Transcript Essentials of Finance - University of South Florida

Capital Budgeting Techniques
How do firms make decisions about whether to
invest in costly, long-lived assets?
How does a firm make a choice between two
acceptable investments when only one can be
purchased?
How are different capital budgeting techniques
related?
Which capital budgeting methods do firms actually
use?
1
Capital Budgeting
Introduction to Capital Budgeting
Payback Period—traditional and
discounted
Net Present Value (NPV)
Internal Rate of Return (IRR)
Modified IRR
Comparison of NPV and IRR
NPV/IRR Ranking Conflicts/Cautions
2
Capital Budgeting
Capital Budgeting Basics and Techniques
Given
 r—firm’s required rate of return
 CF—cash flows generated by an investment
Capital Budgeting—cash flows and risk
Compute
 r—firm’s required rate of return
 CF—cash flows generated by an investment
3
Capital Budgeting Basics
Importance of capital budgeting decisions
 long-term effect—capital, or long-term funds, raised by
the firms are used to invest in assets that enable the firm
to generate revenues several years into the future.
 timing of a decision is important—decisions impact the
firm for several years.
Generating ideas for capital budgeting
 employees, customers, suppliers, and so forth
 based on needs and experiences of the firm and these
groups
4
Capital Budgeting Basics
Project classifications—replacement decisions versus
expansion decisions
 replacement decision—intended to maintain existing levels of
operations
 expansion decision—a decision concerning whether the firm
should expand operations
Project classifications—independent projects versus
mutually exclusive projects
 independent project—accepting one independent project
does not affect the acceptance of any other project
 mutually exclusive projects—only one project can be
purchased
5
Capital Budgeting Basics—
Capital Budgeting Versus Asset Valuation
Value of an asset = PV of the cash flows the asset
is expected to generate during its life:



A sset
Value

C F1
1
(1  r)

C F2
2
(1  r)

C Fn
(1  r)n
An asset is an acceptable investment if the cost of
the asset is less than its value:
Acceptable if: PV of CFs > Cost
6
Capital Budgeting Techniques
Payback period
Net present value
Internal rate of return
7
Capital Budgeting Techniques
Illustrative Investment
Year
0
1
2
3
4

Cash Flow, CF t
(7,000)
2,000
1,000
5,000
3,000
r = 15%
8
Capital Budgeting Example
Cash Flow Time Line
0
1
2
3
4
2,000
1,000
5,000
3,000
15%
(7,000.00)
1,739.13
S PV =
7,498.11
756.14
3,287.58
1,715.26
498.11 =




CF0  PV of CF1  PV of CF2  PV of CF3  PV of CF4
9
Capital Budgeting Techniques
Payback Period
Number of years it takes to recapture the
initial investment.
Year
0
1
2
3
4
Cash Flow
$(7,000)
2,000
1,000
5,000
3,000
Cumulative CF
$(7,000)
(5,000)
(4,000) } 2<Payback<3
1,000
4,000
10
Capital Budgeting Techniques
Payback Period
Year
0
1
2
3
4
Cash Flow
$(7,000)
2,000
1,000
5,000
3,000
Cumulative CF
$(7,000)
(5,000)
(4,000)
} 2<Payback<3
1,000
4,000
$ investment remaining
# of years before
to be recaptured
Payback  full recovery of

period
$ cash flow in
original investment
year of payback

2
 2.80 years

$4,000
$5,000
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Capital Budgeting Techniques
Payback Period
Accept the project if Payback, PB < some
number of years established by the firm
PB = 2.8 years is acceptable if the firm has
established a maximum payback of 4.0 years
12
Capital Budgeting Techniques
Payback Period
Advantages:
Simple
Cash flows are used
Provides an indication of the liquidity of a
project
Disadvantages:
Does not use time value of money concepts
Cash flows beyond the payback period are
ignored
13
Capital Budgeting Techniques
Payback Period
Year
0
1
2
3
4
5
Cash Flow
$(7,000)
2,000
1,000
5,000
3,000
1,000,000
Cumulative CF
$(7,000)
(5,000)
(4,000) } PB = 2.80 yrs
1,000
4,000
1,004,000
14
Capital Budgeting
Net Present Value (NPV)
NPV = present value of future cash flows less the
initial investment



CF1
CF 2
CF n

 
NPV  CF0 
1
2 
(1  r) (1  r)
(1  r) n
n

t 0

CF t
(1  r) t
An investment is acceptable if NPV > 0
15
Capital Budgeting—NPV
$2,000 $1,000 $5,000 $3,000



NPV  -$7,000 
1
2
3
(1.15) (1.15) (1.15) (1.15) 4
 -$7,000  $1,739.13 $756.14  $3,287.58  $1,715.26
 $498.11
NPV = $498.11 > 0, so the project is acceptable
16
Capital Budgeting Example
Cash Flow Time Line
0
1
2
3
4
2,000
1,000
5,000
3,000
15%
(7,000.00)
1,739.13
756.14
3,287.58
1,715.26
498.11 = NPV
17
Capital Budgeting—NPV
Advantages:
Cash flows rather than profits are analyzed
Recognizes the time value of money
Acceptance criterion is consistent with the goal
of maximizing value
Disadvantage:
Detailed, accurate long-term forecasts are
required to evaluate a project’s acceptance
18
Solving for NPV
Numerical (equation) solution
Financial Calculator solution
Spreadsheet solution
19
Solving for NPV
Numerical Solution
$2,000 $1,000 $5,000 $3,00



NPV  -$7,000 
1
2
3
(1.15) (1.15) (1.15) (1.15) 4
 -$7,000  $1,739.13 $756.14  $3,287.58  $1,715.26
 $498.11
20
Solving for NPV
Financial Calculator Solution
Input the following into the cash flow register:
CF0
= -7,000
CF1
= 2,000
CF2
= 1,000
CF3
= 5,000
CF4
= 3,000
Input I = 15
Compute NPV = 498.12
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Capital Budgeting
Discounted Payback Period
Payback period computed using the present values of
the future cash flows.
Year
0
1
2
3
4
Cash Flow
$(7,000)
2,000
1,000
5,000
3,000
Cumulative
PV of CF @15% PV of CF
$(7,000.00)
$(7,000.00)
1,739.13
(5,260.87)
756.14
(4,504.73)
3,287.58
(1,217.14)
1,715.26
498.12
} PBdisc= 3.71
A project is acceptable if PBdisc < project’s life
22
Capital Budgeting
Internal Rate of Return (IRR)
If NPV>0, project’s return > r
IRR > 15%
 Example:
Initial investment
= $7,000.00
PV of future cash flows = $7,498.12
NPV = $498.12
r = 15%
If IRR = project’s rate of return
IRR = the rate of return that causes the NPV of the
project to equal zero, or where the present value of
the future cash flows equals the initial investment.
23
Capital Budgeting
Internal Rate of Return (IRR)



CF 1
CF 2
CF n


0
NPV  CF0 
1
2
n
(1  IRR)
(1  IRR)
(1  IRR)



CF 1
CF 2
CF n


CF0 
1
2
(1  IRR)
(1  IRR)
(1  IRR) n
A project is acceptable if its IRR > r
24
Capital Budgeting
Internal Rate of Return (IRR)
NPV  -7,000 
$7,000 
2,000
1,000
5,000
3,000



0
1
2
3
4
(1  IRR)
(1  IRR)
(1  IRR)
(1  IRR)
$2,000
$1,000
$5,000
$3,000



(1  IRR)1 (1  IRR) 2 (1  IRR) 3 (1  IRR) 4
25
Internal Rate of Return (IRR)
Cash Flow Time Line
0
1
2
3
4
2,000
1,000
5,000
3,000
IRR = ?
(7,000)
S of PVs = 7,000
0 = NPV
26
Capital Budgeting—IRR
Advantages:
Cash flows rather than profits are analyzed
Recognizes the time value of money
Acceptance criterion is consistent with the goal of
maximizing value
Disadvantages:
Detailed, accurate long-term forecasts are required
to evaluate a project’s acceptance
Difficult to solve for IRR without a financial
calculator or spreadsheet
27
Solving for IRR
Numerical Solution
Using the trial-and-error method plug in values for
IRR until the left and right side of the following
equation become equal.
$7,000 
$2,000
$1,000
$5,000
$3,000



(1  IRR)1 (1  IRR) 2 (1  IRR) 3 (1  IRR) 4
28
Solving for IRR
Numerical Solution
Rate of Return
15%
16
17
18
19
NPV
498.12
327.46
162.72
3.62
(150.08)
} 18<IRR<19
29
Solving for IRR
Financial Calculator Solution
Input the following into the cash flow register:
CF0
=
-7,000
CF1
=
2,000
CF2
=
1,000
CF3
=
5,000
CF4
=
3,000
Compute IRR = 18.02%
30
NPV versus IRR
When NPV > 0, a project is acceptable because
the firm will increase its value, which means the
firm earns a return greater than its required rate
of return (r) if it invests in the project.
When IRR > r, a project is acceptable because the
firm will earn a return greater than its required
rate of return (r) if it invests in the project.
When NPV > 0, IRR > r for a project—that is, if a
project is acceptable using NPV, it is also
acceptable using IRR.
31
Accept/Reject Decisions Using NPV,
Discounted Payback, and IRR
Technique
NPV
IRR
Discounted PB
Evaluation Result
Acceptable?
YES
NPV > 0
YES
IRR > r
YES
PBdisc < project’s life
32
NPV Profile
A graph that shows the NPVs of a project
at various required rates of return.
Rate of Return
15%
16
17
18
19
20
21
NPV
498.12
327.46
162.72
3.62
(150.08)
(298.61)
(442.20)
33
NPV Profile
NPV
$5,000
$4,000
$3,000
IRR = 18.02%
$2,000
$1,000
NPV > 0
$0
($1,000)
5%
10%
15%
20%
NPV < 0
r
25%
($2,000)
34
Capital Budgeting Techniques
Illustrative Projects A & B

Cash Flow, C Ft
Year
Project A
Project B
0
(7,000.00)
(8,000.00)
1
2,000.00
6,000.00
2
1,000.00
3,000.00
3
5,000.00
1,000.00
4
3,000.00
500.00
Trad PB =2.80
1.67
NPV =
498.12
429.22
IRR =
18.02%
19.03%
r = 15%
35
NPV Profiles for Projects A & B
NPV
5000
4000
Project A
3000
Crossover = 16.15
2000
1000
Project B
IRRB = 19.03
r
0
5%
-1000
-2000
10%
15%
20%
25%
IRRA = 18.02
36
NPV Profile—Projects A & B
Rate of Return
NPVA
NPVB
15%
16
17
18
19
20
21
498.12
327.46
162.72
3.62
(150.08)
(298.61)
(442.20)
429.22
318.71
210.94
105.82
3.26
(96.84)
(194.55)
37
Capital Budgeting Techniques
Illustrative Projects A & B

Cash Flow, C Ft
Year
Project A
Project B
CFA - CFB
0
1
2
3
4
(7,000)
2,000
1,000
5,000
3,000
(8,000)
6,000
3,000
1,000
500
1,000
(4,000)
(2,000)
4,000
2,500
IRR of (CFA – CFB) Cash Flow Stream = 16.15%
At r = 16.15%, NPVA = NPVB = 302.37
38
NPV/IRR Ranking Conflicts
Traditional PB
Discounted PB
NPV
IRR
Asset A
2.80 yrs
3.71 yrs
$498.12
18.02%
Asset B
1.67 yrs
2.78 yrs
$429.22
19.03%
Which asset(s) should be purchased?
Asset A, because it has the higher NPV.
39
NPV/IRR Ranking Conflicts
Ranking conflicts result from:
 Cash flow timing differences
 Size differences
 Unequal lives
Reinvestment rate assumptions
 NPV—reinvest at the firm’s required rate of
return
 IRR—reinvest at the project’s internal rate of
return, IRR
40
Multiple IRRs
Conventional cash flow pattern—cash outflow(s) occurs
at the beginning of the project’s life, followed by a series
of cash inflows.
Unconventional cash flow pattern—cash outflow(s)
occurs during the life of the project, after cash inflows
have been generated.
An IRR solution occurs when a cash flow pattern is
interrupted; if a cash flow pattern is interrupted more
than once, then more than one IRR solution exists.
41
Multiple IRRs—Example
Year
Cash Flow
0
(15,000)
1
40,150
2
(13,210)
3
(16,495)
IRR1 = 22.5%
IRR2 = 92.0%
42
Modified Internal Rate of Return (MIRR)
Generally solves the ranking conflict and the
multiple IRR problem
PV of cash outf lows=
FV of cash outf lows
(1+ MIRR)n
n
n
 (1  r) t
t 0
COFt


CIFt (1  r ) n - t
t 0
(1  MIRR) n
43
MIRR—Example
Year
0
1
2
3
4
Discounted PB
NPV
IRR
Project A
(7,000)
2,000
1,000
5,000
3,000
Project B
(8,000)
6,000
3,000
1,000
500
3.71 yrs
$498.12
18.02%
2.78 yrs
$429.22
19.03%
44
MIRR—Example
Year
0
1
2
3
4
Project A
(7,000)
2,000
1,000
5,000
3,000
Project B
(8,000)
6,000
3,000
1,000
500
2,000(1.15) 3  1,000(1.15) 2  5,000(1.15)1  3,000(1.15) 0
13,114.25
7,000 

(1  MIRR A )
(1  MIRR A )
Project A—calculator solution: N = 4, PV = -7,000, PMT =
0, FV = 13,114.25; I/Y = 16.99 = MIRRA
Project B—calculator solution: N = 4, PV = -8,000, PMT =
0, FV = 14,742.75; I/Y = 16.51 = MIRRB
45
Capital Budgeting—The Answers
How do firms make decisions about whether
to invest in costly, long-lived assets?
 Firms use decision-making methods that are
based on fundamental valuation concepts
How does a firm make a choice between two
acceptable investments when only one can be
purchased?
 The decision should be consistent with the goal of
maximizing the value of the firm
46
Capital Budgeting—The Answers
How are different capital budgeting
techniques related?
 All techniques except traditional payback period
(PB) are based on time value of money
Which capital budgeting methods do firms
actually use?
 Most firms rely heavily on NPV and IRR to make
investment decisions
47