Transcript Chapter 14 -- Risk and Managerial Options in Capital Budgeting

Risk and Managerial
Options in Capital
Budgeting
14-1
An Illustration of Total
Risk (Discrete Distribution)
ANNUAL CASH FLOWS: YEAR 1
PROPOSAL A
State
Deep Recession
Mild Recession
Normal
Minor Boom
Major Boom
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Probability
.05
.25
.40
.25
.05
Cash Flow
$ -3,000
1,000
5,000
9,000
13,000
Probability Distribution
of Year 1 Cash Flows
Proposal A
Probability
.40
.25
.05
3,000
1,000
5,000
9,000
Cash Flow ($)
14-3
13,000
Expected Value of Year 1
Cash Flows (Proposal A)
CF1
$ - 3,000
1,000
5,000
9,000
13,000
14-4
P1
.05
.25
.40
.25
.05
S=1.00
(CF1)(P1)
$ -150
250
2,000
2,250
650
CF1=$5,000
Variance of Year 1
Cash Flows (Proposal A)
14-5
(CF1)(P1)
(CF1 - CF1)2(P1)
$ -150
250
2,000
2,250
650
$5,000
( -3,000 - 5,000)2 (.05)
( 1,000 - 5,000)2 (.25)
( 5,000 - 5,000)2 (.40)
( 9,000 - 5,000)2 (.25)
(13,000 - 5,000)2 (.05)
Variance of Year 1
Cash Flows (Proposal A)
14-6
(CF1)(P1)
(CF1 - CF1)2*(P1)
$ -150
250
2,000
2,250
650
$5,000
3,200,000
4,000,000
0
4,000,000
3,200,000
14,400,000
Summary of Proposal A
The standard deviation =
SQRT (14,400,000) = $3,795
The expected cash flow = $5,000
14-7
An Illustration of Total
Risk (Discrete Distribution)
ANNUAL CASH FLOWS: YEAR 1
PROPOSAL B
State
Deep Recession
Mild Recession
Normal
Minor Boom
Major Boom
14-8
Probability
.05
.25
.40
.25
.05
Cash Flow
$ -1,000
2,000
5,000
8,000
11,000
Probability Distribution
of Year 1 Cash Flows
Proposal B
Probability
.40
.25
.05
-3,000
1,000
5,000
9,000
Cash Flow ($)
14-9
13,000
Expected Value of Year 1
Cash Flows (Proposal B)
CF1
$ -1,000
2,000
5,000
8,000
11,000
14-10
P1
.05
.25
.40
.25
.05
S=1.00
(CF1)(P1)
$
-50
500
2,000
2,000
550
CF1=$5,000
Variance of Year 1
Cash Flows (Proposal B)
(CF1)(P1)
$
-50
500
2,000
2,000
550
$5,000
14-11
(CF1 - CF1)2(P1)
( -1,000 - 5,000)2 (.05)
( 2,000 - 5,000)2 (.25)
( 5,000 - 5,000)2 (.40)
( 8,000 - 5,000)2 (.25)
(11,000 - 5,000)2 (.05)
Variance of Year 1
Cash Flows (Proposal B)
(CF1)(P1)
$
-50
500
2,000
2,000
550
$5,000
14-12
(CF1 - CF1)2(P1)
1,800,000
2,250,000
0
2,250,000
1,800,000
8,100,000
Summary of Proposal B
The standard deviation =
SQRT (8,100,000) = $2,846
The expected cash flow = $5,000
The standard deviation of
Proposal B < Proposal A.
( $2,846 < $3,795 )
14-13
Coefficient of variation(COV)
The
ratio of the standard
deviation of a distribution to the
expected value of the
distribution.
Higher
the COV, higher the
relative risk would be.
14-14