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 riskadjusted 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 McGrawHill 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 McGrawHill 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)
817
Some important capital budgeting concepts:
◦ Sunk costs
Costs that have already been incurred
◦ Opportunity costs
What a resource is worth in its nextbest 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)
819
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)
820
• CF = Cash flow
• NPV = Net present value
• IRR = Internal rate of return
822
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 McGrawHill 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 riskfree Tbill is 7%?
0
1
7%
$350,000
$400,000
$400,000/(1+0.07) = $373,832
NPV = $23,832
LO1
© 2016 McGrawHill 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 McGrawHill 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 riskfree, 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 preset 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 McGrawHill Education Limited
Chapter 8  14
Example: A company has the following cash flows. If the cutoff 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 McGrawHill 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 McGrawHill 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 McGrawHill Education Limited
Chapter 8  17
LO2
© 2016 McGrawHill Education Limited
Chapter 8  18
For a multiperiod 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 shortlived equipment
◦ The replacement problem
LO4
© 2016 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill Education Limited
Chapter 8  34
Year
0
New Machine
25
Equivalent 5year
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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill 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 McGrawHill Education Limited
Chapter 8  41
© 2016 McGrawHill 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 McGrawHill 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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