Acb III-conflict Bw Npv vs Irr

8/6/2019 Acb III-conflict Bw Npv vs Irr

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CONFLICT IN CASE OFCONFLICT IN CASE OF

RANKINGRANKING

MUTUALLY EXCLUSIVE

PROJECTS


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CONFLICT IN CASE OF RANKING

MUTUALLY EXCLUSIVE PROJECTS

NPV and IRR methods yield the same result in case ofconventional independent projects. But in case ofmutually exclusive projects IRR can be misleading.

Investment projects are said to be mutually exclusivewhen only one investment could be accepted andothers would have to be excluded.Under such situation, the more profitable out of two ormore alternatives shall be selected.This type of exclusiveness is called technical

exclusiveness.


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CONFLICT IN CASE OF RANKING MUTUALLYCONFLICT IN CASE OF RANKING MUTUALLY

EXCLUSIVE PROJECTSEXCLUSIVE PROJECTS

Two independent projects may also bemutually exclusive if financial constraint isimposed. This is called. Financialexclusiveness or capital rationing.


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CONFLICT IN CASE OF RANKING MUTUALLYCONFLICT IN CASE OF RANKING MUTUALLY

EXCLUSIVE PROJECTS (cont..)EXCLUSIVE PROJECTS (cont..)

The NPV and IRR rules will give conflictingranking under following circumstances

The cash flow pattern of the projects may

differ.The cash outlays of the project may differ.

The projects may have different expected

lives.


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TIMING OF CASH FLOWSTIMING OF CASH FLOWS

The common reason for the conflict between IRR &NPV is the difference in the timing of cash flows.

Project 0 1 2 3 NPV @9%

IRR

M -1680 1400 700 140 301 23%

N -1680 140 840 1510 321 17%


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NPV PROFILES OF M& NNPV PROFILES OF M& N

DISCOUNT RATE()

PROJECT M PROJECT N

56 8

5 4 5

76 76

5 5 7

54 - 6

5 -4 - 57

- 5 - 88


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TIMING OF CASH FLOWSTIMING OF CASH FLOWS

NPV of N falls rapidly as discount rateincreases.

Reason is this is its largest cash flows comelate in life when compounding effect of time ismore significant.


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Scale of investmentScale of investment

NPV and IRR methods will give contradictory ranking whenthe cash outlays are of different sizes.

Project As NPV is low. But IRR is high

Project Bs NPV is high. But IRR is low.

PROJECTS

co c NPV IRR

A - 5 64 5

B -


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PROJECT LIFE SPANPROJECT LIFE SPAN

Difference in the life span of two mutually exclusiveprojects give rise of conflict between IRR and NPV.

Project

C C C C C4 C5 NPV

IRR

X - - - - -

Y - - - - - 4 5


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FISHERS INTERSECTIONFISHERS INTERSECTION

Fishers intersection occurs at the discountrate where NPVs of two projects are equal.

NPVs of M & N intersect at discountrate. This is called Fishers intersection


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NPV VS. IRR-FISHERS INTERSECTION

NPV PROFILES OF PROJECTS M & N

-500

0

500

1000

DISCOUNT RATE (%)

NPVProject M

Project N

Project M 560 409 276 159 54 -40 -125

Project N 810 520 276 70 -106 -257 -388

0 5 10 15 20 25 30


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Fishers intersectionFishers intersection

The formula n (Ct)M/(1+r*)t (Co)M= n (Ct)N/(1+r*)t (Co)Nt=1 t=1

NPVM = NPVN


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ILLUSTRATION determination of discount rate at which fishersintersection occurs

- 68 + 4 /( +r*) + 7 /( +r*) + 4 /( +r*)

- 68 + 4 /( +r*) +84 /( +r*) + 5 /( +r)

Simplify

- 6 /( +r*) + 4 /( +r*) + 5 /( +r*) =

By trial & error, r* =


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At discount rate lessthan intersection rate( ), Project N has

more NPV but low IRR Greater than , M

has more NPV andhigher IRR.

Discountrate ( )

Project M Project N

56 8

5 4 576 76

5 5 7

54 - 65 -4 - 57

- 5 - 88


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MULTIPLE INTERNAL RATE OF

RETURN

A serious short coming of the IRR method, when used to evaluatenon-conventional investments, is that it can yield multipleInternal Rate of Return.

Lorie and savage were first to point out that certainconfigurations of cash flow

A necessary, but not sufficient condition for this occurrence is

that the cash flow stream changes sign more than once.


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Multiple IRR (cont.)

The formula for finding IRR is :n

NPV = Ct - Co = 0t=1 (1+r)t

In case of conventional investment only one positive value for rexists.In case of non-conventional project, there is a possibility ofmultiple roots of r.


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Multiple IRR (cont..)

Let us consider the following

project:

When we solve for the IRR we find

two rates i.e.25% & 400%(NPV is

zero at these rates)This is an example of Multiple IRR.

Similarly, Let us see the

this table and chart -

Year

Cashflow

-$ 6 $ -$

Project

A-Year

Cashflows

- 4 - 75


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MULTIPLE IRR

DUAL RATE OF RETURN

-800

-600

-400

-200

0

200

0 50 100 150 200

DISCOUNT RATE

NPV

NPV


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It is clear that Project Ayields dual rate of return5 & 5

At these rates, NPV of theproject is zero.

At zero rate of discount, theNPV is simply the differenceof undiscounted cash flows.

As discount rate increases,the negative NPVdiminishes and becomes

zero at 5

DUAL RATE OF RETURN

-800

-600

-400

-200

0

200

0 50 100 150 200

DISCOUNT RATE

NPV NPV


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MULTIPLE IRR The positive NPV increases

as discount rate exceeds5 , but after reachingmaximum it startsdecreasing and at 5 it

again becomes zero. In case of projects having

multiple changes in signboth lending borrowing areinvolved.

DUAL RATE OF RETURN

-800

-600

-400

-200

0

200

0 50 100 150 200

DISCOUNT RATE

NPV NPV


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Although reversal in signs is a necessary condition for multiple

IRR, it is not sufficient for such an occurrence.

The occurrence of multiple IRR also depends on the magnitude

of cash flows.

When there are multiple IRRs none of them will work

satisfactorily.

In such cases, an alternative method must be used. The simple

alternative is to use NPV rule.

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Acb III-conflict Bw Npv vs Irr