npv & irr chapter_11 (1)

Chapter 11 Net Present Value and Other

Investment Criteria

California State University-East Bay

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Good Decision Criteria• We need to ask ourselves the following

questions when evaluating decision criteria 1. Does the decision rule adjust for the time

value of money? 2. Does the decision rule adjust for risk? 3. Does the decision rule provide information

on whether we are creating value for the firm?


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Net Present Value• The difference between the market value

of a project and its cost• How much value is created from

undertaking an investment?1. Estimate the expected future cash flows.2. Estimate the required return for projects of

this risk level.3. The third step is to find the present value of

the cash flows and subtract the initial investment.


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Net Present Value 0 1 2 3 4 50 1 2 3 4 5 |----------|----------|----------|----------|----------| -250 -100 -100 -100 -100 -100 +200 +200 +200 +200 +200 +100 +100 +100 +100 +100

If conventional CFs,

0 1 2 3 4 50 1 2 3 4 5 |----------|----------|----------|----------|----------| (-) (+) (+) (+) (+) (+)


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Net Present Value

1 2

0 21 1 1nn

CC CNPV Cr r r


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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.


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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

• Your required return for assets of this risk is 12%.


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Computing NPV for the Project

• Using the formulas:

NPV = 63,120/(1.12) + 70,800/(1.12)2 + 91,080/(1.12)3 – 165,000 = 12,627.42

• Do we accept or reject the project?


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Computing NPV for the Project

• Using the calculator:

CF, 2nd [CLR WORK]CF0 = -165,000 ENTER ” C01 = 63,120 ENTER ”F01 = 1 ” C02 = 70,800 ENTER ”F02 = 1 ”C03 = 91,080 ENTER ”NPV, I = 12 ENTER ”CPT => 12,627.41


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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?• NPV rule is our primary decision.


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IRR – Definition and Decision Rule

• Definition: the return that makes the NPV = 0

• Decision Rule: Accept the project if the IRR is greater than the required return

1 2

0 201 1 1

nn

CC CNPV CIRR IRR IRR


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Computing IRR For The Project

• This is a trial and error process• Calculator

CF, 2nd [CLR WORK]CF0 = -165,000 ENTER ” C01 = 63,120 ENTER ”F01 = 1 ” C02 = 70,800 ENTER ”F02 = 1 ”C03 = 91,080 ENTER ”IRRCPT => 16.13

• Do we accept or reject the project?


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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

NPV

IRR = 16.13%


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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?


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Advantages of IRR• Knowing a return is intuitively appealing (This is

why it is often used in practice)• It is a simple way to communicate the value of a

project to someone who doesn’t know all the estimation details

• It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere

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


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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


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IRR and Non-conventional Cash Flows

• When the cash flows change sign more than once, there could be 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?


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IRR – Definition and Decision Rule

• Definition: the return that makes the NPV = 0

1 2

0 201 1 1

nn

CC CNPV CIRR IRR IRR


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IRR and Non-conventional Cash Flows

If Non-conventional CFs,

0 1 2 3 4 50 1 2 3 4 5 |----------|----------|----------|----------|----------| (-) (+) (-) (+) (+) (-)

Descartes Rule: There could be as many IRRs as there are sign changes.


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Non-conventional CFs Example

• 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?


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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

NPV

IRR = 10.11% and 42.66%


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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


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IRR and Mutually Exclusive Projects

• Mutually exclusive projects– If you choose one, you can’t choose the other– Example: You can choose to attend graduate

school next year at either Harvard or Stanford, but not both

• Intuitively you would use the following decision rules:– NPV – choose the project with the higher NPV– IRR – choose the project with the higher IRR


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Example: 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?


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Example: Mutually Exclusive ProjectsA: CF, 2nd [CLR WORK] CF0 = -500 ENTER ” C01 = 325 ENTER ”F01 = 1 ” C02 = 325 ENTER ” NPV, I = 10 ENTER ”CPT => 64.05 IRR CPT => 19.43

B: CF, 2nd [CLR WORK] CF0 = -400 ENTER ” C01 = 325 ENTER ”F01 = 1 ” C02 = 200 ENTER ” NPV, I = 10 ENTER ”CPT => 60.74 IRR CPT => 22.17


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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

NPV

A B

IRR for A = 19.43%

IRR for B = 22.17%

Crossover Point = 11.8%


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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


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npv & irr chapter_11 (1)

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