Slides developed by:Pamela L. Hall, Western Washington University

Capital Budgeting

Chapter 9

2

Introduction

Capital budgeting involves planning and justifying large expenditures on long-term projects Projects can be classified as:

• Replacement • New business ventures

3

Characteristics of Business Projects Project Types and Risk

Capital projects have increasing risk according to whether they are replacements, expansions or new ventures

Stand-Alone and Mutually Exclusive Projects A stand-alone project has no competing alternatives

• The project is judged on its own viability

Mutually exclusive projects are involved when selecting one project excludes selecting the other

4

Characteristics of Business Projects Project Cash Flows

The first and usually most difficult step in capital budgeting is reducing projects to a series of cash flows

Business projects involve early cash outflows and later inflows• The initial outlay is required to get started

The Cost of Capital A firm’s cost of capital is the average rate it pays its investors for

the use of their money• In general a firm can raise money from two sources: debt and

equity

• If a potential project is expected to generate a return greater than the cost of the money to finance it, it is a good investment

5

Capital Budgeting Techniques

There are four basic techniques for determining a project’s financial viability: Payback (determines how many years it takes to

recover a project’s initial cost) Net Present Value (determines by how much the

present value of the project’s inflows exceeds the present value of its outflows)

Internal Rate of Return (determines the rate of return the project earns [internally])

Profitability Index (provides a ratio of a project’s inflows vs. outflows—in present value terms)

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Capital Budgeting Techniques—Payback The payback period is the time it takes to

recover early cash outflows Shorter paybacks are better

Payback Decision Rules Stand-alone projects

• If the payback period < (>) policy maximum accept (reject) Mutually Exclusive Projects

• If PaybackA < PaybackB choose Project A

Weaknesses of the Payback Method Ignores the time value of money Ignores the cash flows after the payback period

7

Capital Budgeting Techniques—Payback Consider the following cash flows

Year

0 1 2 3 4

Cash flow (Ci) ($200,000) $60,000 $60,000 $60,000 $60,000

Cumulative cash flows

($200,000) ($140,000) ($80,000) ($20,000) $40,000

Payback period occurs at 3.33 years.

Year

0 1 2 3 4

Cash flow (Ci) ($200,000) $60,000 $60,000 $60,000 $60,000

Payback period is easily visualized by the cumulative cash flows

8

Capital Budgeting Techniques—Payback—Example

Q: Use the payback period technique to choose between mutually exclusive projects A and B.

Exa

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e

800200C5

800200C4

350400C3

400400C2

400400C1

($1,200)($1,200)C0

Project BProject A

A: Project A’s payback is 3 years as its initial outlay is fully recovered in that time. Project B doesn’t fully recover until sometime in the 4th year. Thus, according to the payback method, Project A is better than B.

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Capital Budgeting Techniques—Payback Why Use the Payback Method?

It’s quick and easy to apply Serves as a rough screening device

The Present Value Payback Method Involves finding the present value of the

project’s cash flows then calculating the project’s payback

10

Capital Budgeting Techniques—Net Present Value (NPV)

NPV is the sum of the present values of a project’s cash flows at the cost of capital

outflows

inflows

1 2 n0 1 2 n

C C C C NPV

1+k 1+k 1+kPV

PV

If PVinflows > PVoutflows, NPV > 0

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Capital Budgeting Techniques—Net Present Value (NPV) NPV and Shareholder Wealth

A project’s NPV is the net effect that undertaking a project is expected to have on the firm’s value

• A project with an NPV > (<) 0 should increase (decrease) firm value

Since the firm desires to maximize shareholder wealth, it should select the capital spending program with the highest NPV

12

Capital Budgeting Techniques—Net Present Value (NPV)

Decision Rules Stand-alone Projects

• NPV > 0 accept• NPV < 0 reject

Mutually Exclusive Projects• NPVA > NPVB choose Project A over B

13

Capital Budgeting Techniques—Net Present Value (NPV) Example

Q: Project Alpha has the following cash flows. If the firm considering Alpha has a cost of capital of 12%, should the project be undertaken?

Exa

mpl

e $3,000C3

$2,000C2

$1,000C1

($5,000)C0

A: The NPV is found by summing the present value of the cash flows when discounted at the firm’s cost of capital.

Alpha 1 2 3

1,000 2,000 3,000 -5,000 NPV

1.12 1.12 1.12

-5,000 892.90 1,594.40 2,135.40

-5,000 4,622.70

($377.30)

Since Alpha’s NPV<0, it

should not be undertaken.

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Techniques—Internal Rate of Return (IRR) A project’s IRR is the return it generates on the

investment of its cash outflows For example, if a project has the following cash flows

0 1 2 3

-5,000 1,000 2,000 3,000

• The IRR is the interest rate at which the present value of the three inflows just equals the $5,000 outflow

The “price” of receiving the inflows

15

Techniques—Internal Rate of Return (IRR) Defining IRR Through the NPV Equation

The IRR is the interest rate that makes a project’s NPV zero

outflows

inflows

1 2 n0 1 2 n

C C C: C IRR

1 IRR 1 IRR 1 IRRPV

PV

16

Techniques—Internal Rate of Return (IRR) Decision Rules

Stand-alone Projects• If IRR > cost of capital (or k) accept• If IRR < cost of capital (or k) reject

Mutually Exclusive Projects• IRRA > IRRB choose Project A over Project B

17

Techniques—Internal Rate of Return (IRR) Calculating IRRs

Finding IRRs usually requires an iterative, trial-and-error technique

• Guess at the project’s IRR• Calculate the project’s NPV using this interest rate

• If NPV is zero, the guessed interest rate is the project’s IRR

• If NPV > (<) 0, try a new, higher (lower) interest rate

18

Techniques—Internal Rate of Return (IRR)—Example

Q: Find the IRR for the following series of cash flows:

If the firm’s cost of capital is 8%, is the project a good idea? What if the cost of capital is 10%?

Exa

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e

$1,000

C1

($5,000)

C0

$2,000

C2

$3,000

C3

A: We’ll start by guessing an IRR of 12%. We’ll calculate the project’s NPV at this interest rate.

1 2 3

1,000 2,000 3,000 -5,000 NPV

1.12 1.12 1.12

-5,000 892.90 1,594.40 2,135.40

-5,000 4,622.70

($377.30)

Since NPV<0, the project’s

IRR must be < 12%.

19

Techniques—Internal Rate of Return (IRR)—Example

We’ll try a different, lower interest rate, say 10%. At 10%, the project’s NPV is ($184). Since the NPV is still less than zero, we need to try a still lower interest rate, say 9%. The following table lists the project’s NPV at different interest rates.

Exa

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e

Since NPV becomes positive somewhere

between 8% and 9%, the project’s IRR must be

between 8% and 9%. If the firm’s cost of capital is 8%, the project is marginal. If the firm’s cost of capital is 10%, the project is not a

good idea.$1307

$228

($83)9

($184)10

($377)12%

Calculated NPV

Interest Rate Guess

The exact IRR can be calculated using a financial calculator. The financial calculator uses the iterative process just demonstrated; however it is capable of guessing and recalculating much more quickly.

20

Techniques—Internal Rate of Return (IRR) Technical Problems with IRR

Multiple Solutions• Unusual projects can have more than one IRR

• Rarely presents practical difficulties

• The number of positive IRRs to a project depends on the number of sign reversals to the project’s cash flows

• Normal pattern involves only one sign change

The Reinvestment Assumption• IRR method implicitly assumes cash inflows will be

reinvested at the project’s IRR• For projects with extremely high IRRs, this is unlikely

21

NPV Profile

A project’s NPV profile is a graph of its NPV vs. the cost of capital

It crosses the horizontal axis at the IRR

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Figure 9.1: NPV Profile

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Comparing IRR and NPV

NPV and IRR do not always provide the same decision for a project’s acceptance Occasionally give conflicting results in mutually exclusive

decisions If two projects’ NPV profiles cross it means below a

certain cost of capital one project is acceptable over the other and above that cost of capital the other project is acceptable over the first The NPV profiles have to cross in the first quadrant of the

graph, where interest rates are of practical interest The NPV method is the preferred decision-making

criterion because the reinvestment interest rate assumption is more practical

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Figure 9.2: Projects for Which IRR and NPV Can Give Different Solutions

At a cost of capital of k1, Project A is better

than Project B, while at k2 the opposite is true.

25

NPV and IRR Solutions Using Financial Calculators

Modern financial calculators and spreadsheets remove the drudgery from calculating NPV and IRR Especially IRR

The process involves inputting a project’s cash flows and then having the calculators calculate NPV and IRR Note that a project’s interest rate is needed to

calculate NPV

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Spreadsheets

NPV function in Microsoft Excel =NPV(interest rate, Cash Flow1:Cash Flown) +

Cash Flow0

• Every cash flow within the parentheses is discounted at the interest rate

IRR function in Microsoft Excel =IRR(Cash Flow0:Cash Flown)

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Projects with a Single Outflow and Regular Inflows Many projects have one outflow at time 0 and

inflows representing an annuity stream For example, consider the following cash flows

C0 C1 C2 C3

($5,000) $2,000 $2,000 $2,000

In this case, the NPV formula can be rewritten as• NPV = C0 + C[PVFAk, n]

The IRR formula can be rewritten as• 0 = C0 + C[PVFAIRR, n]

28

Projects with a Single Outflow and Regular Inflows—Example

Q: Find the NPV and IRR for the following series of cash flows:

Exa

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e

A: Substituting the cash flows into the NPV equation with annuity inflows we have:

NPV = -$5,000 + $2,000[PVFA12, 3]NPV = -$5,000 + $2,000[2.4018] = -$196.40

Substituting the cash flows into the IRR equation with annuity inflows we have:

0 = -$5,000 + $2,000[PVFAIRR, 3]Solving for the factor gives us:

$5,000 $2,000 = [PVFAIRR, 3]The interest factor is 2.5 which equates to an interest rate between 9% and 10%.

$2,000

C1

($5,000)

C0

$2,000

C2

$2,000

C3

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Profitability Index (PI)

The profitability index is a variation on the NPV method

It is a ratio of the present value of a project’s inflows to the present value of a project’s outflows

Projects are acceptable if PI>1 Larger PIs are preferred

30

Profitability Index (PI)

Also known as the benefit/cost ratio Positive future cash flows are the benefit Negative initial outlay is the cost

1 2 n

1 2 n

0

C C C

1+k 1+k 1+kPI

C

or

present value of inflowsPI

present value of outflows

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Profitability Index (PI)

Decision Rules Stand-alone Projects

• If PI > 1.0 accept• If PI < 1.0 reject

Mutually Exclusive Projects• PIA > PIB choose Project A over Project B

Comparison with NPV With mutually exclusive projects the two

methods may not lead to the same choices

32

Comparing Projects with Unequal Lives If a significant difference exists between

mutually exclusive projects’ lives, a direct comparison of the projects is meaningless

The problem arises due to the NPV method Longer lived projects almost always have

higher NPVs

33

Comparing Projects with Unequal Lives Two solutions exist

Replacement Chain Method• Extends projects until a common time horizon is reached

• For example, if mutually exclusive Projects A (with a life of 3 years) and B (with a life of 5 years) are being compared, both projects will be replicated so that they each last 15 years

Equivalent Annual Annuity (EAA) Method• Replaces each project with an equivalent perpetuity that

equates to the project’s original NPV

34

Comparing Projects with Unequal Lives—Example

Q: Which of the two following mutually exclusive projects should a firm purchase?

Exa

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e

Short-Lived Project (NPV = $432.82 at an 8% discount rate; IRR = 23.4%)

$750$750$750$750$750$750($2,600)

-

C5

-

C4

$750

C3

Long-Lived Project (NPV = $867.16 at an 8% discount rate; IRR = 18.3%)

$750

C1

($1,500)

C0

$750

C2

-

C6

A: The IRR method argues for undertaking the Short-Lived Project while the NPV method argues for the Long-Lived Project. We’ll correct for the unequal life problem by using both the Replacement Chain Method and the EAA Method. Both methods will lead to the same decision.

35

Comparing Projects with Unequal Lives—Example

The Replacement Chain Method involves replicating all projects (if needed) until each project being evaluated has a common time horizon. If the Short-Lived Project is replicated for a total of two times, it will have the same life (6 years) as the Long-Lived Project. This involves buying the Short-Lived Project again in year 3 and receiving the same stream of cash flows as originally expected for the following three years. This stream of cash flows is represented in the table below.

Exa

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e

($750)

Short-Lived Project replicated for a total of two times

$750$750$750($1,500)

-

C5

-

C4

$750

C3

$750

C1

($1,500)

C0

$750

C2

-

C6

Thus, buying the Long-Lived Project is a better decision than buying the Short-Lived Project twice.

The NPV of this stream of cash

flows is $776.41.

36

Comparing Projects with Unequal Lives—Example

The EAA Method equates each project’s original NPV to an equivalent annual annuity. For the Short-Lived Project the EAA is $167.95 (the equivalent of receiving $432.82 spread out over 3 years at 8%); while the Long-Lived Project has an EAA of $187.58 (the equivalent of receiving $867.16 spread out over 6 years at 8%). Since the Long-Lived Project has the higher EAA, it should be chosen. This is the same decision reached by the Replacement Chain Method.

Exa

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e

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Capital Rationing

Capital rationing exists when there is a limit (cap) to the amount of funds available for investment in new projects

Thus, there may be some projects with +NPVs, IRRs > discount rate or PIs >1 that will be rejected, simply because there isn’t enough money available

How do you choose the set of projects in which to invest? Use complex mathematical process called constrained

maximization

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Figure 9.6: Capital Rationing