1

Chapter 11Capital Budgeting and Net Present Value

Should we build thisplant?

2Ch 13: Capital Budgeting Techniques

Payback period rule Discounted Cash Flow Approaches

Discounted payback period Net present value (NPV) Internal rate of return (IRR)

• Modified internal rate of return (MIRR) Profitability index (PI)

Why is the NPV the best? NPV vs. Payback period NPV vs. IRR

• Mutually exclusive projects• Multiple IRRs

NPV vs. PI The practice of capital budgeting

3

What is capital budgeting? Capital budgeting: Total process of planning,

evaluating, and selecting on capital expenditures for long-lived assets. Usually requires a large amount of capital expenditures. It could be anything that requires lots of money.

“In February 2000, Corning, Inc., announced plans to spend $170 million to expand by 50 percent its manufacturing capacity of optical fiber, a crucial component of today’s high-speed communications networks.”

To do or not to do? That is the question!

Is there any financial method that Corning can use to make this investment decision?

4

Capital Budgeting: Steps

1. Estimate CFs (inflows & outflows).

2. Assess riskiness of CFs.

3. Determine r = WACC for project.

4. Find NPV, IRR and/or others.

5. Accept or reject project based on the results from sep 4.

5

Example 1 Coca Cola and Procter & Gamble just announced that

they will consider a joint venture (JV) for new beverage and snack business. The new idea is to form a limited-liability company, with 50-50 ownership, that will develop and market juice-based drinks and snacks. Coca-Cola will invest $2 billions and the investments will be deprecated on a straight-line basis with zero salvage value for four-year investment period. You are a CFO of Coca Cola and just created a pro forma income statement for this project. Previously, Coca Cola hired the consulting company to study market research for new beverage and snack business, and paid $300,000. The tax rate is 30 percent. The similar project with a similar risk level yields 10%. Your job is to evaluate this project. Is this project acceptable?

6

Coca Cola Pro Forma Income Statement

Year 2002 2003 2004 2005

Sales $2,000 $2,000 $2,000 $2,000

Cost of Goods Sold

1,000 1,000 1,000 1,000

Gross Profit 1,000 1,000 1,000 1,000

Operating Expenses

50 50 50 50

Depreciation 500 500 500 500

EBT 450 450 450 450

Taxes (30%) 135 135 135 135

Net Income 315 315 315 315

What is a pro forma income statement?Coca Cola

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Q1. What is the operating cash flow (OCF)?

Operating Cash Flow (OCF)

= EBIT (1 – T) + Depreciation

=

- Why operating cash flow, instead of accounting income?

8Q2. Is the consulting fee of $300,000

relevant in capital budgeting decision? What is the sunk cost?

9

Time Line for the Joint Venture

0

815

1

815

2

815

3r = 10%

815

4

-2,000

10

Q3. Is this project acceptable?

We will use several capital budgeting techniques to evaluate new projects. Payback period Discounted cash flow (DCF) approaches

• Discounted payback period• Net Present Value (NPV) - most important• Internal rate of return (IRR) – most popular

Modified Internal Rate of Return

• Profitability index (PI)

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Q3. Is this project acceptable?Payback period

Payback Period: Length of time until initial investment is recovered, or “How long will it take to recover initial investments?”

Computation: 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

Payback period of JV=

12

Payback Period Computation

CFt

Cumulative

Payback

815 815815

0 1 2 3

-2,000

=

-2,000 -1,185 -370 0

2 + 370/815 = 2.454 years

2.454

4

815

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Q3. Is this project acceptable?Discounted payback period

Discounted Payback Period: Use discounted CFs rather than raw CFs.

Computation: Subtract the future discounted cash flows from the initial cost until the initial investment has been recovered

Decision Rule: Accept if the discounted payback period is less than some preset limit

Discounted payback period of JV=

14

815 815815

0 1 2 3

CFt

Cumulative -2000 -1259 -586 27

Discountedpayback 2 + 586 / 612 = 2.96 yrs

Discounted Payback Period

PVCFt -2000

-2000

10%

741 674 612

=

Still this method requires arbitrary cut-off point and ignores cash flows occurring later than cut-off point

4

815

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Q3. Is this project acceptable?Net present value (NPV)

Net Present Value (NPV) = PVs of inflows – PVs of outflows, or= PVs of inflows – Initial Investment (usually occurs in year 0)=

Decision criteria: 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’s wealth, NPV is a direct measure of how well this project will meet our goal.

Should we accept or reject new joint venture proposal?

16

0

.1

nt

tt

CFNPV

r

Cost often is CF0 and is negative.

01

.1

nt

tt

CFNPV CF

r

NPV (continued)

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What’s JV’s NPV?

815

0 1 2 3r =10%

Project JV:

-2,000

741

674

612

$584 = NPV

4

815 815 815

557

Since NPV > 0, Accept!

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NPV (continued)Calculator Solution

Enter in CFj for JV:

-2,000

815

815

815

815

10

CF0

CF1

NPV

CF2

CF3

I/YR = 583.44

CF4

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Q3. Is this project acceptable?Internal rate of return (IRR)

Definition: IRR is the return that makes the NPV = 0

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

Internal Rate of Return (IRR) of JV = Should we accept or reject new joint venture

proposal?

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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.

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0

.1

nt

tt

CFNPV

r

t

nt

t

CF

IRR

0 10.

NPV: Enter r, solve for NPV.

IRR: Enter NPV = 0, solve for IRR.

22Coca Cola Example: IRRSensitivity Analysis: NPV

($600.00)

($400.00)

($200.00)

$0.00

$200.00

$400.00

$600.00

$800.00

$1,000.00

$1,200.00

$1,400.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Discount Rate (%)

NP

V

NPV >0 ACCEPT!

NPV < 0REJECT!

IRR = 22.87%

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Computing IRR For The Project

If you do not have a financial calculator, then this becomes a trial and error process

Calculator Enter the cash flows as you did with NPV Press IRR If IRR > 10%, required return, then

accept the project.Should we accept or reject the new JV?

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Rationale for the IRR Method

If IRR > WACC, then the project’s rate of return is greater than its cost-- some return is left over to boost stockholders’ returns.

Example: WACC = 10%, IRR = 22.87%.Profitable.

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Q3. Is this project acceptable?Profitability Index (PI)

Definition: PV of future cash flows @ R (discount rate)

divided by Initial Investment “Bang for the buck” Benefit-cost ratio

Decision rule: If PI > 1 then accept project PI of JV = Should we accept or reject the JV?

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Profitability Index

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

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

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Q4: What are the relationships among NPV, IRR, and PI?

The discount rate is 10%. Are the discount rate, opportunity cost, and cost of capital the same things?

In this case, the IRR is 22.87%. When you use 22.87% as new discount rate, what is the new NPV?

What if the discount rate is 20%? What is the new NPV? What if the discount rate is 24%? Does the higher discount rate means the lower NPV? If so, why ?

When NPV > 0, IRR > r? When NPV > 0, PI >1? In general, if NPV > 0, then IRR > R and PI > 1.

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So far,So far,

We learned payback period, discounted We learned payback period, discounted payback period, NPV, IRR and PI to payback period, NPV, IRR and PI to evaluate new projects.evaluate new projects.

Now, we will be making a case that the Now, we will be making a case that the NPV is the best, and NPV is the best, and

We will see why it is the best.We will see why it is the best.Also, we will see some cases that NPV Also, we will see some cases that NPV

and other criteria lead us to conflicting and other criteria lead us to conflicting results.results.

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Example 2: NPV vs. Payback period

0 1 2 3 4 PaybackPayback NPVNPV

A -100 20 30 50 60 3 yr3 yr 21.5221.52

B -100 50 30 20 60 3 yr3 yr 26.2626.26

C -100 50 30 20 6,000 3 yr3 yr ??

Discount rate, r = 10%

30Advantages and Disadvantages of

Payback

Advantages Easy to understand Provides an

indication of a project’s liquidity.

Disadvantages Ignores the time value of

money Requires an arbitrary cutoff

point Ignores cash flows beyond the

cutoff date Biased against long-term

projects, such as research and development, and new projects

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Special cases: What is the difference between independent and mutually exclusive projects?

Projects are:

independent, if the cash flows of one are unaffected by the acceptance of the other.

mutually exclusive, if the cash flows of one can be adversely impacted by the acceptance of the other.

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An Example of Mutually Exclusive Projects

BRIDGE vs. BOAT to get products across a river.

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Example 3: NPV vs. IRR (Mutually Exclusive Projects)

Option #1: You give me $1 now and I’ll give you $1.50 back at the end of the class period.

Option #2: You give me $10 now and I’ll give you $11 back at the end of the class period.

You can choose only one of two options. Assume a zero rate of interest because our class lasts only 2 hours. Which option would you choose?

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Example 4: NPV vs. IRR (Mutually Exclusive Projects)

Project 0 1 2 3 IRRIRR NPV NPV @5%@5%

Long -100 10 60 80 18.1%18.1% $33$33

HigherHigher

Short -100 70 50 20 23.6%23.6%

HigherHigher

$29$29

Which one should we take?

Suppose r = 5%.

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Construct NPV Profiles

Enter CFs in CFj and find NPVL andNPVS at different discount rates:

r

0

5

10

15

20

NPVL

50

33

19

7

NPVS

40

29

20

12

5 (4)

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-10

0

10

20

30

40

50

60

0 5 10 15 20 23.6

NPV ($)

Discount Rate (%)

IRRL = 18.1%

IRRS = 23.6%

Crossover Point = 8.7%

Microsoft Excel Worksheet

Double click on the icon

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To Find the Crossover Rate

1. Find cash flow differences between the projects. See data at beginning of the case.

2. Enter these differences in CFj register, then press IRR. Crossover rate = 8.68%, rounded to 8.7%.

3. Can subtract S from L or vice versa, but better to have first CF negative.

4. If profiles don’t cross, one project dominates the other.

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Which project(s) should be accepted at r=5%?

If S and L are independent, accept both. NPV > 0. IRRS and IRRL > r = 5%.

If Projects S and L are mutually exclusive, accept L because NPVS < NPVL at r = 5%, although IRRS > IRRL . Conflict!!!

Choose between mutually exclusive projects on basis of higher NPV. Adds most value in dollar.

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NPV and IRR always lead to the same accept/reject decision for independent projects:

r > IRRand NPV < 0.

Reject.

NPV ($)

r (%)IRR

IRR > rand NPV > 0

Accept.

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Mutually Exclusive Projects

r 8.7 r

NPV

%

IRRS

IRRL

L

S

r < 8.7: NPVL> NPVS , IRRS > IRRL

CONFLICT r> 8.7: NPVS> NPVL , IRRS > IRRL

NO CONFLICT

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Reinvestment Rate Assumptions

NPV assumes reinvest at r (opportunity cost of capital).

IRR assumes reinvest at IRR.Reinvest at opportunity cost, r, is more

realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects.

reinvestment assumption

4242

Another Problem with IRRAnother Problem with IRR

IRR has another problem so-called IRR has another problem so-called “Multiple IRRs.”“Multiple IRRs.”

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Normal Cash Flow Project:

Cost (negative CF) followed by aseries of positive cash inflows. One change of signs.

Nonnormal Cash Flow Project:

Two or more changes of signs.Most common: Cost (negativeCF), then string of positive CFs,then cost to close project.Nuclear power plant, strip mine.

Two kinds of Cash Flows

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Inflow (+) or Outflow (-) in Year

0 1 2 3 4 5 N NN

- + + + + + N

- + + + + - NN

- - - + + + N

+ + + - - - N

- + + - + - NN

45

Example 5: NPV vs. IRR (Multiple IRRs)

0 1 2 3 4 5 NPV @5.62%

NPV @27.78%

NPV @10%

-22 15 15 15 15 -40 ? ? $0.7M

Greenspan Mining Co. is considering a project to strip mine coal. The project requires an investment of $22 million and is expected to produce a cash inflow of $15 million in each Year 1 through 4. However, the Company is obligated to pay $40 million in Year 5 to restore the terrain. The Company’s opportunity cost of capital is 10%. What are the IRR(s) and NPV?

46

Multiple IRRs

($2.00)

($1.50)

($1.00)

($0.50)

$0.00

$0.50

$1.00

$1.50

1.00% 4.00% 7.00% 10.00% 13.00% 16.00% 19.00% 22.00% 25.00% 28.00% 31.00%

Discount Rate

NP

V

47

Could find IRR with calculator:

1. Enter CFs as before.

2. Enter a “guess” as to IRR by storing the guess. Try 10%:

10 STO

IRR = 6% = lower IRR

Now guess large IRR, say, 30%:

30 STO

IRR = 28% = upper IRR

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Multiple IRRs (continued)

The previous slides shows that there are two IRRs Multiple IRRs

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

Rely on NPV instead of IRR in this case

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Managers like rates--prefer IRR to NPV comparisons. Can we give

them a better IRR?

Yes, MIRR is the discount rate whichcauses the PV of a project’s terminalvalue (TV) to equal the PV of costs.TV is found by compounding inflowsat WACC.

Thus, MIRR assumes cash inflows are reinvested at WACC.

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MIRR = 16.5%

10.0 80.060.0

0 1 2 310%

66.0 12.1

158.1

Example 6: Starbucks estimates the cash flows for the new project, “Mocha.” Find MIRR. r = 10%.

-100.010%

10%

TV inflows-100.0

PV outflowsMIRRL = 16.5%

$100 = $158.1

(1+MIRRL)3

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To find TV with a calculator, enter in CFj:

I = 10

NPV = 118.78 = PV of inflows.

Enter PV = -118.78, N = 3, I = 10, PMT = 0.Press FV = 158.10 = FV of inflows.

Enter FV = 158.10, PV = -100, PMT = 0, N = 3.Press I = 16.50% = MIRR.

CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80

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Accept Project ?

YES. Reject because MIRR = 16.50% > r= 10%.

Also, if MIRR > r, NPV will be positive: NPV = +$18.78.

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Why use MIRR rather than IRR?

MIRR correctly assumes reinvestment at opportunity cost = WACC. MIRR also avoids the problem of multiple IRRs.

Managers like rate of return comparisons, and MIRR is better for this than IRR.

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Advantages and Disadvantages of IRR

Advantages closely related to NPV, often leading to

identical decisions 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

Disadvantages may lead to incorrect decisions in comparisons

of mutually exclusive investments – to be explained later

May result in multiple answers (so-called, Multiple IRRs)

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Summary: NPV vs. IRR NPV and IRR will generally give us the same

decision Exceptions: IRR is unreliable in the following

situations 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 Whenever there is a conflict between NPV and

another decision rule, you should always use NPV

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NPV (continued)

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

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

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

Does the NPV have serious flaws?

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Example 7: NPV vs. PIMutually Exclusive Projects

0 1 2 PV@12% PI@

12%

NPV@12%

A $-20M 70M 10M $70.5M $3.52 $50.5

Higher

B $-10M 15M 40M $45.3M $4.53

Higher

$35.3

Suppose Project A and B are mutually exclusive.

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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 (so-called, capital rationing, to be explained later)

Disadvantages May lead to incorrect

decisions in comparisons of mutually exclusive investments (To be explained later)

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Capital Rationing: “imposing maximum capital expenditures”

Capital rationing occurs when a company chooses not to fund all positive NPV projects.

The company typically sets an upper limit on the total amount of capital expenditures that it will make in the upcoming year.

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Reason: Companies want to avoid the direct costs (i.e., flotation costs) and the indirect costs of issuing new capital. Or companies avoid a high debt ratio or earnings dilution.

Solution: Increase the cost of capital by enough to reflect all of these costs, and then accept all projects that still have a positive NPV with the higher cost of capital. Or, Use profitability index, instead of NPVs.

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Capital Rationing Example

Projects 0 1 2 3 r NPV PIRank NPV

Rank PI

A -100 50 60 50 10% 33$ 1.33$ 4 1B -200 100 80 100 10% 32$ 1.16$ 5 2C -300 100 200 120 10% 46$ 1.15$ 2 3D -400 100 200 250 10% 44$ 1.11$ 3 5E -500 100 200 410 10% 64$ 1.13$ 1 4Total Required -1500 Total NPV 97$ 111$

What if the company has only $700 million? Which project(s) should you choose?

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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.

Use more than one Also exercise qualitative judgments in conjunction

with quantitative analysis.

63Summary – Discounted Cash Flow Criteria Net present value

Difference between PV of future cash flows 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 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 useful to rank projects in the presence of capital rationing

64A challenging problem incorporating beta, WACC, and capital budgeting.

Returns on the market and Company Y's stock during the last 3 years are shown below:

Year Market Company Y 2001 –24% – 22% 2002 10 13 2003 22 36

The risk-free rate is 5 percent, and the required return on the market is 11 percent. You are considering a low-risk project whose project beta is 0.5 less than the company's overall corporate beta. You finance only with equity, all of which comes from retained earnings. The project has a cost of $500 million, and it is expected to provide cash flows of $100 million per year at the end of Years 1 through 5 and then $50 million per year at the end of Years 6 through 10. What is the project's NPV (in millions of dollars)?

65Market Y M-mean Y-mean Product Weight Product*weight

-24% -22% -26.67% -31.00% 8.27% 33.33% 2.76%

10% 13% 7.33% 4.00% 0.29% 33.33% 0.10%

22% 36% 19.33% 27.00% 5.22% 33.33% 1.74%

Mean 2.67% 9.00% 4.59%

SD 19.48% 4.59% COV COV

VAR 3.80% 1.21 BETA

Regression Statistics

Multiple R 0.9886929

R Square 0.9775136

Adjusted R Square0.9550272

Standard Error0.0619369

Observations 3

ANOVA

df SS MS F Significance F

Regression 1 0.166764 0.166764 43.47129 0.0958256

Residual 1 0.003836 0.003836

Total 2 0.1706

CoefficientsStandard Error t Stat P-value Lower 95% Upper 95%Lower 95.0%Upper 95.0%

Intercept 0.0577283 0.036093 1.599445 0.355715 -0.400871 0.516328 -0.40087 0.516328

X Variable 1 1.2102 0.183549 6.593276 0.095826 -1.12201 3.542385 -1.12201 3.542385