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Capital Budgeting

- For 9.220

Outline

- Introduction
- Net Present Value (NPV)
- Payback Period Rule (PP)
- Discounted Payback Period Rule
- Average Accounting Return (AAR)
- Internal Rate of Return Rule (IRR)
- Profitability Index Rule (PI)
- Special Situations
- Mutually Exclusive, Differing Scales
- Capital Rationing
- Summary and Conclusions

Recall the Flows of funds and decisions important

to the financial manager

Financing Decision

Investment Decision

Reinvestment

Refinancing

Financial Manager

Financial Markets

Real Assets

Returns from Investment

Returns to Security Holders

Capital Budgeting is used to make the Investment

Decision

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.

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.

The Net Present Value (NPV) Rule

- Net Present Value (NPV)
- Total PV of future CFs - 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 gt 0
- Ranking Criteria Choose the highest NPV

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.

The Time Line NPV of Project X

0

1

2

3

4

Initial outlay (1,100)

Revenues 2,000 Expenses 1,300 Cash flow 700

Revenues 1,000 Expenses 500 Cash flow 500

Revenues 2,200 Expenses 2,700 Cash flow (500)

Revenues 2,600 Expenses 1,400 Cash flow 1,200

1,100.00 454.54 578.51 -375.66 819.62 377.

02

1 500 x 1.10

1 700 x 1.10 2

1 - 500 x

1.10 3

1 1,200 x

1.10 4

NPV

NPV -C0 PV0(Future CFs) -C0

C1/(1r) C2/(1r)2 C3/(1r)3 C4/(1r)4

______ ______ ______ _______ _______

377.02 gt 0

NPV in your HP 10B Calculator

First, clear previous data, and check that your

calculator is set to 1 P/YR

CLEAR ALL

The display should show 1 P_Yr Input data (based

on above NPV example)

INPUT

Yellow

Display should show CF 0

/-

CFj

1,100

Key in CF0

Display should show CF 1

CFj

500

Key in CF1

Display should show CF 2

CFj

700

Key in CF2

Display should show CF 3

Key in CF3

/-

CFj

500

Display should show CF 4

CFj

1,200

Key in CF4

I/YR

Key in r

10

NPV

Display should show 377.01659723

Compute NPV

PRC

Yellow

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.

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

Discounted Payback - An Example

- Initial outlay -1,000
- r 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

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 gt some target book rate of return, then

accept the project

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

Calculating Projected NI

Year 1 Year 2 Year 3 Sales 140 160 200 Expenses

120 100 90 E.B.D. Depreciation E.B.T. Taxes

(40) NI

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 gt Average BV

(divide by 4 - not 3) (iii) The

Average Accounting Return AAR

44.44 Conclusion If target AAR lt 44.44 gt

accept If target AAR gt 44.44 gt reject

The Internal Rate of Return (IRR) Rule

- IRR the discount rate that sets the NPV to zero
- Minimum Acceptance Criteria
- Accept if IRR gt 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

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

(1IRR)1 (1IRR)2

(1IRR)3 (1IRR)4

800 900 500

1,600 2,200

(1IRR)1 (1IRR)2 (1IRR)3

(1IRR)4

IRR in your HP 10B Calculator

First, clear previous data, and check that your

calculator is set to 1 P/YR

CLEAR ALL

The display should show 1 P_Yr Input data (based

on above NPV example)

INPUT

Yellow

Display should show CF 0

/-

CFj

2,200

Key in CF0

Display should show CF 1

CFj

800

Key in CF1

Display should show CF 2

CFj

900

Key in CF2

Display should show CF 3

CFj

500

Key in CF3

Display should show CF 4

CFj

1,600

Key in CF4

IRR/YR

Display should show 23.29565668

Compute IRR

CST

Yellow

Internal Rate of Return and the NPV Profile

- 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

gt accept the project (e.g. r 15) - If required rate of return (r) is higher than IRR

gt reject the project (e.g. r 25)

The Net Present Value Profile

Net present value

Year Cash flow 0 2,200

1 800 2 900 3 500 4 1,600

1,600.00

1,126.47

739.55

419.74

159.62

Discount rate

0

72.64

2

6

10

14

18

22

IRR23.30

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

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

(1IRR)1 (1IRR)2 (1IRR)3

-1,200 -800

-3,500 - 4,000

(1IRR)1 (1IRR)2 (1IRR)3

Internal Rate of Return and the NPV Profile for a

Financing Project

- 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

gt reject the project (e.g. r 10) - If required rate of return (r) is higher than IRR

gt accept the project (e.g. r 15)

The NPV Profile for a Financing Project

Multiple Internal Rates of Return

Example 1

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 IRRs and the NPV Profile - Example 1

IRR272.25

IRR1-29.35

Multiple IRRs in your HP 10B Calculator

First, clear previous data, and check that your

calculator is set to 1 P/YR

CLEAR ALL

The display should show 1 P_Yr Input data (based

on above NPV example)

INPUT

Yellow

Display should show CF 0

/-

CFj

900

Key in CF0

Display should show CF 1

CFj

1,200

Key in CF1

Display should show CF 2

CFj

1,300

Key in CF2

Display should show CF 3

CFj

/-

1,200

Key in CF3

IRR/YR

Display should show 72.252175

CST

Yellow

Compute 1st IRR

IRR/YR

STO

CST

Yellow

/-

RCL

Yellow

30

Compute 2nd IRR by guessing it first

Display should show -29.352494

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 - -- -- ---

Multiple Internal Rates of Return

Example 2

Assume you are considering a project for which

the cash flows are as follows Year Cash

flows 0 -260 1 250 2

300 3 20 4 -340

Multiple IRRs and the NPV Profile - Example 2

IRR229.84

IRR111.52

Multiple Internal Rates of Return

Example 3

Assume you are considering a project for which

the cash flows are as follows Year Cash

flows 0 660 1 -650

2 -750 3 -50 4

850

Multiple IRRs and the NPV Profile - Example 3

IRR18.05

IRR233.96

The Profitability Index (PI) Rule

- PI
- Total Present Value of future CFs / Initial

Investment - Minimum Acceptance Criteria Accept if PI gt 1
- Ranking Criteria Select alternative with highest

PI

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
- Whats the NPV
- Whats the Profitability Index (PI)

- 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.

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

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. - NPV0 IRRhurdle rate PI1
- 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 firms available

funds. PI is especially useful here.

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

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.

Using IRR and PI correctly when projects are

mutually exclusive and are of differing scales

Using IRR and PI correctly when projects are

mutually exclusive and are of differing scales

- 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).

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

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

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 firms

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).

Capital Rationing Example(All numbers are in

thousands)

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 NPVEDB6,181.82
- PI rankings (best to worst)
- E, D, C, B, A
- E, D, C use up the available capital
- Overall NPV NPVEDC6,381.82
- The PI rankings produce the best set of

investments to accept given the capital rationing

constraint.

Capital Rationing Conclusions

- PI is best for initial ranking of independent

projects under capital rationing. - Comparing NPVs of feasible combinations of

projects would also work. - IRR may be useful if the capital rationing

constraint extends over multiple periods (see

project C).

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.

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