Transcript Capital Budgeting For 9.220 Outline  Introduction  Net Present Value (NPV)  Payback Period Rule (PP)      Discounted Payback Period Rule Average Accounting Return (AAR) Internal Rate.

Capital Budgeting
For 9.220
1
Outline
 Introduction
 Net Present Value (NPV)
 Payback Period Rule (PP)





Discounted Payback Period Rule
Average Accounting Return (AAR)
Internal Rate of Return Rule (IRR)
Profitability Index Rule (PI)
Special Situations


Mutually Exclusive, Differing Scales
Capital Rationing
 Summary and Conclusions
2
Recall the Flows of funds and decisions
important to the financial manager
Investment
Decision
Financing
Decision
Reinvestment
Real Assets
Refinancing
Financial
Manager
Returns from Investment
Financial
Markets
Returns to Security Holders
Capital Budgeting is used to make the Investment Decision
3
Introduction
 Capital Budgeting is the process of determining which real
investment projects should be accepted and given an
allocation of funds from the firm.
 To evaluate capital budgeting processes, their consistency
with the goal of shareholder wealth maximization is of
utmost importance.
4
Capital Budgeting
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.
5
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
6
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.
7
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
$2,600
1,400
Cash flow $1,200
1
1.10
$700 x
+578.51
Revenues
Expenses
1
1.10 2
- $500 x
1
1.10 3
-375.66
$1,200 x
1
1.10 4
+819.62
+$377.02 NPV
NPV = -C0 + PV0(Future CFs)
= -C0 + C1/(1+r) + C2/(1+r)2 + C3/(1+r)3 + C4/(1+r)4
= ______ + ______ + ______ + _______ + _______
= $377.02 > 0
8
NPV in your HP 10B Calculator
First, clear previous data, and check that your calculator is set to 1 P/YR:
CLEAR ALL
Yellow
INPUT
Key in CF0
1,100
Key in CF1
500
Key in CF2
700
Key in CF3
Key in CF4
Key in r
The display should show: 1 P_Yr
Input data (based on above NPV example)
+/-
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
CFj
Display should show:
CF 4
NPV
Compute NPV
Yellow
PRC
Display should show:
377.01659723
9
NPV: Strengths and Weaknesses


Strengths

Resulting number is easy to interpret: shows how wealth
will change if the project is accepted.

Acceptance criteria is consistent with shareholder wealth
maximization.

Relatively straightforward to calculate
Weaknesses

An improper NPV analysis may lead to the wrong choices
of projects when the firm has capital rationing – this will
be discussed later.
10
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
11
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
12
Average Accounting Return (AAR)
Also known as Accounting Rate of Return (ARR)
Method: using accounting data on profits and
book value of the investment

AAR = Average Net Income / Average Book
Value
If AAR > some target book rate of return, then
accept the project
13
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
Year 2
160
100
60
Year 3
200
90
110
14
Calculating Projected NI
Sales
Expenses
E.B.D.
Depreciation
E.B.T.
Taxes (40%)
NI:
Year 1
140
120
Year 2
160
100
Year 3
200
90
15
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
16
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
17
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
+
800
2,200 =
______
(1+IRR)2
+
900
+
(1+IRR)1
(1+IRR)3
_______
+
500
+
(1+IRR)2
(1+IRR)3
(1+IRR)4
1,600
+
(1+IRR)4
18
IRR in your HP 10B Calculator
First, clear previous data, and check that your calculator is set to 1 P/YR:
CLEAR ALL
Yellow
INPUT
Key in CF0
2,200
Key in CF1
800
Key in CF2
900
The display should show: 1 P_Yr
Input data (based on above NPV example)
+/-
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
IRR/YR
Compute IRR
Yellow
CST
Display should show:
23.29565668%
19
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%)
20
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%
21
IRR: Strengths and Weaknesses
 Strengths


IRR number is easy to interpret: shows the
return the project generates.
Acceptance criteria is generally consistent with
shareholder wealth maximization.
 Weaknesses



Does not distinguish between investing and
financing scenarios
IRR may not exist or there may be multiple IRR
Problems with mutually exclusive investments
22
IRR for Investment and Financing Projects
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
-1,200
- 4,000 =
(1+IRR)1
(1+IRR)2
_______
+
(1+IRR)3
-800
+
(1+IRR)2
-3,500
+
(1+IRR)3
23
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%)
24
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 (%)
25
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
26
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 (%)
27
Multiple IRRs in your HP 10B Calculator
First, clear previous data, and check that your calculator is set to 1 P/YR:
CLEAR ALL
Yellow
INPUT
Key in CF0
900
Key in CF1
1,200
Key in CF2
Key in CF3
1,300
1,200
The display should show: 1 P_Yr
Input data (based on above NPV example)
+/-
Compute 2nd IRR
by guessing it first
Yellow
30
Display should show:
CF 0
CFj
Display should show:
CF 1
CFj
Display should show:
CF 2
+/-
Display should show:
CF 3
IRR/YR
Compute 1st IRR
CFj
CST
+/-
CFj
Display should show:
72.252175%
STO
Yellow
RCL
Yellow
Display should show:
-29.352494%
IRR/YR
CST
28
No or Multiple IRR Problem – What to do?
 IRR cannot be used in this circumstance, the only
solution is to revert to another method of
analysis. NPV can handle these problems.
 How to recognize when this IRR problem can
occur

When changes in the signs of cash flows happen more
than once the problem may occur (depending on the
relative sizes of the individual cash flows).
•
Examples: +-+ ; -+- ; -+++-; +---+
29
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
30
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 (%)
31
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
32
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 (%)
33
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
34
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)?
35
 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.
36
The Profitability Index (PI) Rule
Disadvantages:
 Problems with mutually exclusive investments (to
be discussed later)
Advantages:
 May be useful when available investment funds
are limited (to be discussed later).
 Easy to understand and communicate
 Correct decision when evaluating independent
projects
37
Special situations
 When projects are independent and the firm has few constraints on
capital, then we check to ensure that projects at least meet a minimum
criteria – if they do, they are accepted.

NPV≥0; IRR≥hurdle rate; PI≥1
 Sometimes a firm will have plenty of funds to invest, but it must
choose between projects that are mutually exclusive. This means that
the acceptance of one project precludes the acceptance of any others.
In this case, we seek to choose the one highest ranked of the acceptable
projects.
 If the firm has capital rationing, then its funds are limited and not all
independent projects may be accepted. In this case, we seek to choose
those projects that best use the firm’s available funds. PI is especially
useful here.
38
Using IRR and PI correctly when projects are
mutually exclusive and are of differing scales
 Consider the following
two mutually
exclusive projects.
Assume the
opportunity cost of
capital is 12%
Year
Cash flows
of Project A
Cash flows
of Project B
0
-$100,000
-$50
1
+$150,000
+$100
39
Incremental Cash Flows: Solving the
Problem with IRR and PI
 As you can see, individual IRRs and PIs are not good for
comparing between two mutually exclusive projects.
 However, we know IRR and PI are good for evaluating
whether one project is acceptable.
 Therefore, consider “one project” that involves switching
from the smaller project to the larger project. If IRR or PI
indicate that this is worthwhile, then we will know which
of the two projects is better.
 Incremental cash flow analysis looks at how the cash flows
change by taking a particular project instead of another
project.
40
Using IRR and PI correctly when projects
are mutually exclusive and are of differing
scales
Incremental
Cash flows of Cash flows of Cash flows of A
Year
Project A
Project B
instead of B
(i.e., A-B)
0
-$100,000
-$50
-$99,950
1
+$150,000
+$100
+$149,900
41
Using IRR and PI correctly when projects
are mutually exclusive and are of differing
scales
 IRR and PI analysis of incremental cash flows
tells us which of two projects are better.
 Beware, before accepting the better project, you
should always check to see that the better project
is good on its own (i.e., is it better than “do
nothing”).
42
IRR, NPV, and Mutually Exclusive Projects
200
Year
150
0
100
2
3
4
Project A:
– $350
50
100
150
200
Project B:
– $250
125
100
75
50
IRRB  17.80%
50
NPV ($)
1
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
43
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)
44
Capital Rationing



Recall: If the firm has capital rationing, then its funds are
limited and not all independent projects may be accepted. In
this case, we seek to choose those projects that best use the
firm’s available funds. PI is especially useful here.
Note: capital rationing is a different problem than mutually
exclusive investments because if the capital constraint is
removed, then all projects can be accepted together.
Analyze the projects on the next page with NPV, IRR, and
PI assuming the opportunity cost of capital is 10% and the
firm is constrained to only invest $50,000 now (and no
constraint is expected in future years).
45
Capital Rationing – Example
(All $ numbers are in thousands)
Year
Proj. A
Proj. B
Proj. C
Proj. D
Proj. E
0
-$50
-$20
-$20
-$20
-$10
1
$60
$24.2
-$10
$25
$12.6
2
$0
$0
$37.862
$0
$0
NPV
$4.545
$2.0
$2.2
$2.727
$1.4545
IRR
20%
21%
14.84%
25%
26%
PI
1.0909
1.1
1.11
1.136
1.145
46
Capital Rationing Example:
Comparison of Rankings
 NPV rankings (best to worst)

A, D, C, B, E
• A uses up the available capital
• Overall NPV = $4,545.45
 IRR rankings (best to worst)

E, D, B, A, C
• E, D, B use up the available capital
• Overall NPV = NPVE+D+B=$6,181.82
 PI rankings (best to worst)

E, D, C, B, A
• E, D, C use up the available capital
• Overall NPV = NPVE+D+C=$6,381.82
 The PI rankings produce the best set of investments to accept given the
capital rationing constraint.
47
Capital Rationing Conclusions
 PI is best for initial ranking of independent
projects under capital rationing.
 Comparing NPV’s of feasible combinations
of projects would also work.
 IRR may be useful if the capital rationing
constraint extends over multiple periods
(see project C).
48
Summary and Conclusions
 Discounted Cash Flow (DCF) techniques are the
best of the methods we have presented.
 In some cases, the DCF techniques need to be
modified in order to obtain a correct decision. It
is important to completely understand these cases
and have an appreciation of which technique is
best given the situation.
49