14.Risk In capital Budgeting.pptxparthas

Portfolio Management

1. 14-1
Chapter 14
Risk and Managerial
Options in Capital
Budgeting
©2001 Prentice-Hall, Inc.
Fundamentals of Financial Management, 11/e
Created by: Gregory A. Kuhlemeyer, Ph.D.
Carroll College, Waukesha, WI

2. 14-2
Risk and Managerial
Options in Capital Budgeting
The Problem of Project Risk
Total Project Risk
Contribution to Total Firm Risk:
Firm-Portfolio Approach
Managerial Options

3. 14-3
An Illustration of Total Risk
(Discrete Distribution)
ANNUAL CASH FLOWS: YEAR 1
PROPOSAL A
State Probability Cash Flow
Deep Recession .05 $ -3,000
Mild Recession .25 1,000
Normal .40 5,000
Minor Boom .25 9,000
Major Boom .05 13,000

4. 14-4
Probability Distribution
of Year 1 Cash Flows
.40
.05
.25
Probability
-3,000 1,000 5,000 9,000 13,000
Cash Flow ($)
Proposal A

5. 14-5
CF
1 P
1 (CF
1)(P
1)
$ -3,000 .05 $ -150
1,000 .25 250
5,000 .40 2,000
9,000 .25 2,250
13,000 .05 650
S=1.00 CF
1=$5,000
Expected Value of Year 1
Cash Flows (Proposal A)

6. 14-6
(CF
1)(P
1) (CF
1-CF
1)
2
(P
1)
$ -150 ( -3,000 -5,000)
2
(.05)
250 ( 1,000 -5,000)
2
(.25)
2,000 (5,000 -5,000)
2
(.40)
2,250 ( 9,000 -5,000)
2
(.25)
650 (13,000 -5,000)
2
(.05)
$5,000
Variance of Year 1
Cash Flows (Proposal A)

7. 14-7
Variance of Year 1
Cash Flows (Proposal A)
(CF
1)(P
1) (CF
1-CF
1)
2
*(P
1)
$ -150 3,200,000
250 4,000,000
2,000 0
2,250 4,000,000
650 3,200,000
$5,000 14,400,000

8. 14-8
Summary of Proposal A
The standard deviation =
SQRT (14,400,000) = $3,795
The expected cash flow = $5,000

9. 14-9
An Illustration of Total Risk
(Discrete Distribution)
ANNUAL CASH FLOWS: YEAR 1
PROPOSAL B
State Probability Cash Flow
Deep Recession .05 $ -1,000
Mild Recession .25 2,000
Normal .40 5,000
Minor Boom .25 8,000
Major Boom .05 11,000

10. 14-10
Probability Distribution
of Year 1 Cash Flows
.40
.05
.25
Probability
-3,000 1,000 5,000 9,000 13,000
Cash Flow ($)
Proposal B

11. 14-11
Expected Value of Year 1
Cash Flows (Proposal B)
CF
1 P
1 (CF
1)(P
1)
$ -1,000 .05 $ -50
2,000 .25 500
5,000 .40 2,000
8,000 .25 2,000
11,000 .05 550
S=1.00 CF
1=$5,000

12. 14-12
(CF
1)(P
1) (CF
1-CF
1)
2
(P
1)
$ -50 ( -1,000 -5,000)
2
(.05)
500 ( 2,000 -5,000)
2
(.25)
2,000 ( 5,000 -5,000)
2
(.40)
2,000 ( 8,000 -5,000)
2
(.25)
550 (11,000-5,000)
2
(.05)
$5,000
Variance of Year 1
Cash Flows (Proposal B)

13. 14-13
Variance of Year 1
Cash Flows (Proposal B)
(CF
1)(P
1) (CF
1-CF
1)
2
(P
1)
$ -50 1,800,000
500 2,250,000
2,000 0
2,000 2,250,000
550 1,800,000
$5,000 8,100,000

14. 14-14
Summary of Proposal B
The standard deviation of
Proposal B < Proposal A.
( $2,846< $3,795)
The standard deviation =
SQRT (8,100,000)= $2,846
The expected cash flow = $5,000

15. 14-15
Total Project Risk
Projects have risk
that may change
from period to
period.
Projects are more
likely to have
continuous, rather
than discrete
distributions.
Cash Flow ($)
1 2 3
Year

16. 14-16
Probability Tree Approach
A graphic or tabular approach for
organizing the possible cash-flow
streams generated by an
investment. The presentation
resembles the branches of a tree.
Each complete branch represents
one possible cash-flow sequence.

17. 14-17
Probability Tree Approach
Basket Wonders is
examining a project that will
have an initial cost today of
$900. Uncertainty
surrounding the first year
cash flows creates three
possible cash-flow
scenarios in Year 1.
-$900

18. 14-18
Probability Tree Approach
Node 1: 20% chance of a
$1,200cash-flow.
Node 2: 60% chance of a
$450cash-flow.
Node 3: 20% chance of a
-$600cash-flow.
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3

19. 14-19
Probability Tree Approach
Each node in
Year 2
represents a
branchof our
probability
tree.
The
probabilities
are said to be
conditional
probabilities.
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
(.60)$1,200
(.30) $ 900
(.10) $2,200
(.35)$ 900
(.40)$ 600
(.25)$ 300
(.10)$ 500
(.50)-$ 100
(.40)-$ 700
Year 2

20. 14-20
Joint Probabilities [P(1,2)]
.02 Branch 1
.12 Branch 2
.06 Branch 3
.21 Branch 4
.24 Branch 5
.15 Branch 6
.02 Branch 7
.10 Branch 8
.08 Branch 9
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25)$ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2

21. 14-21
Project NPV Based on
Probability Tree Usage
The probability
tree accounts for
the distribution
of cash flows.
Therefore,
discount all cash
flows at onlythe
risk-freerate of
return.
The NPV for branch i of
the probability tree for two
years of cash flows is
NPV = S(NPV
i)(P
i)
NPV
i=
CF
1
(1 + R
f)
1
(1 + R
f)
2
CF
2
-ICO
+
i = 1
z

22. 14-22
NPV for Each Cash-Flow
Stream at 5% Risk-Free Rate
$ 2,238.32
$ 1,331.29
$ 1,059.18
$ 344.90
$ 72.79
-$ 199.32
-$ 1,017.91
-$ 1,562.13
-$ 2,106.35
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25)$ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2

23. 14-23
NPV on the Calculator
Remember, we can
use the cash flow
registry to solve
these NPV problems
quickly and
accurately!

24. 14-24
Actual NPV Solution Using
Your Financial Calculator
Solving for Branch #3:
Step 1: Press CF key
Step 2: Press 2
nd
CLR Work keys
Step 3: For CF0Press -900Enter keys
Step 4: For C01Press1200Enter keys
Step 5: For F01Press 1 Enter keys
Step 6: For C02Press 900 Enter keys
Step 7: For F02Press 1 Enter keys

25. 14-25
Actual NPV Solution Using
Your Financial Calculator
Solving for Branch #3:
Step 8: Press   keys
Step 9: Press NPV key
Step 10: For I=, Enter5Enter keys
Step 11: Press CPT key
Result:Net Present Value= $1,059.18
You would complete this for EACH branch!

26. 14-26
Calculating the Expected
Net Present Value (NPV)
Branch NPV
i
Branch 1 $ 2,238.32
Branch 2 $ 1,331.29
Branch 3 $ 1,059.18
Branch 4 $ 344.90
Branch 5 $ 72.79
Branch 6 -$ 199.32
Branch 7 -$ 1,017.91
Branch 8 -$ 1,562.13
Branch 9 -$ 2,106.35
P(1,2) NPV
i* P(1,2)
.02 $ 44.77
.12 $159.75
.06 $ 63.55
.21 $ 72.43
.24 $ 17.47
.15 -$ 29.90
.02 -$ 20.36
.10 -$156.21
.08 -$168.51
Expected Net Present Value = -$ 17.01

27. 14-27
Calculating the Variance
of the Net Present Value
NPV
i
$ 2,238.32
$ 1,331.29
$ 1,059.18
$ 344.90
$ 72.79
-$ 199.32
-$ 1,017.91
-$ 1,562.13
-$ 2,106.35
P(1,2) (NPV
i-NPV)
2
[P(1,2)]
.02 $ 101,730.27
.12 $ 218,149.55
.06 $ 69,491.09
.21 $ 27,505.56
.24 $ 1,935.37
.15 $ 4,985.54
.02 $ 20,036.02
.10 $ 238,739.58
.08 $ 349,227.33
Variance = $1,031,800.31

28. 14-28
Summary of the
Decision Tree Analysis
The standard deviation =
SQRT ($1,031,800) = $1,015.78
The expected NPV = -$ 17.01

29. 14-29
Simulation Approach
An approach that allows us to test
the possible results of an
investment proposal before it is
accepted. Testing is based on a
model coupled with probabilistic
information.

30. 14-30
Simulation Approach
Market analysis
Market size, selling price, market
growth rate, and market share
Investment cost analysis
Investment required, useful life of
facilities, and residual value
Operating and fixed costs
Operating costs and fixed costs
Factors we might consider in a model:

31. 14-31
Simulation Approach
Each variableis assigned an appropriate
probability distribution. The distribution for
the selling price of baskets created by
Basket Wonders might look like:
$20$25 $30$35$40$45$50
.02.08.22 .36.22 .08.02
The resulting proposal value is dependent
on the distribution and interaction of
EVERYvariable listed on slide 14-30.

32. 14-32
Simulation Approach
Each proposal will generate aninternal rate of
return. The process of generating many, many
simulations results in a large set of internal
rates of return. The distributionmight look like
the following:
INTERNAL RATE OF RETURN (%)
PROBABILITY
OF OCCURRENCE

33. 14-33
Combining projects in this manner reduces
the firm risk due to diversification.
Contribution to Total Firm Risk:
Firm-Portfolio Approach
CASH FLOW
TIME TIMETIME
Proposal A Proposal B
Combination of
Proposals AandB

34. 14-34
NPV
P= S( NPV
j)
NPV
Pis the expected portfolio NPV,
NPV
jis the expected NPV of the jth
NPV that the firm undertakes,
mis the total number of projects in
the firm portfolio.
Determining the Expected
NPV for a Portfolio of Projects
m
j=1

35. 14-35
s
P= S S s
jk
s
jk
is the covariance between possible
NPVs for projects jand k,
s
jk= s
j s
k r
jk
.
s
j
is the standard deviation of project j,
s
k
is the standard deviation of project k,
r
jkis the correlation coefficient between
projects jand k.
Determining Portfolio
Standard Deviation
m
j=1
m
k=1

36. 14-36
E: Existing Projects
8 Combinations
EE+ 1E+ 1 + 2
E+ 2 E+ 1 + 3
E+ 3 E+ 2 + 3
E+ 1 + 2 + 3
A, B, and Care
dominatingcombinations
from the eight possible.
Combinations of
Risky Investments
A
B
C
E
Standard Deviation
Expected Value of NPV

37. 14-37
Managerial (Real) Options
Management flexibility to make
future decisions that affect a
project’s expected cash flows, life,
or future acceptance.
Project Worth = NPV +
Option(s) Value

38. 14-38
Managerial (Real) Options
Expand (or contract)
Allows the firm to expand (contract) production
if conditions become favorable (unfavorable).
Abandon
Allows the project to be terminated early.
Postpone
Allows the firm to delay undertaking a project
(reduces uncertainty via new information).

39. 14-39
Previous Example with
Project Abandonment
Assume that
this project
can be
abandoned at
the end of the
first year for
$200.
What is the
project
worth?
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2

40. 14-40
Project Abandonment
Node 3:
(500/1.05)(.1)+
(-100/1.05)(.5)+
(-700/1.05)(.4)=
($476.19)(.1)+
-($ 95.24)(.5)+
-($666.67)(.4)=
-($266.67)
-$900
(.20)$1,200
(.20) -$600
(.60)$450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2

41. 14-41
Project Abandonment
-$900
(.20)$1,200
(.20) -$600
(.60)$450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2
The optimal
decision at the
end of Year 1 is
to abandon the
project for
$200.
$200>
-($266.67)
What is the
“new” project
value?

42. 14-42
Project Abandonment
$ 2,238.32
$ 1,331.29
$ 1,059.18
$ 344.90
$ 72.79
-$ 199.32
-$ 1,280.95
-$900
(.20) $1,200
(.20) -$400*
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35)$ 900
(.40) $ 600
(.25) $ 300
(1.0)$ 0
Year 2
*-$600 + $200 abandonment

43. 14-43
Summary of the Addition
of the Abandonment Option
* For “True” Project considering abandonment option
The standard deviation*=
SQRT (740,326) = $857.56
The expectedNPV* = $71.88
NPV* = Original NPV +
Abandonment Option
Thus,$71.88 = -$17.01 +Option
Abandonment Option = $ 88.89