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B280F Introduction to Financial Management

Capital-Budgeting DecisionCriteria

By Charles Chiu, PhD, CFA

Lecture 6

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Capital Budget The list of planned investment projects.

Capital budgeting is the process of analyzing alternative long term investments and making long-term investment decisions.

What is Capital Budgeting?

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Capital budgeting:Analyzing alternative long-

term investments and deciding which assets to acquire or sell.

Outcomeis uncertain.

Large amounts ofmoney are usually

involved.

Investment involves along-term commitment.

Decision may bedifficult or impossible

to reverse.

About Capital Budgeting Decisions

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Types of Investment Decisions

Selection decisions concerning proposed projects such as

investments in long-term assets. i.e., property, plant, and equipment, or resource commitments in the form of new product development, market research, re-funding of long-term debt, and introduction of a computer.

Replacement decisions such as replacement of existing facilities

with new facilities.

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?

?

?

PlantExpansion

NewEquipment

OfficeRenovation

I will choose theproject with the mostprofitable return on

available funds.

LimitedInvestment

Funds

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Decision Process

1. Develop and rank all investment projects

2. Authorize projects based on: Government regulation Production efficiency Capacity requirements NPV

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Employee morale

Environmental concerns Corporate image

Employee working conditions

Product quality

Nonfinancial Considerations

How do we decide if a

capital investment

project should be accepted or rejected?

The ideal evaluation method should:

1. include all cash flows that occur during the life of the project,

2. consider the time value of money, and

3. incorporate the required rate of return on the project.

Decision-making Criteria in Capital Budgeting

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Decision-making Criteria in Capital Budgeting

Payback Period Discounted Payback Period Net Present Value (NPV) Profitability Index (PI) Internal Rate of Return (IRR) Modified Internal Rate of Return

(MIRR)

Decision Rule

All of these techniques attempt to compare the costs and benefits of a project

The over-riding rule of capital budgeting is to accept all projects for which the cost is less than, or equal to, the benefit: Accept if: Cost Benefit Reject if: Cost > Benefit

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How long will it take for the project to generate enough cash to pay for itself?

The payback period measures the length of time to recover the amount of initial investment. It is computed by dividing the initial investment by the cash inflows through increased revenues or cost savings.

Payback Period

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Assume: Cost of investment $18,000 Annual free cash flows $ 3,000

Payback period =

initial investment cost $18,000

increased revenues or cost savings $ 3,000= = 6 years

Decision rule: Choose the project with the shorter payback period, because the shorter the payback period, the less risky the project, and the greater the liquidity.

Example

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Consider two projects whose free cash inflows are not even. Assume each project costs $1,000.

When cash inflows are not even, the payback period has to be found by trial and error.

Year A ($) B ($)1 100 5002 200 4003 300 3004 400 1005 5006 600

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The payback period of project A is 4 years. ($1,000 = $100 + $200 + $300 + $400 )

The payback period of project B is: ($1000 = $500 + $400 + $100) or

The payback period of project B is 2.33 years.

$100$300

= 0.33 years.

Project B is the project of choice in this case, since it has the shorter payback period.

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Advantages It deals with cash flows rather than accounting

profits and therefore focuses on the true timing of the project’s benefits and costs.

It is simple to compute and easy to understand. It can be used as a rough screening device,

eliminating projects whose returns do not materialize until later years.

Shortcomings It ignores the time value of money. It does not consider any required rate of return It ignores the impact of cash inflows received after

the payback period

Discounted Payback Period

Discounts the cash flows at the firm’s required rate of return.

Payback period is calculated using these discounted net cash flows.

Discounted Payback Period

0 1 2 3 4 5

(500) 250 250 250 250 250

Discounted

Year Cash Flow CF (14%)

0 -500 -500.00

1 250 219.30 1 year 280.70 2 250 192.37 2 years 88.33 3 250 168.74 2.52

years

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Net Present Value

Net present value (NPV) is the excess of the present value (PV) of cash inflows generated by the project over the amount of the initial outlay (IO):

Advantages It recognizes the time value of money. It is easy to compute whether the cash

flows form an annuity or vary from period to period

n

ttt IOk

FCFNPV

1 1

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Choose a discount rate – the minimum required rate of return.

Calculate the presentvalue of cash inflows.

Calculate the presentvalue of cash outflows.

NPV = -

Computation

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General decision rule . . .If the Net Present Value is . . . Then the Project is . . .

Positive . . . Acceptable, since it promises a return greater than the required

rate of return.

Zero . . . Acceptable, since it promises a return equal to the required rate

of return.

Negative . . . Not acceptable, since it

promises a return less than the required rate of return.

Decision Rule

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Foundation of the NPV Approach

The market value of the firm is based on the present value of the cash flows it is expected to generate.

Additional investments are “good” if the present value of the incremental expected cash inflows exceeds their cost.

Thus, “good” projects are those which increase firm value - or, good projects are those projects that have positive NPVs!

Conclusion - Invest only in projects with non-negative NPV.

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Sources of NPV

o Economies of Scaleo Cost Advantageso Product differentiationo Distribution Advantageo Regulatory Protection

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Profitability Index (Benefit/Cost Ratio)

The profitability index is the ratio of the total PV of future cash inflows to the initial investment

This index is used as a means of ranking projects in descending order of attractiveness.

Decision rule: If the profitability index is greater than or equal to 1.00, then accept the project.

IOk

FCF

PI

n

ttt

1 1

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Internal Rate of Return

Internal rate of return (IRR) is defined as the rate of interest that equates I with the PV of future cash inflows.

At IRR: NPV = 0

Decision rule: Accept the project if the IRR is greater than or equal to the required rate of return or hurdle rate. Otherwise, reject it.

n

tt

t IOIRR

FCF

1 1

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Advantage IRR is a good decision-making tool as long

as cash flows are conventional. (- + + + + +)

Shortcoming If there are multiple sign changes in the

cash flow stream, we could get multiple IRRs. (- + + - + +)

0 1 2 3 4 5

(500) 200 100 (200) 400 300

1 2 3

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A project is said to be mutually exclusive if the acceptance of one project automatically excludes the acceptance of one or more other projects.

In the case where one must choose between mutually exclusive investments, the NPV and IRR methods may result in contradictory indications.

Mutually Exclusive Investments

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Projects that have different life expectancies.

Projects that have different sizes of investment.

Projects whose cash flows differ over time. For example, the cash flows of one project increase over time, while those of another decrease.

Contradictions May Occur When

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The contradictions result from different assumptions with respect to the reinvestment rate on cash flows from the projects.

The NPV method discounts all cash flows at the cost of capital, thus implicitly assuming that these cash flows can be reinvested at this rate.

The IRR method implies a reinvestment rate at IRR. Thus, the implied reinvestment rate will differ from project to project.

The NPV method generally gives correct ranking, since the cost of capital is a more realistic reinvestment rate.

Causes for Contradiction

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Modified Internal Rate of Return(MIRR)

IRR assumes that all cash flows are reinvested at the IRR.

MIRR provides a rate of return measure that assumes cash flows are reinvested at the required rate of return.

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MIRR Steps

1. Calculate the PV of the cash outflows. Using the required rate of return.

2. Calculate the FV of the cash inflows at the last year of the project’s time line. This is called the terminal value (TV).

Using the required rate of return.

3. MIRR: the discount rate that equates the PV of the cash outflows with the PV of the terminal value, ie, that makes:

PVoutflows = PVinflows

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Suppose we are considering investing in an asset that yields $1000 in year one, $1100 in year two, $1500 in year three and $3200 in year four. If your required rate of return is 12%, and the asset costs $5000, determine the IRR and MIRR.

$4000 = $1000/(1+IRR) + $1100/(1+IRR)2

+ $1500/(1+IRR)3 + $3200/(1+IRR)4

IRR =20.09%

Example

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To find the Modified IRR

$4000 = [$1000(1.12)3 + $1100(1.12)2 + $1500(1.12) + $3200]/(1 + MIRR)4

$4000 = [$1405 + $1380 + $1680 +$3200]/(1 + MIRR)4

$4000(1 + MIRR)4 = $7665 (1 + MIRR) = 1.1766

MIRR = 17.66%

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Importance of Capital Budgeting

Capital budgeting is probably the most important issues in corporate finance Identifying investment opportunities

which offer more value to the firm than their cost - the value of the future cash flows need to be greater than the investment required

estimating the size, timing and risk of future cash flows is the most challenging aspect of capital budgeting

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