Chapter 9
Net Present Value and Other Investment Criteria
Good Decision Criteria

We need to ask ourselves the following
questions when evaluating capital budgeting
decision rules:



Does the decision rule adjust for the time value of
money?
Does the decision rule adjust for risk?
Does the decision rule provide information on
whether we are creating value for the firm?
9-1
Net Present Value

The difference between the market value of a project and
its cost


Net Present Value (NPV) =
Total PV of future CF’s + Initial Investment
How much value is created today from undertaking an
investment?



The first step is to estimate the expected future cash flows.
The second step is to estimate the required return for projects
of this risk level.
The third step is to find the present value of the cash flows and
subtract the initial investment.
9-2
Project Example Information

You are reviewing a new project and have estimated
the following cash flows:






Year 0:CF = -165,000
Year 1:CF = 63,120; NI = 13,620
Year 2:CF = 70,800; NI = 3,300
Year 3:CF = 91,080; NI = 29,100
Average Book Value = 72,000
Your required return for assets of this risk level is
12%.
9-3
NPV – Decision Rule



If the NPV is positive, accept the project
If the NPV is negative, reject the project
If the NPV is zero, Indifferent between taking the
investment and not taking it

A positive NPV means that the project is expected to add
value to the firm and will therefore increase the wealth of the
owners.

Ranking Criteria: Choose the highest NPV
9-4
Computing NPV for the Project

Using the formulas:



Using the calculator:


NPV = 63,120/(1.12) + 70,800/(1.12)2 + 91,080/(1.12)3 –
165,000 = 12,627.42
This is the increase in the value of the firm from the
project
CF0 = -165,000; C01 = 63,120; F01 = 1; C02 = 70,800;
F02 = 1; C03 = 91,080; F03 = 1; NPV; I = 12; CPT NPV
= 12,627.42
Do we accept or reject the project?
7-5
Calculating NPVs with a Spreadsheet


Spreadsheets are an excellent way to compute NPVs,
especially when you have to compute the cash flows
as well.
Using the NPV function



The first component is the required return entered as a
decimal
The second component is the range of cash flows
beginning with year 1
Subtract the initial investment after computing the NPV
9-6
The Payback Period Method

How long does it take the project to “pay
back” its initial investment?

Computation




Estimate the cash flows
Subtract the future cash flows from the initial cost until
the initial investment has been recovered
Payback Period = number of years to recover initial costs
Decision Rule :

Set by management: Accept projects that
“payback” in the desired time frame.
7-7
Computing Payback For The Project

Assume we will accept the project if it pays
back within two years.




Year 1: 165,000 – 63,120 = 101,880 still to
recover
Year 2: 101,880 – 70,800 = 31,080 still to recover
Year 3: 31,080 – 91,080 = -60,000 project pays
back in year 3
Do we accept or reject the project?
7-8
The Payback Period Method

Disadvantages:
Ignores the time value of money
 Ignores cash flows after the payback period
 Requires an arbitrary acceptance criteria
 A project accepted based on the payback
criteria may not have a positive NPV


Advantages:
Easy to understand
 Biased toward liquidity

7-9
The Discounted Payback Period

How long does it take the project to “pay back” its initial
investment, taking the time value of money into account?

Take PV of cash flows – then calculate payback

Decision rule: Accept the project if it pays back on a
discounted basis within the specified time.

By the time you have discounted the cash flows, you might as
well calculate the NPV.

Still flawed:


Ignores cash flows after the payback period
Requires an arbitrary cutoff point
7-10
Computing Discounted Payback

Assume we will accept the project if it pays back on a
discounted basis in 2 years.

Compute the PV for each cash flow and determine the
payback period using discounted cash flows




Year 1: 165,000 – 63,120/1.121 = 108,643
Year 2: 108,643 – 70,800/1.122 = 52,202
Year 3: 52,202 – 91,080/1.123 = -12,627 project pays back in year 3
Do we accept or reject the project?
9-11
Internal Rate of Return

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
found elsewhere
9-12
Internal Rate of Return

Definition: IRR is the return that makes the NPV = 0


It is the rate that makes the PV of Cash inflow equals the
PV of Cash outflow
Decision Rule:


Accept when IRR > Required Return
Reject when IRR < Required Return
7-13
Computing IRR for the Project

If you do not have a financial calculator, then this
becomes a trial and error process

Calculator




Enter the cash flows as you did with NPV
Press IRR and then CPT
IRR = 16.13% > 12% required return
Do we accept or reject the project?
9-14
Calculating IRRs With A Spreadsheet

You start with the cash flows the same as you did for
the NPV

You use the IRR function



You first enter your range of cash flows, beginning with
the initial cash flow
You can enter a guess, but it is not necessary
The default format is a whole percent – you will normally
want to increase the decimal places to at least two
9-15
Summary of Decisions for the Project
Summary
Net Present Value
Accept
Payback Period
Reject
Discounted Payback Period
Reject
Internal Rate of Return
Accept
9-16
IRR: Example
Consider the following project:
0
-$200
$50
$100
$150
1
2
3
The internal rate of return for this project is 19.44%
$ 50
$ 100
$ 150
N P V  0   200 


2
(1  IRR ) (1  IRR )
(1  IRR ) 3
7-17
NPV Payoff Profile
0%
4%
8%
12%
16%
20%
24%
28%
32%
36%
40%
44%
$100.00
$73.88
$51.11
$31.13
$13.52
($2.08)
($15.97)
($28.38)
($39.51)
($49.54)
($58.60)
($66.82)
NPV
If we graph NPV versus the discount rate, we can see the IRR
as the x-axis intercept.
$120.00
$100.00
$80.00
$60.00
$40.00
$20.00
$0.00
($20.00)
-1%
($40.00)
($60.00)
($80.00)
IRR = 19.44%
9%
19%
29%
39%
Discount rate
7-18
Internal Rate of Return (IRR)

Advantages:

Easy to understand and communicate

Closely related to NPV, often leading to identical
decisions

Knowing a return is intuitively appealing
7-19
NPV vs. IRR


NPV and IRR will generally give us the same
decision
Exceptions (Problems with IRR)


Does not distinguish between investing and borrowing
Nonconventional cash flows – cash flow signs change
more than once


IRR may not exist, or there may be multiple IRRs
Problems with mutually exclusive investments

The Scale Problem: Initial investments are substantially different

The Timing Problem: Timing of cash flows is substantially
different
9-20
 With
some cash flows the NPV of the project
increases as the discount rate increases
Project
C0
C1
IRR
NPV @ 10%
A
 1,000  1,500  50%
 364
B
 1,000  1,500  50%
 364
7-21

Certain cash flows can generate NPV= 0 at two different
discount rates.

The following cash flow generates NPV=$ 3.3 million at
10%. It has IRRs of (-44%) and +11.6%.
Cash Flows
C0
 60
C1...... ......C9
12
12
C10
 15
7-22
NPV
600
IRR=11.6%
300
Discount
Rate
0
-30
IRR=-44%
-600
7-23
23
Pitfall - Nonconventional Cash Flows:

It is possible to have no IRR and a positive
NPV
Project
C
C0
C1
C2
 100  200  150
IRR
NPV @ 10%
None
 42
7-24
-0,1
-0,05
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
0,5
0,55
0,6
0,65
0,7
0,75
0,8
0,85
0,9
0,95
1
1,05
1,1
1,15
1,2
1,25
1,3
1,35
1,4
1,45
1,5
NPV
$70,00
$60,00
$50,00
$40,00
$30,00
$20,00
$10,00
$0,00
Discount
Rate
7-25
Another Example – Nonconventional
Cash Flows

Suppose an investment will cost $90,000 initially and
will generate the following cash flows:





Year 1: 132,000
Year 2: 100,000
Year 3: -150,000
The required return is 15%.
Should we accept or reject the project?
9-26
NPV Profile
IRR = 10.11% and 42.66%
$4,000.00
$2,000.00
NPV
$0.00
($2,000.00)
0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55
($4,000.00)
($6,000.00)
($8,000.00)
($10,000.00)
Discount Rate
9-27
Summary of Decision Rules



The NPV is positive at a required return of
15%, so you should Accept
If you use the financial calculator, you would
get an IRR of 10.11% which would tell you to
Reject
You need to recognize that there are nonconventional cash flows and look at the NPV
profile
9-28
Modified IRR

The Modified IRR (MIRR) method handles
the multiple IRR problem by combining CFs
until only one change in sign remains.

Benefits: single answer and specific rates
7-29
Modified IRR

Example: Suppose the CFs from a project are:
(-100, 230, -132) r = 14%

This project has 2 IRRs: 10% & 20%

Solution: NPV or Modified IRR
7-30
Modified IRR

Modified IRR: The value of the last CF (-132) is: -132/1.14 =
-$115.79 as of date 1

The adjusted CF at date 1 is: 230 – 115.79 = $114.21

The MIRR approach produces the following 2 CF project:
(-100, 114.21)
The IRR of this project is 14.21% > 14% => Accept Project
7-31
IRR and Mutually Exclusive Projects

Independent Projects: accepting or rejecting one project does
not affect the decision of the other projects.

Mutually exclusive projects



Only ONE of several potential projects can be chosen  If
you choose one, you can’t choose the other(s)
Example: You can choose to attend graduate school at
either Harvard or Stanford, but not both
RANK all alternatives, and select the best one.
9-32
The Scale Problem
Would you rather make 100% or 50% on your
investments?
What if the 100% return is on a $1
investment, while the 50% return is on a
$1,000 investment?
7-33
The Scale Problem
IRR sometimes ignores the magnitude of the project.

The required return for both projects is 10%.
Project

C0
C1
IRR
NPV @10%
D
 10,000  20,000 100%
 8,182
E
 20,000  35,000  75%
 11,818
Correct Choice: Choose the Project with the highest NPV
7-34
The Scale Problem
 Incremental
IRR (Crossover Rate): Calculate the
incremental CF from choosing the large budget instead of
small budget.
 The
incremental IRR is the IRR on the incremental
investment from choosing the large project instead of the
small project.
 NPV
of the incremental CF can also be calculated.
7-35
The Scale Problem

To calculate Incremental IRR  Subtract the smaller
project’s CFs from the bigger project’s CFs.
Project
ED
C0
C1
IRR
 10,000  15,000 50%
NPV @10%
 3,636
=> It is beneficial to invest an additional $10,000 in order to
receive an additional $15,000 at date 1.
7-36
The Scale Problem

1)
2)
3)

Mutually exclusive projects can be handled in 1 of 3
ways:
Compare the NPVs of the 2 projects  Choose project with higher NPV
Calculate the incremental NPV  If NPV is +ve, choose the largebudget project
Compare the incremental IRR to the discount rate  If incremental IRR
> discount rate, choose the large budget project
All 3 approaches always give the same decision
7-37
The Timing Problem
$10,000
$1,000
$1,000
Project A
0
1
2
3
-$10,000
$1,000
$1,000
$12,000
Project B
0
1
2
3
-$10,000
7-38
The Timing Problem
$5,000.00
Project A
$4,000.00
Project B
$3,000.00
NPV
$2,000.00
10.55% = crossover rate
$1,000.00
$0.00
($1,000.00) 0%
10%
20%
30%
40%
($2,000.00)
($3,000.00)
($4,000.00)
($5,000.00)
12.94% = IRRB
16.04% = IRRA
Discount rate
7-39
Calculating the Crossover Rate
Compute the incremental IRR for either project “A-B” or “B-A”
NPV
Year Project A
0
($10,000)
1
$10,000
2
$1,000
3
$1,000
$2 500,00
$2 000,00
$1 500,00
$1 000,00
$500,00
$0,00
($500,00) 0%
($1 000,00)
($1 500,00)
Project B Project B-A
($10,000)
$0
$1,000
($9,000)
$1,000
$0
$12,000
$11,000
10.55% = IRR
B-A
5%
10%
15%
20%
Discount rate
7-40
The Timing Problem

1)
2)
3)

Mutually exclusive projects can be handled in one of 3
ways: (Assuming Incremental Cf is calculated for project
B-A)
Compare the NPVs of the 2 projects  Given the discount rate, choose
project with higher NPV
Calculate the incremental NPV  If NPV is +ve, choose B (given the
discount rate)
Compare the incremental IRR to the discount rate  If incremental IRR
(crossover rate) > discount rate, choose B
All 3 approaches always give the same decision
7-41
Mutually Exclusive Projects - Summary

Mutually exclusive projects should not be ranked
based on their returns

Looking at IRRs can be misleading

Look at NPVs to choose correctly
o

We are ultimately interested in creating value for the
shareholders, so the option with the higher NPV is
preferred, regardless of the relative returns.
Note: You can also look at incremental IRR or
incremental NPV to choose correctly
9-42

IRR is better than payback method or discounted payback
method

If IRR and NPV give different results  Use NPV

For mutually exclusive projects, if different projects have
the same NPV  Choose the project with the highest IRR
Project
C0
C1
C2
C3
NPV @
8%
IRR
A
-9,000
2,900
4,000
5,400
1,400
15.58%
B
-9,000,000
2,560,000
3,540,000
4,530,000
1,400
8.01%
7-43
Profitability Index (PI)
To tal P V o f F uture C ash F lo w s
PI 
Initial Investent


Measures the benefit per unit cost, based on the time
value of money

The PI gives the dollar return for the $1 invested

A profitability index of 1.1 implies that for every $1 of
investment, we create an additional $0.10 in value
Decision Rule:

Accept if PI > 1
9-44
Profitability Index (PI)
Project
C0
C1
C2
A
-$20
70
10
B
-10
15
40
NPV @
12%
PI
$70.5
$50.5
3.53
45.3
$35.3
4.53
PV @ 12% of
future CFs
 The problem with the profitability index for mutually exclusive
projects is the same as the scale problem with the IRR
7-45
Advantages and Disadvantages of Profitability
Index

Advantages
 Closely related to
NPV, generally
leading to
identical decisions
 Easy to
understand and
communicate

Disadvantages
 May lead to
incorrect
decisions in
comparisons of
mutually
exclusive
investments
9-46
Summary – DCF Criteria

Net present value






Internal rate of return





Difference between market value and cost
NPV directly measures the increase in value to the firm
Take the project if the NPV is positive
Has no serious problems
Preferred decision criterion  Whenever there is a conflict between NPV and
another decision rule, you should always use NPV
Discount rate that makes NPV = 0
Take the project if the IRR is greater than the required return
Same decision as NPV with conventional cash flows
IRR is unreliable with nonconventional cash flows or mutually exclusive
projects
Profitability Index



Benefit-cost ratio
Take investment if PI > 1
Cannot be used to rank mutually exclusive projects
9-47
Summary – Payback Criteria

Payback period




Length of time until initial investment is recovered
Take the project if it pays back within some specified period
Doesn’t 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
9-48
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 required payback is 4 years.
 What is the payback period?
 What is the NPV?
 What is the IRR?
 Should we accept the project?
What decision rule should be the primary decision
method?
When is the IRR rule unreliable?
9-49
Problem

Consider the following cashflows on two
mutually exclusive projects for the Bahamas
Recreation Corporation. Both require an
annual return of 15%.
Year
Deepwater
Fishing
New Submarine
Ride
0
-750,000
-2,400,000
1
360,000
1,700,000
2
420,000
800,000
3
340,000
850,000
7-50
If
your decision is based on IRR, which
project should you choose?
What
mistake did you just make? Show how
to fix it using only IRR.
Now,
compute the NPV. Is this consistent
with the IRR?
7-51
51