capital budgeting, part i - lakehead...

Capital Budgeting, Part I

Gitman & Hennessey, Chapter 12

November 2003

Capital Budgeting Techniques

1. Net Present Value

2. The Payback Rule

3. The Internal Rate of Return

4. The Profitability Index

5. The Practice of Capital Budgeting

2

Net Present Value

Thenet present value (NPV)of a project measures the difference

between the present value of the project’s future cash flows and

the present value of its costs.

The process of valuing an investment by discounting its future

cash flows is often calleddiscounted cash flow (DCF) valuation.

3

Net Present Value: An Example

Consider a project with an initial cost of $30 and subsequent

costs of $14 per year. That is, some equipment is purchased at

time 0 for $30 and will cost $14 per year to operate.

The project is expected to generate a cash flow of $24 per year

for eight years.

At the end of the eighth year, the equipment used in the project

will be sold for $2 (salvage value).

What is the net present value of this project?

4


Timing of Cash Flows

0 1 2 3 4 5 6 7 8Year

Initial cost

Inflows

Outflows

Salvage

Net cash flow

-30

-30

24

-14

10

24

-14

10

24

-14

10

24

-14

10

24

-14

10

24

-14

10

24

-14

10

24

-14

2

12

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This project’s cash flows can be divided in three parts:

1. An outlay of $30 at time 0;

2. An annuity of $10 per year for eight year, the first payment

taking place in year 1;

3. A lump-sum payment of $2 at the end of year 8.

6


Using a discount rate of 12%, the net present value of this project

is

NPV = −30 +10.12

(1−

(1

1.12

)8)

+2

(1.12)8 = $20.48.

The NPV Rule: An investment should be accepted if its net

present value is positive and should be rejected otherwise.

7

The Payback Rule

Thepayback periodof a project is the time it takes to recover the

project’s initial cost.

The payback rule does not consider the time value of money.

In the previous example, the payback period is exactly 3 years.

8

The Payback Rule

What is the payback period for each of these projects?

0 1 2 3 4 5 6 7 8Year

Project 1

Project 2

-50 12 12 12 12 12 12 12 12

-50 20 15 10 6 4 3 2 2

9

The Payback Rule

Let CCFi ≡ cumulative cash flow from projecti.

0 1 2 3 4 5 6 7 8Year

Project 1

CCF1

Project 2

CCF2

-50 12 12 12 12 12 12 12 12-50 -38 -26 -14 -2 10 22 34 46

-50 20 15 10 6 4 3 2 2-50 -30 -15 -5 1 5 8 10 12

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The Payback Rule

Project 1’s cost is paid back between year 4 and year 5. The

exact time can be approximated as follows:

Payback period= 4 +2

10− (−2)= 4 +

212

= 4.17years.

Project 2’s cost is paid back between year 3 and year 4. The

exact time can be approximated as follows:

Payback period= 3 +5

1− (−5)= 3 +

56

= 3.83years.

11

The Payback Rule

The Payback Rule:Accept any investment with a payback

period below some prespecified number of years.

Project 2 pays itself back before project 1. Is project 2 better than

project 1?

12

The Payback Rule

Let the discount rate be 12%. Then

NPV of project 1 = $9.61.

NPV of project 2 = −$3.75.

That is, if the payback rule were “Only accept projects with a

payback period under 4 years”, then project 2 would be accepted

and project 1 would be rejected, even though

NPV of project 2< 0 < NPV of project 1.

13

The Payback Rule

Advantages of the Payback Rule

1. Easy to understand.

2. Adjusts for uncertainty of later cash flows.

3. Biased toward liquidity.

14

The Payback Rule

Disadvantages of the Payback Rule

1. Ignores the time value of money.

2. requires an arbitrary cutoff point.

3. Ignores cash flows beyond the cutoff date.

4. Biased against long-term projects.

15

The Discounted Payback Rule

Thediscounted payback periodof a project is the time it takes to

repay the project’s initial cost with thediscountedfuture cash

flows.

This rule thus takes into account the time value of money.

The rule is that a project is accepted if its discounted payback

period is below some prespecified number of years.

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The Payback Rule

Supposer = 12%, and let CDCFi ≡ cumulative discounted cash

flow from projecti. Then

0 1 2 3 4 5 6 7 8Year

Project 1

CCF1

CDCF1

Project 2

CCF2

CDCF2

-50 12 12 12 12 12 12 12 12

-50 -38 -26 -14 -2 10 22 34 46-50 -39.3 -29.7 -21.2 -13.6 -6.7 -0.7 4.8 9.6

-50 20 15 10 6 4 3 2 2

-50 -30 -15 -5 1 5 8 10 12-50 -32.1 -20.2 -13.1 -9.3 -7.0 -5.5 -4.6 -3.8

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The discounted payback period for project 1 is between year 6

and year 7, whereas project 2 never pays back its initial cost with

its discounted cash flows.

The discounted payback rule never selects projects with negative

net present value.

18


Advantages of the Discounted Payback Rule

1. Takes the time value of money into account.

2. Easy to understand.

3. Does not accept projects with negative NPV.

4. Biased toward liquidity.

19


Disadvantages of the Discounted Payback Rule

1. May reject projects with positive NPV.

2. requires an arbitrary cutoff point.

3. Ignores cash flows beyond the cutoff date.

4. Biased against long-term projects.

20

The Internal Rate of Return

Theinternal rate of return (IRR)is the most important alternative

to NPV.

It provides the discount rate at which an investment has a zero

net present value.

The IRR Rule: If the IRR of an investment is greater than the

required rate of return, then the investment is worth undertaking.

21

The Internal Rate of Return: An Example

0 1 2 3 4 5Year

Cash flow -50 11 13 15 15 14

The internal rate of return in this example is 10.71%:

−50 +11

1.1071+

13(1.1071)2 +

15(1.1071)3 +

15(1.1071)4 +

14(1.1071)5 ≈ 0.

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With an IRR of 10.71%, will the project be undertaken?

If the firm requires a return of 12%, say, or higher on any of its

projects, then this one won’t be undertaken.

If, on the other hand, the firm requires a return of 9% or higher

on any of its projects, then this one will be undertaken.

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• There exists a positive IRR to any project with a positive

NPV.

• A project with a negative NPV, i.e. a project that never pays

back the initial investment, has a negative IRR.

• Given a certain discount rate, the fact that projectA, say, has

a greater NPV than projectB does not imply thatA’s IRR is

greater thanB’s IRR, and vice versa.

• A single project may have more than one IRR.

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Problems with the IRR

Multiple IRRs

Consider the following stream of cash flows:

0 1 2Year

Cash flow -60 155 -100

This project would have two IRRs: 25% and 33.33%.

The maximum number of IRRs a project can have is equal to the

number of times cash flows change sign.

25


Mutually Exclusive Investments

Is the IRR the right rule to use when a firm has access to

mutually exclusive projects?

Consider the two following projects:

0 1 2 3 4 5 6 7 8Year

ProjectA

ProjectB

-50 8 10 11 12 14 15 15 17

-50 16 13 12 12 12 11 10 8

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From these cash flows, we find:

IRRA = 16.71% and IRRB = 18.69%.

Is projectB better than projectA?

The NPV ofB is not always greater than that ofA.

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Rate NPVA NPVB

5% 30.39 27.40

7% 23.56 22.03

9% 17.53 17.23

11% 12.20 12.94

13% 7.47 9.07

15% 3.25 5.59

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ProjectA and projectB have the same NPV when the discount

rate is around 9.5458%. This is the crossover rate.

The Crossover rate is the internal rate of return ofA−B.

Let rc denote the crossover rate. Then, whenr = rc,

NPVA = NPVB ⇒ NPVA − NPVB = 0.

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Let CFA,t and CFB,t denote the cash flow at timet of projectA

and projectB, respectively. Then

NPVA − NPVB =8

∑t=0

CFA,t

(1+ r)t −8

∑t=0

CFB,t

(1+ r)t

=8

∑t=0

CFA,t −CFB,t

(1+ r)t

= NPVA−B.

30



0 1 2 3 4 5 6 7 8Year

ProjectA

ProjectB

A−B

-50 8 10 11 12 14 15 15 17

-50 16 13 12 12 12 11 10 8

0 -8 -3 -1 0 2 4 5 9

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Whenr < 9.5458%, then NPVA > NPVB and thus the IRR rule

may contradict the NPV rule.

There is no conflict when Whenr > 9.5458%.

Looking at different streams of cash flows, can you tell whether

the IRR and the NPV rules contradict each other?

32

The IRR Rule

Advantages

• Closely related to the NPV rule.

• Easy to understand and communicate.

Disadvantages

• May provide multiple answers.

• May provide the wrong answer when comparing mutually

exclusive projects.

33

The Profitability Index

Theprofitability index (PI)is a benefit/cost ratio.

If a project costs $25 and the present value of its future cash

flows is $37.5, then this project has a profitability index of

37.525

= 1.5.

A project with a positive NPV will have a PI greater than one.

A project with a negative NPV will have a PI smaller than one.

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This measure may also lead to the wrong decision when selecting

among mutually exclusive projects.

Suppose projectA costs $5 and pays off $11 in one year.

Suppose projectB costs $100 and pays off $121 in one year.

If the discount rate is 10%, then

PIA = 2 > 1.1 = PIB but NPVA = 5 < 10 = NPVB.

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Advantages

• Closely related to the NPV rule.

• Easy to understand and communicate.

• Useful when capital available is limited.

Disadvantages

• May lead to incorrect decisions when comparing mutually

exclusive projects.

36

The Practice of Capital Budgeting

Since the NPV tells us what we want to know, why do these

other measures exist?

The NPV is only an approximation. The actual cash flows may

be different from what is expected. Firms usually use multiple

criteria to evaluate a proposal.

For instance, a positive NPV, a short payback period and a high

AAR mean that the project is probably a good one.

If, on the other hand, the firm receives conflicting signals

(positive NPV, long payback period and low AAR), then it must

be more careful when making its decision.

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