Fundamentals
of Corporate
Finance
Third Canadian Edition
prepared by:
Sujata Madan
McGill University
Copyright © 2006 McGraw Hill Ryerson Limited
2-1
Chapter 7 NPV and Other
Investment Criteria
 Net Present Value (NPV)
 Other Investment Criteria
 Mutually Exclusive Projects
 Capital Rationing
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Net Present Value
 Capital Budgeting Decision
 Which investments should the firm invest in?
 Known as the capital budgeting decision or
the investment decision.
 This chapter discusses various criteria used to
evaluate investments.
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Net Present Value
 Capital Budgeting Decision
 Suppose you had the opportunity to buy a
building for $350,000 today.
 Assume that you could sell it for $400,000
guaranteed next year.
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Net Present Value
 Capital Budgeting Decision
0
1
r%
-$350,000
$400,000
?
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?

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Net Present Value
 Capital Budgeting Decision
Assume the interest rate on the risk-free T-bill is 7%.
0
1
7%
-$350,000
$400,000
$4,000/(1+0.07) = $373,832
NPV = $23,832
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Net Present Value
 Net Present Value
 Present value of cash flows minus initial
investment.
 Opportunity Cost of Capital
 Expected rate of return given up by investing in a
project.
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Net Present Value
NPV = PV - required investment
C1
C2
Ct
NPV  C0 

...
1
2
t
(1  r )
(1  r )
(1  r )
where
Ct = Cash flow at time t
r = Opportunity cost of capital
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Net Present Value
 Risk and Net 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 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
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Net Present Value
 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.
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Net Present Value
 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.
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Other Investment Criteria
 Net Present Value vs Other Criteria
 Use of the NPV criterion for accepting or
rejecting investment projects will maximize the
value of a firm’s shares.
 Other criteria are sometimes used by firms
when evaluating investment opportunities.
 Some of these criteria can give wrong answers!
 Some of these criteria simply need to be used with
care if you are to get the right answer!
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Other Investment Criteria
 Payback
 Payback is the time period it takes for the cash
flows generated by the project to cover the
initial investment in the project.
 Payback Rule
 Accept a project if its payback period is less
than the specified cutoff period.
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Other Investment Criteria
 Payback
 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.
a
Cash Flows in Dollars
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
-
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Other Investment Criteria
Payback
Project:
C0
C1
C2
C3
Payback
NPV @10%
a
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
-
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Other Investment Criteria
Payback
Project:
C0
C1
C2
C3
Payback
NPV @10%
a
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
-
Only Project A increases shareholder value
and should be accepted!
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Other Investment Criteria
 Discounted Payback
 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.
a
 Although better than payback, it still ignores
all cash flows after an arbitrary cutoff date.
 Therefore it will reject some positive NPV projects.
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Other Investment Criteria
 Book Rate of Return
 Book rate of return equals the company’s
accounting income divided by its assets.
a
Book Rate of Return = Book Income / Book Assets
Note: These components reflect historic costs and
accounting income, not market values and cash flows.
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a
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Other Investment Criteria
 Internal Rate of Return (IRR)
 IRR is the discount rate at which the NPV of
the project equals zero.
 IRR Rule
 Accept a project if it offers a rate of return
higher than the opportunity cost of capital.
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Other Investment Criteria
Internal Rate of Return (IRR)
 Revisiting our building example, we
discovered the following:
Discount Rate
NPV of Project
7%
$23,382
12%
$7,143
At what rate of return will the NPV
of this project be equal to zero?
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Other Investment Criteria
Internal Rate of Return (IRR)
 If we solve for “r” in the equation below,
we find the IRR for this project is
14.3%:
NPV = [C1/(1+r)] - C0
0 = [$400,000/(1+r)] - 350,000
 r = 14.3%
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r
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Other Investment Criteria
Internal Rate of Return (IRR)
 Another way of solving for IRR is to
graph the NPV at various discount rates.
 The point where this NPV profile crosses
the “x” axis will be the IRR for the
project.
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IRR BY GRAPH
NPV Profile for this Project
NPV ($)
$60,000
$50,000
IRR = 14.3%
$40,000
$30,000
(occurs where NPV = 0)
$20,000
$10,000
$0
($10,000)
5%
10%
15%
20%
($20,000)
Discount Rate
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Other Investment Criteria
Multi-period IRR
 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?
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Other Investment Criteria
Multi-period IRR
0
-$350,000
1
$16,000
2
$16,000
3
$466,000
16,000
16,000
466,000
0   350,000 


1
2
(1  IRR )
(1  IRR )
(1  IRR ) 3
By trial and error; or using a financial calculator,
IRR = 12.96%
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Project Interactions
Pitfalls with IRR – Lending vs Borrowing
 Project J involves lending $100 at 50%
interest.
 Project K involves borrowing $100 at 50%
interest.
 Which option should you choose?
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Project Interactions
 Pitfalls with IRR – Lending vs Borrowing
 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.
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Project Interactions
 Pitfalls with IRR – Multiple Rates of Return
 Certain cash flows can generate NPV=0 at
more than one discount rate.
 The IRR rule would not work in this case; NPV
works!
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Project Interactions
 Pitfalls with IRR – Mutually Exclusive
Projects
 Two or more projects that cannot be pursued
simultaneously are called mutually exclusive.
 When choosing amongst mutually exclusive
projects, choose the one with the highest NPV.
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Project Interactions
 Pitfalls with IRR – Mutually Exclusive
Projects
 Calculate the IRR and NPV for the following projects:
Cash Flows in Dollars
Project:
H
I
C0
C1
C2
C3
-350
-350
400
16
16
466
IRR
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.
NPV @ 6%
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Project Interactions
 Pitfalls with IRR – Mutually Exclusive
Projects
 Calculate the IRR and NPV for the following projects:
Cash Flows in Dollars
Project:
H
I
C0
C1
C2
C3
IRR
-350
-350
400
16
16
466
14.29%
12.96%
NPV @ 6%
$24,000
$59,000
Choose Project I since it makes a greater contribution
to the value of the firm!
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Project Interactions
 Pitfalls with IRR
 Higher IRR for a project does not necessarily
mean a higher NPV.
 You goal should be to maximize the value of
the firm.
 NPV is the most reliable criterion for project
evaluation.
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Project Interactions
 The Investment Timing Decision
 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.
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Project Interactions
 The Investment Timing Decision
 You can buy a computer system today for $50,000.
Based on the savings it provides to you, the NPV of
this investment ~ $20,000.
 However, you know that these systems are dropping
in price every year.
 When should you purchase the computer?
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Project Interactions
Year of
Purchase
t=0
t=1
t=2
t=3
t=4
t=5
Cost
$50
$45
$40
$36
$33
$31
PV of
Savings
$70
$70
$70
$70
$70
$70
NPV at
Year of
Purchase
$20
$25
$30
$34
$37
$39
NPV
Today
$20.0
$22.7
$24.8
$25.5
$25.3
$24.2
Decision rule for investment timing:
Choose the investment date which results
in the highest NPV today.
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Project Interactions
 Long- vs Short-Lived Equipment
 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?
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Project Interactions
 Long- vs Short-Lived Equipment
Cash Costs [outflows] in Dollars
Project:
C0
C1
C2
C3
PV @ 6%
Machine D
15
4
4
4
$25.69
Machine E
10
6
6
-
$21.00
a
We cannot compare the PV of costs of assets
with different lives.
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Project Interactions
 Long- vs Short-Lived Equipment
 For comparing assets with different lives, we
need to compare their Equivalent Annual
Costs.
 The Equivalent Annual Cost is the cost per
period with the same PV as the cost of the
machine.
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a
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Project Interactions
 Calculating Equivalent Annual Cost:
Cash Flows in Dollars
Project:
C0
C1
C2
C3
Machine D
15
4
4
4
$25.69
9.61
?
9.61
?
9.61
?
$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
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Project Interactions
Long- vs Short-Lived Equipment
 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.
Cash Flows in Dollars
Project:
PV @ 6%
Equivalent Annual Cost
D
$25.69
$9.61
E
$21.00
$11.45
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Capital Rationing
 Capital Rationing
 Limit is set on the amount of funds available to
a firm for investment.
 Soft Rationing
 Limits imposed by senior management.
 Hard Rationing
 Limits imposed by the unavailability of funds in
the capital markets.
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Capital Rationing
Rules for Project Selection
 A firm maximizes its value by accepting all
positive NPV projects.
 With capital rationing, you need to select a group of
projects which
 is
within the company’s resources and
 gives
the highest NPV.
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Capital Rationing
Profitability Index (PI)
 The solution is to pick the projects that give
the highest NPV per dollar of investment.
 We do this by calculating the Profitability
Index:
PI = NPV / Initial Investment (C0)
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Capital Rationing
Profitability Index (PI)
 Suppose your firm had the following projects and only
$20 million to spend:
Project
L
M
N
O
P
Budget
C0
-3.00
-5.00
-7.00
-6.00
-4.00
-25.00
C1
2.20
2.20
6.60
3.30
1.10
C2
2.42
4.84
4.84
6.05
4.84
NPV @
10%
1.00
1.00
3.00
2.00
1.00
Which Projects should your firm select?
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Capital Rationing
Profitability Index
Project
L
M
N
O
P
C0
3.00
5.00
7.00
6.00
4.00
NPV @
10%
1.00
1.00
3.00
2.00
1.00
PI
1/3 = 0.33
1/5 = 0.20
3/7 = 0.43
2/6 = 0.33
1/4 = 0.25
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ACCEPT
ACCEPT
ACCEPT
ACCEPT
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Summary of Chapter 7
 NPV is the only measure which always gives
the correct decision when evaluating projects.
 The other measures can mislead you into
making poor decisions if used alone.
 The other measures are:





IRR
Payback
Discounted Payback
Book Rate of Return
Profitability Index (PI)
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Summary of Chapter 7
Type of Decision:
NPV
IRR
Payback
Discounted
Payback
Book Rate
of Return
Profitability
Index
Independent
Projects
Mutually
Exclusive
Projects
Capital
Rationing


















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