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Fin650:Project Appraisal

Lecture 4-5

Project Appraisal Under Uncertainty andAppraising Projects with Real Options

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Project Analysis Under

Certainty: Recap

Discounted cash flow techniques

The ideal investment decision makin

technique is !et Present "alue#

! P " measures the equivalent presentwealth contri$uted $% the investment#

!P"&& relates directl% to the firm's oal of

wealth ma(imi)ation

&& emplo%s the time value of mone%

&& can $e used in all t%pes of investments

&& can $e adjusted to incorporate risk#

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Other Project EvaluationTechniques

*nternal +ate of +eturn , calculates

The discount rate that ives the

project an !P" of 0# *f the *++ is

reater than the required rate- theproject is accepted# *++

is iven as . pa#

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Other Project EvaluationTechniques/odified *nternal +ate of +eturn ,calculates the discount rate that ivesthe project an !P" of 0- when future

cash flows can $e re&invested at the+e&*nvestment +ate- a rate differentfrom the *++# *f the /*++ is reaterthat the required rate- the project is

accepted# /*++ is iven as . pa#

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Other Project Evaluation

Techniques!on&Discounted 1ash Flow Techniques

Accountin +ate of +eturn& measures the ratio

of annual averae accountin income to anasset $ase value# A++ is iven as . pa#

Pa%$ack Period , measures the lenth of time

required to retrieve the initial cash outla%#Pa%$ack is iven as num$er of %ears#

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Selection of Techniques

!P" is the technique of choice2 it satisfies the

requirements of: the firm's oal- the time value of

mone%- and the a$solute measure of investment#

*++is useful in a sinle asset case- where the

1ash flow pattern is an outflow followed $% all

positive inflows# *n other situations the *++ ma%

not rank mutuall% e(clusive assets properl%- or

ma% have )ero or man% solutions#

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Selection of Techniques

/*++ is useful in the same situations asthe *++- $ut requires the e(tra predictionof a re&investment rate#

A++ allows man% valuations of the asset$ase- does not account for the time valueof mone%- and does not relate to the firm'soal# *t is not a recommended method#

P3 does not allow for the time value ofmone%- and does not relate to the firm'soal# *t is not a recommended methode(cept for situations of uncertaint%#

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The Notion of Certainty

1ertaint% assumption Financial decision makers are rational- risk&averse-

wealth ma(imi)ers Financial markets are efficient and competitive

Future is certain- outcome is known 1ertaint% allows demonstration and evaluation

of the capital $udetin techniques- whilstavoidin the comple(ities involved with risk#

1ertaint% requires forecastin- $ut forecasts

which are certain# 1ertaint% is useful for calculation practice# +isk is added as an adaption of an evaluation

model developed under certaint%#

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NP Applications

Asset retirement

Asset replacement

Correct ranking of mutually exclusiveprojects.

Where projects have different lives.

Where projects have different outlays.

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Class Exercise: Asset

Replacement

1$

4nd of %ear !et operatininflow

alvae value

5 - 22%$$$

!%$$$ 1!%5$$

! %4$$ 14%3!5

" 4%25$ "#"$

Assu&e that '(U Ltd) has an asset with a*out three years o+

Operating li+e re&aining% today *eing the asset,s +i+th year)he net operating in+lows are shown in the ta*le *elow) .henshould the asset *e retired/

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alue

T4 model to use in all investment

evaluations#7ther criteria- such as *++- /*++-A++-and Pa%$ack ma% $e used ascomplementar% measures#

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Class Exercise

0onsider the +ollowing three cash +low pro+iles

ear ending

$ 1 2 3 4 5

Project 1 -1$$ 2$ 2$ 2$ 2$ 12$

Project 2 -1$$ 33)44 33)44 33)44 33)44 33)44

Project 3 -1$$ "5)22 "5)22 "5)22 "5)22 -3$$

0alculate RR% (P% and Pay*ac periods +or the projects

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Class Exercise

Project RR678 (P Pay*ac

1 2$ 3!)# 5

2 2$ 2)" 3

3 1#)#% 44)4 -1)4 1)2

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Pitfalls in Project Appraisal 'peci+ying project,s incre&ental cash +low

re9uires care Rele:ant e;pected a+ter-ta; cash +low associated with

two &utually e;clusi:e scenarios% without and with theproject

Allocation o+ o:erheads 4(pected:ersus most likel%cash +lows

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Pitfalls in Project Appraisal he pay*ac period is o+ten a&*iguous

=oes not re+lect the ti&e :alue o+ &oney gnores cash +lows a+ter the pay*ac period Unsuita*le +or projects re9uiring in:est&ent o:er a period o+

years

=iscount rates are +re9uently wrong >allacy o+ single discount rate% projects ha:e widely di++ering

riss

Rising in+lation rates are dangerous Use o+ a no&inal rate to discount no&inal cash +lows and use

o+ a real rate to discount real cash +lows All cash +lows do not change e9ually with the rate o+ in+lation n+lation increases the re9uired in:est&ent in no&inal woring

capital n+lation increases corporate ta; rate

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Pitfalls in Project Appraisal he precise ti&ing o+ cash +lows is i&portant

0ash +lows occur at the end o+ the year assu&ption

wo &ethods +or precise discounting Use &onthly discount rates

>or e;a&ple 1)5 ?year discount +actor

>orecasting is o+ten untruth+ul ncrease the hurdle rate *y the a:erage +orecasting *ias

'u*sidiary +orecast

Ris adds :alue to real options Real options a++ect the (P rule

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Critique of DCF gnores riss inherent in capital projects

Uses the sa&e discount rate to cash +lows withdi++erent riss

Uses the sa&e discounts rates throughout theli+e o+ the project

0onsiders in:est&ent one-ti&e irre:ersi*ledecision

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Project Analysis UnderRis!

*ncorporatin risk into projectanal%sis throuh adjustments to the

discount rate- and $% the certaintyequivalent factor#

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"ntroduction: #hat is

Ris!$ +isk is the variation of futuree(pectations around an e(pectedvalue#

+isk is measured as the rane ofvariation around an e(pected value#

+isk and uncertaint% areinterchanea$le words#

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#here %oes Ris! Occur$

*n project anal%sis- risk is thevariation in predicted future cashflows#

End of End of End of End of

Year 0 Year 1 Year 2 Year 3

-$760 ? -$876 ? -$546 ?

-$235 ? -$231 ? -$231 ?

-$1,257 $127 ? $186 ? $190 ?

$489 ? $875 ? $327 ?

$945 ? $984 ? $454 ?

Varying Cash !o"s

ore#as Esi%aes of

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&andlin' Ris!

Risk may be accounted for by evaluating the project

using sensitivity and breakeven analysis.

Risk may be accounted for by (1 applying a

discount rate commensurate !ith the riskiness ofthe cash flo!s" and (#" by using a certainty

e$uivalent factor

%here are several approaches to handling risk&

Risk may be accounted for by evaluating the

project under simulated cash flo! and discount

rate scenarios.

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Usin' a Ris! Adjusted%iscount Rate The structure of the cash flow

discountin mechanism for risk is:&

%he ' amount used for a risky cash flo!) is theexpected dollar value for that time period.

A risk adjusted rate) is a discount rate calculated to

include a risk premium. %his rate is kno!n as the

RA*R" the Risk Adjusted *iscount Rate.

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%e(nin' a Ris! Adjusted

%iscount Rate

1onceptuall%- a risk adjusted discountrate- k- has three components:&

8# A risk&free rate (r), to account for the

time value of mone%9# An averae risk premium (u),to

account for the firm's $usiness risk

# An additional risk factor (a)- with a

positive- )ero- or neative value- toaccount for the risk differential$etween the project's risk and thefirms' $usiness risk#

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Calculatin' a

Ris! Adjusted %iscountRateA risk% discount rate is conceptuall% defined

as:

k = r + u + a

+nfortunately" k,is not easy to estimate.

%!o approaches to this problem are&

1. +se the firm)s overall Weighted Average Cost of

Capital" after tax" as k. %he WACC is the overall rateof return re$uired to satisfy all suppliers of capital.

2.A rate estimating (r, u is obtained from the

Capital Asset -ricing odel" and thena

is added.

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Calculatin' the #ACC

Assume a firm has a capital structure of:

50. common stock- 80. preferred stock-

;0. lon term de$t#

Rates of return re$uired by the holders of each are &

common" 1/0 preferred" 20 pre3tax debt" 40.

%he firm)s income tax rate is 5/0.

WACC 6 (/.7 x /.1/ , (/.1/ x /./2 ,

(/.8/ x (/./4x (13/.5/

6 4.490 pa" after tax.

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The Capital Asset Pricin'

)odel This model esta$lishes the covariance$etween market returns and returnson a sinle securit%#

The covariance measure can $e usedto esta$lish the risk% rate of return- r-for a particular securit%- ivene(pected market returns and the

e(pected risk free rate#

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Calculatin' r fro* theCAP)

The equation to calculate r- for asecurit% with a calculated 3eta is:

Where & is the re$uired rate ofreturn being calculated" is the risk freerate& is the :eta of the security" and

is the expected return on the market.

( )rE~fR

mR

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+eta is the Slope of anOrdinary ,east Squares

Re'ression ,ine&hare 'e$(rns 'egressed )n *ar+e$

'e$(rns

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

0,10

0,12

-0,10 -0,05 0,00 0,05 0,10 0,15 0,20

'e$(rns on *ar+e$, - .a

'e$(rnsof&hare,

-

.a

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The Re'ression Process

%he value of :eta can be estimated as the regression coefficient

of a simple regression model. %he regression coefficient a)

represents the intercept on the y3axis" and b) represents :eta"

the slope of the regression line.

itmtiit urbar ++=

Where" 6 rate of return on individual firm i)s shares at time t

6 rate of return on market portfolio at time t

6 random error term (as defined in regression

analysis

mtr

uit

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The Certainty Equivalent

)ethod:Adjustin' the cash-o.s to their /certain0equivalents%he Certainty ;$uivalent method adjusts the

cash flo!s for risk" and then discounts thesecertain) cash flo!s at the risk free rate.

( ) ( )

COetc

r

bCF

r

bCFNPV

+

+

+

=

2

2

1

1

11

Where& bis the certainty coefficient) (established by

management" and is bet!een / and 1 and r is the

risk free rate.

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Analysis Under Risk

:Summary +isk is the variation in future cash flows

around a central e(pected value#

+isk can $e accounted for $% adjustin the!P" calculation discount rate: there are twomethods , either the

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Appraisin Projects !it" Real#ptions@0ritics o+ the =0> criteria argue thatcash +low analysis +ails to account +or+le;i*ility in *usiness decisions)

@Real option &odels are &ore +ocused ondescri*ing uncertainty and in particularthe &anagerial +le;i*ility inherent in&any in:est&ents

@Real options gi:e the +ir& theopportunity *ut not the o*ligation to taecertain action

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$"at is Real #ptions% Application o+ +inancial options theory to

in:est&ent in a non-+inancial 6real8 asset

ence the na&e real options

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Real #ptions: &ink 'et!een(n)estments and *lack+Sc"oles(nputs

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Real #ptions in Capital

Projects en real options to n:est in a +uture capital project =elay in:esting in a project 0hoose the project,s initial capacity

B;pand capacity o+ the project su*se9uent to theoriginal in:est&ent 0hange the project,s technology 0hange the use o+ project during its li+e 'hutdown the project with the intention o+ restarting it

later A*andon or sell the project B;tend the li+e o+ the project n:est in +urther projects contingent on in:est&ent in

the initial project

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Real #ptions in Capital

Projects 'i&ply adjusting the discount rate +or the risdoes not account +or the +ull i&pact o+ uncertainty

Uncertainty a++ects in:est&ent in two ways Uncertainty a*out in:est&ent 68 re9uired

Uncertainty a*out the present :alue 6P8 that the +uturein:est&ent &ight generate

'ince the +uture :alues 6>s8 o+Iand PV &ay*oth *e uncertain% we need to si&pli+y *y

co&*ing the& into a single :aria*lePro+ita*ility inde; C Present :alueDn:est&ent

PIC PV/I

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Real #ptions in Capital

Projects Real option and pro+ita*ility inde; B;ercise real option only i+ PI turns out to *e

greater than o+ e9ual to Eero

Otherwise% eep the +undsIin:ested in the+inancial &aret where PI :irtually alwayse9uals 1)$$

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Uncertainty and Real#ptions ,alue n the year 2$$$ FRO.0O had a prospecti:e project

under de:elop&ent he decision to in:est will not *e &ade until 2$$3 n:est&ent in the project is contingent upon PI *eing

greater than 1 here+ore% in 2$$$ the potential to in:est in 2$$3 was a

real option +or FRO.0O RH= *udget to &ae the project ready is G 1 &illion per

year) he actual siEe o+ the in:est&ent is uncertain% it depended

on &aret in+or&ation +ully a:aila*le until 2$$3 Real options payo++ histogra&

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Real #ptions in CapitalProjects

$ $)4 $)"

Pro*a*ility

1)$ 1)4 1)" 2)$

Real Option Payo++ istogra&

P

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Calculation of t"e Expected P(of Payo- he +irst colu&n shows selected inter:als o+ the PIused in

the histogra& he second colu&n is the a:erage :alue o+ the PI +or each

inter:al he third colu&n gi:es the pro*a*ility &anage&ent

assigned to each inter:al he +ourth colu&n gi:es the :alue o+ the PIo+ the payo++

depending on whether or not &anage&ent would e;ercisethe in:est&ent option

he +inal colu&n gi:es the product o+ the PI and its

pro*a*ility +or each inter:al he su& at the *otto& o+ the colu&n gi:es the e;pected

PIo+ the payo++

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Calculation of t"e Expected P(of Payo- >or e;a&ple% in the +ourth row PI+alls *etween 1)2 and 1) he second colu&n shows the a:erage :alue o+ the inter:al% 1)4 he third colu&n shows the pro*a*ility &anage&ent assigned to

this inter:al% $)21 Iecause the a:erage inter:al :alue o+ 1)4 is greater than 1%

&anage&ent would intend to in:est in this inter:al% gaining an

a:erage PI:alue o+ 1)4 with pro*a*ility o+ $)21 he +inal colu&n gi:es the product o+ the PI:alue 61)48 and its

pro*a*ility6$)218i)e) $)2#4 he +irst two rows PI:alue is less than 1% &anage&ent under

these circu&stances would in:est in +inancial &aret and get a:alue o+ 1)$$% as shown in the +ourth colu&n

he third row has an inter:al :alue o+ 1) here+ore we useweighted a:erage $)5;1)1J$)5;1C1)$5 he e;pected :alue o+ the in:est&ents PI with option payo++ is

1)225 as shown at the *otto& row

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Calculation of expected P(of payo-nter:al nter:al :alue Pro*a*ility P o+ payo++ B;pected P o+ payo++

$K;KC$)4 $)2 $)1 1)$$ $)1$

$)4K;KC$)" $) $)21 1)$$ $)21$

$)"K;KC1)2 1 $)2 1)$5 $)2!3

1)2K;KC1) 1)4 $)21 1)4$ $)2#4

1)K;KC2 1)" $)1 1)"$ $)2""

1)$$ 1)225

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Risk .eutral ,aluation of Real#ptions C Ris adjust&ent +actor +or PVD Ris adjust&ent +actor +orI

Ris adjust&ent +actor +or PVC 61JR>8D 61JRP8

Ris adjust&ent +actor +orIC 61JR>8D 61JR8

here+ore% > C 61JR8D 61JRP8 % where

R represents the discount rate +or +uture in:est&ente;penditure and RP is the Project,s discount rate

Assu&ing RC $)5 and RPC$)1$% we get >C$)"!$

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Real #ptions in CapitalProjects

$ $)4 $)"

Pro*a*ility

1)$

1)12 1)4# 1)"!

Ris adjusted istogra&

P

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Risk+neutral ,aluation of t"eexpected P( !it" payo-

nter:al Ris-neutralinter:al

nter:al:alue

Pro*a*ility P o+ payo++ B;pected P o+ payo++

$K;KC$)4 $K;KC$)3! $)1" $)1 1)$$ $)1$

$)4K;KC$)" $)3!K;KC$)!4 $)55 $)21 1)$$ $)21$

$)"K;KC1)2 $)!4K;KC1)1$ $)#2 $)2 1)$1 $)24

1)2K;KC1) 1)1$K;KC1)4! 1)2# $)21 1)2# $)2!1

1)K;KC2 1)4!K;KC1)"4 1) $)1 1) $)25

1)$$ 1)1#

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Risk .eutral ,aluation of Real#ptions Re-calculate other :alues using the ris-neutral inter:als)

he result is a s&aller e;pected PI payo++ 1)1# Present :alue o+ the optionC Present :alue o+ the

e;pected in:est&ent e;penditure 6Present :alue o+ theP-18

C G25D61J$)$!83=61)1#-18C G3)44# &illion RH= *udget to &ae the project ready is G 1 &illion per

year) he present :alue o+ this three year annuitydiscounted at 57 is G2)!23 &illion

here+ore% addition to shareholder :alue% due toe;ercising this option% is G3)44# - G2)!23 &illion C$)!2 &illion

RH= should go ahead