Chapter 6
Capital Budgeting Criteria for Investments Projects
Mutually Exclusive versus Independent Project
 Mutually Exclusive Projects: only ONE of several
potential projects can be chosen, e.g. acquiring an
accounting system.

RANK all alternatives and select the best one.
 Independent Projects: accepting or rejecting one project
does not affect the decision of the other projects.

Must exceed a MINIMUM acceptance criteria.
Jacoby, Stangeland and Wajeeh, 2000
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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
Jacoby, Stangeland and Wajeeh, 2000
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NPV - An Example
 Assume you have the following information on
Project X:
Initial outlay -$1,100
Required return = 10%
Annual cash revenues and expenses are as follows:
Year
Revenues
Expenses
1
$1,000
$500
2
2,000
1,300
3
2,200
2,700
4
2,600
1,400
 Draw a time line and compute the NPV of project X.
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The Time Line & NPV of Project X
0
1
2
3
4
Initial outlay Revenues
($1,100)
Expenses
$1,000
500
Revenues
Expenses
$2,000
1,300
Revenues
Expenses
$2,200
2,700
Cash flow
$500
Cash flow
$700
Cash flow
(500)
– $1,100.00
$500 x
+454.54
Revenues
Expenses
$2,600
1,400
Cash flow $1,200
1
1.10
$700 x
1
1.10 2
+578.51
1
- $500 x
1.10 3
-375.66
$1,200 x
1
1.10 4
+819.62
NPV = -C0 + PV0(Future CFs)
= -C0 + C1/(1+r) + C2/(1+r)2 + C3/(1+r)3 + C4/(1+r)4
=-
+
= $377.02 > 0
+
+
+
4
NPV in your HP 10B Calculator
First, clear previous data, and check that your calculator is set to 1 P/YR:
Yellow
The display should show: 1 P_Yr
Input data (based on above NPV example)
C
C ALL
Key in CF0
1,100
Key in CF1
500
Key in CF2
700
Key in CF3
Key in CF4
Key in r
Compute NPV
+/-
CFj
Display should show:
CF 0
CFj
Display should show:
CF 1
CFj
Display should show:
CF 2
500
+/-
Display should show:
CF 3
1,200
CFj
10
I/YR
Yellow
PRC
NPV
CFj
Display should show:
CF 4
Display should show:
377.01659723
5
The Payback Period Rule
How long does it take the project to “pay
back” its initial investment?
Payback Period = # of years to recover costs
of project
Minimum Acceptance Criteria: set by
management
Ranking Criteria: set by management
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Discounted Payback - An Example
Year
1
2
3
4
Year
1
2
3
4
Initial outlay -$1,000
r = 10%
PV of
Cash flow
Cash flow
$ 200
$ 182
400
331
700
526
300
205
Accumulated
discounted cash flow
$ 182
513
1,039
1,244
Discounted payback period is just under 3 years
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Average Accounting Return (AAR)
 You want to invest in a machine that produces squash balls.
 The machine costs $90,000.
 The machine will ‘die’ after 3 years (assume straight line depreciation,
the annual depreciation is $30,000).
 You estimate for the life of the project:
Sales
Expenses
EBD
Year 1
140
120
20
Jacoby, Stangeland and Wajeeh, 2000
Year 2
160
100
60
Year 3
200
90
110
8
Calculating Projected NI
Sales
Expenses
E.B.D.
Year 1
140
120
Year 2
160
100
Year 3
200
90
Depreciation
E.B.T.
Taxes (40%)
NI:
Jacoby, Stangeland and Wajeeh, 2000
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We calculate:
 6 18 48  60  20
(i) Average NI =
3
3
(ii) Average book value (BV) of the investment (machine):
time-0 time-1 time-2 time-3
BV of investment:
90
=> Average BV = 90  60  30  0  45
4
60
30
0
(divide by 4 - not 3)
(iii) The Average Accounting Return:
20
AAR = 45 = 44.44%
Conclusion: If target AAR < 44.44% => accept
If target AAR > 44.44% => reject
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The Internal Rate of Return (IRR) Rule
 IRR: the discount rate that sets the NPV to zero
 Minimum Acceptance Criteria:
Accept if: IRR > required return
 Ranking Criteria: Select alternative with the highest IRR
 Reinvestment assumption: the IRR calculation assumes that all future
cash flows are reinvested at the IRR
 Disadvantages:
 Does not distinguish between investing and financing
 IRR may not exist or there may be multiple IRR
 Problems with mutually exclusive investments
 Advantages:
 Easy to understand and communicate
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Internal Rate of Return - An Example
Initial outlay = -$2,200
Cash flow
Year
1
2
3
4
800
900
500
1,600
Find the IRR such that NPV = 0
0=-
+
(1+IRR)1
+
(1+IRR)2
+
(1+IRR)3
+
(1+IRR)4
Or:
800
2,200 =
(1+IRR)1
900
+
(1+IRR)2
500
+
(1+IRR)3
Jacoby, Stangeland and Wajeeh, 2000
1,600
+
(1+IRR)4
12
IRR in your HP 10B Calculator
First, clear previous data, and check that your calculator is set to 1 P/YR:
Yellow
The display should show: 1 P_Yr
Input data (based on above NPV example)
C
C ALL
Key in CF0
2,200
Key in CF1
800
Key in CF2
900
+/-
CFj
Display should show:
CF 0
CFj
Display should show:
CF 1
CFj
Display should show:
CF 2
Key in CF3
500
CFj
Display should show:
CF 3
Key in CF4
1,600
CFj
Display should show:
CF 4
Yellow
CST
IRR/YR
Compute IRR
Display should show:
23.29565668%
Jacoby, Stangeland and Wajeeh, 2000
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Internal Rate of Return and the NPV Profile
The NPV Profile
Discount rates
NPV
0%
$1,600.00
5%
1,126.47
10%
739.55
15%
419.74
20%
152.62
25%
-72.64

IRR is between 20% and 25% -- about 23.30%

If required rate of return (r) is lower than IRR => accept the project (e.g. r = 15%)

If required rate of return (r) is higher than IRR => reject the project (e.g. r = 25%)
Jacoby, Stangeland and Wajeeh, 2000
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The Net Present Value Profile
Net present
value
Year
Cash flow
1,600.00
0
1
2
3
4
1,126.47
– $2,200
800
900
500
1,600
739.55
419.74
159.62
0
– 72.64
2%
6%
10%
14%
18%
22%
Discount
rate
IRR=23.30%
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IRR: Investment vs. Financing Project
Initial outlay = $4,000
Cash flow
Year
1
2
3
-1,200
-800
-3,500
Find the IRR such that NPV = 0
0=
+
(1+IRR)1
+
(1+IRR)2
+
(1+IRR)3
Or:
-1,200
- 4,000 =
(1+IRR)1
-800
+
(1+IRR)2
-3,500
+
(1+IRR)3
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Internal Rate of Return and the NPV Profile for a Financing Project
The NPV Profile of a Financing Project:
Discount rates
NPV
0%
-$1,500.00
5%
-891.91
10%
-381.67
15%
50.2
20%
418.98

IRR is between 10% and 15% -- about 14.37%
For a Financing Project, the required rate of return is the cost of financing, thus

If required rate of return (r) is lower than IRR => reject the project (e.g. r = 10%)

If required rate of return (r) is higher than IRR => accept the project (e.g. r = 15%)
Jacoby, Stangeland and Wajeeh, 2000
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The NPV Profile for a Financing Project
$2,000.00
$1,500.00
$1,000.00
NPV ($)
$500.00
$0.00
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
-$500.00
-$1,000.00
-$1,500.00
-$2,000.00
Rate of Return (%)
18
Multiple Internal Rates of Return
Example 1
Assume you are considering a
project for which the cash flows are
as follows:
Year
Cash flows
0
-$900
1
2
3
1,200
1,300
-1,200
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Multiple IRRs and the NPV Profile - Example 1
$600.00
$400.00
IRR1=-29.35%
IRR2=72.25%
$200.00
NPV ($)
$0.00
-60%
-40%
-20%
0%
20%
40%
60%
80%
100%
120%
140%
-$200.00
-$400.00
-$600.00
-$800.00
-$1,000.00
Rate of Return (%)
20
Multiple IRRs in your HP 10B Calculator
First, clear previous data, and check that your calculator is set to 1 P/YR:
Yellow
The display should show: 1 P_Yr
Input data (based on above NPV example)
C
C ALL
Key in CF0
900
Key in CF1
1,200
Key in CF2
Key in CF3
Compute 1st IRR
Compute 2nd IRR
by guessing it first
+/-
CFj
Display should show:
CF 0
CFj
Display should show:
CF 1
CFj
Display should show:
CF 2
1,200
+/-
Display should show:
CF 3
Yellow
CST
IRR/YR
1,300
30
+/-
CFj
Display should show:
72.252175%
Yellow
RCL
STO
Yellow
Display should show:
-29.352494%
CST
IRR/YR
21
Multiple Internal Rates of Return
Example 2
Assume you are considering a
project for which the cash flows are
as follows:
Year
Cash flows
0
-$260
1
2
3
4
250
300
20
-340
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Multiple IRRs and the NPV Profile - Example 2
$10.00
$0.00
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
-$10.00
NPV ($)
-$20.00
IRR1=11.52%
IRR2=29.84%
-$30.00
-$40.00
-$50.00
-$60.00
-$70.00
-$80.00
Rate of Return (%)
23
Multiple Internal Rates of Return
Example 3
Assume you are considering a
project for which the cash flows are
as follows:
Year
Cash flows
0
$660
1
2
3
4
-650
-750
-50
850
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Multiple IRRs and the NPV Profile - Example 3
$200.00
NPV($)
$150.00
$100.00
IRR1=8.05%
$50.00
IRR2=33.96%
$0.00
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
-$50.00
Rate of Return (%)
Jacoby, Stangeland and Wajeeh, 2000
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IRR, NPV, and Mutually Exclusive Projects
200
Year
150
0
100
2
3
4
Project A:
– $350
50
100
150
200
Project B:
– $250
125
100
75
50
50
NPV ($)
1
IRRB  17.80%
0
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
-50
-100
-150
-200
IRRA  12.91%
Rate of Return (%)
Project A
Project B
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IRR, NPV, and the Incremental Project
Year
200
150
0
1
2
3
4
Project A:
– $350
50
100
150
200
Project B:
– $250
125
100
75
50
100
(A-B):
NPV ($)
50
0
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
-50
-100
The Crossover Rate
= IRRA-B = 8.07%
-150
Rate o Return (%)
-200
Project A
Project B
Incremental (A-B)
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The Profitability Index (PI) Rule
PI =
Total Present Value of future CF’s / Initial Investment
Minimum Acceptance Criteria: Accept if PI > 1
Ranking Criteria: Select alternative with highest PI
Disadvantages:
 Problems with mutually exclusive investments
Advantages:
 May be useful when available investment funds are
limited
 Easy to understand and communicate
 Correct decision when evaluating independent projects
Jacoby, Stangeland and Wajeeh, 2000
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Profitability Index - An Example

Consider the following information on Project Y:
Initial outlay -$1,100
Required return = 10%
Annual cash benefits:
Year


Cash flows
1
$ 500
2
1,000
What’s the NPV?
What’s the Profitability Index (PI)?
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 The NPV of Project Y is equal to:
NPV = (500/1.1) + (1,000/1.12) - 1,100 = ($454.54 + 826.45) - 1,100
= $1,280.99 - 1,100 = $180.99.
 PI = PV Cashflows/Initial Investment
=
 This is a good project according to the PI rule. Can you explain why?
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