12
Part 4 Investing in Long-Term Assets: Capital Budgeting
FIGURE 13.1
Analysis of a Growth Option (Dollars in Thousands)
A
B
D
E
F
G
H
13
50%
NPV@
12%
$603
-$358
$122
$480
3.93
4
5 Part 1. Project Without the Growth Option
6
Cash Flow at End of Period
7
Outcome Prob.
0
1
2
3
8
Good
-$3,000 $1,500 $1,500
$1,500
19
Bad
50% -$3,000 $1,100 $1,100 $1,100
10
Expected NPV
11
Standard Deviation (a)
12
Coefficient of Variation = CV=0 / Expected NPV
13
14 Part II. Project With the Growth Option
15
Cash Flow at End of Period
16
0
1
2
3
17
Cash flows, initial investment _$3,000 $1,500 $1,500 $1,500
18
Cash flows, growth investment
__$1,000 $5,000
19
Good
50% -$3,000 $1,500
$500 $6,500
20
Bad
-$3,000 $1.100 $1,100 $1,100
21
Expected NPV
22
Standard Deviation (o)
23
Coefficient of Variation = CV = g / Expected NPV
24
25 Part III. Value of the Option
26
Expected NPV with the growth option
27
Expected NPV without the growth option
NPV@
12%
50%
$3,364
-$358
$1,503
$1,861
1.24
$1.503
$122
$1,381
CASE 1: If the expected NPV without the growth option is positive, then
28
Value of the Option =
Expected NPV with the
Expected NPV without
29
growth option
the growth option
30
31
CASE 2: If the expected NPV without the growth option is negative, then
Value of the Option =
Expected NPV with the
0
32
growth option
33
Note: If the expected NPV without the growth option is negative, the project would not be
34 undertaken, in which case the project would have no effect on firm value (NPV = 0).
35
36
VALUE OF OPTION=
NA
$1,381
considering an embedded real option to expand the project. GRE would invest
$3 million at Time 0. Because this is considered a relatively risky investment, a
WACC of 12% is used. There is a 50% probability of success, in which case the
project will yield positive cash inflows of $1.5 million per year for 3 years.
COMMODO
'All બાકી પણ હા, મજીદા નગારીનું કામ કરી ગયા મારા પગ દબાણ ગણ મન મારા કામમાં મારા મન માં ગાયા,
DLL
F
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Chapter 13 Real Options and Other Topics in Capital Budgeting
445
FIGURE 13.2
Analysis of an Abandonment Option (Dollars in Thousands)
A
B
C
D
E
F
G
H н
3 Part I. Cannot Abandon
4
5 Outcome Prob.
6 Best Case 2596
7 Base Case 50%
8
Worst Case 25%
9
10
11
12
$400
Cash Flow at End of Period
0
1
2
3
4
-$1,000 $400 $600
$800 $1300
-$1,000 $200
$500 $600
-$1,000 -$280 H$280
-$280
$280
Expected NPY
Standard Deviation (o)
Coefficient of Variation = CV=0 / Expected NPV
NPV @
10%
$1,348
$298
|_$1,888
$14
$1,179
83.25
13 Part II. Can Abandon
14
15 Outcome Prob.
16 Best Case 25%
17 Base Case 50%
18 Worst #1 0%
19 Worst #2 25%
20
21
22
23
24 Part II. Value of the Option
25
Cash Flow at End of Period
0
1
2
3
4
-$1,000 $400 $600 $800 $1,300
_$1,000 $200 $400 $500 $600
_$1,000 $280
$280 -$280 -$280
_$1,000 -$280
$0
$0
Expected NPV
Standard Deviation (a)
Coefficient of Variation = CV=0 / Expected NPV
NPV @
10%
$1,348
$298
-$1,888 Don't Use
-$1,089 Use
$214
$866
4.05
$200
26
Expected NPV with the abandonment option
Expected NPV without the abandonment option
$214
$14
$200
217 CASE 1: If the expected NPV without the abandonment option is positive, then
Expected NPV with
Expected NPV without
Value of the Option= the abandonment
the abandonment
option
28
option
29
30
CASE 2: If the expected NPV without the abandonment option is negative, then
Expected NPV with
Value of the Option = the abandonment
0
31
option
32
Note: If the expected NPV without the abandonment option is negative, the project
would not be undertaken in which case the project would have no effect on firm
33 value (NPV = 0).
134
135
VALUE OF OPTION
NA
ਦਾ
$200
des
G4.204
mars
Tગામનગર આ વાતમાં જ મારી મધ્ય માણવામાલ સાગરમા ગરમ સરગામ ગામ માર માં ગામ ના ગાતા ગાતા ને
DLL
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Chapter 13 Real Options and Other Topics in Capital Budgeting
447
FIGURE 13.3
Analysis of a Timing Option (Dollars in Thousands)
H
NPV@
1296
$1,804
_$1,919
$58
$1,861
32.23
А
B
D
E
G
|3|Part 1. Project Without the Timing Option
4
Cash Flow at End of Period
5
Outcome Prob.
0
1
2
6
Good 50% -$3,000 $2,000 $2,000 $2,000
17
Bad
50% -$3,000
$450 $450 $450
8
Expected NPV
9
Standard Deviation (0)
10
Coefficient of Variation = CV = 0 / Expected NPV
11
12 Part II. Delay the Decision Until We Know the Market Conditions
1113
Cash Flow at End of Period
14
Outcome
Prob.
0
2
3
15
Good
50%
SO
--$3,000 $2,000 $2,000
16
Bad
50%
$0
$0
$0
$0
17
Expected NPY
18
Standard Deviation (0)
19
Coefficient of Variation = CV = c/ Expected NPVT
20
21 Part 1. Value of the Option
22
Expected NPV with the timing option
23
Expected NPV without the timing option
24
25
CASE 1: If the expected NPV without the timing option is positive, then
Value of the Option =
Expected NPV with the
Expected NPV without
timing option
the timing option
26
127
28
CASE 2: If the expected NPV without the timing option is negative, then
Value of the Option =
Expected NPV with the
29
timing option
GO
NPV
12%
$339
$0
$170
$170
1.00
$170
$58
NA
$170
Note: If the expected NPV without the timing option is negative, the project would not be
undertaken, in which case the project would have no effect on firm value (NPV = 0).
31
32
33
VALUE OF OPTION =
$170
134
Note: Under the Delay situation, we must find the NPV as of t = 0. If we set the cash flow for t= 0 at 50,
then using a calculator or Excel, we automatically find the NPV at t = 0. However, if we let
CFC-3000, CF = 2000, N = 2. and I/YR = 12, we get an NPV = 5380 under the Good outcome and an
expected NPV of $190. Note, though, that these NPVs are as of t= 1, so we must discount them back
1 year at 12% to achieve comparability with the NPV calculated for not delaying the project and arrive
35 at the correct answer.
Hab
பேயாயபபாயா
DLL
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Chapter 13 Real Options and Other Topics in Capital Budgeting
449
FIGURE 13.4
Analysis of a Flexibility Option Dollars in Thousands)
А
B
C
D
E
F
G
H
J
3 Part I. Project Without the Flexibility Option
Cash Flow at End of Period
4
Outcome
Prob.
0
1
2
3
5 Strong demand
6 Weak demand
NPV@
1296
$1,005
$1,397
50%
$2,500
_$5,000
-$5,000
$2,500
$1,500
50%
$2,500
$1,500
$1,500
Expected NPV
-$196
Cash Flow at End of Period
NPV@
7
8
9 Part II. Project With the Flexibility Option
10
Outcome
11 Strong demand
12 Weak demand Switch products
13
14
Prob.
0
1
2
3
12%
50%
-$5,100
-$5,100
$2.500
$1,500
50%
$2,500 $2,500
$2,250
$2,250
Expected NPV
$905
|_$366
$270
15 Part III. Value of the Option
16
$270
17
Expected NPV with the flexibility option
Expected NPV without the flexibility option
-$196
18
119
CASE 1: If the expected NPV without the flexibility option is positive, then
Value of the
Option =
Expected NPV with
the flexibility option
20
Expected NPV
without the flexibility
option
NA
21
I
22
CASE 2: If the expected NPV without the flexibility option is negative, then
Value of the Expected NPV with
Option the flexibility option
23
$270
24
Note: If the expected NPV without the flexibility option is negative, the project would not be
25 undertaken, in which case the project would have no effect on firm value (NPV = 0).
26
27
VALUE OF OPTION =
$270
SEE TEST
2
What are input flexibility options and output flexibility options?
How do flexibility options affect projects NPVs and risk?
DI
e
DALL
F5
F6
F7
N
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