Capital Budgeting
Rules for Sensible Investment
Decisions!!
Cost vs. Benefits
• Investment typically has two components:
– Outflow of cash (cost)
– Inflow of cash (benefits)
• TVM requires all cash flows to be compared at
the same point in time
– Most convenient is time 0
Recall Forbes Example
• Tax savings: $500,000 forever
• Campaign Costs: $40 million
• r = 10%
• PV of Benefits: .5 mill / .10 = $5 million
• Cost: $40 million
• Benefit - Cost = 5- 40 = -$35 million
Forbes example...
• Obviously this is a lousy investment
• What you just used in analyzing this ‘investment’
proposal is NPV rule!
• It turns out the NPV rule is the most sensible
rule to use for evaluating projects
Examples of Capital Budgeting
Projects
• To open a corner latte stand
• To replace replace a 486 computer used in
business with a Pentium computer
• To decide between a coal-fired and a nuclear
fuel power plant costing $1 billion
• To add 5 stories to an existing office tower
• To shut down an aging factory making ball
bearings
Evaluating Investments
• There are many ways to evaluate investments
• Among all the investment rules we will
consider, NPV rule is the only rule that
always gives correct answer in all situations!!
• Other rules may or may not give an answer
consistent with NPV rule
Net Present Value
• NPV = PV of Benefits - PV of Costs
• Accept project if NPV > 0
• Reject project if NPV < 0
Another Example...
0
1
Initial outlay
($1,100)
2
Revenues $1,000
Expenses
500
Revenues $2,000
Expenses
1,000
Cash flow
Cash flow $1,000
– $1,100.00
$500 x
$500
1
1.10
+454.54
$1,000 x
1.10 2
+826.45
+$180.99
1
NPV
NPV Formula
CF1
CF2
CF3
CFn
NPV  CF0 


 ....
2
3
n
1  r (1  r )
(1  r )
(1  r )
• ‘r’ has many names:
– ‘r’ is called the discount rate or
– ‘r’ is called the required return or
– ‘r’ is called the cost of capital
Computing NPV on calculator
• Use the CFj key
– First entry is at time 0
– Subsequent entries are time 1, 2, 3, ... and so on
– make sure the cash flows have the proper signs
• Enter ‘r’ as the I/YR
NPV
• Use the
That’s it!!
keys
Another Example..
Time
Cash Flow
0
-$718
1
$250
2
$575
3
$100
r = 12%
4
NPV = $ _______
Accept / Reject Project ?
Another Example...
• The cash flows are
Year
0
Cash flow
-$252
1
1431
2
-3035
3
2850
4
-1000
r = 10%
NPV = _______
Accept / Reject ??
Example continued...
• This was an example of unconventional cash
flows
• Conventional Cash Flows: Only one change
in sign (from + to - or vice versa)
e.g.
+
+
+
+
• Unconventional Cash Flows: More than one
change in sign
e.g. +
+
+
-
Importance of NPV
• NPV is the dollar value added to the enterprise
– it’s the amount by which the enterprise is richer!
• For public companies, NPV is the increase in
total market value of equity
• Managers should not take negative NPV
projects since it reduces the firm value
Other Rules
• Alternative rules of evaluating investments
are:
–
–
–
–
–
Internal Rate of Return (IRR)
Payback
Discounted Payback
Profitability Index
Accounting Rate of Return
IRR Rule
• IRR: the discount rate that makes NPV = 0
CF3
CFn
CF1
CF2
0  CF0 


 ....
2
3
1  IRR (1  IRR)
(1  IRR)
(1  IRR) n
• Rule: Accept if IRR > required return
Reject if IRR < required return
IRR and Required Return
• Required return also called the ‘Hurdle Rate’
• Required return is the cost of investment funds
– i.e. what it costs to borrow money or raise equity
capital for investments
– it is the same cost of capital ‘r’ used in NPV
calculations
IRR on Calculator
• Enter the cash flows as before
• Use the
IRR/YR
keys
• That’s it!
• Without financial calculator, IRR is computed
by trial and error
IRR Example
Year
Cash flow
0
-200
1
2
3
50
100
150
50
Hurdle rate = 9%
100
150
0 = -200 + (1+IRR)1 + (1+IRR)2 + (1+IRR)3
IRR = ______%
Accept / reject?
Another Example
0
1
2
3
4
5
6
-256
+31
+128
+194
+61
+55
+108
• What is the IRR?
Ans: _____
• What is the NPV if r = 16%
Ans: _____
• Do IRR and NPV give the same answer?
Net Present Value Profile
Net present value
120
Year
100
0
1
2
3
4
80
60
40
Cash flow
– $275
100
100
100
100
NPV>0
20
0
NPV < 0
– 20
– 40
Discount rate
2%
6%
10%
14%
18%
IRR
22%
IRR and Unconventional Cash Flows
 The
cash flows are
Year
Cash flow
0
-$252
1
2
3
4
1431
-3035
2850
-1000
IRR = ?
Example continued....
• What’s the IRR?
at 25.00%:
NPV = _______
at 33.33%:
NPV = _______
at 42.86%:
NPV = _______
at 66.66%:
NPV = _______
• Two questions:
– 1. What’s going on here?
– 2. How many IRRs can there be?
NPV Profile - Multiple IRR Problem
NPV
$0.06
$0.04
$0.02
IRR = 25%
$0.00
($0.02)
IRR =
33.3%
IRR =
42.8%
($0.04)
IRR =
66.6%
($0.06)
($0.08)
0.2
0.28
0.36
0.44
0.52
Discount rate
0.6
0.68
Problem 1 with IRR Rule
• IRR Rule does not always give a clear answer
with unconventional cash flows
• In the above example, there are multiple IRRs
• The accept/reject decision in the example
depends on required rate of return
Another Problem with IRR
Year
0
1
2
3
4
Project A:
– $350
50
100
150
200
Project B:
– $250
125
100
75
50
If the projects are mutually exclusive (i.e. can take
one or the other, but not both), which project to take?
Example Continued...
Project A
Project B
IRR
12.9%
17.8%
NPV @ 5%
$82.44
$65.67
NPV @ 14%
-$9.53
$16.82
Decision with mutually exclusive
projects

IRR Rule does not always give a correct
answer with mutually exclusive projects

In the above example, it seems we would
prefer Project ________ (higher IRR)
Mutually Exclusive… (contd.)
• But always take the project with higher NPV!!
• If r = 5%, then accept project A
• If r = 14%, then accept project B
IRR, NPV, and Mutually Exclusive Projects
Net present value $
160
140
Project A
120
100
80
Project B
60
40
20
NPV A >NPV B
0
– 20
– 40
– 60
NPV B >NPV A
– 80
– 100
0
2%
Crossover rate
6%
10%
16%
IRR A < IRR B
20%
24%
Discount
rate %
Cross-over Rate
• the discount rate that makes NPV of two
projects equal
• the interest rate at which you are indifferent
between two mutually exclusive projects
Finding Crossover Rate
• Take difference between cash flows of two
projects and find IRR (of these incremental
cash flows)
Year
0
1
2
3
4
Project A:
– $350
150
120
150
200
Project B:
– $250
125
100
75
165
Difference:
–$100
25
20
75
35
IRR (difference) = _______ %
Another example
Year
Project A
Project B
0
-$400
-$500
1
250
320
2
280
340
• Find the crossover rate of these two projects
• Answer: _________
IRR - Criticisms
• Not a measure of dollar value added
• Does not consider the scale of the project
• Interim cash flows are assumed to be reinvested
at the IRR which is unrealistic
• Does not give correct answer when
– you have mutually exclusive project
– unconventional cash flows
Payback Rule
• Measure of the length of time until the sum of
future cash flows equals the initial investment
– Time it takes to get you money back
• Accept: if payback period is less than some prespecified benchmark
Payback Example
 The
Payback = 2 yrs
cash flows are
Year Proj. A
Proj. B
0
-$100
-$100
1
2
3
4
90
15
10
10
15
90
10
20
Problem with Payback
Payback rule
ignores
these cash
flows
Year Proj. A
Proj. B
0
-$100
-$100
1
2
3
4
90
15
10
10
15
90
100
2000
Although both projects have the same payback,
Proj. B is clearly superior
Payback Rule - Criticisms
• It does not take into account time value of
money (i.e. no discounting of cash flows)
• Payback rule ignores all the cash flows that
occur after the payback period
• Required payback benchmark is arbitrary
Discounted Payback
• Length of time until present value of future
cash flows equals the intial investment
– avoids the time value criticism of simple payback
rule
• Accept if discounted payback less than prespecified benchmark
• Does not avoid other criticisms of payback
rule
Disc. Payback Example
 The
cash flows are
Year Proj. A
discounted
payback
= 3 years
PV (r=10%)
0
-$100
-$100
1
2
3
4
90
15
10
10
81.82
12.40
7.51
6.83
Discounted Payback - criticism
• Incorporates time value in decision in
contrast with simple payback,
BUT
• It still ignores all cash flows occuring after
the required payback period
• Benchmark is still arbitrary
Profitability Index
PV ( Benefits) PV ( Inflows)
P. I . 

PV (Costs)
PV (Outflows)
• Ratio of PV of benefits to PV of costs
– “Bang for the buck”
• Rule:
Accept Project if
Reject project if
PI > 1
PI < 1
P. I. Example
Year
0
CashFlow -200
r = 10%
1
50
2
100
3
150
• P. I. = ______
=________
200
• Interpretation: NPV of $0.204 is added for
each $1 of investiment.
Problems with P. I.
• As with IRR, it does not consider the scale of
the project.
– Not a measure of total $ value added to firm
• With mutually exclusive projects, P. I. can give
wrong rankings
Another Example
Project A
Project B
-$100
-$200
NPV
$50
$80
P. I.
1.5
1.4
Cost (t=0)
• Although Proj. A has higher P. I., Proj. B should
be accepted because NPV is higher
Average Accounting Return
• Measure of avg. accounting profit divided by
avg. accounting value of investment:
A. A. R. =
avg. net income
avg. book value of invest.
• Accept if AAR > benchmark return
Reject if
AAR < benchmark return
A. A. R. Example
 Average net income:
Year
1
2
3
Sales
$440
$240
$160
Costs
220
120
80
Gross profit
220
120
80
Depreciation
80
80
80
140
40
0
35
10
0
$105
$30
$0
Earnings before taxes
Taxes (25%)
Net income
Average net income = (105 + 30 + 0)/3 = $45
Example continued
 Average book value:
Initial investment = $240
Average investment = ($240 + 160 + 80 + 0)/4 = $120
(or) = $240/2 = $120
 Average accounting return (AAR):
Average net income
AAR =
Average book value
$45
=
$120
= 37.5%
Problems with AAR
• Does not use cash flows
• Ignores timing of income
• Pre-specified benchmark is arbitrary
Summary
• Of all the rules considered, NPV consistently
gives the correct answers
• Other rules may or may not give the same
answer as NPV
• Decisions based on NPV rule are always correct!
Summary
• Why study other rules?
• Corporations often use more than one rule
• However, most corporations have adopted
the NPV rule
• In practice, IRR is the strongest challenge to
the NPV rule
• managers seem to prefer talking about
investment ‘returns’ rather than NPV
Major remaining issues
• So far we have ignored from where we got
the cash flows and ‘r’:
• How do you compute the correct cash flows
to use in NPV?
– accounting income vs. relevant cash flows
• How do you determine the correct cost of
capital ‘r’?
– risk and return