capital budgeting chapter 9 © 2003 south-western/thomson learning

Capital Budgeting

Chapter 9

© 2003 South-Western/Thomson Learning

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Introduction

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

• Replacement • New business ventures

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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

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Characteristics of Business Projects Project Cash Flow

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

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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

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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

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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

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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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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

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Decision Rules Stand-alone Projects

• NPV > 0 accept• NPV < 0 reject

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

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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

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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

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• 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

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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

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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

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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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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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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]

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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

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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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• 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

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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

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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

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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

capital budgeting chapter 9 © 2003 south-western/thomson learning

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