BUSI 3360 Finance for Business Quiz Questions Please complete Quiz2 using the method in the courseware. I posted the related documents below, please contact me if you have any questions FINANCE 1 – BUSI 3360

Quiz #2

Due March 23rd by 6pm.

1) Best Darn Glasses (BDR) is thinking of investing in a sandblasting machine for its

glassware. It provides you with the following information:

The initial investment for this project would be $235,000 in specialized machinery.

According to CRA, this machine falls into a CCA class of 8%. There is the possibility

of salvage of $6,000, although it’s not for sure. The risk-adjusted cost of capital is

12% and the company’s tax rate is 25%.

Calculate the CCA tax shield under both scenarios – with and without salvage.

2) Using the information from above, calculate the project’s NPV if the following

information were also provided to you:

Cost of maintenance of the sandblasting machine is $35,000 per year, and the

machine will only last 10 years. The salvage value, at that point, will be zero. The

company’s revenues will be $170,000 per year with direct production costs of

$27,000.

Please show all calculations and workings. If you are going to use Excel, please put

both questions on the same sheet. You may also use Word. Please also name your

file with your name before you submit it.

Chapter 8

Net Present Value

and Other

Investment Criteria

Prepared by

Tanya Willis

Saint Mary’s University

© 2016 McGraw-Hill Education Limited

Chapter 8 – 1

After studying this chapter, you should be able to:

LO1 Calculate the net present value of an investment.

LO2 Calculate the internal rate of return of a project and know what to look

out for when using the internal rate of return rule.

LO3 Explain why the payback and discounted payback rules don’t always

make shareholders better off.

LO4 Use the net present value rule to analyze three common problems that

involve competing projects: (a) when to postpone an investment

expenditure, (b) how to choose between projects with unequal lives, and (c)

when to replace equipment.

LO5 Calculate the profitability index and use it to choose between projects

when funds are limited.

© 2016 McGraw-Hill Education Limited

Chapter 8 – 2

Capital budgeting is the process that companies use for decision making

on capital projects — those projects with a life of a year or more.

◦ Replacement projects

The easier capital budgeting decision.

◦ Expansion projects

May involve more uncertainties than expansion projects.

◦ New products and services

Involve even more uncertainties than any other projects

◦ Regulatory, safety and environmental projects

May generate no revenues but may incur significant costs

◦ Other

Pet projects of someone

Source: Clayman, Fridson and Troughton (2012)

8-17

Some important capital budgeting concepts:

◦ Sunk costs

Costs that have already been incurred

◦ Opportunity costs

What a resource is worth in its next-best use

◦ Incremental cash flow

Cash flow with a decision minus the cash flow without the decision; the

additional operating cash flow that a company receives from taking on a new

project.

◦ Externality

Cannibalization

◦ Conventional vs Nonconventional cash flows

Source: Clayman, Fridson and Troughton (2012)

8-19

Several types of project interactions make the incremental cash

flow analysis challenging:

◦ Independent vs. mutually exclusive projects

Independent projects are projects whose cash flows are independent of each

other. Mutually exclusive projects compete directly with each other.

◦ Project sequencing

Many projects are sequenced through time, so that investing in a project

creates the option to invest in future project.

◦ Unlimited funds vs capital rationing

Capital rationing exist when the company has a fixed amount of funds to

invest.

Source: Clayman, Fridson and Troughton (2012)

8-20

• CF = Cash flow

• NPV = Net present value

• IRR = Internal rate of return

8-22

Capital Budgeting is the process of determining what

investments will maximize the value of the firm.

◦ Suppose, you are given the opportunity to buy a building today for

$350,000 and a guarantee of being able to sell it next year for $400,000.

Should you take it?

0

1

r%

-$350,000

$400,00

0

?

LO1

© 2016 McGraw-Hill Education Limited

Chapter 8 – 3

What discount rate do we use to value this stream of cash flows?

What else could we have done with the $350,000?

What other opportunity are we giving up by investing in the

building?

What if the interest rate on the risk-free T-bill is 7%?

0

1

7%

-$350,000

$400,000

$400,000/(1+0.07) = $373,832

NPV = $23,832

LO1

© 2016 McGraw-Hill Education Limited

Chapter 8 – 4

NPV = PV of cash flows minus initial investment.

Expected rate of return given up by investing in a project is

the opportunity cost of capital.

Ct

C1

C2

NPV = C0 +

+

+ … +

1

2

(1 + r ) (1 + r )

(1 + r )t

Where:

Ct = Cash flow at time t

r = Opportunity cost of capital

LO1

© 2016 McGraw-Hill Education Limited

Chapter 8 – 5

Risk and Present Value

◦ The discount rate used to discount a set of cash flows must match the

risk of the cash flows.

◦ Instead of being risk-free, if the building investment in the previous

example was estimated to be as risky as the stock market yielding 12%,

the NPV would be:

NPV

=PV – C0

= [$400,000/(1+.12)] – $350,000

= $357,143 – $350,000 = $7,143

LO1

© 2016 McGraw-Hill Education Limited

Chapter 8 – 6

Valuing long lived projects:

◦ The NPV rule works for projects of any duration.

◦ The critical problems in any NPV problem are to determine:

The amount and timing of the cash flows

The appropriate discount rate

Net Present Value Rule:

◦ Managers increase shareholders’ wealth by accepting all projects

that are worth more than they cost.

◦ Therefore, they should accept all projects with a positive net

present value.

LO1

© 2016 McGraw-Hill Education Limited

Chapter 8 – 7

Example: A company is considering the purchase of a piece of production

equipment to increase volume. The equipment has a cost of $500,000

and will produce annual cash flows over the next 3 years of $150,000 in

year 1, $200,000 in year 2, and $250,000 in year 3. If the required return

on investment is 10%, should the company purchase the equipment?

NPV = C0 +

Ct

C1

C2

+

+

…

+

(1 + r )1 (1 + r ) 2

(1 + r ) t

150,000 200,000 250,000

NPV = −500,000 +

+

+

1

2

(1.10)

(1.10)

(1.10) 3

NPV = −500,000 + 136,364 + 165,289 + 187,829

NPV = −500,000 + 489481 = −10,519

LO1

© 2016 McGraw-Hill Education Limited

Chapter 8 – 8

Using the NPV Rule to Choose Among Projects

◦ Most companies must choose between multiple projects. If

doing one project precludes you from doing the other the

projects are said to be mutually exclusive.

◦ If projects are mutually exclusive, determine NPV and choose the

project with the higher positive NPV.

LO1

© 2016 McGraw-Hill Education Limited

Chapter 8 – 9

Other criteria are sometimes used by firms when evaluating

investment opportunities.

Most commonly used alternatives are: Payback, Discounted

Payback and Internal Rate of Return (IRR)

Payback and Discounted payback are rough guides to an

investment’s worth and often give an incorrect decision.

Internal rate of return will usually lead to the same decision as

NPV however there are exceptions.

LO2, LO3

© 2016 McGraw-Hill Education Limited

Chapter 8 – 10

Payback

◦ Payback is the time period it takes for the cash flows

generated by the project to cover the initial investment in

the project. If the payback period is less than a specified

cutoff point, the project should be accepted.

LO3

© 2016 McGraw-Hill Education Limited

Chapter 8 – 11

Example: A company has the following three investment opportunities.

The company accepts all projects with a 2 year or less payback period and

uses a 10% discount rate.

Project

C0

C1

C2

C3

A

-2,000

+1,000

+1,000

+10,000

B

-2,000

+1,000

+1,000

–

C

-2,000

–

+2,000

–

LO3

© 2016 McGraw-Hill Education Limited

Chapter 8 – 12

Project C0

C1

C2

C3

Payback

NPV @ 10%

A

-2,000 +1,000

+1,000

+10,000

2

$7,249

B

-2,000 +1,000

+1,000

–

2

-$264

C

-2,000 –

+2,000

–

2

-$347

Although all the projects have a payback period of 2 years and are

therefore acceptable, the use of NPV shows us that only the first

project will create value for the shareholders. Therefore, only

Project A should be chosen.

LO3

© 2016 McGraw-Hill Education Limited

Chapter 8 – 13

Discounted Payback Period

◦ Discounted payback is the time period it takes for the discounted

cash flows generated by the project to cover the initial

investment in the project. The acceptance rule is still the same –

the discounted payback should be less than a pre-set cutoff

point.

◦ Although better than payback, it still ignores all cash flows after

an arbitrary cutoff date.

◦ Therefore it will reject some positive NPV projects.

LO3

© 2016 McGraw-Hill Education Limited

Chapter 8 – 14

Example: A company has the following cash flows. If the cut-off is

2 years, should the project be accepted?

Year

CF

Discounted CF Cumulative Discounted

@ 10%, $

CF @ 10%, $

0

-2,000

-2,000

-2,000

1

+1,000

909

1,091

2

+1,000

827

264

3

+10,000

7513

+7,249

NPV=7,249

LO3

© 2016 McGraw-Hill Education Limited

Chapter 8 – 15

Internal Rate of Return (IRR)

◦ IRR is the discount rate at which the NPV of the project

equals zero.

◦ A project is acceptable if the IRR is more than the cost of

capital of the project.

◦ Recall the NPV example we used earlier, where the NPV was

$23,832 at a discount rate of 7% and $7,143 at a rate of

12%.

◦ At what discount rate will the NPV be equal to 0?

LO2

© 2016 McGraw-Hill Education Limited

Chapter 8 – 16

IRR Calculation: If we solve for the “r” in the equation below, we

will find the IRR.

NPV = C0 +

C1

(1 + r )1

400,000

(1 + r )1

r = .142857 14.3%

0 = −350,000 +

Another way of finding IRR is using the NPV profile. By finding out

where the profile crosses the X axis, we can find out the IRR.

LO2

© 2016 McGraw-Hill Education Limited

Chapter 8 – 17

LO2

© 2016 McGraw-Hill Education Limited

Chapter 8 – 18

For a multi-period case, we can solve the IRR either by trial and

error or by a financial calculator.

◦ Example: You can purchase a building for $350,000. The

investment will generate $16,000 in cash flows (i.e. rent) during

the first three years. At the end of three years you will sell the

building for $450,000. What is the IRR on this investment?

◦ We can picture the project in the following way:

0

-$350,000

1

$16,000

3

2

$16,000

$466,000

LO2

© 2016 McGraw-Hill Education Limited

Chapter 8 – 19

In this case, what we are trying to do is to solve the following

equation:

16,000

16,000

466,000

0 = − 350,000 +

+

+

1

2

(1 + IRR )

(1 + IRR )

(1 + IRR ) 3

• By trial and error or by financial calculator, we find:

IRR = 12.96%

LO2

© 2016 McGraw-Hill Education Limited

Chapter 8 – 20

Borrowing vs. Lending:

◦ Let’s say project J involves lending $100 at 50% interest. Project K

involves borrowing $100 at 50% interest. Which one will you

choose?

According to the IRR rule, both projects have a 50% rate of return and

are thus equally desirable.

However, you lend in Project J, and earn 50%; you borrow in Project

K, and pay 50%.

Pick the project where you earn more than the opportunity cost of

capital.

LO2

© 2016 McGraw-Hill Education Limited

Chapter 8 – 21

Mutually Exclusive Projects – Timing of Cash Flows:

◦ Calculate the IRR and NPV for the following projects:

◦ Cash flows in $000’s

Project

C0

H

I

C1

C2

C3

IRR

NPV @ 7%

-350 400

–

–

14.29%

$24,000

-350 16

16

466

12.96%

$59,000

Project H has a higher IRR but is not the best choice at a discount rate of 7%

as NPV is higher for Project I.

LO2

© 2016 McGraw-Hill Education Limited

Chapter 8 – 22

The decision depends on the discount rate used. If we plot the NPV

of each project as a function of the discount rate, the two profiles

cross at an interest rate of 12.26%.

At discount rates above 12.26%, project H with its rapid cash inflow

would provide a higher NPV.

At discount rates below 12.26%, project I, with more total cash

flow but received later, would provide a higher NPV.

LO2

© 2016 McGraw-Hill Education Limited

Chapter 8 – 23

Mutually Exclusive projects – Size of Project

◦ A small project may have a high IRR but a low NPV.

◦ A large project may have a low IRR but a high NPV.

Example: Would you rather earn 50% on a $1 investment or 10%

on a $100 investment?

LO2

© 2016 McGraw-Hill Education Limited

Chapter 8 – 24

Multiple Rates of Return:

◦ Projects with cash flows that change direction more than once,

will have more than one discount rate at which the NPV will be

zero. That means, there are multiple IRRs for projects with nonconventional cash flows.

◦ The IRR rule would not work in this case; NPV works!

LO2

© 2016 McGraw-Hill Education Limited

Chapter 8 – 25

Choosing between competing projects can be tricky. We will

look at three important but challenging problems:

◦ The Investment timing project

◦ The choice between long- and short-lived equipment

◦ The replacement problem

LO4

© 2016 McGraw-Hill Education Limited

Chapter 8 – 26

Sometimes you have the ability to defer an investment and select a

time that is more ideal at which to make the investment decision.

The decision rule is to choose the investment date that results in

the highest NPV today.

Example:

◦ You can buy a computer system today for $50,000 which will last

4 years from date of installment. Based on the PV of savings it

provides to you ($70,000), the NPV of this investment is $20,000.

◦ However, you know that these systems are dropping in price

every year.

◦ When should you purchase the computer?

LO4

© 2016 McGraw-Hill Education Limited

Chapter 8 – 27

The decision rule for investment timing is to choose the investment

date that results in the highest NPV today.

LO4

© 2016 McGraw-Hill Education Limited

Chapter 8 – 28

Suppose you must choose between buying two machines

with different lives.

Machines D and E are designed differently, but have identical

capacity and do the same job.

Machine D costs $15,000 and lasts 3 years. It costs $4,000 per

year to operate.

Machine E costs $10,000 and lasts 2 years. It costs $6,000 per

year to operate.

◦ Which machine should the firm acquire?

LO4

© 2016 McGraw-Hill Education Limited

Chapter 8 – 29

Costs, $000s

Machine

C0

C1

C2

C3

PV of costs @ 6%

Machine D

15

4

4

4

25.69

Machine E

10

6

6

–

21.00

We cannot compare the PV of costs of assets with different lives.

LO4

© 2016 McGraw-Hill Education Limited

Chapter 8 – 30

For comparing assets with different lives, we need to compare

their Equivalent Annual Costs (EAC).

The Equivalent Annual Cost is the cost per period with the

same PV as the cost of buying and operating the machine.

LO4

© 2016 McGraw-Hill Education Limited

Chapter 8 – 31

Calculating equivalent annual cost for Machine D

Machine

Co

C1

C2

C3

Machine D

15

4

4

4

$25.69

?

?

?

$25.69

Equivalent

Annual Cost

PV @ 6%

The equivalent annual cost is calculated as follows:

Equivalent Annual Cost

= PV of Costs / Annuity Factor

= $25.69 / 3 Year Annuity Factor

= $25.69 / 2.673

= $9.61 per year

LO4

© 2016 McGraw-Hill Education Limited

Chapter 8 – 32

If mutually exclusive projects have unequal lives, then you

should calculate the equivalent annual cost of the projects.

Picking the lowest EAC allows you to select the project which

will maximize the value of the firm.

Machine PV @ 6%

Equivalent Annual Cost

D

$25.69

$9.61

E

$21.00

$11.45

LO4

© 2016 McGraw-Hill Education Limited

Chapter 8 – 33

Example:

◦ You are operating an old machine that will last two more years before it

will be worthless.

◦ It costs $12,000 per year to operate.

◦ You can replace it now with a new machine, which costs $25,000 but is

much more efficient ($8,000 per year in operating costs) and will last

for five years.

◦ Should you replace it now or wait a year?

◦ The opportunity cost of capital is 6%.

LO4

© 2016 McGraw-Hill Education Limited

Chapter 8 – 34

Year

0

New Machine

-25

Equivalent 5-year

annuity

1

2

3

4

5

PV @ 6%

8

8

8

8

8

58.70

13.93

13.93

13.93

13.93

13.93

58.70

Cash flow will be $13,930 for new machine

Cash flow will be $12,000 for old machine

Why replace an old machine with a new one that will cost $1,930

more to run?

Decision: Do not replace – wait the two years.

LO4

© 2016 McGraw-Hill Education Limited

Chapter 8 – 35

We refer to the limit set on the amount of funds available for

investment as capital rationing. A limit may be set for 2

reasons:

Soft Rationing: Imposed by the senior management.

Hard Rationing: Imposed by the unavailability of capital in the

market. For example, the limit set during the 2008 credit

crunch crisis.

LO5

© 2016 McGraw-Hill Education Limited

Chapter 8 – 36

Example: A company has an opportunity cost of capital of 10%

and total resources of $20 million. Which projects should the firm

select?

Cash Flows, $ Millions

Project

C0

C1

C2

PV @ 10%

NPV

L

-3

+2.2

+2.42

$4

$1

M

-5

+2.2

+4.84

6

1

N

-7

+6.6

+4.84

10

3

O

-6

+3.3

+6.05

8

2

P

-4

+1.1

+4.84

5

1

LO5

© 2016 McGraw-Hill Education Limited

Chapter 8 – 37

The solution is to pick the projects that give the highest NPV per

dollar of investment.

We do this by calculating the Profitability Index: The ratio of NPV

to initial investment.

The company will select the projects with the highest possible

NPV within the budget.

LO5

© 2016 McGraw-Hill Education Limited

Chapter 8 – 38

Project

PV

Investment

NPV

PI

Decision

L

$3

$3

$1

1/3=.33

accept

M

5

5

1

1/5=.20

reject

N

7

7

3

3/7=.43

accept

O

6

6

2

2/6=.33

accept

P

4

4

1

1/4=.25

accept

All projects would be acceptable if sufficient funds were available.

• Project N with highest PI is picked first.

• Projects L and O are picked next, both with PI of .33.

• Project P is last with a PI of .25

• These 4 projects add up to $20 million (the budget) and will provide

the highest increases in value to shareholders.

LO5

© 2016 McGraw-Hill Education Limited

Chapter 8 – 39

Profitability Index will not always be reliable when choosing

between mutually exclusive projects (just like with IRR).

•

•

A small project may have a high PI but a low NPV.

A large project may have a low PI but a high NPV.

A higher NPV is always preferable to a higher PI.

LO5

© 2016 McGraw-Hill Education Limited

Chapter 8 – 40

NPV is the best decision criteria.

It tells you whether an investment will increase the value of

the firm and by how much.

The only exception is when the firm is facing capital

rationing.

Despite the advantages of discounted cash flow methods,

many corporations use payback.

© 2016 McGraw-Hill Education Limited

Chapter 8 – 41

© 2016 McGraw-Hill Education Limited

Chapter 8 – 42

NPV measures the difference between a projects cost and its

benefits (all in today’s dollars).

It is the only measure which always gives the correct decision

when evaluating projects.

IRR is the discount rate that results in an NPV of zero. The

project should be accepted if the IRR exceeds the opportunity

cost of capital.

© 2016 McGraw-Hill Education Limited

Chapter 8 – 43

Be careful using IRR when: (1) early cash flows are positive,

(2) more than one change in the sign of the cash flows occurs,

or (3) projects are mutually exclusive.

Payback and discounted payback methods ignore cash flows

that occur beyond…

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