7-1
Chapter 7
NPV and Other Investment Criteria
Chapter Outline


Net Present Value (NPV)
Other Investment Criteria
IRR (Internal Rate of Return)
Payback and Discounted Payback
 Book Rate of Return




Investment Criteria When Projects Interact
Pitfalls with IRR
Capital Rationing
Semih Yildirim
ADMS 3530
7-2
Net Present Value
• Capital



Budgeting Decision
Central to the success of any company is the
investment decision, also known as the
capital budgeting decision.
Assets acquired as a result of the capital
budgeting decision can determine the
success of the business for many years.
It is extremely important that we ensure that
the correct capital budgeting decision is
made!
Semih Yildirim
ADMS 3530
7-3
Net Present Value
• Capital

Budgeting Decision
Suppose you had the opportunity to buy a
Tbill (Treasury Bill) which would be worth
$400,000 one year from today.
 Interest

rates on Tbills are a risk free 7%.
What would you be willing to pay for this
investment?
-$400,000
PV today:
0
1
2
$400,000 / (1.07) = $373,832
Semih Yildirim
ADMS 3530
7-4
Net Present Value
• Capital



Budgeting Decision
You would be willing to pay $373,382 for a risk free
$400,000 a year from today.
Suppose this were, instead, an opportunity to
construct a building, which you could sell in a year for
$400,000 with certainty (That means the project is
risk free.)
Since this investment has the same risk and promises
the same cash flows as the Tbill, it is also worth the
same amount to you:
$373,282
Semih Yildirim
ADMS 3530
7-5
Net Present Value
• Capital



Budgeting Decision
Now, assume you could buy the land for
$50,000 and construct the building for
$300,000. Is this a good deal?
Sure! If you would be willing to pay $373,382
for this investment and can acquire it for only
$350,000, you have found a very good deal!
You are better off by:
$373,382 - $350,000 = $23,832
Semih Yildirim
ADMS 3530
7-6
Net Present Value
• Capital


Budgeting Decision
We have just developed a way of evaluating
an investment decision which is known as Net
Present Value (NPV).
NPV is defined as the PV of the cash flows
from an investment minus the initial
investment.
NPV = PV – Required Investment (C0)
= [$400,000/(1+.07)] - $350,000
= $23,832
Semih Yildirim
ADMS 3530
7-7
Net Present Value
• Capital

Budgeting Decision
This discount rate is known as the
opportunity cost of capital.
 It


is called this because it is the return you give up
by investing in the project.
 In this case, you give up the money you could
have used to buy a 7% tbill so that you can
construct a building.
But, a Tbill is risk free! A construction project is not!
We should use a higher opportunity cost of capital.
Semih Yildirim
ADMS 3530
7-8
Net Present Value
• Risk




and Net Present Value
Suppose instead you believe the building project is as
risky as a stock which is yielding 12%.
Now your opportunity cost of capital would be 12%
and the NPV of the project would be:
NPV = PV – IC0
= [$400,000/(1+.12)] - $350,000
= $357,143 - $350,000 = $7,142.86
The project is significantly less attractive once you
take account of risk.
This leads to a basic financial principal: A risky dollar
is worth less than a safe one.
Semih Yildirim
ADMS 3530
7-9
Net Present Value
•
Valuing long lived projects

The NPV rule works for projects of any duration:
 Simply discount the cash flows at the appropriate opportunity cost of
capital and then subtract the cost of the initial investment.

The critical problems in any NPV problem are to determine:


The amount and timing of the cash flows.
The appropriate discount rate.
NPV Rule: Accept Projects with Positive NPVs
Semih Yildirim
ADMS 3530
7-10
Net Present Value
Semih Yildirim
ADMS 3530
7-11
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!
Semih Yildirim
ADMS 3530
7-12
Other Investment Criteria
•
Internal Rate of Return (IRR)

IRR is simply the discount rate at which the NPV of the project
equals zero.

You can calculate the rate of return on a project by:
1. Setting the NPV of the project to zero.
2. Solving for “r”.

Unless you have a financial calculator, this calculation must be
done by using trial and error!
Semih Yildirim
ADMS 3530
7-13
Other Investment Criteria
• Internal

Rate of Return (IRR)
To go back to our office example, we
discovered the following:
Discount Rate
NPV of Project
7%
$23,382
12%
$7,143
At what rate of return will the NPV
of this project be equal to zero?
Semih Yildirim
ADMS 3530
7-14
Other Investment Criteria
• Internal

Rate of Return (IRR)
If we solve for “r” in the equation below, we
find the IRR for this project is 14.29%:
• IRR
Decision Rule: Accept Projects withr IRR
which exceeds the opportunity cost of capital
Semih Yildirim
ADMS 3530
7-15
Other Investment Criteria
• Internal
Rate of Return (IRR)
Another way of solving for IRR is to
graph the NPV at various discount rates.
 The point where this NPV profile
crosses the “x” axis will be the IRR for
the project.

Semih Yildirim
ADMS 3530
7-16
IRR BY GRAPH
NPV ($)
NPV Profile for this Project
$60,000
$50,000
$40,000
$30,000
$20,000
$10,000
$0
($10,000)
($20,000)
IRR = 14.3%
(occurs where NPV = 0)
5%
10%
15%
Discount Rate
Semih Yildirim
ADMS 3530
20%
7-17
Other Investment Criteria
• Internal


The NPV Rule states that you invest in any project which
has a positive NPV when its cash flows are discounted at
the opportunity cost of capital.
The Rate of Return Rule states that you invest in any
project offering a rate of return which exceeds the
opportunity cost of capital.



Rate of Return (IRR) vs NPV:
i.e., if you can earn more on a project than it costs to undertake,
then you should accept it!
The NPV and IRR rules will give the same accept/reject
answer about a project as long as the NPV of a project
declines smoothly as the discount rate increases.
Do not confuse IRR and the opportunity cost of capital
Semih Yildirim
ADMS 3530
7-18
Other Investment Criteria
•
Payback

Payback is the time period it takes for the cash flows generated
by the project to recover the initial investment in the project.
Example: You are paying $150 a month to park a car in your
apartment’s garage. You can purchase a parking spot for $5,400.
What is the payback for this “project”?

3 years  $5,400 / (12 * $150)
The Payback Rule states that a project should be accepted if its
payback is less than a specified cutoff period.



For example, if your cutoff were 4 years to payback, then you would
buy the parking spot.
If it were 2 years, you wouldn’t buy the parking spot:
 3 years is longer than you consider desirable to get your money
out of a project.
Semih Yildirim
ADMS 3530
7-19
Other Investment Criteria
• Payback

Payback is a very poor way of determining a project’s
acceptability:



It ignores all cashflows after your cutoff date.
It ignores TVM principle: it does not discount CFs
a
Calculate the payback and NPV for the following
projects if the discount rate is 10%:
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
-
Semih Yildirim
ADMS 3530
7-20
Other Investment Criteria
Project:
Payback (years)
NPV @ 10%
A
2
$7,248.69
B
2
- 264.46
C
2
- 347.11
• Payback
vs NPV … what to do?
 Under
NPV, only project A is acceptable. B and C have
negative NPV’s and are thus both unacceptable.
 But if your payback period is 2 years, then all the
projects are acceptable.
NPV and payback disagree … what is the correct answer?
Semih Yildirim
ADMS 3530
7-21
Other Investment Criteria
• Payback

Payback gives the same weight to all CFs which
occur before the cutoff period, while it completely
ignores the CFs after the cutoff





The firm decision will be biased towards too many short
term lived projects
And against some long-lived projects.
NPV gives the correct answer:


vs NPV … what to do?
Only project A will increase shareholder value.
Therefore, it should be the only project accepted.
Lesson:
Use NPV if you want to make the correct
investment decision!
Semih Yildirim
ADMS 3530
7-22
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.


It offers an important advantage over Payback: if a project is
acceptable with the Discounted Payback, it must have a
positive NPV (if the ignored Cashflows are all positive!)
Therefore it will reject some positive NPV projects.
NPV is thus always preferable to discounted payback
in evaluating projects!
Semih Yildirim
ADMS 3530
7-23
Discounted Payback Example
(OCC=10%, cut-off = 4 years)
Semih Yildirim
ADMS 3530
7-24
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
Managers rarely use this
measurement to make decisions:
The components reflect historic costs and
accounting income, not market
values and cash flows.
Semih Yildirim
a
ADMS 3530
7-25
Project Interactions
• Investment Criteria When Projects Interact
 NPV has proven to be the only reliable measure of a
project’s acceptability.
 But, what happens when we must choose among
projects which interact?
 The NPV rule can be adapted to deal with the
following situations:




Mutually Exclusive Projects
The Investment Timing Decision
Long- vs Short-Lived Equipment (Unequal Lives)
Replacing an Old Machine
Semih Yildirim
ADMS 3530
7-26
Project Interactions
• Mutually

Most projects you deal with will be either-or
propositions.



Exclusive Projects
For example, you own a vacant piece of land.
You have many either-or choices:
 You could construct a townhouse or a condo.
 You could heat it with oil or with natural gas.
If you choose one of the options, you cannot pursue the
other. They cannot be realized simultaneously.


Calculate the NPV of each project
From those, chose the project with the highest (positive) NPV.
Semih Yildirim
ADMS 3530
7-27
Project Interactions
•
Mutually Exclusive Projects

In Example 7.4, you are going to replace your office network.


You can choose between a cheaper, slower package or a more
expensive, faster option.
Calculate the NPV for the two projects if the discount rate is 7%:
a
Cash Flows in Dollars
Project:
C0
C1
C2
C3
NPV @7%
Faster
$ (800)
$ 350
$ 350
$ 350
$ 118.50
Slower
$ (700)
$ 300
$ 300
$ 300
$


87.30
Both projects have a positive NPV, thus both are acceptable.
However, you cannot do both of the these projects!
Since the faster system would make a greater contribution to the
value of the firm, it should be your preferred choice.
Semih Yildirim
ADMS 3530
7-28
Project Interactions
• The


Investment Timing Decision
Sometimes your choice is start a project now
or wait and do it at a later date.
In Example 7.1, you looked at purchasing a
new computer system.
 Its
cost today was $50,000 and its NPV was
$19,740.
 However, you know that these systems are
dropping in price every year.
 From the numbers on the next slide, when should
you purchase the computer?
Semih Yildirim
ADMS 3530
7-29
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
The decision rule for investment timing is to
choose the investment date which results
in the highest net present value today.
Semih Yildirim
ADMS 3530
7-30
Project Interactions
• Long
vs Short-Lived Equipment
Suppose you must choose between buying
Machine D and E.
 The
two machines are designed differently, but
have identical capacity and do the same job.
 The difference?
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?
Semih Yildirim
ADMS 3530
7-31
Project Interactions
• Long

vs Short-Lived Equipment
So far, this looks like a mutually exclusive
choice like problem 7.4
Calculate PV of the costs for the projects if the
discount rate is 6%:
a
Cash OutFlows in Dollars
Project:
C0
C1
C2
C3
PV @ 6%
Machine D
15000
4000
4000
4000
$25,692.5
Machine E
10000
6000
6000
-
$21,000
Should you accept Machine E
because the PV of its costs are lower?
.
Semih Yildirim
ADMS 3530
7-32
Project Interactions
•
Long- vs Short-Lived Equipment
•
Choosing Machine E may not be the best decision. Why not?



All we know is that Machine E costs less to run over 2 years than
Machine D does over 3 years.
D is being penalized by having one extra year of costs charged
against it!
What we should be asking is: How much would it cost per year to use
a
Machine E as versus Machine D?
•
We solve this problem by calculating the Equivalent Annual
Cost (EAC) of the two machines.
• The EAC is the cost per period with the same PV as the cost of
the machine.



.
Think of it as calculating the annual rental charge for the machine.
There will be equal annual payments (an annuity).
The PV of these payments must equal the PV of the cost of the
machine.
Semih Yildirim
ADMS 3530
7-33
Project Interactions
• Calculating
Equivalent Annual Cost:
Cash Flows in Dollars
Project:
C0
C1
C2
C3
Machine D
15000
4000
4000
4000
Equivalent
Annual cost:

9,611.5
9,611.5
9,611.5
?
?
?
PV @ 6%
$25,692.5
$25,692.5
The equivalent annual cost is calculated as follows:
Equivalent Annual Cost = PV of Costs / Annuity Factor
= $25,692.5 / 3 Year Annuity Factor
= $25,692.5 / 2.673
= $9,611.5 per year
.
Semih Yildirim
ADMS 3530
7-34
Project Interactions
Cash Flows in Dollars
Project:
PV @ 6%
D
$25,692.5
E
$21,000
• Long-
Equivalent Annual Cost
$9,611.50
$11,454.37
vs Short-Lived Equipment
 We
see from the equivalent annual costs that D is
actually the better choice because its annual cost is
lower than for Machine E.
 If mutually exclusive projects have unequal lives, then
you should calculate the equivalent annual cost of the
projects.
 This will allow you to select the project which will
maximize the value of the firm.
Semih Yildirim
ADMS 3530
7-35
Project Interactions
• Replacing


an old machine
When should existing equipment be
replaced?
For example:
 You
are operating an old machine which will last 2
more years.
 It costs $12,000 per year to operate.
 A new machine costs $25,000 to buy, but is more
efficient and can be operated for $8,000 per year.
 It will last for 5 years.
Should you replace the old machine?
.
Semih Yildirim
ADMS 3530
7-36
Project Interactions
• Replacing an old machine
 Solve these problems by calculating for the new machine
the PV of the cash flows and its equivalent annual cost:
Cash Flows in Dollars
Project:
C0
C1
C2
C3
C4
C5 PV @ 6%
New Machine
Equivalent
Annual cost:
25
8
8
8
8
8
?
13.93
? 13.93
?
?
?
13.93
13.93
13.93
$58.70
$58.70
Your choice: pay $12,000 per year to run the old
machine or $13,930 per year for the new machine.
Obviously, it’s cheaper to keep your old machine!
.
Semih Yildirim
ADMS 3530
7-37
Project Interactions
• Pitfalls


with IRR: 1-Mutually Exclusive Projects
IRR can mislead you when choosing among 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 @ 7%
$24,000
$59,000
Project H has a higher IRR …
but Project I contributes more to the value of the firm.
Obviously, you should prefer Project I!
.
Semih Yildirim
ADMS 3530
7-38
Project Interactions
• Pitfalls




with IRR
Remember: a high IRR is not an end in itself!
Higher IRR for a project does not necessarily
mean a higher NPV.
You goal should be to maximize the value of
the firm.
Remember:
 NPV
is the most reliable criterion for project
evaluation.
 Only NPV measures the amount by which a project
would increase the value of the firm.
.
Semih Yildirim
ADMS 3530
7-39
Project Interactions
• Pitfalls

with IRR: 2 – Lending vs Borrowing
Calculate the IRR and NPV for the projects below:
Cash Flows in Dollars
Project:
J
K
C0
C1
IRR
-100
+100
+150
-150
50%
50%
NPV @ 10%
+ $36.4
- $36.4
Both projects have the same IRR …
but Project J contributes more to the value of the firm.
Obviously, you should prefer Project J!
.
Semih Yildirim
ADMS 3530
7-40
Project Interactions
• Pitfalls


Project J involves lending $100 at 50% interest.
Project K involves borrowing $100 at 50% interest.



.
When you lend money, you want a high rate of return.
When you borrow money, you want a low rate of return.
The IRR calculation shows that both projects have a
50% rate of return and are equally desirable.


Which option should you choose?
Remember:


with IRR – Lending vs Borrowing
You should see that this is a trap!
The NPV rule correctly warns you away from a project
which involves borrowing money at 50%.
Semih Yildirim
ADMS 3530
7-41
Project Interactions
• Other
Pitfalls with IRR
3. Some projects will generate multiple internal
rates of return.
 Look
at Figure 7.4 on page 218 for an example.
4. Some projects have no internal rate of return.
 Look
at Footnote #6 on page 219 for an example.
How should you evaluate a project in cases like this?
You should calculate NPV!
.
Semih Yildirim
ADMS 3530
7-42
Capital Rationing
• Capital

Occurs when a limit is set on the amount of
funds available to a firm for investment.
• Soft

Rationing
Occurs when these limits are imposed by
senior management.
• Hard

Rationing
Rationing
Occurs when these limits are imposed by the
capital markets.
Semih Yildirim
ADMS 3530
7-43
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.

This is done with the Profitability Index (PI)
 pick
the projects that give the highest NPV per
dollar of investment.
PI = NPV / Initial Investment (C0)
Semih Yildirim
ADMS 3530
7-44
Capital Rationing
• Profitability

Index (PI)
For example: 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?
Semih Yildirim
ADMS 3530
7-45
Capital Rationing
• Profitability
Project
L
M
N
O
P
Index
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
Semih Yildirim
ACCEPT
ACCEPT
ACCEPT
ACCEPT
ADMS 3530
7-46
Summary of Chapter 6



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)

See the next slide for a summary.
Semih Yildirim
ADMS 3530
7-47
Summary of Chapter 6
Type of Decision:
NPV
IRR
Payback
Discounted
Payback
Book Rate
of Return
Profitability
Index
Independent
Projects
Mutually
Exclusive
Projects *
Capital
Rationing


















* Includes: Investment T iming Decision, Unequal Lives
and Replacement Decision
Semih Yildirim
ADMS 3530
7-48
Summary of Chapter 6

It should be noted that when capital rationing
is in place, NPV by itself, cannot lead you to
the correct decision.
 You
must combine NPV with the Profitability Index.
 Ranking the projects this way will allow you to
choose the package of projects which will offer the
highest NPV per dollar of investment.

In summary:
NPV should always be used when
evaluating project acceptability!
Semih Yildirim
ADMS 3530