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FUNDAMENTALS OF FINANCE

Lecture 5: Investment Evaluation Techniques

Presented by: Dr Balasingham Balachandran Professor of Finance Department of Finance, La Trobe Business School

Investment Evaluation Techniques

2 These slides have been drafted by the La Trobe University School of Economics & Finance based on Berk (2011).

Topic Overview

 Introduction to capital budgeting and investment

evaluation

 Net Present Value (NPV)

 Internal Rate of Return (IRR)

 Payback Period (PP)

 Accounting Rate of Return (ARR)

 Choosing between projects when resources are

limited

These slides have been drafted by the Department of Finance, La Trobe Business School based on Berk (2014).

Investment Evaluation Techniques

Learning Objectives

 Understand alternative decision rules and their

drawbacks

 Choose between mutually exclusive investments

 Rank projects when a company’s resources are

limited so that it cannot take all positive- NPV

projects

Investment Evaluation Techniques

 The investment decision entails deciding which projects or investments

should be undertaken

 Companies need to use investment evaluation techniques to determine

the value of the projects available to them

 The final decision as to which projects a company should undertake is

known as ‘capital budgeting’

 In this topic we will apply a number of techniques to the valuation of

individual projects

Investment evaluation and capital budgeting

Investment Evaluation Techniques

 When a corporation allocates funds to long-term investment projects, the outlay is made in the expectation of generating future cash flows

 In making the decision to invest in a project, the key consideration is whether or not the proposal provides an adequate return to investors

 The process used to select projects to invest – capital budgeting – is essentially a process to decide on the optimum use of scarce resources

Investment evaluation and capital budgeting

Investment Evaluation Techniques

There are three fundamental stages in making capital budgeting

decisions:  Stage 1 is the forecasting of costs and benefits associated with a project – the most

important being the financial ones

 Stage 2 involves the application of an investment evaluation technique to decide

whether a project is acceptable, or optimal amongst alternative projects

 Stage 3 is the ultimate decision to accept or reject a project

The capital budgeting process

Investment Evaluation Techniques

 In this lecture we will discuss the four best-known

investment evaluation techniques

 Two of these are based on the discounted cash flow

(DCF) model:  Net present value (NPV)

 Internal rate of return (IRR)

 The other two are accounting-based techniques:  Payback

 (Average) accounting rate of return (ARR)

Investment evaluation techniques

Investment Evaluation Techniques

 In evaluating projects, it is important to keep in mind the

type of projects being considered

 Projects can be:

 Independent

 Mutually exclusive

 Independent projects can be evaluated separately, and

as long as there are sufficient funds are available, a

company should invest in all acceptable independent

projects

Types of projects

Investment Evaluation Techniques

 If two or more projects are mutually exclusive, a company can

only choose one of them – the one that is ranked highest by

the evaluation technique being used

 Projects could be neither mutually exclusive nor independent,

in the sense that accepting one project affects the cash flows

of another

 Project evaluation in this case is complex and largely beyond

the scope of this subject

Types of projects

Investment Evaluation Techniques

 This technique involves calculating the present value of all future cash

inflows and cash outflows that will result from undertaking a project

 These positive and negative present values are then netted off

against one another to determine the net present value of the project

 The firm should accept all positive-NPV projects and reject negative-

NPV projects, because NPV measures the increase in value from the

project

Net Present Value (NPV)

Investment Evaluation Techniques

 If the NPV of a project is zero, the firm would be indifferent between

undertaking the project or paying the available cash back to

shareholders

 This is because zero NPV indicates that the project yields the same

future cash that the investors could obtain by investing themselves

 A project is acceptable if the accumulated cash flow at the end of the

project exceeds the cash flow that investors could have generated

Net Present Value (NPV)

Investment Evaluation Techniques

 Most firms measure values in terms of net present value–that is, in

terms of cash today.

The NPV decision rule

NPV = PV (Benefits) – PV (Costs)

(Eq. 8.1)

Investment Evaluation Techniques

where:

CFt = cash flow generated by the project in year t

r = the opportunity cost of capital

CF0 = the cost of the project (initial cash flow, if any)

n = the life of the project in years

The net present value of a project is calculated as

follows:

Net Present Value (NPV)

  0

NPV 1

n t

t t

CF CF

r  

 

Investment Evaluation Techniques

Using the NPV Rule

 Consider an investment project that requires to built a new fertiliser

plant at a cost of $81.6 million.

 Estimated return on the new fertiliser will be $28 million after the first

year, and lasting four years as shown by the timeline below:

Month: 0 1 2 3

Cash Flow: ($81.60) $28 $28 $28 $28

Cost of capital is10%

Investment Evaluation Techniques

 Therefore, given a discount rate r, the NPV of this project is:

 If we replace r with the estimated cost of capital of 10%, we get an NPV of

$7.2 million, which is positive.

 In this case, the project’s benefits outweigh the costs by $7.2 million and will

increase the value of the firm.

Using the NPV Rule

NPV = -81.6 + 28

+ 28

1+r (1+r)2 (1+r)3 (1+r)4

Investment Evaluation Techniques

 The NPV of the project depends on the appropriate cost of capital.

 It is helpful to calculate an NPV profile, which graphs the project’s NPV over

a range of discount rates.

NPV Profile

 Based on this data the NPV

is positive only when the

discount rates are less than 14%.

Investment Evaluation Techniques

Net Present Value (NPV)

Example:

A company is considering whether to outlay $500,000 for a machine

that will generate $150,000 p.a. over the next 5 years. What is the

NPV of this project, given an opportunity cost of capital of 10%?

Investment Evaluation Techniques

 The strengths of the NPV technique are:  It always ensures the selection of projects that maximise the wealth of

shareholders

 It takes into account the time value of money

 It considers all cash flows expected to be generated by a project

 Two possible weaknesses are:  It requires extensive forecasts of the costs and benefits of a project,

which can be problematic

 The concept is difficult for non-finance-trained managers to understand

Net Present Value (NPV)

Investment Evaluation Techniques

Payback Period

• Payback period is the amount of time required for an investment to generate cash flows to recover its initial cost.

• Steps in estimating the payback period are:  Estimate the cash flows.

 Accumulate the future cash flows until they equal the initial investment.

 Work out how long this takes to happen.

• An investment is acceptable if its calculated payback is less than some prescribed number of years.

Investment Evaluation Techniques

 The payback is given by:

The payback technique

year before full recovery

cost to be recovered at start of year

cash flow during year

Payback 



Investment Evaluation Techniques

The payback technique

Example:

Calculate the payback period for the following project.

Year 0 1 2 3 4 5 6

Project A -1000 100 200 800 100 100 100

Investment Evaluation Techniques

The payback technique

Example:

Calculate the payback period for the following project.

Year 0 1 2 3 4 5 6

Project A -1000 100 200 800 100 100 100

Cum NCF

Investment Evaluation Techniques

The payback technique

Example:

Calculate the payback period for the following project.

Year 0 1 2 3 4 5 6

Project A -1000 100 200 800 100 100 100

Cum NCF -900

Investment Evaluation Techniques

The payback technique

Example:

Calculate the payback period for the following project.

Year 0 1 2 3 4 5 6

Project A -1000 100 200 800 100 100 100

Cum NCF -900 -700

Investment Evaluation Techniques

The payback technique

Example:

Calculate the payback period for the following project.

Year 0 1 2 3 4 5 6

Project A -1000 100 200 800 100 100 100

Cum NCF -900 -700 100

Investment Evaluation Techniques

The payback technique

Example:

Calculate the payback period for the following project.

Year 0 1 2 3 4 5 6 Payback

Project A -1000 100 200 800 100 100 100

Cum NCF -900 -700 100 200 300 400 2.88 yrs

At the end of the third year, the sign of the cumulative net cash flow

has changed from negative to positive. Therefore the payback

occurred during the third year. If we assume the year 3 cash flow

is earned evenly

during year 3, the

payback period is: years88.2

800

700 2 

A Payb ack

Investment Evaluation Techniques

Example

Cash flows for projects A to F are given

below:

Year A B C D E F 0 -900 -900 -900 -900 -900 -900

1 300 300 100 600 600 300

2 300 300 200 200 200 300

3 300 300 600 100 100 300

4 - 300 - - 100

Calculate the payback period for these projects A-F.

Which one is the best investment?

Investment Evaluation Techniques

Example

Cash flows for projects I and D are given

below:

Year Project I Project D

0 (100) (100)

1 10 70

2 60 50

3 80 20

Investment Evaluation Techniques

Example continued

The significant cash flows occur in later years!

10 80 60

0 1 2 3

– 100

Cumulative – 100 – 90 – 30 50

PBPI 2 + 30/80 = 2.375

years

2.375

Project I

Investment Evaluation Techniques

Example Continued

The significant cash flows come early!

70 20 50

0 1 2 3

– 100

Cumulative – 100 – 30 20 40

PBPD 1 + 30/50 = 1.6 years

1.6

Project D

Investment Evaluation Techniques

Decision Criteria Test - Payback

• Does the payback rule account for the time value of money?

• Does the payback rule account for the risk of the cash flows?

• Does the payback rule provide an indication about the increase in value?

• Should we consider the payback rule for our primary decision rule?

Investment Evaluation Techniques

Evaluation of Payback Period

 Advantages:

 Easy to understand.

 Adjusts for uncertainty of later cash flows.

 Disadvantages:

 Time value of money and risk ignored.

 Ignores cash flows beyond the cut-off date.

 Biased against long-term projects or Lacks a decision criterion grounded in

economics.

 Arbitrary determination of acceptable payback period.

Investment Evaluation Techniques

 The discounted payback period is similar to the normal payback period, except that the cash flows are discounted to present value

 The discounted payback period is the time taken to recover the outlay from discounted cash flows

 This takes account of the time value of money (for cash flows within the payback period) but does not allow for risk, ignores cash flows after the pay- back period and is subject to an arbitrary cut-off

The discounted payback technique

Investment Evaluation Techniques

The discounted payback technique

Example:

Calculate the discounted payback period for the following project

(discounting cash flows at a required rate of return of 10%).

Year 0 1 2 3 4 5 6

Project A -1000 100 200 800 100 100 100

Disc CF

Cum NCF

Investment Evaluation Techniques

The discounted payback technique

Example:

Calculate the discounted payback period for the following project

(discounting cash flows at a required rate of return of 10%).

Year 0 1 2 3 4 5 6

Project A -1000 100 200 800 100 100 100

Disc CF -1000

Cum NCF

Investment Evaluation Techniques

The discounted payback technique

Example:

Calculate the discounted payback period for the following project

(discounting cash flows at a required rate of return of 10%).

Year 0 1 2 3 4 5 6

Project A -1000 100 200 800 100 100 100

Disc CF -1000

Cum NCF

1.1

100

Investment Evaluation Techniques

The discounted payback technique

Example:

Calculate the discounted payback period for the following project

(discounting cash flows at a required rate of return of 10%).

Year 0 1 2 3 4 5 6

Project A -1000 100 200 800 100 100 100

Disc CF -1000

= 91

Cum NCF

1.1

100

Investment Evaluation Techniques

The discounted payback technique

Example:

Calculate the discounted payback period for the following project

(discounting cash flows at a required rate of return of 10%).

Year 0 1 2 3 4 5 6

Project A -1000 100 200 800 100 100 100

Disc CF -1000

= 91

Cum NCF

1.1

100 2

1.1

200

Investment Evaluation Techniques

The discounted payback technique

Example:

Calculate the discounted payback period for the following project

(discounting cash flows at a required rate of return of 10%).

Year 0 1 2 3 4 5 6

Project A -1000 100 200 800 100 100 100

Disc CF -1000

= 91

= 165

Cum NCF

1.1

100 2

1.1

200

Investment Evaluation Techniques

The discounted payback technique

Example:

Calculate the discounted payback period for the following project

(discounting cash flows at a required rate of return of 10%).

Year 0 1 2 3 4 5 6

Project A -1000 100 200 800 100 100 100

Disc CF -1000

= 91

= 165

= 601

= 68

= 62

=56

Cum NCF

1.1

100 2

1.1

200 3

1.1

800 4

1.1

100 5

1.1

100 6

1.1

100

Investment Evaluation Techniques

The discounted payback technique

Example:

Calculate the discounted payback period for the following project

(discounting cash flows at a required rate of return of 10%).

Year 0 1 2 3 4 5 6

Project A -1000 100 200 800 100 100 100

Disc CF -1000

= 91

= 165

= 601

= 68

= 62

=56

Cum NCF -909

1.1

100 2

1.1

200 3

1.1

800 4

1.1

100 5

1.1

100 6

1.1

100

Investment Evaluation Techniques

The discounted payback technique

Example:

Calculate the discounted payback period for the following project

(discounting cash flows at a required rate of return of 10%).

Year 0 1 2 3 4 5 6 DPB

Project A -1000 100 200 800 100 100 100

Disc CF -1000

= 91

= 165

= 601

= 68

= 62

=56

Cum NCF -909 -744 -143 -74 -12 44 5.22 yrs

years22.5 56

12 5 

A Payb ackDisc

1.1

100 2

1.1

200 3

1.1

800 4

1.1

100 5

1.1

100 6

1.1

100

Investment Evaluation Techniques

Decision Criteria Test – Discounted Payback

• Does the discounted payback rule account for the time value of money?

• Does the discounted payback rule account for the risk of the cash flows?

• Does the discounted payback rule provide an indication about the increase in value?

• Should we consider the discounted payback rule for our primary decision rule?

Investment Evaluation Techniques

Evaluation of Discounted Payback

Advantages

 - Includes time value of money

 - Easy to understand

- Does not accept negative NPV

investments

Disadvantages

- May reject positive NPV investments

- Arbitrary determination of acceptable

payback period

- Ignores cash flows beyond the cut-off

date

- Biased against long-term investments.

Investment Evaluation Techniques

 The ARR is the percentage return on invested physical capital, and is based on accounting income and historical cost asset figures

 The ARR is given by:

Average Accounting Rate of Return (ARR)

 The ARR is compared with a predetermined ARR target, or “cut- off” rate, to determine whether to proceed with the project

capital invested average

income average ARR

Investment Evaluation Techniques

There are four stages in calculating the ARR:  Step 1:The average income over the life of the asset is estimated (Note that

“income” takes into account not only cash but non-cash items such as depreciation

 Step 2: The average net investment (after depreciation) is estimated

 Step 3: The ARR is found using the equation

 Step 4: If the ARR is greater than target return, the project should be accepted

Average Accounting Rate of Return (ARR)

Investment Evaluation Techniques

Average Accounting Rate of Return (ARR) Example: Step 1

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows of

$53m & $65m in years 1 &

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate average net income

Year 1 2

Cash flow

Less depreciation

Taxable income

Less tax (30%)

Net income

Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 1

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate average net income

Year 1 2

Cash flow 53 65

Less depreciation

Taxable income

Less tax (30%)

Net income

Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 1

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate average net income

Year 1 2

Cash flow 53 65

Less depreciation 50 50

Taxable income

Less tax (30%)

Net income

Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 1

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate average net income

Year 1 2

Cash flow 53 65

Less depreciation 50 50

Taxable income 3 15

Less tax (30%)

Net income

Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 1

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate average net income

Year 1 2

Cash flow 53 65

Less depreciation 50 50

Taxable income 3 15

Less tax (30%) 1 5

Net income

Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 1

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate average net income

Year 1 2

Cash flow 53 65

Less depreciation 50 50

Taxable income 3 15

Less tax (30%) 1 5

Net income 2 10

Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 1

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate average net income

Year 1 2

Cash flow 53 65

Less depreciation 50 50

Taxable income 3 15

Less tax (30%) 1 5

Net income 2 10

Average = (2 + 10) / 2 = 6

Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 2

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate average investment

Year 0 1 2

Machine cost

Less accum.

depreciation

Investment

Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 2

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate average investment

Year 0 1 2

Machine cost 100 100 100

Less accum.

depreciation

Investment

Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 2

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate average investment

Year 0 1 2

Machine cost 100 100 100

Less accum.

depreciation

Investment

Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 2

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate average investment

Year 0 1 2

Machine cost 100 100 100

Less accum.

depreciation

0 50

Investment

Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 2

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate average investment

Year 0 1 2

Machine cost 100 100 100

Less accum.

depreciation

0 50 100

Investment

Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 2

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate average investment

Year 0 1 2

Machine cost 100 100 100

Less accum.

depreciation

0 50 100

Investment 100 50 0

Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 2

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate average investment

Year 0 1 2

Machine cost 100 100 100

Less accum.

depreciation

0 50 100

Investment 100 50 0

Average investment =

(100 + 50 + 0) / 3 = 50

Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 3

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate the ARR

Step 4

Compare the ARR to a target or

“cut-off” rate to accept or reject

Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 3

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate the ARR

Step 4

Compare the ARR to a target or

“cut-off” rate to accept or reject

%12 50

capital invested Avg

income Avg



Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 3

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate the ARR

Step 4

Compare the ARR to a target or

“cut-off” rate to accept or reject

%12 50

capital invested Avg

income Avg



Investment Evaluation Techniques

Average Accounting Rate of Return (ARR)

Example: Step 3

Calculate the ARR for a 2-

year project involving a

machine that costs $100m

and will yield cash flows

of $53m & $65m in years

1 & 2.

The machine is to be

depreciated on a straight-

line basis, and the

corporate tax rate is 30%.

Calculate the ARR

Step 4

Compare the ARR to a target or

“cut-off” rate to accept or reject

%12 50

capital invested Avg

income Avg



Investment Evaluation Techniques

The ARR technique has a number of disadvantages,

including the fact that it:

 Is based on accounting figures, which are not necessarily related to

cash flows and are based on accounting techniques that may vary

from company to company

 Ignores the time value of money

 Requires an arbitrary target or “cut-off” rate, but there is little

theoretical or other guidance in setting an appropriate target ARR

Average Accounting Rate of Return (ARR)

Investment Evaluation Techniques

 The IRR technique is also based on a DCF model, but focuses on the

rate of return in the DCF equation rather than the NPV

 The IRR is defined as the discount rate that equates the present value

of a project’s cash inflows with the present value of its cash outflows

 This is the equivalent of saying that the IRR is the discount rate at

which the NPV of the project is equal to 0

Internal Rate of Return (IRR)

Investment Evaluation Techniques

Stated formally:

Internal Rate of Return (IRR)

  0

0 1

n t

t t

F CF

r  

 

where:

Ft = cash flow generated by the project in year t

C0 = the cost of the project (initial cash flow, if any)

n = the life of the project in years

r = the internal rate of return on the project

Investment Evaluation Techniques

 The unknown variable (r) can be solved using a financial calculator or

by trial-and-error

 The decision rule is to accept a project if its IRR is greater than the

cost of capital and reject it if its IRR is less than the cost of capital

 It is clear from a comparison of the NPV and IRR equations that these

methods use the same framework and inputs, so they should result in

the same accept/reject decision

Internal Rate of Return (IRR)

Investment Evaluation Techniques

Internal Rate of Return (IRR)

Example:

Apply the IRR rule to a project that costs $100 million and yields

$106 million in one year when the opportunity cost of capital is

7%.

Investment Evaluation Techniques

Internal Rate of Return (IRR)

Example:

Apply the IRR rule to a project that costs $100 million and yields

$106 million in one year when the opportunity cost of capital is

7%.

  0

0 1

106 0 100

n t

t t

CF CF

irr

m m



  

   

 



Investment Evaluation Techniques

Internal Rate of Return (IRR)

Example:

Apply the IRR rule to a project that costs $100 million and yields

$106 million in one year when the opportunity cost of capital is

7%.

  0

0 1

106 0 100

n t

t t

CF CF

irr

m m



  

   

 



Investment Evaluation Techniques

Internal Rate of Return (IRR)

Example:

Apply the IRR rule to a project that costs $100 million and yields $106

million in one year when the opportunity cost of capital is 7%.

If the hurdle rate is set at

the cost of capital (7%),

the project is not

acceptable since the IRR

is below the hurdle rate.

  0

0 1

106 0 100

n t

t t

CF CF

irr

m m



  

   

 



Investment Evaluation Techniques

 Given that the IRR technique uses the same structure is the NPV

technique, it shares most of the latter’s advantages

 IRR is a percentage rate of return that is intuitive to most, and can

easily be compared with rates of return on alternative investment

Internal Rate of Return (IRR)

Investment Evaluation Techniques

Example —IRR

Initial investment = –$200

Year Cash flow

1 $ 50

2 100

3 150

n Find the IRR such that NPV = 0

50 100 150 0 = –200 + + + (1+IRR) 1 (1+IRR) 2 (1+IRR) 3

50 100 150 200 = + + (1+IRR) 1 (1+IRR) 2 (1+IRR) 3

Investment Evaluation Techniques

a is a discount rate which gives a positive NPV

b is a discount rate which gives a negative NPV

c is the positive NPV at the discount rate a

d is the negative NPV at the discount rate b

)( )(

c abaIRR

 

IRR - Trial and Error Method

Investment Evaluation Techniques

Example —IRR (continued)

Trial and Error

Discount rates NPV

0% $100

5% 68

10% 41

15% 18

20% –2

IRR is just under 20%

Investment Evaluation Techniques

Example

What is the project’s IRR?

10 80 60

0 1 2 3 IRR = ?

– 100

PV3

PV2

PV1

0 = NPV

IRR = 18.13% (by calculator)

Investment Evaluation Techniques

Example - Calculator Solution

100 – ve CFi (C0)

10 CFi (C1)

60 CFi (C2)

80 CFi (C3)

COMP IRR 18.13%

RCL CFi 2nd F C-CE = (clears CF registers)

Investment Evaluation Techniques

Conventional Projects

A cash outflow (the initial cost outlay) occurs at

the beginning of the project

This followed by a series of cash inflows

Hence there is one change of signs (from –ve to

+ve); if so it is classed as conventional

Conventional projects usually have a unique IRR

Investment Evaluation Techniques

Non-conventional Projects

The most common is a cash outflow to set up the project, followed

by a series of cash inflows, then a terminal cost to complete the

project (e.g., repair a damaged site)

Hence there can be two or more changes of signs

Multiple, or no internal rates of return, can occur in these cases

(i.e., where a project has more than one sign change in the series

of CFs)

Investment Evaluation Techniques

Inflow (+) or Outflow (–) in Year

0 1 2 3 4 5 C or NC?

– + + + + + C

– + + + + – NC

– – – + + + C

+ + + – – – C

– + + – + – NC

Examples of Cash Flows

Investment Evaluation Techniques

Multiple Internal Rate of Returns (Multiple IRRs)

    2

230 132 0 100

1 1r r

    

 

Multiple rates of return.

YEAR 0 1 2

Net cash flows -100 230 -132

Solving for the IRR, we find that IRR = 10% or 20%.

If the cost of capital were, say, 15%, it is unclear whether the project should be undertaken using IRR.

An application of the NPV technique would resolve this problem. (NPV = +$64.69).

Investment Evaluation Techniques

Example

Suppose an investment will cost $90,000 initially

and will generate the following cash flows:

 Year 1: $132,000

 Year 2: $100,000

 Year 3: – $150,000

The required return is 15%

Should the project be accepted or rejected?

Investment Evaluation Techniques

Example continued

Since the cash flows are non-conventional and indicate two sign

changes, there could be (at most) two IRRs – which is correct?

NPV = $1,769.54, so this suggests the project should be accepted

Need to check to see if there are two IRRs

Can do this by drawing an NPV profile, i.e., calculate NPV for different

values of the company cost of capital, r

Investment Evaluation Techniques

Example continued

r (%) NPV ($) 0 – 8,000.00

5 – 3,158.41

10 – 52.59

15 1769.54

20 2,638.89

25 2,800.00

30 2,435.14

35 1,681.15

40 641.40

45 – 605.60

NPV @ 15%

Investment Evaluation Techniques

Example continued

($10,000.00)

($8,000.00)

($6,000.00)

($4,000.00)

($2,000.00)

$0.00

$2,000.00

$4,000.00

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

Discount Rate

N P

 NPV = $1,769.54, and IRR = 10.11% and 42.66%

IRR

NPV

Graph of NPV Profile

Investment Evaluation Techniques

Example continued

 If we calculate IRR and get 42.66%, we

would accept the project

 However, if we get 10.11%, we would reject

 Which is correct?

 Remember, NPV > 0 which implies we

should accept

Investment Evaluation Techniques

Example - No IRR

Year Cash Flows

0 – 9,000

1 8,000

2 2,000

3 4,000

4 12,000

5 – 20,000

NPV is negative at all discount rates  no IRR (Try various values of r and see what happens to NPV!)

Investment Evaluation Techniques

Independent Projects

 Both IRR and NPV lead to the same

accept/reject decision, except for those non-

conventional projects where the CF patterns

result in either multiple, or no, internal rate of

return

Investment Evaluation Techniques

 NPV and IRR always lead to the same accept/reject decision for independent projects

IRR < r

and NPV 

Reject

NPV

($)

r (%)

IRR

IRR > r

and NPV > 0

Independent Projects continued

Investment Evaluation Techniques

Mutually Exclusive Projects

 Since only one can be accepted, we need to rank them in order of

acceptability

 NPV and IRR methods can provide a different ranking order

 In cases where doubt exists (i.e., where there are differences in the

scale or timing of the CFs), ranking should be based on NPV

 NPV is the superior method for mutually exclusive projects, and is

preferred

Investment Evaluation Techniques

Example - Mutually Exclusive Projects With Different Scale of CFs

Cash flows for Projects I and D:

Year Project I Project D Project I-D

0 (100) (100) 0

1 10 70 (60)

2 60 50 10

3 80 20 60

 Given what has been said, this could be a

problem case, and so we need to check it!

Investment Evaluation Techniques

Example - Construct NPV Profiles

 Find NPVI, and NPVD using different discount rates, and

IRRI and IRRD, and the crossover point (i.e., IRRI-D), and

graph them:

NPVI

– 4

NPVD

Investment Evaluation Techniques

Example - Crossover Point

1. Find the difference between the CFs of the

projects (see data for Project I – D on slide 60)

2. Calculate the IRR for these CF differences

3. Can subtract cash flow of project D from project I or vice versa

4. If the profiles don’t cross, then one project dominates the other

Investment Evaluation Techniques

Example - Graph of NPV Profiles

-10

0 5 10 15 20 23.6

NPV ($)

Discount Rate, r (%) IRRI = 18.1%

IRRD =

23.6%

Crossover Point =

8.7%

Investment Evaluation Techniques

Example - Mutually Exclusive Projects

r1 8.7 r2

NPV $

r %

IRRD =

23.6%

IRRI = 18.1%

r1 < 8.7: NPVI > NPVD , IRRD > IRRI

 conflict

r2 > 8.7: NPVD > NPVI , IRRD > IRRI

 no conflict

Crossover

point = 8.7%

Investment Evaluation Techniques

 Size (scale) differences

 Smaller projects free up funds at t = 0 for other profitable

investments

 The higher the opportunity cost, the more valuable are these

funds, so a high r favours smaller projects

 Timing differences

 Projects with a faster payback period provide more CFs in the

early years for reinvestment

 If r is high, the early CFs are especially good (larger, because

they are discounted over shorter periods), and so NPVD >

NPVI

Why Do NPV Profiles Cross?

Investment Evaluation Techniques

The higher the opportunity cost, the more valuable are these funds, so

a high r favours smaller projects

The IRR does not take into account the size of projects.

YEAR 0 1 IRR Which project is better if the

opportunity cost of

capital is 5%?

Small project -10 15 50%

Large project -100 122 22%

 If a corporation has $100m to spend, takes on the small project, and

returns $90m to shareholders, which is then reinvested at the

opportunity cost of capital (5%), their total wealth at the end of the year

will be $109.5m (90  1.05 + 15).

 Investing $100m in the large project will generate $122m.

 Lower opportunity cost of capital favours larger project

Investment Evaluation Techniques

Internal Rate of Return (IRR)

The IRR does not take into account the size of projects.

YEAR 0 1 IRR Which project is better if the

opportunity cost of

capital is 20%?

Small project -10 15 50%

Large project -100 122 22%

The small project is favoured by the IRR technique. However:

 If a corporation has $100m to spend, takes on the small project, and returns $90m to

shareholders, which is then reinvested at the opportunity cost of capital (20%), their

total wealth at the end of the year will be $133m (90  1.20 + 15).

 Investing $100m in the large project will generate $122m.

 Higher opportunity cost of capital favours smaller project

Investment Evaluation Techniques

100

Example - Mutually Exclusive Projects

Period Project A ($) Project B ($)

0 – 500 – 400

1 325 325

2 325 200

IRR 19.43% 22.17%

NPV $64.05 $60.74

 The required return for both projects is 10%

 Which project should you accept and why?

Investment Evaluation Techniques

101

Example continued

($40.00)

($20.00)

$0.00

$20.00

$40.00

$60.00

$80.00

$100.00

$120.00

$140.00

$160.00

0 0.05 0.1 0.15 0.2 0.25 0.3

Discount Rate

N P

V A

Crossover Point =

11.8%

IRRA = 19.43%

IRRB =

22.17%

Investment Evaluation Techniques

102

Summary re NPV vs. IRR

NPV and IRR will generally give the same decision

Exceptions:

 Non-conventional cash flows – where cash flow signs

change more than once

 Mutually exclusive projects

 Scale of cash flows is substantially different

 Timing of cash flows is substantially different

Investment Evaluation Techniques

103

Drawbacks or Problems with IRR

 Multiple IRRs

 Are We Borrowing or Lending

 No IRRs

 Mutually exclusive projects  The Scale Problem

 The Timing Problem

Investment Evaluation Techniques

 While we have pointed out the shortcomings of using the

IRR rule to make investment decisions, the IRR itself

remains a very useful tool.

 The IRR measures the sensitivity of the NPV to estimation

error in the cost of capital and the average return of the

investment.

 Thus knowing the IRR can be very useful, but relying on it to

make investment decisions can be hazardous.

104

IRR Versus the IRR Rule

Investment Evaluation Techniques

 The bottom line on IRR

 Even when projects have the same scale, differences in timing of cash flows can lead to ranking projects incorrectly using the IRR.

 As these examples make clear, picking the investment opportunity with the largest IRR can lead to a mistake.

 In general, it is dangerous to use the IRR in cases where you are choosing between projects, or anytime when your decision to accept or reject one project would affect your decision on another project. In such a situation, always rely on NPV.

105

Choosing Between Projects

Investment Evaluation Techniques

Choosing Between Projects when Resources are Limited

 In some situations, different investment opportunities demand

different amounts of a particular resource.

 If there is a fixed supply of the resource so that you cannot

undertake all possible opportunities, simply picking the highest-NPV

opportunity might not lead to the best decision.

106

Investment Evaluation Techniques

107

Choosing Between Projects when Resources are Limited

 Profitability Index

 Measures ‘bang for your buck’ - the NPV per unit

of resources consumed.

FORMULA

– 8.4

PI = Value created

= NPV

Resources consumed Resource consumed

Investment Evaluation Techniques

Table 8.4: Possible projects for $200 million budget

Choose B and C instead of A to maximize NPV

108

Investment Evaluation Techniques

Problem:

 Your division at NetIt, a large networking company, has put together a project proposal to develop a new home networking router.

 The expected NPV of the project is $17.7 million, and the project will require 50 software engineers.

 NetIt has a total of 190 engineers available, and is unable to hire additional qualified engineers in the short run.

 Therefore, the router project must compete with the following other projects for these engineers:

109

Example 7.5 Profitability Index with a Human Resource Constraint

Investment Evaluation Techniques

Problem: How should NetIt prioritise these projects?

110

Example 7.5 Profitability Index with a Human Resource Constraint

Project NPV ($ millions) Engineering Headcount

Router 17.7 50

Project A 22.7 47

Project B 8.1 44

Project C 14.0 40

Project D 11.5 61

Project E 20.6 58

Project F 12.9 32

Total 107.5 332

Investment Evaluation Techniques

Solution:

Plan:

 The goal is to maximize the total NPV we can create with 190 employees (at most).

 We can use Eq. 8.4 to determine the profitability index for each project.

 In this case, since engineers are our limited resource, we will use Engineering Headcount in the denominator. Once we have the profitability index for each project, we can sort them based on the

index.

111

Example 7.5 Profitability Index with a Human Resource Constraint

Investment Evaluation Techniques

Execute:

112

Example Profitability Index with a Human Resource Constraint

Investment Evaluation Techniques

Execute (cont’d):

 We now assign the resource to the projects in descending order according to the profitability index.

 The final column shows the cumulative use of the resource as each project is taken on until the resource is used up.

 To maximize NPV within the constraint of 190 employees,

NetIt should choose the first four projects on the list.

113

Example 7.5 Profitability Index with a Human Resource Constraint

Investment Evaluation Techniques

Evaluate

 By ranking projects in terms of their NPV per engineer, we find the most value we can create, given our 190 engineers.

 There is no other combination of projects that will create more value without using more engineers than we have.

 This ranking also shows us exactly what the engineering constraint costs us—this resource constraint forces NetIt to forgo three otherwise valuable projects (C, D, and B) with a total NPV of $33.6

million.

114

Example 7.5 Profitability Index with a Human Resource Constraint

Investment Evaluation Techniques

115

 Surveys of capital budgeting practices in Australia in

recent years indicate that:

 Most of the corporations surveyed used more than one

technique

 All four of the techniques we have seen are used

 The techniques relying on DCF (i.e. IRR and NPV) are the

most popular, and have become more prevalent in recent

times

 The payback method has also increased in popularity

Which technique is used in practice?

Investment Evaluation Techniques

The most popular decision rules used by Aus CFOs -

116

Investment Evaluation Techniques

117

1. Explain the NPV rule for stand-alone projects.

2. Under what conditions will the IRR rule lead to the same decision as the NPV rule?

3. What is the most reliable way to choose between mutually exclusive projects?

4. Explain why choosing the option with the highest NPV is not always correct when the options have different lives.

5. What does the profitability index tell you?

Lecture quiz