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Chapter 8Capital Budgeting and Net Present Value

Should we build thisplant?

2Issues in Ch 8

Chapter 8: Capital Budgeting Techniques 8.1 Payback Period Rule8.2 Average Accounting Return 8.3 Net Present Value8.4 Internal Rate of Return8.5 Profitability Index8.6 Why is the NPV the best?8.7 The Practice of Capital Budgeting

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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?

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Capital Budgeting: Steps

1. Estimate CFs (inflows & outflows).

2. Assess riskiness of CFs.

3. Determine the discount rate, R (To be

discussed in Ch 12).

4. Find NPV, IRR and/or others.

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

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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?

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Coca Cola Pro Forma Income Statement

Year 2006 2007 2008 2009

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

Coca Cola ExampleWhat is a pro forma income statement?

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

Remember from Ch2:

Operating Cash Flow (OCF)

= EBIT + Depreciation expense – Tax

=

- 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?

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Time Line for the Joint Venture

0

815

1

815

2

815

3R=10%

815

4

-2,000

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Q3. Is this project acceptable?

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

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

13Q3. Is this project acceptable?

Average accounting return There are many different definitions for average accounting

return The one used in the book is:

Average net income / average book value (or average investment)

Note that the average book value depends on how the asset is depreciated.

Similar to return on assets measure Decision Rule: Accept the project if the AAR is greater than

a preset rate. Average Accounting Return (AAR) of JV

= average net income / average book value = /

=

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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?

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.10

tt

n

t R

CFNPV

Cost often is CF0 and is negative.

.1 0

1

CFR

CFNPV

tt

n

t

NPV (continued)

16What’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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NPV (continued)

The best approachWe will make the case that the NPV is the

best later.

Understanding NPV Suppose you borrow $1,000 from Citi Bank for one-year loan today

This means that you need to pay back $1,100 in one year.

Suppose with $1,000, you invest on AAPL stocks today. In one year, you sell AAPL stocks for $1,100.

Will you make a profit or loss? You are break-even!!!

How? The present value of $1,100 at 10% is $1,000. NPV = $1,000 (PV of $1,100) - $1,000 (cost) = $0 !!! IRR = 10% from investment, and the cost of capital is 10%

Break-even

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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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Coca Cola Example: IRR

($600)

($400)

($200)

$0

$200

$400

$600

$800

$1,000

$1,200

$1,400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 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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Internal Rate of Return

This is the most important alternative to NPV

Widely accepted in practice. Managers like rates.

IRR: What it really means? Suppose you are a big time real estate developer, and the following cash

flows represents cash returns as well as investment costs: CF 0 ~ 2 = - $10m per year (building materials +

labors) CF 3 ~ 5 = $8m per year (rental income) CF 6 = $15m (estimated selling price) Question: What would my annual compound rate of return on this

investment be? Find IRR!

• IRR is the rate that make the present value of cost equal to the present value of income.

• IRR = 7.26% using your TED.

Or, alternatively, • PV of cash outflow = $28.02m• FV of cash inflow = $42.66m• Find Rate =?• N=6, PV=-28.02, FV=42.66, I=7.26%

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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 Often called “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 farSo far

We learned payback period, average We learned payback period, average accounting return, NPV, IRR and PI to accounting return, NPV, IRR and PI to evaluate new projects.evaluate new projects.

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

We will see why it is the best.We will see why it is the best.

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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%

31Advantages and Disadvantages of

Payback

Advantages Easy to understand Biased towards

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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Advantages and Disadvantages of AAR

Advantages Easy to calculate

Disadvantages Not a true rate of return;

time value of money is ignored

Uses an arbitrary benchmark cutoff rate

Based on accounting net income and book values, not cash flows and market values (from Ch 2)

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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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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

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Example 3: 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?

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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

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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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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???

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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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Example

In which of following causes a project to have multiple IRRs? A. The project has a large initial outlay.

B. With mutually exclusive investments.

C. The opportunity cost is greater than sunk cost.

D. The present value of future cash flow is greater than initial outlay.

E. A ten-year project has a negative cash flow in the last year of the project’s life.

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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 4: 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 1 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 18.13%18.13% 3333

higherhigher

Short -100 70 50 20 23.56%23.56%higherhigher

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Which one should we take?

Suppose r = 5%.

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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%

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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 accept a job next

year from either IBM or GM, 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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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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Example 6: 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.

51Capital Rationing There is one case that the PI is preferred to the NPV.

It is called “capital rationing” situation. Capital rationing occurs when a company chooses not

to fund all positive NPV projects. Or simply the firm does not have sufficient funds to

undertake all positive NPV project. In these cases, the company typically sets an upper

limit on the total amount of capital expenditures that it will make in the upcoming year.

In some cases, companies believe that the project’s managers forecast unreasonably high cash flow estimates, so companies “filter” out the worst projects by limiting the total amount of projects that can be accepted.

Use profitability index, instead of NPVs. Why?

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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 -500 100 200 400 10% 57$ 1.11$ 1 4Total Required -1500

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

53Advantages 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 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.

55Summary – 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

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