1 Capital Budgeting For 9.220. 2 Outline §Introduction §Net Present Value (NPV) §Payback Period...

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Capital Budgeting

For 9.220

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Outline IntroductionNet Present Value (NPV)Payback Period Rule (PP)

Discounted Payback Period RuleAverage Accounting Return (AAR) Internal Rate of Return Rule (IRR)Profitability Index Rule (PI)Special Situations

Mutually Exclusive, Differing Scales Capital Rationing

Summary and Conclusions

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Recall the Flows of funds and decisions important to the financial manager

Financial Manager

Financial Markets

Real Assets

Financing Decision

Investment Decision

Returns from Investment Returns to Security Holders

Reinvestment Refinancing

Capital Budgeting is used to make the Investment Decision

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Introduction

Capital Budgeting is the process of determining which real investment projects should be accepted and given an allocation of funds from the firm.

To evaluate capital budgeting processes, their consistency with the goal of shareholder wealth maximization is of utmost importance.

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Capital Budgeting Mutually Exclusive versus Independent Project

Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g. acquiring an accounting system.

RANK all alternatives and select the best one.

Independent Projects: accepting or rejecting one project does not affect the decision of the other projects.

Must exceed a MINIMUM acceptance criteria.

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The Net Present Value (NPV) Rule Net Present Value (NPV) =

Total PV of future CF’s - Initial Investment

Estimating NPV: 1. Estimate future cash flows: how much? and when? 2. Estimate discount rate 3. Estimate initial costs

Minimum Acceptance Criteria:

Accept if: NPV > 0

Ranking Criteria: Choose the highest NPV

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NPV - An Example

Assume you have the following information on

Project X:

Initial outlay -$1,100 Required return = 10%

Annual cash revenues and expenses are as follows:

Year Revenues Expenses

1 $1,000 $500

2 2,000 1,300

3 2,200 2,700

4 2,600 1,400

Draw a time line and compute the NPV of project X.

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The Time Line & NPV of Project X0 1 2

Initial outlay($1,100)

Revenues $1,000Expenses 500

Cash flow $500

Revenues $2,000Expenses 1,300

Cash flow $700

– $1,100.00

+454.54

+578.51

-375.66

+819.62

+$377.02

1$500 x 1.10

1$700 x 1.10

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NPV

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Cash flow (500)

1- $500 x 1.10

3

4


Cash flow $1,200

1$1,200 x 1.10

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NPV = -C0 + PV0(Future CFs)= -C0 + C1/(1+r) + C2/(1+r)2 + C3/(1+r)3 + C4/(1+r)4

= ______ + ______ + ______ + _______ + _______ = $377.02 > 0

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First, clear previous data, and check that your calculator is set to 1 P/YR:NPV in your HP 10B Calculator

INPUT

CLEAR ALL

Yellow

CFj

I/YR

Key in CF0

Key in CF4

Key in r

Key in CF3 +/- CFj500

1,200

CFjKey in CF1500

CFjKey in CF2700

+/- CFj1,100

The display should show: 1 P_YrInput data (based on above NPV example)

Display should show: CF 0





PRCCompute NPVDisplay should show:

377.01659723

10

Yellow

NPV

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NPV: Strengths and Weaknesses

Strengths Resulting number is easy to interpret: shows how wealth

will change if the project is accepted. Acceptance criteria is consistent with shareholder wealth

maximization. Relatively straightforward to calculate

Weaknesses An improper NPV analysis may lead to the wrong choices

of projects when the firm has capital rationing – this will be discussed later.

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The Payback Period Rule

How long does it take the project to “pay back” its initial investment?

Payback Period = # of years to recover costs of project

Minimum Acceptance Criteria: set by management

Ranking Criteria: set by management

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Discounted Payback - An Example

Initial outlay -$1,000r = 10%

PV of Year Cash flow Cash flow 1 $ 200 $ 182 2 400 331 3 700 526 4 300 205

Accumulated Year discounted cash flow 1 $ 182 2 513 3 1,039 4 1,244

Discounted payback period is just under 3 years

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Average Accounting Return (AAR)

Also known as Accounting Rate of Return (ARR)

Method: using accounting data on profits and book value of the investment

AAR = Average Net Income / Average Book Value

If AAR > some target book rate of return, then accept the project

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Average Accounting Return (AAR)

You want to invest in a machine that produces squash balls. The machine costs $90,000.

The machine will ‘die’ after 3 years (assume straight line depreciation, the annual depreciation is $30,000).

You estimate for the life of the project:

Year 1 Year 2 Year 3

Sales 140 160 200

Expenses 120 100 90

EBD 20 60 110

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Year 1 Year 2 Year 3

Sales 140 160 200

Expenses 120 100 90

E.B.D.

Depreciation

E.B.T.

Taxes (40%)

NI:

Calculating Projected NI

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We calculate:

(i) Average NI =

(ii) Average book value (BV) of the investment (machine):

time-0 time-1 time-2 time-3

BV of investment: 90 60 30 0

=> Average BV = (divide by 4 - not 3)

(iii) The Average Accounting Return:

AAR = = 44.44%

Conclusion: If target AAR < 44.44% => accept

If target AAR > 44.44% => reject

203

603

48186

454

0306090

4520

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The Internal Rate of Return (IRR) Rule

IRR: the discount rate that sets the NPV to zero Minimum Acceptance Criteria:

Accept if: IRR > required return

Ranking Criteria: Select alternative with the highest IRR

Reinvestment assumption: the IRR calculation assumes that all future cash flows are reinvested at the IRR

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Internal Rate of Return - An Example

Initial outlay = -$2,200

Year Cash flow

1 800 2 900 3 500 4 1,600

Find the IRR such that NPV = 0

______ _______ ______ _______

0 = + + + + (1+IRR)1 (1+IRR)2 (1+IRR)3 (1+IRR)4

800 900 500 1,600

2,200 = + + + (1+IRR)1 (1+IRR)2 (1+IRR)3 (1+IRR)4

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First, clear previous data, and check that your calculator is set to 1 P/YR:IRR in your HP 10B Calculator

INPUT

CLEAR ALL

Yellow

CFj

CFj500

1,600

CFj800

CFj900

+/- CFj2,200







CSTCompute IRRDisplay should show:

23.29565668%Yellow

IRR/YR

Key in CF0

Key in CF4

Key in CF3

Key in CF1

Key in CF2

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The NPV Profile

Discount rates NPV

0% $1,600.00

5% 1,126.47

10% 739.55

15% 419.74

20% 152.62

25% -72.64

IRR is between 20% and 25% -- about 23.30%

If required rate of return (r) is lower than IRR => accept the project (e.g. r = 15%)

If required rate of return (r) is higher than IRR => reject the project (e.g. r = 25%)

Internal Rate of Return and the NPV Profile

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Year Cash flow

0 – $2,200 1 800 2 900 3 500 4 1,600

The Net Present Value Profile

Discount rate2% 6% 10

%14% 18%

1,600.00

1,126.47

739.55

419.74

Net present value

159.62

– 72.64 22%

IRR=23.30%

0

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IRR: Strengths and Weaknesses Strengths

IRR number is easy to interpret: shows the return the project generates.

Acceptance criteria is generally consistent with shareholder wealth maximization.

Weaknesses Does not distinguish between investing and

financing scenarios IRR may not exist or there may be multiple IRR Problems with mutually exclusive investments

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IRR for Investment and Financing Projects

Initial outlay = $4,000

Year Cash flow

1 -1,200 2 -800 3 -3,500

Find the IRR such that NPV = 0

_______ _______ _______

0 = + + + (1+IRR)1 (1+IRR)2 (1+IRR)3

-1,200 -800 -3,500

- 4,000 = + + (1+IRR)1 (1+IRR)2 (1+IRR)3

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The NPV Profile of a Financing Project:

Discount rates NPV

0% -$1,500.00

5% -891.91

10% -381.67

15% 50.2

20% 418.98

IRR is between 10% and 15% -- about 14.37%

For a Financing Project, the required rate of return is the cost of financing, thus

If required rate of return (r) is lower than IRR => reject the project (e.g. r = 10%)

If required rate of return (r) is higher than IRR => accept the project (e.g. r = 15%)

Internal Rate of Return and the NPV Profile for a Financing Project

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The NPV Profile for a Financing Project

-$2,000.00

-$1,500.00

-$1,000.00

-$500.00

$0.00

$500.00

$1,000.00

$1,500.00

$2,000.00

0% 5% 10% 15% 20% 25% 30% 35% 40% 45%

Rate of Return (%)

NP

V (

$)

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Assume you are considering a project for which the cash flows are as follows:

Year Cash flows

0 -$900

1 1,200

2 1,300

3 -1,200

Multiple Internal Rates of Return

Example 1

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-$1,000.00

-$800.00

-$600.00

-$400.00

-$200.00

$0.00

$200.00

$400.00

$600.00

-60% -40% -20% 0% 20% 40% 60% 80% 100% 120% 140%

Rate of Return (%)

NP

V (

$)Multiple IRRs and the NPV Profile - Example 1

IRR2=72.25%IRR1=-29.35%

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First, clear previous data, and check that your calculator is set to 1 P/YR:Multiple IRRs in your HP 10B Calculator

INPUT

CLEAR ALL

Yellow

CFj1,200

CFj1,200

CFj1,300

+/- CFj900






CSTCompute 1st IRRDisplay should show:

72.252175%Yellow

IRR/YR

+/-

CSTCompute 2nd IRR by guessing it first

Display should show: -29.352494%

Yellow

IRR/YR

30 +/- RCLYellow

STO

Key in CF0

Key in CF3

Key in CF1

Key in CF2

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No or Multiple IRR Problem – What to do?

IRR cannot be used in this circumstance, the only solution is to revert to another method of analysis. NPV can handle these problems.

How to recognize when this IRR problem can occur When changes in the signs of cash flows happen more

than once the problem may occur (depending on the relative sizes of the individual cash flows). • Examples: +-+ ; -+- ; -+++-; +---+

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Year Cash flows

0 -$260

1 250

2 300

3 20

4 -340


Example 2

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-$80.00

-$70.00

-$60.00

-$50.00

-$40.00

-$30.00

-$20.00

-$10.00

$0.00

$10.00

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Rate of Return (%)

NP

V (

$)Multiple IRRs and the NPV Profile - Example 2

IRR1=11.52%IRR2=29.84%

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Year Cash flows

0 $660

1 -650

2 -750

3 -50

4 850


Example 3

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-$50.00

$0.00

$50.00

$100.00

$150.00

$200.00

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Rate of Return (%)

NP

V($

)Multiple IRRs and the NPV Profile - Example 3

IRR1=8.05%IRR2=33.96%

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The Profitability Index (PI) Rule PI =

Total Present Value of future CF’s / Initial Investment

Minimum Acceptance Criteria: Accept if PI > 1

Ranking Criteria: Select alternative with highest PI

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Profitability Index - An Example

Consider the following information on Project Y:

Initial outlay -$1,100

Required return = 10%

Annual cash benefits:

Year Cash flows

1 $ 500

2 1,000

What’s the NPV? What’s the Profitability Index (PI)?

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The NPV of Project Y is equal to:

NPV = (500/1.1) + (1,000/1.12) - 1,100 = ($454.54 + 826.45) - 1,100

= $1,280.99 - 1,100 = $180.99.

PI = PV Cashflows/Initial Investment =

This is a good project according to the PI rule.

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The Profitability Index (PI) Rule Disadvantages:

Problems with mutually exclusive investments (to be discussed later)

Advantages: May be useful when available investment funds

are limited (to be discussed later). Easy to understand and communicate Correct decision when evaluating independent

projects

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Special situations

When projects are independent and the firm has few constraints on capital, then we check to ensure that projects at least meet a minimum criteria – if they do, they are accepted.

NPV≥0; IRR≥hurdle rate; PI≥1

Sometimes a firm will have plenty of funds to invest, but it must choose between projects that are mutually exclusive. This means that the acceptance of one project precludes the acceptance of any others. In this case, we seek to choose the one highest ranked of the acceptable projects.

If the firm has capital rationing, then its funds are limited and not all independent projects may be accepted. In this case, we seek to choose those projects that best use the firm’s available funds. PI is especially useful here.

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Using IRR and PI correctly when projects are mutually exclusive and are of differing scales

Consider the following two mutually exclusive projects. Assume the opportunity cost of capital is 12%

YearCash flows of Project A

Cash flows of Project B

0 -$100,000 -$50

1 +$150,000 +$100

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Incremental Cash Flows: Solving the Problem with IRR and PI

As you can see, individual IRRs and PIs are not good for comparing between two mutually exclusive projects.

However, we know IRR and PI are good for evaluating whether one project is acceptable.

Therefore, consider “one project” that involves switching from the smaller project to the larger project. If IRR or PI indicate that this is worthwhile, then we will know which of the two projects is better.

Incremental cash flow analysis looks at how the cash flows change by taking a particular project instead of another project.

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YearCash flows of

Project ACash flows of

Project B

Incremental Cash flows of A

instead of B (i.e., A-B)

0 -$100,000 -$50 -$99,950

1 +$150,000 +$100 +$149,900

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IRR and PI analysis of incremental cash flows tells us which of two projects are better.

Beware, before accepting the better project, you should always check to see that the better project is good on its own (i.e., is it better than “do nothing”).

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-200

-150

-100

-50

0

50

100

150

200

0% 5% 10% 15% 20% 25% 30% 35% 40% 45%

Rate of Return (%)

NP

V (

$)

Project A Project B

IRR, NPV, and Mutually Exclusive Projects

Year

0 1 2 3

4

Project A: – $350 50 100 150 200

Project B: – $250 125 100 75 50%80.17BIRR

%91.12AIRR

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-200

-150

-100

-50

0

50

100

150

200

0% 5% 10% 15% 20% 25% 30% 35% 40% 45%

Rate o Return (%)

NP

V (

$)

Project A Project B Incremental (A-B)

IRR, NPV, and the Incremental Project Year

0 1 2 3

4

Project A: – $350 50 100 150 200

Project B: – $250 125 100 75 50

(A-B):

The Crossover Rate = IRRA-B = 8.07%

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Capital Rationing

Recall: If the firm has capital rationing, then its funds are limited and not all independent projects may be accepted. In this case, we seek to choose those projects that best use the firm’s available funds. PI is especially useful here.

Note: capital rationing is a different problem than mutually exclusive investments because if the capital constraint is removed, then all projects can be accepted together.

Analyze the projects on the next page with NPV, IRR, and PI assuming the opportunity cost of capital is 10% and the firm is constrained to only invest $50,000 now (and no constraint is expected in future years).

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Capital Rationing – Example(All $ numbers are in thousands)

Year Proj. A Proj. B Proj. C Proj. D Proj. E

0 -$50 -$20 -$20 -$20 -$10

1 $60 $24.2 -$10 $25 $12.6

2 $0 $0 $37.862 $0 $0

NPV $4.545 $2.0 $2.2 $2.727 $1.4545

IRR 20% 21% 14.84% 25% 26%

PI 1.0909 1.1 1.11 1.136 1.145

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Capital Rationing Example: Comparison of Rankings

NPV rankings (best to worst) A, D, C, B, E

• A uses up the available capital• Overall NPV = $4,545.45

IRR rankings (best to worst) E, D, B, A, C

• E, D, B use up the available capital• Overall NPV = NPVE+D+B=$6,181.82

PI rankings (best to worst) E, D, C, B, A

• E, D, C use up the available capital• Overall NPV = NPVE+D+C=$6,381.82

The PI rankings produce the best set of investments to accept given the capital rationing constraint.

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Capital Rationing Conclusions

PI is best for initial ranking of independent projects under capital rationing.

Comparing NPV’s of feasible combinations of projects would also work.

IRR may be useful if the capital rationing constraint extends over multiple periods (see project C).

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Summary and Conclusions

Discounted Cash Flow (DCF) techniques are the best of the methods we have presented.

In some cases, the DCF techniques need to be modified in order to obtain a correct decision. It is important to completely understand these cases and have an appreciation of which technique is best given the situation.

1 Capital Budgeting For 9.220. 2 Outline §Introduction §Net Present Value (NPV) §Payback Period...

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