Weighing Net Present Value and
Other Capital Budgeting Criteria
Chapter 13
Fin 325, Section 04 - Spring 2010
Washington State University
1
Introduction
 In previous chapters we learned how to
 Calculate the firm’s cost of capital
 Estimate a project’s cash flows
 Now, we need to finish the analysis of the
project to determine whether the firm should
proceed with a potential project.
2
Capital Budgeting Techniques
 Most commonly-used methods to evaluate projects:






Net Present Value (NPV)
Payback (PB)
Discounted Payback (DPB)
Internal Rate of Return (IRR)
Modified Internal Rate of Return (MIRR)
Profitability Index (PI)
 NPV is generally the preferred technique for most
project evaluations
 There are situations where you may want to use one
of the other techniques in conjunction with NPV
3
Net Present Value
 NPV represents the “purest” of the capital
budgeting rules
 It measures the amount of value created by the
project
 NPV is completely consistent with the overall goal
of the firm: to maximize firm value
4
 NPV is the sum of the present value of every
project cash flow (including the initial
investment)
CF0
CFN
CF1
NPV 

 ... 
0
1
(1  i)
(1  i)
(1  i) N
N
CFn

n
n  0 (1  i )
5
 NPV Benchmark
 NPV includes all of the project’s cash flows, both
inflows and outflows
 Since it involves finding the present values of every
cash flow using the appropriate cost of capital as
the discount rate, anything greater than zero
represents the amount of value added above and
beyond the required return
 Accept project if NPV > 0
 Reject project if NPV < 0
6
Example
 A project has a cost of $25,000, and annual
cash flows as shown. Calculate the NPV of
the project if the discount rate is 12 percent
i=12%
0
(25,000)
1
8,500
2
12,000
3
13,500
4
15,000
7
 Financial Calculator solution:
CF0 = (25,000)
CF1 = 8,500
CF2 = 12,000
CF3 = 13,500
CF4 = 15,000
I = 12 percent
NPV = 11,297.42
8
 Interpretation:
 Do we like this project?



Yes – it has a positive NPV
If the market agrees with our analysis, the value of our
firm will increase by $11,297 due to this project
When will the value-added occur? When the
project is complete?
 NO – it will occur immediately upon the
announcement that we are taking the project
9
10
NPV Strengths and Weaknesses
 Strengths
 NPV not only provides a go/no-go decision, but it
also quantifies the dollar amount of the value added
 NPV is not a ratio
 It works equally well for independent projects and
for choosing between mutually-exclusive projects

Accept the project with the highest positive NPV
 Weakness
 Misinterpretation
 Comparing NPV to the cost of the project is wrong!
 Not understanding that the cost is already incorporated into
the NPV
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Payback
 Answers the question: How long will it take us
to recoup our costs?
 Has intuitive appeal
 Remains popular because it is easy to compute
 Built-in assumptions:


Cash flows are normal
Assumes cash flows occur smoothly throughout the year
12
Example
 Refer to the problem we worked earlier. Compute
the payback.
i=12%
0
(25,000)
Cumulative (25,000)
1
2
8,500
12,000
(16,500)
(4,500)
3
13,500
4
15,000
Payback will occur during the 3rd year
Payback = 2 + 4,500/13,500
= 2.33 years
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 Payback Benchmark
 Firms set some maximum allowable payback

Often set arbitrarily – one of payback’s greatest
weaknesses
 Accept project if calculated payback < Maximum
allowable payback
 Reject project if calculated payback > Maximum
allowable payback
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Discounted Payback
 One of the major problems with payback is
that it ignores the time value of money
 It treats all cash flows equally regardless of when
they occur
 Discounted payback fixes this particular
problem
 We convert the raw cash flows to their present
values, and then calculate payback like before
using these discounted cash flows
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Example
i=12%
0
2
3
4
(25,000) 8,500
12,000
13,500
15,000
CF present values (25,000) 7,589
9,566
9,609
9,533
Cumulative
1
(25,000) (17,411)
(7,845)
Discounted Payback will occur during the 3rd year
Discounted Payback = 2 + 7,845/9,609
= 2.82 years
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 Discounted Payback benchmark
 Like payback, management will likely set an
arbitrary benchmark
 Notice that for normal projects DPB will be larger
than PB
 The cash flows that are “chipping away” at the
initial cost are the smaller discounted cash flows,
so it takes longer
 Hopefully, the arbitrary benchmark would at least
take that effect into account
17
PB and DPB Strengths and Weaknesses
 Strengths:
 Easy to calculate
 Intuitive
 Weaknesses:
 Both methods have severe weaknesses that make
them unsuitable to be the primary method used to
select projects
1) PB ignores the time value of money
2) Both methods rely on arbitrary accept/reject
benchmarks
3) Both methods ignore cash flows that occur after the
payback period. This is perhaps the most serious
flaw of all
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Internal Rate of Return
 IRR is the most popular technique to analyze
projects
 Often referred to as “the return on the project”
 IRR is generally consistent with Net Present
Value
 Problems occur if cash flows are not normal
 Problems can occur when choosing among
mutually exclusive projects
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 IRR is so closely related to NPV that it is actually
defined in terms of NPV
 IRR is the discount rate that results in a zero NPV
N
CF0
0
n
n 0 (1  IRR)
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 Internal Rate of Return benchmark
 Once we calculate IRR, we must compare it to the
cost of capital (investors’ required return) to see if
the project is acceptable
 We only want to invest in projects where the rate we
expect to get (IRR) exceeds the rate investors
require (i)
21
Example
 Refer to our previous problem. Calculate the IRR
of the project.
i=12%
0
(25,000)
1
8,500
2
12,000
3
13,500
4
15,000
22
 Financial Calculator solution:
CF0 = (25,000)
CF1 = 8,500
CF2 = 12,000
CF3 = 13,500
CF4 = 15,000
IRR = ?
= 30.08%
Do we like this project?
Yes – the IRR is greater than the required return
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Problems with IRR
 IRR will be consistent with NPV as long as:
 The project has normal cash flows
 Projects are independent
 NPV profiles
 The NPV profile is a graph of NPV versus different
discount rates
 It can help us determine if we may encounter a
problem with IRR
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 For normal cash flows, the NPV profile slopes
downward
 IRR can be found where the profile crosses the xaxis (i.e. where NPV = 0, the definition of IRR)
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 For non-normal cash flows there will be
multiple IRRs for the same project
 IRRs represent the solution to a mathematical
series. These solutions are called ‘roots’, and a
series will have as many roots as there are sign
changes. This is Descartes’ Rule of Signs,
discovered in 1637.
 For us, this means that there will be as many IRRs
as there are sign changes in the cash flows.
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 Examples:
 In our normal project, we have one IRR because
we have one sign change
-++++
 What if a project involves a cleanup at the end?
We might have two sign changes (and two
IRRs):
-+++ What if a project has to shut down in the 3rd
year for maintenance, and then starts up again?
We might have three sign changes:
-++-++
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 Here is a sample NPV profile for a project
with non-normal cash flows. Notice that
the line crosses the x-axis twice:
 Fortunately, we can fix the problem of
multiple IRRs using a technique called
Modified Internal Rate of Return (MIRR)
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Calculating MIRR
 Calculating MIRR is a three-step process:
Step 1: Calculate the PV of the cash outflows using
the required rate of return.
Step 2: Calculate the FV of the cash inflows at the last
year of the project’s time line using the required
rate of return.
Step 3: Calculate the MIRR, which is the discount
rate that equates the PV of the cash outflows with
the PV of the terminal value, ie, that makes
PVoutflows = PVinflows
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Example
 Calculate the MIRR of the following project:
0 i = 9%
-10,000
1
2
3
4
5
4,000
6,000
-5,000
12,000
15,000
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 Step 1: PV of outflows = -13,861
 Step 2: FV of inflows = 41,497
 Step 3: Calculate MIRR
INPUT
OUTPUT
5
N
-13,861
I/YR
PV
24.52
0
PMT
41,497
FV
 MIRR = 24.52%
 Exceeds the required return of 9%, so accept project
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Profitability Index
 Based on NPV
NPV
PI 
CF0
 Measures “bang per buck invested”
 PI benchmark:
 Accept project if PI > 0
 Reject project if PI < 0
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Example
 Calculate the PI of our example
i=12%
0
(25,000)
1
8,500
2
12,000
3
13,500
4
15,000
 Recall that the NPV = $11,297
 PI = 11,297 / 25,000
 = 45.19%
 PI indicates that we should accept the project
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