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Lecture 7

Chapter 10 Textbook

Fundamentals of Capital Budgeting

COMMONWEALTH OF AUSTRALIA

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Yong,H, Dempsey,M , Morkel-Kingbury,N, Ekanayake,S, Kofoed,J and Murray,J (2014), Fundamentals of Corporate Finance, 2nd Edition,

John Wiley & Sons Australia, Ltd

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Topic 5 Review

1. Why are shares harder to value than bonds using the

discounted cash flow method?

2. Today is the 30th of July 2013. Westpac shares have

annual dividends which are expected to grow at the same

rate as the last dividend increased by forever. The required

return on these shares is 7%. What is the price today?

Date Dividends

09/11/2012 0.90

09/11/2013 0.93

P0 = D1 / (R – g)

Topic 5 Review 2.

a) Dividends from 2012 to 2013 have increased:

%∆= (0.93-0.9)/0.9= 3.33%

b) Value the share using the Constant Growth in Dividends Formula:

• Do is the latest dividend

• Would you buy this share today? Go to http://au.finance.yahoo.com

P0 = D1 / (R – g)

P0 = 0.93*(1.0333) / (0.07 – 0.0333)

P0 = $26.18

http://au.finance.yahoo.com/

Topic 7

An introduction to capital

budgeting • Capital budgeting decisions are the most significant

investment decisions made by management.

• The goal of these decisions is to select capital projects

that will ➔

• Key reasons for Capital Investment

➢ Renewal: Modernize, Overhaul, Retrofit

➢ Replacement: Replace worn out equipment

➢ Expansion: Adding physical capacity

➢ Other: A variety of corporate objectives.

Increase firm value

What is capital budgeting?

• Capital budgeting techniques help management to systematically analyze potential business opportunities in order to decide which are worth undertaking.

• Capital investments are important because they involve substantial cash outlays and, once made, are not easily reversed.

• Capital budgeting decisions are long-term decisions

• Very important to a firm’s future

Classification of Investment

Projects

1. Independent Projects

• Projects are independent when their cash flows are unrelated

• If two projects are independent, accepting or rejecting one project has no bearing on the decision on the other

2. Mutually Exclusive Projects

• When two projects are mutually exclusive, accepting one automatically precludes the other

• Mutually exclusive projects typically perform the same function

Definitions

• Cost of Capital

➢The cost of capital is the minimum return that

a capital budgeting project must earn for it to

be accepted

➢ It is an opportunity cost since it reflects the

rate of return investors can earn on financial

assets of similar risk

➢Also known as the “Hurdle Rate” and

“Opportunity Cost”

• Capital Rationing

➢Capital rationing implies that a company

does not have the resources necessary to

fund all of the available projects

➢It implies that funding needs exceed funding

resources

➢Thus, the available capital will be allocated to

the projects that will benefit the company and

its shareholders the most

Capital Budgeting Methods

1. The Payback Period

2. The Discounted Payback

3. The Net Present Value (NPV)

4. The Internal Rate of Return

(IRR)

PBP is the period of time required for

the cumulative expected cash flows

from an investment project to equal

the initial cash outflow.

0 1 2 3 4 5

CF0 CF1 CF2 CF3 CF4 CF5

1. The Payback Period

• It is one of the most widely used tools for evaluating capital projects

• To calculate the payback period, we need to know the project’s cost and estimate its future net cash flows

Decision Rule: Accept a project if its payback period is below some pre-specified threshold

recovery ofyear theduringflowCash

recovery beforeyear in recover tocostRemaining covcos += eryretbeforeYearsPB

PB = 3 + 3 / 10

= 3.3 Years

Example: Payback period

yeartheduringflowCash

erretotmaining eryretbeforeYearsPB

covcosRe covcos +=

• The management of Basket Wonders has set a

maximum PB of 3.5 years for projects of this type.

• Should this project be accepted?

Payback Period with Various Cash Flow Patterns

1. Why do some projects have two pay back periods?

2. Which project has the shortest single pay back period? Do

you think this is the best project to undertake? Why or why

not?

➢Weaknesses of ordinary payback period

➢One of the weaknesses of the ordinary payback period is that it ignores all cash flows after the arbitrary cut-off period

➢Payback period method also does not take into account the time value of money

Solution? ➔ The discounted payback period calculation calls for the future cash flows to be discounted by the company’s cost of capital

DPBP is the period of time required for

the cumulative discounted expected cash

flows from an investment project to equal

the initial cash outflow.

0 1 2 3 4 5

2. The Discounted Payback

Period

FV PV

)1( + =

CF0 CF1 CF2 CF3 CF4 CF5

• Similar calculation and rule to the payback period rule.

• To calculate the discounted payback period, we need to know the project’s cost and estimate its future net cash flows

Decision Rule: Accept a project if its discounted payback period is below some pre-specified threshold

yeartheduringflowCashDiscounted

erretotmaining eryretbeforeYearsDPB

covcosRe covcos +=

Example: The Discounted Payback

At 14% p.a.

$7,000

$7,500

($18,000)

Now

$8,000

$8,500

Discounted CF $6,140 $5,771 $5,400 $5,033

Cumulative DCF($11,860) ($6,089) ($689) $4,344

A project requires an initial investment of $18,000. It is

expected to generate following cash flows, $7,000, $7,500,

$8,000, and $8,500 at the end of year 1, 2, 3, and 4,

respectively. What is this project’s discounted payback period

at 14% p.a.?

FV PV

)1( + =

Discounted Payback = 3 years + ($689 / $5,033) = 3.1 years

Evaluating both payback techniques Summary of Payback & Discounted Payback Methods

Decision Rule: Payback period ≤ Payback rule  Accept the project. Payback period > Payback rule  Reject the project.

Key Advantages Key Disadvantages

1. Easy to calculate and understand for people without strong finance backgrounds.

2. A simple measure of a project’s liquidity.

1. Most common version does not account for time value of money.

2. Does not consider cash flows past the payback period

3. Bias against long-term projects such as research and development and new products.

4. Arbitrary cut-off point.

3. Net Present Value (NPV) ➢The basic concept • The present value of a project is the difference between the

present value of the expected future cash flows and the initial cost of the project

NPV = PV(Project’s future cash flows) – PV(Cost of the project)

• Accepting a positive NPV project leads to an increase in shareholder wealth, while accepting a negative NPV project leads to a decline in shareholder wealth

• Projects that have a NPV equal to zero implies that management will be indifferent between accepting and rejecting the project

NPV = −CFo+σ𝑡 𝑇 𝐶𝐹𝑡

(1+𝑖)𝑡

Sample Worksheet for Net Present Value Analysis

NCF

NCF NCFNPV

)1( ...

)1(1

1 2

2 0

+ ++

+ +

+ +−= NPV = −CFo+σ𝑡

𝑇 𝐶𝐹𝑡

(1+𝑖)𝑡

A five step approach is used to calculate the

NPV

1. Determine the cost of the project:

• Identify and add up all expenses related to the cost of the project

• While most project’s entire cost occurs at the start of the project, note that some projects may have costs occurring beyond the first year

• The cash flow in year 0 (NCF0) is negative, indicating a cost

Sample Worksheet for Net Present Value Analysis

($ thousands)

NPV = −CFo+σ𝑡 𝑇 𝐶𝐹𝑡

(1+𝑖)𝑡

2.Estimate the project’s future cash

flows over its forecasted life:

• Both cash inflows (CIF) and cash outflows are

likely in each year of the project. Estimate the

net cash flow (NCFt) = CIFt – COFt for each

year of the project

• Remember to recognise any salvage value from

the project in its terminal year

• We will do this in Topic 8

Sample Worksheet for Net Present Value Analysis

($ thousands)

3.Determine the riskiness of the project and estimate the appropriate cost of capital:

• The cost of capital is the discount rate used in determining the present value of the future expected cash flows

• The riskier the project, the higher the cost of capital for the project

• In this example, we assume that the discount rate is 15%

• We will learn how to do this in Topics 10

4.calculate the project’s NPV

• Determine the difference between the present

value of the expected cash flows from the project

and the cost of the project

5.Make a decision

• Accept the project if it produces a positive NPV or

reject the project if NPV is negative

91.16$ )15.1(

110

)15.1(

15.1

80 300

5432 −=

+ +

+ +−=NPV

Sample Worksheet for Net Present Value Analysis

Decision: Due to the negative NPV, reject the project.

If it is accepted, the project will destroy shareholders’ wealth

You can also use the annuity formula.

NCF

NCF NCFNPV

)1( ...

)1(1

1 2

2 0

+ ++

+ +

+ +−=

NPV = 2,423.84 29

Example:

$20,000

$14,000

($35,000)

Now

( )ni FV

PV +

= 1

Given: Initial Outlay = ($35,000)

CF1 = $20,000; CF2 = $14,000; CF3 = $11,000

Discount rate = 11% p.a.

$11,000

PV = $20,000 = $18,018.02

(1+0.11)

PV = $14,000 = $11,362.71

(1+0.11)2

PV = $11,000 = $8,043.11

(1+0.11)3

PV = -$35,000

ACCEPT the project

as its NPV is positive

A B

2 Year Cash Flow

3 0 -$35,000

4 1 $20,000

5 2 $14,000

6 3 $11,000

7 11%

8 NPV 2,423.84

Formula used =NPV(B7,B4:B6)+B3

NPV Using spreadsheet

See “Lecture 7 Excel Case Study” for how to solve for

NPV and IRR on excel

NPV Formula

• What does the net present value formula do?

➢Discount all cash flows to project to time 0 by the cost of capital and compare them 1. Why do we compare the cash flows at time 0?

2. Why do we NOT discount the initial cash outflow?

• How do we write the general NPV formula?

• How can we adjust the NPV formula if the cash flows after year 0 are an annuity stream?

NPV = −CFo+σ𝑡 𝑇 𝐶𝐹𝑡

(1+𝑖)𝑡

NPV = −CFo+ CF i 1−

1+i n

Summary of Net Present Value (NPV) Method

Decision Rule: NPV > 0: Accept the project. NPV < 0: Reject the project.

Key Advantages Key Disadvantages

1. Uses discounted cash flow valuation technique.

2. A direct measure of how much a capital project will increase the value of the firm.

3. Consistent with the goal of maximising shareholder wealth.

Difficult to understand without an accounting and finance background.

• The NPV decision criteria can be summed up

as follows:

NPV = −CFo+σ𝑡 𝑇 𝐶𝐹𝑡

(1+𝑖)𝑡

4. Internal rate of return • The IRR is the discount rate that makes the NPV

to equal zero

• The IRR is an expected rate of return, much like

the yield to maturity calculation that was made

on bonds

PV(Project’s future cash flows) = PV(Cost of

the project)

Decision Rule: Accept the project if IRR > Cost of

Capital

0 )1(

... )1(1 2

21 0 =

+ ++

+ +

+ +−=

IRR

NCF

IRR

NCF

IRR

NCF NCFNPV

Example: IRR Given: Initial Outlay = ($560)

CF1 = $240; CF2 = $240; CF3 = $240

Required return = 12% p.a.

$0 = - $560

+ $240 / (1 + IRR)

+ $240 / (1 + IRR)2

+ $240 / (1 + IRR)3

Trial and Error

IRR =?

You will not

have to

calculate the

IRR in an exam

A B

2 Year Cash Flow

3 0 -$560

4 1 $240

5 2 $240

6 3 $240

7 12%

8 IRR 13.70%

Formula used =IRR(B3:B6)

IRR Using spreadsheet

See “Lecture 7 Excel Case Study” for how to solve for

NPV and IRR on excel

➢When IRR and NPV methods agree

➢The two methods will always agree when

the projects are independent and the

projects’ cash flows are conventional

➢Conventional cash flows - After the initial

investment is made (cash outflow), all the

cash flows in each future year are

positive (inflows)

➢Example:

➢When IRR and NPV methods disagree

•The IRR and NPV methods can produce different accept/reject

decisions due to:

1. Unconventional cash flows

• the sign of cash flows changes more than once

• For unconventional cash flows the IRR technique can

provide more than one solution

2. Mutually exclusive projects

•IRR and NPV method can disagree when accepting one project

means rejecting another (mutually exclusive projects)

•Possible that the NPVs of the two projects will equal each other

at a certain discount rate

•The point at which the NPVs intersect (equal) is called the

crossover point.

•Depending upon whether the required rate of return is above or

below this crossover point, the ranking of the projects will be

different.

➢When IRR and NPV methods disagree

IRR decision rule

➢ The table below summarizes the IRR decision

making criteria:

Decision Rule: IRR > Cost of capital  Accept the project. IRR < Cost of capital  Reject the project.

Key Advantages Key Disadvantages

(1) intuitively easy to understand (2) based on discounted cash flow

technique

(1) with non conventional cash flows, IRR generates no or multiple answers

(2) with mutually exclusive projects, IRR may provide incorrect investment decisions

➢ IRR versus NPV

• While the IRR has an intuitive appeal to managers because of the output being in the form of a return, the technique has some critical problems

• On the other hand, decisions made based on the project’s NPV are consistent with goal of shareholder wealth maximisation.

• NPV results show management the dollar amount by which each project is expected to increase the value of the company.

1- 40

Quiz 7 1. Net present value: Modena Art Gallery is adding to its existing buildings at a cost of $2 million. The gallery expects to bring in additional cash flows of $520,000, $700,000, and $1,000,000 over the next three years. Given a required rate of return of 10 percent, what is the NPV of this project?

a. $1,802,554

b. $197,446

c. -$1,802,554

d. -$197,446

2. Which ONE of the following statements about the payback method is true?

a. The payback method is consistent with the goal of shareholder wealth maximisation

b. The payback method represents the number of years it takes a project to recover its initial investment plus a required rate of return.

c. There is no economic rationale that links the payback method to shareholder wealth maximisation.

d. None of the above statements are true.

Quiz 7 Indicate which answer is correct.

3. Payback: Barcode Biz has invested in new machinery at a cost of

$1,450,000. This investment is expected to produce cash flows of $640,000,

$715,250, $823,330, and $907,125 over the next four years. What is the

payback period for this project?

a. 2.12 years

b. 1.88 years

c. 4.00 years

d. 3.00 years.

4. Discounted payback: Bendigo Energy Company is installing new

equipment at a cost of $10 million. Expected cash flows from this project over

the next five years will be $1,045,000, $2,550,000, $4,125,000, $6,326,750,

and $7,000,000. The company's discount rate for such projects is 14 percent.

What is the project's discounted payback period?

a. 4.2 years

b. 4.4 years

c. 4.8 years

d. 5.0 years

Quiz 7

5. Which one of the following statements about IRR is NOT true?

a. The IRR is the discount rate that makes the NPV greater than

zero.

b. The IRR is a discounted cash flow method.

c. The IRR is an expected rate of return.

d. None of the above.

6. When evaluating capital projects, the decisions using the NPV

method and the IRR method will agree if:

a. the projects are independent.

b. the cash flow pattern is conventional.

c. the projects are mutually exclusive.

d. both a and b.

Quiz 7

7. Projects are classified as independent when their cash flows are

unrelated. True or false?

8. The goal of the capital budgeting decisions is to select capital

projects that will increase the value of the company. True or false?

9. The net present value technique is an approach that goes against

the goal of shareholder wealth maximisation. True or false?

10. The discount rate used to determine the present value of future

cash flows is called the cost of capital. True or false?

11. The discounted payback period calculation calls for the future cash

flows to be discounted by the company's cost of capital. True or false?

12. When mutually exclusive projects are considered, both NPV and

IRR will always produce the same acceptance decision. True or false?

13. Unconventional cash flow patterns could lead to conflicting

decisions by NPV and IRR. True or false?

Capital budgeting in practice

• Net Present Value is the most popular method in

Australia

• Surprisingly in Australia, over 90 percent of

managers used the payback method

• The technique used may depend on factors such

as a company’s policy, an analyst’s preference,

etc.

Practitioners’ methods of choice

Capital budgeting in practice

“We use a sample survey to analyse the capital-budgeting practices of Australian listed companies. We find that NPV, IRR and Payback are the most popular evaluation techniques. Discounting is typically by the weighted average cost of capital [Topic 10], assumed constant for the life of the project, and with the same discount rate across divisions. The WACC is usually based on target weights for debt and equity. The CAPM is widely used, while other asset pricing models are not.

Projects are usually evaluated using NPV, but the company is likely to also use other techniques such as IRR and payback methods. The project cash flow projections are made from three to ten years into the future…”

Paper: Truong, G., Partington, G. and Peat, M. (2008), “Cost-of-capital estimation and capital-budgeting practice in Australia”, Australian Journal of

Management, Vol. 33 No. 1, pp. 95-122. (Available on portal)

1. Understand the method and different approaches to capital

budgeting

2. Classify investment projects as mutually exclusive, independent or

contingent

3. Understand and apply basic capital budgeting terms such as

incremental cash flows, cost of capital etc.

4. Conduct, interpret and apply to various scenario the listed capital

budgeting methods:

i. Payback Period

ii. Discounted Payback Period

iii. Net Present Value (NPV)

iv. Internal rate of return (IRR)- you do not have to calculate this

5. Evaluate and compare capital Budgeting methods

6. Have an understanding of the use of capital budgeting in practice

Learning Outcomes Topic 7