1

Weighing Net Present Value and Other Capital Budgeting Criteria

Chapter 13Fin 325, Section 04 -

Spring 2010Washington State

University

2

IntroductionIn previous chapters we learned how

toCalculate the firm’s cost of capitalEstimate a project’s cash flows

Now, we need to finish the analysis of the project to determine whether the firm should proceed with a potential project.

3

Capital Budgeting TechniquesMost commonly-used methods to evaluate

projects:Net Present Value (NPV)Payback (PB)Discounted Payback (DPB)Internal Rate of Return (IRR)Modified Internal Rate of Return (MIRR)Profitability Index (PI)

NPV is generally the preferred technique for most project evaluations

There are situations where you may want to use one of the other techniques in conjunction with NPV

4

Net Present ValueNPV represents the “purest” of the

capital budgeting rulesIt measures the amount of value created by

the projectNPV is completely consistent with the

overall goal of the firm: to maximize firm value

5

NPV is the sum of the present value of every project cash flow (including the initial investment)

NN

i

CF

i

CF

i

CFNPV

)1(...

)1()1( 11

00

N

nn

n

i

CF

0 )1(

6

NPV BenchmarkNPV includes all of the project’s cash

flows, both inflows and outflowsSince it involves finding the present values

of every cash flow using the appropriate cost of capital as the discount rate, anything greater than zero represents the amount of value added above and beyond the required returnAccept project if NPV > 0Reject project if NPV < 0

7

ExampleA project has a cost of $25,000, and

annual cash flows as shown. Calculate the NPV of the project if the discount rate is 12 percent

0 1 2 3 4

8,500(25,000)

i=12%

12,000 13,500 15,000

8

Financial Calculator solution:CF0 = (25,000)

CF1 = 8,500

CF2 = 12,000

CF3 = 13,500

CF4 = 15,000

I = 12 percentNPV = 11,297.42

9

Interpretation:Do we like this project?

Yes – it has a positive NPVIf the market agrees with our analysis, the

value of our firm will increase by $11,297 due to this project

When will the value-added occur? When the project is complete?NO – it will occur immediately upon the

announcement that we are taking the project

10

11

NPV Strengths and WeaknessesStrengths

NPV not only provides a go/no-go decision, but it also quantifies the dollar amount of the value added

NPV is not a ratioIt works equally well for independent projects and

for choosing between mutually-exclusive projects Accept the project with the highest positive NPV

WeaknessMisinterpretation

Comparing NPV to the cost of the project is wrong! Not understanding that the cost is already incorporated

into the NPV

12

PaybackAnswers the question: How long will it

take us to recoup our costs?Has intuitive appealRemains popular because it is easy to

computeBuilt-in assumptions:

Cash flows are normal Assumes cash flows occur smoothly throughout

the year

13

ExampleRefer to the problem we worked earlier.

Compute the payback.

0 1 2 3 4

8,500(25,000)

i=12%

12,000 13,500 15,000

(25,000)Cumulative (16,500) (4,500)

Payback will occur during the 3rd year

Payback = 2 + 4,500/13,500 = 2.33 years

14

Payback BenchmarkFirms set some maximum allowable

paybackOften set arbitrarily – one of payback’s

greatest weaknesses

Accept project if calculated payback < Maximum allowable payback

Reject project if calculated payback > Maximum allowable payback

15

Discounted PaybackOne of the major problems with

payback is that it ignores the time value of moneyIt treats all cash flows equally regardless of

when they occur

Discounted payback fixes this particular problem

We convert the raw cash flows to their present values, and then calculate payback like before using these discounted cash flows

16

Example

0 1 2 3 4

8,500(25,000)

i=12%

12,000 13,500 15,000

(25,000) 7,589 9,566

Cumulative

CF present values 9,609 9,533

(25,000) (17,411) (7,845)

Discounted Payback will occur during the 3rd year

Discounted Payback = 2 + 7,845/9,609 = 2.82 years

17

Discounted Payback benchmarkLike payback, management will likely set

an arbitrary benchmarkNotice that for normal projects DPB will be

larger than PBThe cash flows that are “chipping away”

at the initial cost are the smaller discounted cash flows, so it takes longer

Hopefully, the arbitrary benchmark would at least take that effect into account

18

PB and DPB Strengths and WeaknessesStrengths:

Easy to calculateIntuitive

Weaknesses:Both methods have severe weaknesses that

make them unsuitable to be the primary method used to select projects

1)PB ignores the time value of money2)Both methods rely on arbitrary accept/reject

benchmarks3)Both methods ignore cash flows that occur after

the payback period. This is perhaps the most serious flaw of all

19

Internal Rate of ReturnIRR is the most popular technique to

analyze projectsOften referred to as “the return on the

project”

IRR is generally consistent with Net Present ValueProblems occur if cash flows are not normalProblems can occur when choosing among

mutually exclusive projects

20

IRR is so closely related to NPV that it is actually defined in terms of NPV

IRR is the discount rate that results in a zero NPV

N

nnIRR

CF

0

0

)1(0

21

Internal Rate of Return benchmarkOnce we calculate IRR, we must compare it

to the cost of capital (investors’ required return) to see if the project is acceptable

We only want to invest in projects where the rate we expect to get (IRR) exceeds the rate investors require (i)

22

ExampleRefer to our previous problem. Calculate

the IRR of the project.

0 1 2 3 4

8,500(25,000)

i=12%

12,000 13,500 15,000

23

Financial Calculator solution:CF0 = (25,000)

CF1 = 8,500

CF2 = 12,000

CF3 = 13,500

CF4 = 15,000

IRR = ? = 30.08%

Do we like this project?

Yes – the IRR is greater than the required return

24

Problems with IRRIRR will be consistent with NPV as long

as:The project has normal cash flowsProjects are independent

NPV profilesThe NPV profile is a graph of NPV versus

different discount ratesIt can help us determine if we may

encounter a problem with IRR

25

For normal cash flows, the NPV profile slopes downward

IRR can be found where the profile crosses the x-axis (i.e. where NPV = 0, the definition of IRR)

26

For non-normal cash flows there will be multiple IRRs for the same projectIRRs represent the solution to a

mathematical series. These solutions are called ‘roots’, and a series will have as many roots as there are sign changes. This is Descartes’ Rule of Signs, discovered in 1637.

For us, this means that there will be as many IRRs as there are sign changes in the cash flows.

27

Examples:In our normal project, we have one IRR

because we have one sign change- + + + +

What if a project involves a cleanup at the end? We might have two sign changes (and two IRRs):- + + + -

What if a project has to shut down in the 3rd year for maintenance, and then starts up again? We might have three sign changes:- + + - + +

28

Here is a sample NPV profile for a project with non-normal cash flows. Notice that the line crosses the x-axis twice:

Fortunately, we can fix the problem of multiple IRRs using a technique called Modified Internal Rate of Return (MIRR)

29

Calculating MIRRCalculating MIRR is a three-step process:

Step 1: Calculate the PV of the cash outflows using the required rate of return.

Step 2: Calculate the FV of the cash inflows at the last year of the project’s time line using the required rate of return.

Step 3: Calculate the MIRR, which is the discount rate that equates the PV of the cash outflows with the PV of the terminal value, ie, that makes PVoutflows = PVinflows

30

ExampleCalculate the MIRR of the following

project:

i = 9%0 1 2 3 4 5

-10,000 4,000 6,000 -5,000 12,000 15,000

31

Step 1: PV of outflows = -13,861Step 2: FV of inflows = 41,497Step 3: Calculate MIRR

MIRR = 24.52%Exceeds the required return of 9%, so

accept project

INPUT 5 -13,861 0N I/YR PV PMT FV

OUTPUT

41,497

24.52

32

Profitability IndexBased on NPV

Measures “bang per buck invested”PI benchmark:

Accept project if PI > 0Reject project if PI < 0

0CF

NPVPI

33

ExampleCalculate the PI of our example

Recall that the NPV = $11,297PI = 11,297 / 25,000 = 45.19%PI indicates that we should accept the

project

0 1 2 3 4

8,500(25,000)

i=12%

12,000 13,500 15,000