Chapter

McGraw-Hill/Irwin Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.

9•Net Present Value and Other

Investment Criteria•Net Present Value and Other

Investment Criteria

9-2

Key Concepts and Skills

• Be able to compute payback and discounted payback and understand their shortcomings

• Understand accounting rates of return and their shortcomings

• Be able to compute the internal rate of return and understand its strengths and weaknesses

• Be able to compute the net present value and understand why it is the best decision criterion

9-3

What is capital budgeting?

• Process of planning and evaluating expenditures on asset whose cash flows are beyond 1 year.• Decide which are acceptable investments• Decide which actually should be purchased

(or invested)

• Long-term decisions; involve large expenditures.

• Very important to firm’s future.

9-4

Good Decision Criteria

• We need to ask ourselves the following questions when evaluating capital budgeting decision rules• Does the decision rule adjust for the time

value of money?• Does the decision rule adjust for risk?• Does the decision rule provide information on

whether we are creating value for the firm?

9-5

Main criteria

• The Payback

• The Discounted Payback

• Net Present Value

• The Internal Rate of Return

• The Profitability Index

• The Average Accounting Return

9-6

What is the payback period?

The number of years required to recover a project’s cost,

or how long does it take to get the business’s money back?

9-7

Payback for Franchise L(Long: Most CFs in out years)

10 8060

0 1 2 3

-100

=

CFt

Cumulative -100 -90 -30 50

PaybackL 2 + 30/80 = 2.375 years

0100

2.4

9-8

Franchise S (Short: CFs come quickly)

70 2050

0 1 2 3

-100CFt

Cumulative -100 -30 20 40

PaybackS 1 + 30/50 = 1.6 years

100

0

1.6

=

9-9

Payback Period

• Computation• Estimate the cash flows• Subtract the future cash flows from the initial

cost until the initial investment has been recovered

• Decision Rule – Accept if the payback period is less than some preset limit

• If the cut-off point is 2 years, which project should be accepted, which should be rejected?

9-10

Strengths and weaknesses of payback

• Strengths• Provides an indication of a project’s risk and

liquidity.• Easy to calculate and understand.

• Weaknesses• Ignores the time value of money.• Ignores CFs occurring after the payback

period.• requires an arbitrary cut-off point

9-11

Discounted Payback Period

• Compute the present value of each cash flow and then determine how long it takes to payback on a discounted basis

• Compare to a specified required period

• Decision Rule - Accept the project if it pays back on a discounted basis within the specified time

9-12

10 8060

0 1 2 3

CFt

Cumulative -100 -90.91 -41.32 18.79

Discountedpayback 2 + 41.32/60.11 = 2.7 yrs

Discounted Payback: Uses discountedrather than raw CFs. Project L

PVCFt -100

-100

10%

9.09 49.59 60.11

=

Recover invest. + cap. costs in 2.7 yrs.

9-13

Discounted payback period (project S)

• Uses discounted cash flows rather than raw CFs.

Disc PaybackS = 2 + / = 1.88 years

CFt -100 70 50 20

Cumulative -100 -36.36 19.99

0 1 2 3

=

15.03

4.96

PV of CFt -100 63.64 41.32

36.36 41.32

10%

9-14

Advantages and Disadvantages of Discounted Payback

• Advantages• Includes time value of

money• Easy to understand

• Disadvantages• Requires an arbitrary

cutoff point• Ignores cash flows

beyond the cutoff point

9-15

Net Present Value

• The difference between the market value of a project and its cost

• How much value is created from undertaking an investment?• The first step is to estimate the expected

future cash flows.• The second step is to estimate the required

return for projects of this risk level.• The third step is to find the present value of

the cash flows and subtract the initial investment.

9-16

.

10t

tn

t r

CFNPV

NPV: Sum of the PVs of inflows and outflows.

Cost often is CF0 and is negative.

.

10

1

CFr

CFNPV t

tn

t

9-17

NPV – Decision Rule

• If the NPV is positive, accept the project

• A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners.

• Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal.

9-18

What’s Franchise L’s NPV?

10 8060

0 1 2 310%

Project L:

-100.00

9.09

49.59

60.1118.79 = NPVL

9-19

Calculator Solution

Enter in CFLO for L:

-100

10

60

80

10

CF0

CF1

NPV

CF2

CF3

I = 18.78 = NPVL

9-20

What’s Franchise S’s NPV?

70 2050

0 1 2 310%

Project S:

-100.00

63.64

41.32

15.0319.98 = NPVS

9-21

Calculator Solution

Enter in CFLO for S:

-100

70

50

20

10

CF0

CF1

NPV

CF2

CF3

I = 19.98 = NPVS

9-22

Decision Criteria Test - NPV

• Does the NPV rule account for the time value of money?

• Does the NPV rule account for the risk of the cash flows?

• Does the NPV rule provide an indication about the increase in value?

• Should we consider the NPV rule for our primary decision rule?

9-23

Internal Rate of Return

• This is the most important alternative to NPV• It is often used in practice and is intuitively

appealing• It is based entirely on the estimated cash flows

and is independent of interest rates found elsewhere

• Project A: cost $1000, PV of all future cash flows = $1500. What is NPV of A?

• Project B: cost $1,000,000, PV of all future cash flows = $1,500,000. What is NPV of B?

• We might need a rate of return in this case.

9-24

Internal Rate of Return: IRR

0 1 2 3

CF0 CF1 CF2 CF3

Cost Inflows

IRR is the discount rate that forcesPV inflows = cost. This is the sameas forcing NPV = 0.

9-25

.

10

NPVr

CFt

tn

t

t

nt

t

CF

IRR

0 10.

NPV: Enter r, solve for NPV.

IRR: Enter NPV = 0, solve for IRR.

9-26

What’s Franchise L’s IRR?

10 8060

0 1 2 3IRR = ?

-100.00

PV3

PV2

PV1

0 = NPV

Enter CFs in CFLO, then press IRR:IRRL = 18.13%. IRRS = 23.56%.

9-27

Rationale for the IRR Method

If IRR > cost of capital (or required return), then the project’s rate of return is greater than its cost-- some return is left over to boost stockholders’ returns.Example: required return = 10%, IRR = 15%. Profitable.If required return = 10%, should we accept or reject L and S?

9-28

Decision Criteria Test - IRR

• Does the IRR rule account for the time value of money?

• Does the IRR rule account for the risk of the cash flows?

• Does the IRR rule provide an indication about the increase in value?

• Should we consider the IRR rule for our primary decision criteria?

9-29

Advantages of IRR

• Knowing a return is intuitively appealing

• It is a simple way to communicate the value of a project to someone who doesn’t know all the estimation details

• If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task

9-30

NPV Vs. IRR

• NPV and IRR will generally give us the same decision

• Exceptions• Non-conventional cash flows – cash flow signs

change more than once• Mutually exclusive projects

• Initial investments are substantially different• Timing of cash flows is substantially different

9-31

NPV Vs. IRR

• NPV and IRR will generally give us the same decision

• NPV>0 and IRR> required return

• NPV<0 and IRR< required return

• NPV=0 and IRR= required return

9-32

Project Example Information

• You are looking at a new project and you have estimated the following cash flows:• Year 0: CF = -165,000• Year 1: CF = 63,120; • Year 2: CF = 70,800; • Year 3: CF = 91,080;

9-33

NPV profile

• A graphical representation of the relationship between an investment’s NPV and various discount rates (required return)

• IRR = 16.13324%• R = 0, NPV = 60,000• R = 10, NPV = 19,324• R = 16.3224, NPV = 0• R = 18, NPV = -5227• IRR > R, NPV > 0• IRR < R, NPV < 0• Same decision

9-34

NPV Profile For The Project

-20,000

-10,000

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

Discount Rate

NP

V

IRR = 16.13%

9-35

NPV Vs. IRR

• NPV and IRR will generally give us the same decision

• Exceptions• Non-conventional cash flows – cash flow signs

change more than once• Mutually exclusive projects

• Initial investments are substantially different• Timing of cash flows is substantially different

9-36

NPV Vs. IRR

• Non-conventional cash flows – cash flow signs change more than once

• Normal (conventional)Time 0 1 2 3CF -300 150 200 250sign - + + +

• Non-normal (non-conventional)Time 0 1 2 3CF -90,000 132,000 100,000 -

150,000sign - + + -• More than 1 IRR, if the signs change 2 times, we have 2

IRRs, the signs changes 3 times, we have 3 IRRs

9-37

IRR and Non-conventional Cash Flows

• When the cash flows change sign more than once, there is more than one IRR

• When you solve for IRR you are solving for the root of an equation and when you cross the x-axis more than once, there will be more than one return that solves the equation

• If you have more than one IRR, which one do you use to make your decision?

9-38

Example – Non-conventional Cash Flows

• Suppose an investment will cost $90,000 initially and will generate the following cash flows:• Year 1: 132,000• Year 2: 100,000• Year 3: -150,000

• The required return is 15%.

• Should we accept or reject the project?

9-39

Example – Non-conventional Cash Flows

• Calculator: CF0 = -90,000; C01 = 132,000; F01 = 1; C02 = 100,000; F02 = 1; C03 = -150,000; F03 = 1; I = 15; CPT NPV = 1769.54

• Solve for IRR• 0 = -90,000 + 132,000/(1+IRR)1

+100,000/(1+IRR)2 -150,000/(1+IRR)3

• (IRR-0.101102)(IRR-0.426585) = 0• IRR = 10.1102% and IRR = 42.6585%• If you compute the IRR on the calculator, you get

10.1102% because it is the first one that you come to.

9-40

Summary of Decision Rules

• The NPV is positive at a required return of 15%, so you should Accept

• If you use the financial calculator, you would get an IRR of 10.11% which would tell you to Reject

• You need to recognize that there are non-conventional cash flows and look at the NPV profile

• When you have conflict between NPV and IRR, go with the NPV

9-41

NPV Profile

($10,000.00)

($8,000.00)

($6,000.00)

($4,000.00)

($2,000.00)

$0.00

$2,000.00

$4,000.00

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

Discount Rate

NP

V

IRR = 10.11% and 42.66%

9-42

IRR and Mutually Exclusive Projects

• Independent and Mutually exclusive projects• Independent: the decision to accept/reject one project

does not affect the decision to accept/reject another.• Mutually exclusive: If you choose one, you can’t

choose the other• NPV(L) = 18.79, NPV(S) = 19.98

• If L and S are independent, which project should we accept?

• IF L and S are mutually exclusive, which project should we accept?

• Intuitively you would use the following decision rules (if mutually exclusive)• NPV – choose the project with the higher NPV• IRR – choose the project with the higher IRR

9-43

Example With Mutually Exclusive Projects

Period Project A

Project B

0 -500 -400

1 325 325

2 325 200

IRR 19.43% 22.17%

NPV 64.05 60.74

The required return for both projects is 10%.

Which project should you accept and why?

9-44

Period A B A-B

0 -500 -400 -100

1 325 325 0

2 325 200 125

• Cross-over rate is the rate where NPV(A) = NPV(B). It is the IRR of the difference in the cash flows of the 2 projects

• IRR (A-B) = cross over rate = 11.8034%

9-45

NPV Profiles

($40.00)

($20.00)

$0.00

$20.00

$40.00

$60.00

$80.00

$100.00

$120.00

$140.00

$160.00

0 0.05 0.1 0.15 0.2 0.25 0.3

Discount Rate

NP

V AB

IRR for A = 19.43%

IRR for B = 22.17%

Crossover Point = 11.8%

9-46

Example With Mutually Exclusive Projects

Period Project A

Project B

0 -500 -400

1 325 325

2 325 200

IRR 19.43% 22.17%

NPV 64.05 60.74

The required return for both projects is 10%.

Which project should you accept and why?

9-47

Conflicts Between NPV and IRR

• NPV directly measures the increase in value to the firm

• Whenever there is a conflict between NPV and another decision rule, you should always use NPV

• IRR is unreliable in the following situations• Non-conventional cash flows• Mutually exclusive projects

9-48

Profitability Index

• PI = PV of future cash flows/ Intial cost• Measures the benefit per unit cost, based

on the time value of money• A profitability index of 1.1 implies that for

every $1 of investment, we create an additional $0.10 in value

• Can have conflict with NPV in some mutually exclusive projects

• This measure can be very useful in situations in which we have limited capital

9-49

Advantages and Disadvantages of Profitability Index

• Advantages• Closely related to NPV,

generally leading to identical decisions

• Easy to understand and communicate

• May be useful when available investment funds are limited

• Disadvantages• May lead to incorrect

decisions in comparisons of mutually exclusive investments

9-50

Summary – Discounted Cash Flow Criteria

• Net present value• Difference between market value and cost• Take the project if the NPV is positive• Has no serious problems• Preferred decision criterion

• Internal rate of return• Discount rate that makes NPV = 0• Take the project if the IRR is greater than the required return• Same decision as NPV with conventional cash flows• IRR is unreliable with non-conventional cash flows or mutually exclusive

projects• Profitability Index

• Benefit-cost ratio• Take investment if PI > 1• Cannot be used to rank mutually exclusive projects• May be used to rank projects in the presence of capital rationing

9-51

Summary – Payback Criteria

• Payback period• Length of time until initial investment is recovered

• Take the project if it pays back in some specified period

• Doesn’t account for time value of money and there is an arbitrary cutoff period

• Discounted payback period• Length of time until initial investment is recovered on a

discounted basis

• Take the project if it pays back in some specified period

• There is an arbitrary cutoff period

9-52

Capital Budgeting In Practice

• If NPV is superior than all other method, why should we consider IRR, payback, etc?• Convenience• NPV is only an estimate, it depends on future cash

flows and discount rate. Both are estimates. Therefore, we need to compute other criteria to strengthen our decisions

• In theory, NPV is the best• In practice, NPV: 74.9%, IRR: 75.7%, and

payback 56.7%. Small companies use payback, big companies use IRR, NPV

9-53

Capital Budgeting In Practice

• We should consider several investment criteria when making decisions

• NPV and IRR are the most commonly used primary investment criteria

• Payback is a commonly used secondary investment criteria