Net Present Value and
Other Investment Rules
Percent of CFOs who say they use the
following rules to evaluate projects
2
What Makes for a Good Investment Rule?
1.
2.
Recognize the time value of money
Should rely solely on expected future cash
flows and the opportunity cost of capital
-Manager discretion & accounting numbers, are
easy to manipulate
3.
Want to be able to rank projects, and
evaluate portfolios of projects
3
Potential Investment Criteria
Payback Period
 Average Accounting Return
 IRR
 NPV

4
Payback Period

Definition: The number of years before the
project’s cumulative future cash flows equal the
initial investment.
 How

long does it take the project’s to pay for itself?
Decision rule: Accept projects whose payback
period is less than a manager determined cut-off
5
Payback Example


Assume Payback cut-off is 1 year
Which project do we take
Project
Year 0
Year 1
Year 2
A
Cum. CF
-10
10
0
B
-10
0
15
PB
NPV @
10%
Cum. CF
6
The Payback Period Method

Disadvantages:
1. Biased against long-term projects

Ignores cash flows after the payback period
Requires an arbitrary acceptance criteria
3. Ignores the time value of money
2.


A “Good” project may destroy value
Advantages:
1. Easy to understand
2. Biased toward liquidity
7
The Discounted Payback Period

Cash flows are discounted before payback
period is calculated
 Effectively


pick positively NPV project
Very conservative → only very valuable projects
accepted
STILL ignores cash flows after the payback
period
8
Average Accounting Return
Average Net Income
AAR 
Average Book Value of Investment
Decision Rule: If the calculated value is above a
benchmark (Ex. the firm’s current return on
book or the industry average) accept the project.
 Fatally Flawed because:

9
Book Depreciation
This type of depreciation is used to calculate a
company’s Net Income
 Straight line Depreciation:

 (Investment
– Salvage Value) / Expected life
10
AAR Example

A project has net income of $1,200, and
$1,600 a year over its 2-year life. The initial
cost of the project is $5,000, which will be
depreciated using straight-line depreciation
to a book value of zero over the life of the
project. What is the AAR for this project?

Hint: What is the yearly Depreciation?

(Investment – Salvage)/Expected Life
11
AAR example
A project has net income of $1,200, and $1,600 a year over its 2-year life. The
initial cost of the project is $5,000, which will be depreciated using straight-line
depreciation to a book value of zero over the life of the project. What is the AAR
for this project?

0
1
2
Ave
NI
BV

AAR =
12
Average Accounting Return

Disadvantages:
Uses accounting numbers instead of cash flows
2. Ignores the time value of money
3. The benchmark is arbitrary.
1.

Advantages:
The accounting information is easy to obtain
2. Easy to calculate
1.
13
Internal Rate of Return (IRR)

Definition: It is the discount rate that makes a
project’s NPV equal 0.

Decision Rule: Accept all projects with IRR’s
greater than the opportunity cost of capital.
14
IRR’s Underlying Assumptions

All intermediate cash flows can be reinvested
at the IRR
 Is

this reasonable?
That short-term interest rates are equal to longterm interest rates
 Does
not address which to use if they are not equal
15
IRR Notes

To find the IRR of a project lasting t years, solve
the following equation:
 C0+C1/(1+IRR)+C2/(1+IRR)2+….+Ct/(1+IRR)t=0
NPV > 0 implies that IRR > Op Cost
IRR > Op Cost DOES NOT IMPLY that NPV > 0
IRR assumes that causality goes both ways
16
IRR & NPV Investment Example

A firm has a project that requires an initial
investment of $10m. In the first year, it will return
$12m, what is the IRR?

If r=10% do we accept the project based on IRR
and NPV?
17
Internal Rate of Return (IRR)

Disadvantages:
1.
2.
3.
4.
5.

No distinction between investing and borrowing
May have multiple IRR’s, or no IRR
Problems with mutually exclusive investments
Scale Problem
Timing Problem
Advantages:
1.
Easy to understand and communicate
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Loan Example
C0
C1
IRR
Project A
-10
20
100%
Project B
10
-20
100%

NPV @ 10%
According to IRR which project do we pick?
19
No IRR

Example of No IRR
C0
Project 10
C1
-30
C2
25
IRR (%) NPV @10%
None
3.4
20
$200
Multiple IRR
- $800
-$200
If cash flows switch signs more than once then there exists
multiple IRR’s
 There
will be as many IRRs as there are sign changes
 Which IRR do we use?
NPV

$800
$100.00
$50.00
$0.00
-50%
0%
($50.00)
($100.00)
50%
100%
150%
200%
Discount rate
The Scale Problem

Would you rather make 100% or 50% on your
investments?
22
Mutually Exclusive Projects

Choosing between projects
 RANK all alternatives, and select highest IRR
 IRR ignore the amount of wealth generated
C0
Project A -100
C1
150
IRR
50%
NPV @ 10%
36.36
Project B
120
50%
34.09
-75

Which project should we take according to IRR?

Which project do investors prefer?
23
Resource constraint

The firm has $100 to invest, what should it buy?
Project
C0
C0
C0
IRR
NPV 10%
A
-100
300
50
216%
$210
B
-50
50
200
156%
$160
C
-50
50
150
130%
$120
IRR:
 NPV:

24
Verdict on IRR

Gives the same result as NPV if:
 Flat
term structure
 Conventional cash flows
 Independent projects
Otherwise IRR can lead to BAD
decisions
25
The Profitability Index (PI)
Total PV of Future Cash Flows
PI 
Initial Investment

Minimum Acceptance Criteria:
 Accept

if PI > 1
Ranking Criteria:
 Select
alternative with highest PI
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Selection Example

Which projects do we take?
Projects
C0
C1
C2
NPV @ 10%
A
-100
300
50
214
B
-50
50
200
161
C
-50
50
150
119
PI
27
The Profitability Index

Disadvantages:
1. Problems
 Use

when there are additional constraints
linear or integer programming
Advantages:
1. When
funds limited (Capital Rationing),
provides better rankings than NPV
2. Easy to understand and communicate
28
The Net Present Value (NPV) Rule


Net Present Value (NPV) =
Total PV of future CF’s + Initial Investment
Estimating NPV:
1. Estimate future cash flows: how much? and when?
2. Estimate discount rate
3. Estimate initial costs


Minimum Acceptance Criteria: Accept if NPV > 0
Ranking Criteria: Choose the highest NPV
29
Why We Love NPV
NPV recognizes the time value of money
 NPV depends only on future cash flows and
the opportunity cost of capital
 Present value, can be added up, thus allowing
us to evaluate “packages of projects” or a
single project
 Accepting positive NPV projects, increases
wealth

30
Capital Budgeting in Practice
Varies by industry
 The most frequently used technique for large
corporations are: IRR or NPV

 However,
many companies also consider payback
31
Example of Investment Rules
Compute the Payback Period, NPV, and PI for
the following two projects. Assume the required
return is 10%.
Year
Project A
Project B
0
-$200
-$150
1
$200
$50
2
$800
$100
3
-$800
$150
32
Summary – Discounted Cash Flow

Net present value




Internal rate of return




Accept the project if the NPV is positive
Has no serious problems
Yields the best decision
Take the project if the IRR is greater than the required return
Same decision as NPV with conventional cash flows
IRR is unreliable with non-conventional cash flows or mutually
exclusive projects
Profitability Index



Take investment if PI > 1
Cannot be used to rank mutually exclusive projects
Should be used to rank projects in the presence of capital rationing
33
Summary – Payback Criteria

Payback period
 Length
of time until initial investment is recovered
 Take the project if it pays back in some specified period
 Does not account for time value of money, and there is an
arbitrary cutoff period

Discounted payback period
 Length
of time until initial investment is recovered on a
discounted basis
 Take the project if it pays back in some specified period
 There is an arbitrary cutoff period
34
Summary – Accounting Criterion

Average Accounting Return
 Measure
of accounting profit relative to book
value
 Similar to return on assets measure
 Take the investment if the AAR exceeds some
specified return level
 Serious problems and should not be used
35
Quick Quiz

Consider an investment that costs $100,000 and has a
cash inflow of $25,000 every year for 5 years. The
required return is 9%, and payback cutoff is 4 years.
 What
is the payback period?
 What is the discounted payback period?
 What is the NPV?
 What is the IRR?
 Should we accept the project?


What method should be the primary decision rule?
When is the IRR rule unreliable?
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Why We Care
Help you develop your finance intuition
 Showing you common mistakes, so that you
won’t make those mistakes

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