NPV VS. IRRNPV VS. IRRNPV VS. IRRNPV VS. IRR

Mutually exclusiveMutually exclusive

Multiple IRRMultiple IRR

NPV VS. IRR - Introduction

• NPV and IRR are two closely related investment criteria.

• Both are time-adjusted methods of measuring investment worth.

• In case of independent projects, two methods lead to same decisions.

• However, in certain situations, a conflict arises between them.

NPV and IRRNPV and IRRNPV and IRRNPV and IRR

IN CASE OF CONVENTIONAL IN CASE OF CONVENTIONAL

INDEPENDENT PROJECTSINDEPENDENT PROJECTS

It is important to distinguish between conventional and non-conventional

investments while making the comparison between NPV and IRR projects.

CONVENTIONAL INDEPENDENT PROJECTS

A conventional investment is defined as one whose cash flows take the pattern of an initial cash outlay followed by cash inflows.Conventional projects have only one change in the sign of cash flows.For example : - (10000),+2500,+4000

Non-Conventional InvestmentA non- conventional investment is one which has cash outflows mingled with cash inflows throughout the life of the project.Non-conventional investments have more than one change in the signs of cash flows.For example : (160000),+1000000, -1000000

NPV and IRR in case of conventional independent

projectsIn case of conventional investments, which are economically independent of each other,NPV and IRR methods result in same accept or reject decision. (if a firm is not constrained for funds in accepting all profitable projects.)Accept – Projects with positive NPVAccept – Projects with higher IRR than required rate of return.

NPV & IRR IN CASE OF CONVENTIONAL PROJECTS

NPV PROFILE

-5000

0

5000

10000

15000

0 5 10 15 16 20 25

DISCOUNT RATE (%)

NP

V NPV

Marginal project• Marginal/last project is one which

has zero NPV (if NPV method is followed) : NPV=0

• IRR equal to required rate of return(if IRR method if followed) IRR=K

• IRR>k

Lending and Borrowing-type projectsInvestment projects may be borrowing type or

lending type.

Let us see the following example-

Projects

C0 C1 IRR NPV@10%

x -100 120 20% 9

y 100 -120 20% -9

Lending type of project

• For Project X, the NPV declines as the discount rate increases.It is lending type of project.

• NPV is zero at 20%. It is positive for rates lower than 20% & negative for rates higher than 20%

• Project X is lending type project. Higher the rate we earn, the happier we are.

LENDING - TYPE PROJECT

PROJECT Y

-20-15-10-505

10152025

10 20 30 40

DISCOUNT RATE

NP

V

NPV

Borrowing type projectNPV increases with increase in

discount rate.Project Y is borrowing type project.For example, we are borrowing

Rs.100 @ 20% rate of return.20% is return to the lender.For borrower it is a cost. It is better to borrow at less than opportunity cost of capital (10%)

BORROWING-TYPE PROJECT

PROJECT X

-20-15-10-505

10152025

10 20 30 40

DISCOUNT RATE

NP

V

NPV

LENDING VS.BORROWINGThe IRR rule cannot distinguish between lending and borrowing and hence, a high IRR need not necessarily be a desirable thing. Let us consider project A & BThe IRR for project A is 50% and Project B is 75%Project A is attractive project but not project B.This is because Project A involves lending (investing) Rs.4000 @ 50%.B involves borrowing Rs.4000 @ 75%If we go by IRR figures, B appears more attractive than A.

Project C0 C1 IRR NPV@10%

A -4000 +6000 50% 145

B +4000 -7000 75% -236

MULTIPLE INTERNAL RATE OF RETURNA serious short coming of the IRR method, when used to evaluate non-conventional investments, is that it can yield multiple Internal Rate of Return.Lorie and savage were first to point out that certain configurations of cash flowA necessary, but not sufficient condition for this occurrence is that the cash flow stream changes sign more than once.

Multiple IRR (cont.)

The formula for finding IRR is :

n

NPV =∑ Ct - Co = 0 t=1 (1+r)t

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

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 0 1 2

Cash flow

-$1600 $10000

-$10000

Project A- Year

0 1 2

Cash flows

-1000 4000 -3750

MULTIPLE IRR

DUAL RATE OF RETURN

-800

-600

-400

-200

0

200

0 50 100 150 200

DISCOUNT RATE

NP

V

NPV

Multiple IRR (cont..) It is clear that Project

A yields dual rate of return @ 50% & 150%

At these rates, NPV of the project is zero.

At zero rate of discount, the NPV is simply the difference of undiscounted cash flows.

As discount rate increases, the negative NPV diminishes and becomes zero at 50%

DUAL RATE OF RETURN

-800

-600

-400

-200

0

200

0 50 100 150 200

DISCOUNT RATE

NPV NPV

MULTIPLE IRR

The positive NPV increases as discount rate exceeds 50%, but after reaching maximum it starts decreasing and at 150% it again becomes zero.

In case of projects having multiple changes in sign both lending borrowing are involved.

DUAL RATE OF RETURN

-800

-600

-400

-200

0

200

0 50 100 150 200

DISCOUNT RATE

NPV NPV

Multiple IRR (cont..)

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.