!ount the nu*,er of si n !han es in the !u*ulati/e !ashflo+ series

%ust )erfor* ,oth tests to ,e sure of one i H 0

Predicting the likelihood of multiple i* values

8/19/2019 3360 Unit 07.2 2014-I-01

10/21

Unit 7 Rate of Return

2014#I#01 $r. %. &ennett' (.En .' (%(7#10

7.: Co*)osite Rate of Return= Re*o/in

%ulti)le i alues his se!tion intro"u!es the !on!e)t of thecomposite rate of return or the external rate

of return Assu*e that any over-recovered funds fro* an in/est*ent !an ,e in/este" at so*einterest rate ter*e" J cK

8/19/2019 3360 Unit 07.2 2014-I-01

11/21

Unit 7 Rate of Return

2014#I#01 $r. %. &ennett' (.En .' (%(7#11

Co*)osite IRR A))roa!hConsider the following investment

-$10,000

0 1 2 3 45

+$8,000

+$9,000

Determine the I

8/19/2019 3360 Unit 07.2 2014-I-01

12/21

Unit 7 Rate of Return

2014#I#01 $r. %. &ennett' (.En .' (%(7#12

Co*)osite IRR A))roa!h # E;a*)le!he I "n"l#sis reve"ls

Year Cash Flow

0 -$10,0001 $02 $8,0003 $04 $05 $9,000

Sum $7,000

ROR-Guess 0%ROR 1 !82%

i% & 1'(82)*#e"r on thenre overed investment"l"n es over 5 #e"rs

8/19/2019 3360 Unit 07.2 2014-I-01

13/21

Unit 7 Rate of Return

2014#I#01 $r. %. &ennett' (.En .' (%(7#13

Co*)osite IRR A))roa!h= I&?s• The Investment Balances at i* are:

Year Cash Flow "ro#e &ala' es( )* Ra e

0 -$10,000 -$10,000!001 $0 -$11, 81!592 $8,000 -$5, 45!953 $0 -$ ,595!34 $0 -$7,704!435 $9,000 $0!00

Sum $7,000

ROR-Guess 0%ROR 1 !82%

• .ll I/ s "re 0 for#e"rs 0 to 4 "nd itis 0 "fter 5 #e"rs

• Convention"lre investment

8/19/2019 3360 Unit 07.2 2014-I-01

14/21

Unit 7 Rate of Return

2014#I#01 $r. %. &ennett' (.En .' (%(7#14

Co*)osite IRR A))roa!h i% & 1'(82)

-$10,000

0 1 2 3 45

+$8,000

+$9,000

estion Is it re"son" le to"ss me th"t the +8,000 "n einvested forw"rd "t 1'(82)6

Reinvest forward atsome interest rate

8/19/2019 3360 Unit 07.2 2014-I-01

15/21

Unit 7 Rate of Return

2014#I#01 $r. %. &ennett' (.En .' (%(7#1:

Co*)osite IRR A))roa!h

Remember … ROR assumes reinvestment atthe calculated i* rate

What if it is not practical for the +$ !""" tobe reinvested for#ard one ear at %&' ()

ns#er: ppl a reinvestment rate morein line #ith a %, ear investment return-appl this rate onl to the positiveinvestment balances.

8/19/2019 3360 Unit 07.2 2014-I-01

16/21

Unit 7 Rate of Return

2014#I#01 $r. %. &ennett' (.En .' (%(7#16

Rein/est*ent Rates /ost 0rms can reinvest surplus funds atsome conservative mar1et rate of interestin e2ect at the time the surplus fundsbecome available'

Often! the current mar1et rate is less thana calculated IRR value

What then is the 0rm to do #ith the +$ !""" #hen it comes into the 0rm fromthe investment

8/19/2019 3360 Unit 07.2 2014-I-01

17/21

Unit 7 Rate of Return

2014#I#01 $r. %. &ennett' (.En .' (%(7#17

Co*)osite IRR A))roa!h 3onsider a reinvestment rate that is closerto the current mar1et rate for reinvestmentof the $ !""" for the ne4t time period-s.

ssume a reasonable mar1et rate is )per ear

3all this rate an external rate - c

8/19/2019 3360 Unit 07.2 2014-I-01

18/21

Unit 7 Rate of Return

2014#I#01 $r. %. &ennett' (.En .' (%(7#1@

he e;ternal rate ## c

he e;ternal interest rate' !' is a rate that the fir* !anrein/est sur)lus fun"s for at least one ti*e )erio" at ati*e.

!' is often set to e ual !urrent %ARR rate

8/19/2019 3360 Unit 07.2 2014-I-01

19/21

Unit 7 Rate of Return

2014#I#01 $r. %. &ennett' (.En .' (%(7#1D

Co*)osite IRR A))roa!h

5rocedure does the follo#in6:

determine a sin6le! uni7ue i* for a stated c

Techni7ue is called net,investment procedureResult is called the composite rate of return

or i8

8/19/2019 3360 Unit 07.2 2014-I-01

20/21

Unit 7 Rate of Return

2014#I#01 $r. %. &ennett' (.En .' (%(7#20

Co*)osite IRR A))roa!h

9indin6 i8 is a much more involved processthan 0ndin6 i*

5rior to computer solution! onl ver small-n ;

f

8/19/2019 3360 Unit 07.2 2014-I-01

21/21

Unit 7 Rate of Return

2014#I#01 $r % &ennett' ( En ' (%(7#21

u**ary

IRR analysis is often use" ,ut not al+ays +ellun"erstoo" ,y )ra!titioners IRR !an ,e !o*)utationally "iffi!ult *anually a

s)rea"sheet *o"el hel)s re"u!e solution ti*e IRR )ro,le*s *ay in/ol/e *ulti)le i rates. Choosethe lo+er L*ore !o*)li!ate" analyses )ossi,leMWhen !hoosin ,et+een 2 alternati/es' use theINCRE%EN A> IRR analysis