4. NPV vs IRR.ppt

4-1

Chapter 4: Net Present Value vs Internal Rate of Return

NPV vs IRR: Independent Projects NPV vs IRR: Dependent Projects Differences in the Scale of Investment Timing of the Cash flow Reinvestment Rates The Horizon Problem A Theoretical Justification for Net Present

Value Capital Structure Irrelevancy Dividend Policy Irrelevancy Non-conventional Cash Flow Capital Rationing

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If the discussion is limited to conventional projects which are economically independent of one another no problem arises. In this case, both the NPV and IRR rules lead to identical accept or reject decisions. The NPV and IRR rules with respect to conventional independent projects can readily be proven equivalence. The equivalence can be shown in the following graph:

NPV vs IRR: Independent Projects

4-3

NPV

NPV (K1)

NPV (K2)

Increase in productivity

0 Discount rate

R K2

K1

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NPV vs IRR: Dependent Projects

There may be conflicting results in case of conventional projects which are economically dependent of one another. In this case, NPV and IRR rules lead to different accept or reject decisions. The NPV and IRR rules with respect to conventional dependent projects can readily be proven unequivalence. The unequivalence can be shown in the following graph:

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NPV

Discount rate

2700

2000

1089908

ProjectA

ProjectB

0 10% 20% 28%K0

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NPV vs IRR: Dependent Projects

Project

Initial investment

Net cash

inflow

IRR NPV Cost of capital

A 10000 12000 28%

908 10%

B 15000 17700 20%

1089 10%

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Conflictions between NPV & IRR1. Differences in the Scale of Investment

Project

Initial investme

nt

Net cash inflow in year 1

IRR NPV Cost of capital

M 1000000

1280000 28% 163636

10%

N 5000000

6000000 20% 454545

10%

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2. Timing of the Cash Flow

Project

Initial investme

nt

Net cash inflow in year 1

IRR NPV @ 10% CC

Incremental (Δ)

X 1000000 1280000 28% 163636

ΔI0=4000000ΔCF1=47200

00

Y 5000000 6000000 20% 454545

ΔIRR=18%ΔNPV=29090

9

4-9

NPV

Discount rate

Project A

Project B

0 17% 24%

515

4000

15%16.58%

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Timing of the Cash Flow

Project Investment

Cash inflow Y=1

Cash inflow Y=2

NPV @ 10% CC

IRR

A 100 20 120 17.30 20%

B 100 100 32 16.70 25%

A Minus B

0 -80 88 0.60 10.9%

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NPV

40

32

8

010.9% 20% 25%

‘A minus B’

Project A

Project B

Discount rate

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3. Reinvestment Rate

The use of NPV method implicitly assumes that the opportunity rate at which cash flows generated by a project can be reinvested at the cost of capital, whereas use of IRR method implies that the firm has the opportunity to reinvest at the IRR. Thus NPV method evaluates the cash flows at the cost of capital, while the IRR method evaluates cash flows at the project’s IRR.

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Reinvestment Rate

Therefore, we simply must come to the conclusion that the correct reinvestment rate assumption is the cost of capital, which is implicit in the NPV method. This in turn, leads us to prefer the NPV method, at least firms willing and able to obtain capital at a cost reasonably close to their current cost of capital. In addition to this, in case of nonnormal cash flows, IRR is not usable because there is existence of multiple IRR.

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4. Horizon ProblemHorizon problem arises when alternative investment

projects have different lives. Example:

Project

Investment

CF1 CF2 CF3 CF4 NPV @ 10%

IRR

A 100 120 - - - 9 20%

B 100 - - - 174 19 15%

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Horizon Problem

Since project A earns its cash inflow of 120 at the end of the 1st year, while in project B the cash inflow of 174 at the end of 4th year, it has been argued that the appropriate comparison is with the cash flow of the earlier project repeated three more times. Denoting the repetitive project A*, cash flows can be rewritten as follows by assuming reinvestment of earlier years’ cash inflows:

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Horizon Problem

Project

Investment

CF1 CF2 CF3 CF4 NPV @ 10

IRR

A* 100 120-100=20

120-100=20

120-100=20

120 31.7 20%

B 100 - - - 174 19.0 15%

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A Theoretical Justification for Net Present Value

1. It maximizes investors’ utility by maximizing shareholders’ wealth.

2. It takes into account investment size.3. It reinvest interim cash flows at the

relevant rate.4. It can be applied in case of both

conventional and non-conventional cash flows.

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Important Terms:

1. Investment schedule.2. The meaning of indifference curve.3. Optimal investment decisions4. The money market line.5. Separation of investment and financing

decisions

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Second period cash flow

First period cash flow

1,256

950

350200

0W0= 1,000

Project Aa

Project Bb

Project C

c

Project Dd

Investment Opportunity Schedule

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Project

Initial investment (Io

or Co)

Rate of return (IRR)

Future cash inflow (I1 or

C1)

A 400000 15% 460000

B 300000 12% 336000

C 500000 10% 550000

D 800000 8% 864000

Total 2000000 2210000

Investment Opportunity Schedule

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M

M1

N

b

I

I1

C1

0C0

a

Indifference Curve

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I0

I1

I2

W0C0*

C*

d

C1*

Second period cash flow

First period cash flow

0

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Optimum Consumption Decision

Through consideration of investment opportunity schedule and indifference curve – point where these two lines tangent each other i.e. slopes of these two lines are equal.

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C1

C00PV

3PV2PV

1

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Optimum Investment Decision

1. Through consideration of investment opportunity schedule and present value line – point where these two lines tangent each other i.e. slopes of these two lines are equal.

2. Through consideration of investment opportunity schedule and marginal cost of capital line – point where these two lines intersect each other.

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Capital Structure Irrelevancy

Capital structure refers to the proportion of debt and equity used by the firm in financing its investments. This capital structure is irrelevant for investment which means a firm can arbitrarily choose its capital structure. It means regardless of the firm’s financing mix, all investors will maximize their utility by borrowing and lending.

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Dividend Policy Irrelevancy

Theoretically dividend policy is irrelevant for investment which means a firm can arbitrarily choose its dividend decision. It means regardless of the firm’s financing mix, the firm automatically decides its dividend policy. In practice, dividend is relevant since reality is uncertain and the economic content of dividends may be important i.e. dividend may have other uses such as signaling information to the market about the firm’s future earnings potential and stability.

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Non-conventional cash flow

In case of conventional cash flows both NPV and IRR can be applied for making investment decision. Both the methods may provide same accept or reject decision or contradictory decisions. But in case of non-conventional cash flows IRR method can not applied for making investment decision because IRR does not exist. So NPV method can be applied for this project. For example, cash flows are (Tk.100), Tk.200 & (Tk.150) in years 0, 1 & 2 respectively. IRR is imaginary and NPV is calculable.

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Non-conventional cash flow and Multiple IRR

In case of non-conventional cash flows IRR method can not applied for making investment decision because IRR does not exist. Sometimes it may be possible to calculate IRR, but there will be more than one rates that can not be compared with given cost of capital for making accept or reject decision. For example, cash flows are (Tk.16000), Tk.100000 & (Tk.100000) in years 0, 1 & 2 respectively. IRRs are 25% and 400% (by applying quadratic equation) and NPV @ 30% cost of capital is (Tk.1751).

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Capital rationing

Firms commonly operate under capital rationing i.e. they have more acceptable independent projects than they can fund. Management internally imposes capital expenditure constraints to avoid what it deems to be excessive levels of new financing. The objective of capital rationing is to select the group of projects that provides the highest overall net present value and does not require more amount than are budgeted.

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Capital rationing

As prerequisite to capital rationing, the best way to any mutually exclusive projects must be chosen and placed in the group of independent projects. It is occurred when the situation that exists if a firm has positive NPV projects but can not find the necessary financing.

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Capital rationing: Fund available Tk.250000

Projects

Initial investmen

t

PV of Benefits @ 10%

CC

IRR (%)

PI @ 10% CC

Selection

IRR- B, C, E

A 80000 112000 12 1.40 X

B 70000 145000 20 2.07 X

Selection based on PI- D, B, E, AC 100000 119000 16 1.19

X

D 40000 100000 8 2.50 X

E 60000 106500 15 1.78 X

F 110000 60000 11 0.55 X

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Problems: 4.2, 4.3 & 4.5