Lecture 02: NPV and Other Investment Rules

8/18/2019 Lecture 02: NPV and Other Investment Rules

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Corporate FinanceLecture 02: NPV and Other Investment Rules


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1 Why Use Net Present Value?

• Accepting positive NPV projects beneits shareholders!

NPV uses cash lo"s

NPV uses all the cash lo"s o the project

NPV discounts the cash lo"s properl#


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The Net Present Value (NPV) Rule

• Net Present Value $NPV% & 'otal PV o uture ()*s + Initial Investment

• ,inimum Acceptance (riteria: Accept i NPV - 0• Ran.ing (riteria: (hoose the highest NPV

• /stimating NPV:• ! /stimate uture cash lo"s: ho" much1 and "hen1

• 2! /stimate initial costs

• ! /stimate discount rate $opportunit# cost%


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Estimate iscount rate

• (ash lo"s can onl# be estimated3 rather than .no"n!

• As a manager3 #ou e4pect the cash lo" o a project "ith500 initial investment to be 506 ne4t #ear! 'hat is3 the cash

lo" could be higher3 sa# 563 or lo"er3 sa# 576! It is ris.#!

• 8uppose the project is about as ris.# as the stoc. mar.et as a"hole3 "here the e4pected return this #ear is perhaps 0

percent!

• 'hen 0 percent becomes the discount rate!


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'he NPV Rule : /4ample

9 Assume #ou have the ollo"ing inormation onProject :

; Initial outla#

9 Annual cash revenues and e4penses are asollo"s:

?ear Revenues /4penses

53000 5@00 2 23000 300

23200 23600

23B00 300


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'he NPV Rule : /4ample $continued%

Initialoutlay

($1,100)

Revenues $1,000Expenses 500

Cash flow $500

Revenues $2,000Expenses 1,300

Cash flow $700

!"#

$377%02

&1'%2


Cash flow (500)


Cash flow $1,200

0 1 2 3

1$500 !

1%10

1$700 ! 1%10 2

1* $500 ! 1%10 3

1$1,200 ! 1%10

+ $1,100%00

5%5

57&%51

*375%


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NPV = -C0 + PV0(Future CFs)

= -C0 + C1/(1+r) + C2/(1+r)2 + C3/(1+r)

3 + C4/(1+r)4

= -1,100 + 500/1.1 + 700/1.12 + (-500)/1.13 + 1,200/1.14

= $377.02 > 0

'he NPV Rule : /4ample $continued%


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" The Pay#ac$ Perio Rule


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The Pay#ac$ Perio Rule

(continue)


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% The &iscounte Pay#ac$ Perio

Rule

• Co" long does it ta.e the project to Dpa# bac.E its initialinvestment ta.ing the time value o mone# into account1

• G# the time #ou have discounted the cash lo"s3 #ou mightas "ell calculate the NPV!


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'he Fiscounted Pa#bac. Period Rule: /4ample

9 Assume #ou have the ollo"ing inormation onProject :

; Initial outla#

9 Annual that cash lo"s and their PVs are as ollo"s:

?ear (ash lo" PV o (ash lo"

5 200 5 H2

2 00

600 @2B

00 20@


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?ear Accumulated discounted ()

5 H2

2 @

307 32

'he Fiscounted Pa#bac. Period Rule:

/4ample $continued%

9 Fiscounted pa#bac. period is just under #ears


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' nternal Rate o Return (RR) Rule

• 'he most important alternative to NPV rule!

• IRR: the discount that sets NPV to ero!


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RR* +n E!ample

R NPV

+

+−=

1110$100$


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RR* +n E!ample

10.1

110$100$0

12.1

110$100$79.1$

08.1110$100$85.1$

+−=

+−=−

+−=

• Co" to solve or the IRR1 Jse a trial


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' nternal Rate o Return (RR) Rule

• ,inimum Acceptance (riteria:

• Accept i the IRR e4ceeds the re=uired return!• Ran.ing (riteria:• 8elect alternative "ith the highest IRR

• Reinvestment assumption:

• All uture cash lo"s assumed reinvested at the IRR!


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The nternal Rate o Return, E!ample

(onsider the ollo"ing project:

0 1 2 3

$50 $100 $150

-$200

'he internal rate o return or this project is 7!>


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The NPV Payo Proile or This E!ample

Discount Rate NPV

0> 500!00

> 56!0

H> 56!2

2> 526!67

B> 5!B@

20> $5!6%

2> $52!HH%

2H> $522!6%

2> $527!7%

B> $5B!%0> $5!HB%

I "e graph NPV versus discount rate3 "e can see the IRR as

the 4


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0 Pro#lems .ith the RR +pproach

9 Are Ke Gorro"ing or Lending1

9 ,ultiple IRRs!

9 'he 8cale Problem!

9 'he 'iming Problem!


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Pro#lem 1, +re We orro.in- or

2enin-?


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Pro#lem 1, +re We orro.in- or

2enin-?


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Pro#lem ", 3ultiple RRs


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9 In general3 these lip


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To 4anle Pro#lem ", 3oiie RR

9 'he modiied IRR method $,IRR%: combining cash lo"s

until onl# one change in sign remains!

9 (onsider Project C again! Kith a discount rate o >3 thevalue o the last cash lo"3 M523 is as o Fate !

$115.79-$132/1.14- =


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To 4anle Pro#lem ", 3oiie RR

9 'he modiied IRR method $,IRR%: combining cash lo"s

until onl# one change in sign remains!

9 (onsider Project C again! Kith a discount rate o >3 thevalue o the last cash lo"3 M523 is as o Fate !

9 'he DadjustedE cash lo" at Fate is 5!2 $&520 M

@!67% !

9 Ke produced the ollo"ing cash lo"s or this project:

$115.79-$132/1.14- =

)$114.21,100$(−


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3oiie RR (Continue)

9 Ke produced the ollo"ing cash lo"s or this project

using ,IRR:

9 Note that no" "e have onl# one change in sign!

9 'he IRR o these t"o cash lo"s is !2>3 "hich is

larger than the discount rate: >!

9 Although correct3 ,IRR violates the DspiritE o the IRR

approach! 'he number should be internal3 or intrinsic3 to

the project!

)$114.21,100$(−


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Pro#lem %, The /cale Pro#lem


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)or the reasons in the previous e4ample3 8herr#

is correct! Gut ho" to convince 8tanle#1


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Ans"er: use the ,odiied IRR

9 )ormula or computing the incremental IRR:

9 'he e=uation gives us IRR&BB!B6> - the discount rate

2@>

IRR ++−=

1

million25$ million15$0


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8imilarl#3 "e can use the incremental NPV

9 )ormula or computing the incremental NPV:

9 'he incremental NPV is positive!

million5$25.1

million25$

million15$ =+−


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9 'o sum up3 "e have "a#s to deal "ith the NPV

problem:

! (ompare the NPVs o the t"o choices !

2! (alculate the incremental NPV

! (ompare the incremental IRR to the discount rate !


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Pro#lem ', The Timin- Pro#lem

0 1 2 3

$10,000 $1,000

$1,000

-

$10,000

Project A

0 1 23

$1,000 $1,000

$12,000

-

$10,00

0

Project G

'he preerred project in this case depends on the discount

rate3 not the IRR!


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The Timin- Pro#lem

10.55% = crossoer r!te

12."4% = # B 1.04% = # A


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Calculatin- the Crosso5er Rate

(ompute the IRR or either project DA 20>

Fiscount rate

N P V

A


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3utually E!clusi5e 5s6 nepenent

Pro7ect

• ,utuall# /4clusive Projects: onl# ON/ o several potential projects can be chosen3 e!g!3 ac=uiring an accounting s#stem!

• RAN all alternatives and select the best one!

• Independent Projects: accepting or rejecting one project does not aectthe decision o the other projects!

• ,ust e4ceed a ,INI,J, acceptance criteria!


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8 The Proita#ility ne! (P) Rule

• ,inimum Acceptance (riteria:• Accept i PI -

• Ran.ing (riteria:• 8elect alternative "ith highest PI• Fisadvantages:

• Problems "ith mutuall# e4clusive investments

• Advantages:• ,a# be useul "hen available investment unds are limited• /as# to understand and communicate• (orrect decision "hen evaluating independent projects


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(redit Rationing


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9 The Practice o Capital u-etin-

• Varies b# industries!

• Fiscounted cash lo" techni=ues $such as IRR or NPV %are the most re=uentl# used in J8(anada!


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E!ample o n5estment Rules

(ompute the IRR3 NPV3 PI3 and pa#bac. period or the ollo"ing

t"o projects! Assume the re=uired return is 0>!

?ear Project A Project G

0


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E!ample o n5estment Rules

Project A Project G

()0

PI & !207B !B0@


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Relationship et.een NPV an

RRFiscount rate NPV or A NPV or G

0!00 @0!0020> @7!2B 6!72

0> @7!H 2!7 20!H@ 0!00


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Pro&ect 'Pro&ect

($200)

($100)

$0

$100

$200

$300

$400

-15% 0% 15% 30% 45% 70% 100% 130% 10% 1"0%

*scout r!tes

N P V

# 1(') # ()

NPV Proiles

# 2(')

Cross-oer !te


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: /ummary an Conclusions

• 'his chapter evaluates the most popular alternatives to NPV:

• Pa#bac. period

• Internal rate o return

•Proitabilit# inde4

• Khen it is all said and done3 the# are not the NPV rule orthose o us in inance3 it ma.es them decidedl# second

Lecture 02: NPV and Other Investment Rules

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Transcript of Lecture 02: NPV and Other Investment Rules