investment decision under uncertainty

8/17/2019 Investment Decision Under Uncertainty

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Investment DecisionUnder Conditions of

Uncertainty


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decision

• Investment decision is a process of committing company’sfunds into long term projects with an expectation of futurebenets.

• An investment decision would generally include expansion,acquisition, moderniation and replacement of xed asset.

• Investment decision of the rm are alternatively called thecapital budgeting, investment appraisal or capital

expenditure decisions.• Investment decisions are crucial because!

– It involves commitment of large sum of money andmay introduce drastic change in a company

– They have long term implications for the rm – They are usually irreversible


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What is uncertainty?

It refers to a situation whereby theinvestor or nancial analyst can notestimate future returns accurately

Uncertainty occurs where the future

outcome cannot be predicted withany degree of condence from!nowledge of past or e"isting

events# so that no probabilityestimates are available


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In conditions of uncertainty# theprobability of occurrence of

earning is not !nown $omefactors li!e in%ation# governmentpolicies and political stabilityimpose substantial ris! on the

business rm

In%ation ma!es the future cash%ow of a business uncertain

&re'uent changes in governmentalso a(ect the pattern of cash %ow


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• Under conditions of uncertainty# theinvestor cannot accurately predict

what the returns and theprobability of occurrence will be

• To handle uncertainty# the investoridenties the various stages ofnature of the investment and then

attaches a sub)ective probability toeach of these stages


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• These probabilities are sometimessub)ective as may be based onguesswor! though predicated on thee"perience of the analyst in a giveneconomic environment

• The probabilities can# however bemade ob)ective if the pro)ect at hand isnot completely new In this case an

ob)ective probability can be establishedbased on empirical data of relatedpro)ect


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• What is *is!?

*is! occurs where it is not !nown

what the future outcome will be but

where the various possibleoutcomes

may be e"pected with some degreeof

condence from !nowledge of past

or e"isting events

+ f *i ! d


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+easures of *is! andUncertainty

•

The ris! of an investmentpro)ect is measured by thevariability or dispersion of itscash %ow about the e"pected

value ,e"pected cash %ow-

• The common measures of ris!are

variance#standard deviationcoe.cient of variation


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• /ariance is the average of thes'uared deviation from thee"pected value# while the

standard deviation is its positives'uare root0iven as1

"ariance #$ % & ' ()x* $.+

tandard deviation )#* % - of variancehere!

#$ % variance

# % standard deviation

& % outcome

()x* % expected value )outcome*

+ % probability of the outcome


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Illustration A

• /alculate the variance and the

standard deviation from the followingprobability distribution

+roject A +roject 0

/ash1ow

+ /ash1ow

+

234 4.54 3,344 4.$46,444 4.34 6,444 4.34

6,523 4.$4 7$,444 4.54

•


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• o u on! ro ec

•

()&* % 6444• "ariance is % 89,:23

• tandard deviation is ! #$ % - 89,:23

% $69.34

/ash 1ow)x*

+robability

+

&.+ )x '()x**$

)x '()x**$.+

234 4.54 $$3 9$,344 6:234

6,444 4.34 344 4 4

6,523 4.$4 $23 684,9$3

$:,6$3

7 6444

7 89,:23


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/ash1ow

+robability

&.+ )& '()&** $

) & ' ()&* * $ .+

3,344 4.$4 6644 $4$34444

8434444

6444 4.34 344 4 4

7$444 4.54 7944 ;444444 $2444446444 7 9234444

2ro)ect 3


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The pro)ects have the samee"pected cash %ow ,4,"- 5

6777-# but with di(erences intheir variance and standarddeviation

2ro)ect 3 has a higher

deviation# therefore it is moreris!y


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Coe.cient of /ariation

•

Coe.cient of variation is therelationship between thee"pected value and the

standard deviation It iscalculated thus1

Cov 5 89 4,"-

This measures the ris! pernaira of e"pected cash %ow.


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Illustration 32ro)ect

A

2ro)ect 3

4"pectedCash %ow

$34 6444

$tandard

Deviation

64 54

=he coe>cient of variation are!"A % 64?$34 % 4.48

"0 %54?6444 % 4.45

ince "0 is less than "A, we

conclude that project A is more


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e o s o ncorpora ng*is!

• The methods of incorporatingris! in capital budgeting include1

–The paybac! period#

–

*is! Ad)usted discount rate –Certainty e'uivalents

–The e"pected net 2resent

/alue –The variance of net present

value


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2aybac! 2eriod ,232-• =his refers to the length of time it ta@es for

the cash in1ows to repay the outlays. It isused to determine how quic@ly a projectrepays its outlay.

It can be calculated in two dierent ways

depending on its cash 1owsi. Annual constant cash %ow'i.e the same

amount every year. If the annual cash 1ows

are constant, the +0+ is calculated as follows! % Butlay

A//< )Annual constant /ash 1ow*


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ii. :on constant cash %ows, Irregular-1

if the cash 1ows are irregular a recouping approachwill have to be applied as follows.

Until the balance is ;ero A =W

3A>A:C4

7 ,A- @ ,A-

6 3 ,A- 3B C ,A- 3C

D ,A- 3CD

4 ,A-


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E2eriod6 Fero" >td is considering a pro)ect

re'uiring an investment of :67million


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$olutiona. /onstant cash 1ow )+0+* % Butlay % C64m

A//< $.3m

% 8years

b.

+0+ % 6.:

8.3 % 4.8 D 5 yrsE 4.8 yrs % 5.8years

=W

3A>A:C4

7 67m ,67m-

6 B6m ,Hm-

B BHm ,GBm-

m ,6Jm-

Gm @@@@@@@

investment decision under uncertainty

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