Topics Covered
Investment Criteria
Net Present Value (NPV)
Payback Period
 Discounted Payback
 Average Accounting Return (AAR)
 Internal Rate of Return (IRR)
 Profitability Index (PI)

Chapter 9 Net Present Value
and Other Investment Criteria

Konan Chan
Conflicts between NPV and IRR
Financial Management, Spring 2017
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
Multiple rates of return
Mutually exclusive projects
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Net Present Value (NPV)
Net Present Value (NPV)
Present value of all expected cash flows of a
project at the cost of capital (required return)
NPV = PV of future cash flows – initial costs
NPV is the difference between investment’s
market value (i.e., total present value) and its
cost
Cost of capital is the expected return given up by
investing in a project (required return demanded
by investors)
 Cash flows can be positive or negative in any
period

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NPV Rule
NPV Example
Managers increase shareholders’ wealth by
accepting all projects that are worth more
than they cost
Therefore, managers should accept all
projects with positive net present values
That is, accept the project if NPV > 0
You plan to purchase an office building
Then you will lease out the building, and
the tenant will pay $16,000 per year for
three years
At the end of three years you anticipate
selling the building for $450,000.
How much would you be willing to pay for
the building if cost of capital is 7%?
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Net Present Value
NPV Example (continued)
$466,000
$450,000
Present Value 0
$16,000
$16,000
1
2
$16,000
3
If the building is being offered for sale at a
price of $350,000, would you buy the
building and what is the added value
generated by your purchase and
management of the building?
14,953
13,975
380,395
$409,323
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Payback Method
Payback Method - Example
Measures how long to recover a project’s
initial cost
Easy to calculate and a good measure of a
project’s liquidity
Many firms use this rule for its simplicity
Decision rule: accept the project, if
Payback < some prespecified period of time
The three projects below are available. The
company accepts all projects with a 2 year or less
payback period. Show how this decision will
impact the firm value
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Payback Problems
Cash Flows
Project C0
C1
A
-2000 +1000
B
-2000 +1000
C
-2000
0
Financial Management
C2
C3 Payback NPV@10%
+1000 +10000
2
+ 7,249
+1000
0
2
- 264
+2000
0
2
- 347
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Discounted Payback Period
Ignores time value of money
Do not consider the risk of cash flows
Requires an arbitrary cutoff period
Ignores cash flows beyond payback period
Biased against long-term or new projects
Compute the present value of each cash flow
and then determine how long it takes to pay
back on a discounted basis
Decision rule: accept the project, if
Discount payback < some prespecified
period of time
So, it’s not a good decision criterion
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Computing Discounted Payback
Projected cash flows
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Although discounted payback considers the
time value of money, it still maintains the
major problems of payback method
C0 = -165,000, required return = 12%
CF1 = 63,120
CF2 = 70,800
CF3 = 91,080
Compute the PV for each cash flow and determine
the payback period using discounted cash flows
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
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Year 1 cash flow: 165,000 – 63,120/1.121 = 108,643
Year 2 cash flow: 108,643 – 70,800/1.122 = 52,202
Year 3 cash flow: 52,202 – 91,080/1.123 = -12,627
project pays back in year 3 (2.805 to be exact)
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Discounted Payback Problems
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Requires an arbitrary cutoff period
Ignores cash flows beyond payback period
Biased against long-term or new projects
May reject projects with positive (or higher)
NPV
Financial Management
Average Accounting Return
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Decision rule: accept the project, if
AAR > target average accounting return

(13,620 + 3,300 + 29,100) / 3 = 15,340
AAR = 15,340 / 72,000 = .213 = 21.3%
Reject because AAR < target rate
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AAR Problems
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Internal Rate of Return (IRR)
Ignores time value of money, so it’s not a true
measure of return
Requires an arbitrary cutoff rate
Based on accounting net income and book
values, not cash flows and market values
So, it’s not a good decision criterion
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NI 1 = 13,620, NI 2 = 3,300, NI 3= 29,100
Average Book Value = 72,000
Assume target avg. accounting return of 25%
Average Net Income:
Average net income / average book value
 Easy to compute and implement
Financial Management
Computing AAR
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Net Income
AAR= average accounting income divided
by average accounting value
In this course, we use
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Discount rate at which NPV = 0
Project’s expected rate of return
IRR rule: accept the project, if
IRR > cost of capital (required return)
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Internal Rate of Return
IRR Example
This is the most important alternative to
NPV
It is often used in practice and is intuitively
appealing
It is based entirely on the estimated cash
flows and is independent of interest rates
offered elsewhere
You pay $350,000 to buy an office building
which will generate $16,000 per year for
three years, and sell for $450,000 at the end.
What is the IRR on this investment?
IRR = 12.96%
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Internal Rate of Return
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How to Get NPV and IRR
Take office building as an example
Initial cost = 350,000
Lease out for 16,000 for 3 years
Sell at 450,000 at the end of year 3


IRR=12.96%

Enter cash flow worksheet: CF
NPV>0
CF0 = -350,000 Enter ; 
C01 = 16,000 Enter;  F01 = 2 Enter; 
C02 = 466,000 Enter;  F02 = 1 Enter
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NPV<0

Go to NPV worksheet: NPV
NPV profile
let I = 7 Enter,  CPT NPV = 59,323

Go to IRR worksheet: IRR
CPT IRR = 12.96%
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IRR Rule Does Not Work ...
when
IRR and NPV
Multiple rates of return
Generally speaking, when IRR > cost of
capital, NPV will be also positive
However, there are exceptional situations
where NPV and IRR decisions are not
equivalent

Certain cash flows can generate NPV=0 at two
different discount rates
Mutually exclusive projects

IRR sometimes ignores the magnitude of the
project
Financing type project
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the NPV of the project increases s the discount
rate increases
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Project Types
Multiple Rates of Return
Independent vs. mutually exclusive projects
Suppose a project will generate a cash
inflow in the year 1, but an outflow in the
2nd (last) year of the project. ABC’s cost of
capital is 13%.
Independent: acceptance of the project doesn’t
affect acceptance of other projects.
 Mutually Exclusive: projects that accomplish
the same task; cannot be pursued simultaneously

Conventional vs. non-conventional projects
Conventional: cash outflow at the beginning,
and cash inflow thereafter (sign of cash flows
changes only once)
 Non-conventional: sign of cash flows changes
more than once (cash outflow in the middle)

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Multiple Rates of Return
NPV= -1.95, IRR=26.8%
So, take the project or not?
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Mutually Exclusive Projects
NPV rule for two or more projects


Independent projects: Accept all if NPV >0
Mutually exclusive: among the positive NPV projects,
accept the highest NPV project
Example (assume 7% discount rate)
There are two IRRs, one is 26.8% and the other is
373.2%. When discount rate is 13%, the project
has a negative NPV despite IRR > cost of capital
Because of this conflict, don't use IRR to make
decisions for non-conventional projects
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If these two are mutually exclusive, we will choose
the ‘Faster,’ given 7% discount rate
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NPV, IRR Conflicts
Mutually Exclusive Projects
You have two proposals to evaluate: the initial (I)
and revised (R). Using IRR, which do you prefer?
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NPV (,000s)
40
Initial proposal
IRR= 12.96%
IRR= 14.29%
30
20
10
Revised proposal
0
-10
Crossover rate = 12.26%
-20
8
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Financial Management
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14
Discount rate (%)
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Comparison of NPV and IRR
For conventional independent projects, both
methods give same accept/reject decision.

NPV > 0 yields IRR > r, because IRR has to be
greater than r in order to lower NPV to 0.
However, these methods can rank mutually
exclusive projects differently.
So, how do we know there is conflict in
NPV and IRR?
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Determining Conflict Range
If the cost of capital > crossover rate, there
is no conflict between NPV and IRR rules.
If the cost of capital < crossover rate, a
ranking conflict between NPV and IRR
exists.
Then, what do we do if a conflict exists?
Financial Management
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Determining Conflict Range
For each year, subtract one project’s cash flows
from the other.
If there is a change of signs of these cash flow
differences, a ranking conflict exists.
Compute difference in cash flows between projects.
The IRR of these cash flows is the crossover rate.
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Reconcile Ranking Conflicts
Shareholder wealth maximization:

Want to add more value to the firm
Choose the project with highest NPV when
NPV/IRR ranking conflict exists for
mutually exclusive projects
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Investing or Financing?
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Financing type project
With 50% IRR, should we accept both
projects (assume cost of capital is 10%)?
The typical project has inflows after
outflows (investing type, I), but there are
projects with outflows precede inflows
(financing type, F)
For financing type projects, the NPV of the
project increases as the discount rate
increases.
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Financing type project is like borrowing
money, and thus the lower the rate the better
Accept the (financing type) project only if
IRR < cost of capital
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Profitability Index
Profitability Index
Measures the benefit per unit cost
 The ratio of present value to initial cost
A profitability index of 1.1 implies that for
every $1 of investment, we create an
additional $0.10 in value
Pro
Decision Rule: accept if PI > 1
Con
Closely related to NPV, generally leading to
identical decisions
 Easy to understand and communicate
 Maybe useful when investment funds are limited


This measure can be very useful in
situations in which we have limited capital
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Profitability Index - Example
Which of the following projects will be chosen?
May lead to incorrect decisions in comparisons of
mutually exclusive investments
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Summary of Capital Budgeting
Analytically,
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NPV, IRR, PI, discounted payback consider the time
value of money
IRR can give an erroneous decision for nonconventional projects
So, NPV is the best and preferred method
In practice,


If no capital limit, choose all. But with limited
capital, choose projects with higher PI
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We should consider several investment criteria when
making decisions
NPV and IRR are the most commonly used primary
investment criteria
Payback is also used commonly by CFOs
Financial Management
Survey on CFOs
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Ethics Issues
An ABC poll in the spring of 2004 found that one-third of
students age 12 – 17 admitted to cheating and the
percentage increased as the students got older and felt more
grade pressure. If a book entitled “How to Cheat: A User’s
Guide” would generate a positive NPV, would it be proper
for a publishing company to offer the new book?
Should a firm exceed the minimum legal limits of
government imposed environmental regulations and be
responsible for the environment, even if this responsibility
leads to a wealth reduction for the firm? Is environmental
damage merely a cost of doing business?
Should municipalities offer monetary incentives to induce
firms to relocate to their areas?
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