1. Risk and Managerial (Real) Options in Capital Budgeting
Chapter 14
Risk and Managerial (Real) Options in Capital Budgeting

2. After Studying Chapter 14, you should be able to:
Define the "riskiness" of a capital investment project.
Understand how cash-flow riskiness for a particular period is measured, including the concepts of expected value, standard deviation, and coefficient of variation.
Describe methods for assessing total project risk, including a probability approach and a simulation approach.
Judge projects with respect to their contribution to total firm risk (a firm-portfolio approach).
Understand how the presence of managerial (real) options enhances the worth of an investment project.
List, discuss, and value different types of managerial (real) options.

3. 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

4. An Illustration of Total Risk (Discrete Distribution)
ANNUAL CASH FLOWS: YEAR 1
PROPOSAL A
State Probability Cash Flow
Deep Recession $ –3,000
Mild Recession ,000
Normal ,000
Minor Boom ,000
Major Boom ,000

5. Probability Distribution of Year 1 Cash Flows
Proposal A
0.40
0.25
Probability
0.05
–3, , , , ,000
Cash Flow ($)

6. Expected Value of Year 1 Cash Flows (Proposal A)
CF P (CF1)(P1)
$ –3, $ –150 1,
5, ,000
9, ,250
13,
S= CF1=$5,000

7. Variance of Year 1 Cash Flows (Proposal A)
(CF1)(P1) (CF1 – CF1)2(P1)
$ – (–3,000 – 5,000)2 (0.05)
( 1,000 – 5,000)2 (0.25)
2, ( 5,000 – 5,000)2 (0.40)
2, ( 9,000 – 5,000)2 (0.25)
(13,000 – 5,000)2 (0.05)
$5,000

8. Variance of Year 1 Cash Flows (Proposal A)
(CF1)(P1) (CF1 – CF1)2*(P1)
$ – ,200,000
,000,000 2,
2, ,000,000
,200,000
$5, ,400,000

9. Summary of Proposal A
The standard deviation = SQRT (14,400,000) = $3,795
The expected cash flow = $5,000
Coefficient of Variation (CV) = $3,795 / $5,000 = 0.759
CV is a measure of relative risk and is the ratio of standard deviation to the mean of the distribution.

10. An Illustration of Total Risk (Discrete Distribution)
ANNUAL CASH FLOWS: YEAR 1
PROPOSAL B
State Probability Cash Flow
Deep Recession $ –1,000
Mild Recession ,000
Normal ,000
Minor Boom ,000
Major Boom ,000

11. Probability Distribution of Year 1 Cash Flows
Proposal B
0.40
0.25
Probability
0.05
–3, , , , ,000
Cash Flow ($)

12. Expected Value of Year 1 Cash Flows (Proposal B)
CF P (CF1)(P1)
$ –1, $ –50 2,
5, ,000
8, ,000
11,
S= CF1=$5,000

13. Variance of Year 1 Cash Flows (Proposal B)
(CF1)(P1) (CF1 – CF1)2(P1)
$ – (–1,000 – 5,000)2 (0.05)
( 2,000 – 5,000)2 (0.25)
2, ( 5,000 – 5,000)2 (0.40)
2, ( 8,000 – 5,000)2 (0.25)
(11,000 – 5,000)2 (0.05)
$5,000

14. Variance of Year 1 Cash Flows (Proposal B)
(CF1)(P1) (CF1 – CF1)2(P1)
$ – ,800,000
,250,000 2,
2, ,250,000
,800,000
$5, ,100,000

15. Summary of Proposal B
The standard deviation = SQRT (8,100,000) = $2,846
The expected cash flow = $5,000
Coefficient of Variation (CV) = $2,846 / $5,000 = 0.569
The standard deviation of B < A ($2,846< $3,795), so “B” is less risky than “A”.
The coefficient of variation of B < A (0.569<0.759), so “B” has less relative risk than “A”.

16. Projects have risk that may change from period to period.
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 ($)
Year

17. 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.

18. 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

19. Probability Tree Approach
Node 1: 20% chance of a $1,200 cash-flow.
Node 2: 60% chance of a $450 cash-flow.
Node 3: 20% chance of a –$600 cash-flow.
(0.20) $1,200 1
(0.60) $450
–$900 2
(0.20) –$600 3
Year 1

20. Probability Tree Approach
(0.10) $2,200
Each node in Year 2 represents a branch of our probability tree.
The probabilities are said to be conditional probabilities.
(0.20) $1,200
(0.60) $1,200 1
(0.30) $ 900
(0.35) $ 900
(0.60) $450
(0.40) $ 600
–$900 2
(0.25) $ 300
(0.10) $ 500
(0.20) –$600
(0.50) –$ 100 3
(0.40) –$ 700
Year 1
Year 2

21. Joint Probabilities [P(1,2)]
(0.10) $2,200
Branch 1
Branch 2
Branch 3
Branch 4
Branch 5
Branch 6
Branch 7
Branch 8
Branch 9
(0.20) $1,200
(0.60) $1,200 1
(0.30) $ 900
(0.35) $ 900
(0.60) $450
(0.40) $ 600
–$900 2
(0.25) $ 300
(0.10) $ 500
(0.20) –$600
(0.50) –$ 100 3
(0.40) –$ 700
Year 1
Year 2

22. Project NPV Based on Probability Tree Usagez
NPV = S (NPVi)(Pi)
The probability tree accounts for the distribution of cash flows. Therefore, discount all cash flows at only the risk-free rate of return.
i = 1
The NPV for branch i of the probability tree for two years of cash flows is
CF1
CF2
NPVi = +
(1 + Rf )1
(1 + Rf )2
- ICO

23. NPV for Each Cash-Flow Stream at 5% Risk-Free Rate
(0.10) $2,200
$ 2,238.32
$ 1,331.29
$ 1,059.18 $ $ –$
–$ 1,017.91
–$ 1,562.13
–$ 2,106.35
(0.20) $1,200
(0.60) $1,200 1
(0.30) $ 900
(0.35) $ 900
(0.60) $450
(0.40) $ 600
–$900 2
(0.25) $ 300
(0.10) $ 500
(0.20) –$600
(0.50) –$ 100 3
(0.40) –$ 700
Year 1
Year 2

24. NPV on the Calculator
Remember, we can use the cash flow registry to solve these NPV problems quickly and accurately!
Source: Courtesy of Texas Instruments

25. Actual NPV Solution Using Your Financial Calculator
Solving for Branch #3:
Step 1: Press CF key
Step 2: Press 2nd CLR Work keys
Step 3: For CF0 Press – Enter  keys
Step 4: For C01 Press Enter  keys
Step 5: For F01 Press Enter  keys
Step 6: For C02 Press Enter  keys
Step 7: For F02 Press Enter  keys

26. Actual NPV Solution Using Your Financial Calculator
Solving for Branch #3:
Step 8: Press   keys
Step 9: Press NPV key
Step 10: For I=, Enter 5 Enter  keys
Step 11: Press CPT key
Result: Net Present Value = $1,059.18
You would complete this for EACH branch!

27. Calculating the Expected Net Present Value (NPV)
Branch NPVi
Branch 1 $ 2,238.32
Branch 2 $ 1,331.29
Branch 3 $ 1,059.18
Branch 4 $
Branch 5 $
Branch 6 –$
Branch 7 –$ 1,017.91
Branch 8 –$ 1,562.13
Branch 9 –$ 2,106.35
P(1,2) NPVi * P(1,2) $
$159.75 $ $ $ –$ –$
–$156.21
–$168.51
Expected Net Present Value = –$

28. Calculating the Variance of the Net Present Value
NPVi
$ 2,238.32
$ 1,331.29
$ 1,059.18 $ $ –$
–$ 1,017.91
–$ 1,562.13
–$ 2,106.35
P(1,2) (NPVi – NPV )2[P(1,2)]
$ 101,730.27
$ 218,149.55
$ 69,491.09
$ 27,505.56
$ 1,935.37
$ 4,985.54
$ 20,036.02
$ 238,739.58
$ 349,227.33
Variance = $1,031,800.31

29. Summary of the Decision Tree Analysis
The standard deviation = SQRT ($1,031,800) = $1,015.78
The expected NPV = –$

30. 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.

31. Simulation Approach Factors we might consider in a model:
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

32. Simulation Approach
Each variable is assigned an appropriate probability distribution. The distribution for the selling price of baskets created by Basket Wonders might look like:
$ $ $30 $35 $40 $45 $50
The resulting proposal value is dependent on the distribution and interaction of EVERY variable listed on slide

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

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

35. Determining the Expected NPV for a Portfolio of Projects
NPVP = S ( NPVj )
NPVP is the expected portfolio NPV,
NPVj is the expected NPV of the jth NPV that the firm undertakes,
m is the total number of projects in the firm portfolio.
j=1

36. Determining Portfolio Standard Deviation
sP = S S sjk
sjk is the covariance between possible NPVs for projects j and k,
s jk = s j s k r jk .
sj is the standard deviation of project j,
sk is the standard deviation of project k,
rjk is the correlation coefficient between projects j and k.
j=1
k=1

37. Combinations of Risky Investments
E: Existing Projects
8 Combinations
E E E E E E E E
A, B, and C are dominating combinations from the eight possible. C B
Expected Value of NPV E A
Standard Deviation

38. 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

39. 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).

40. Previous Example with Project Abandonment
(0.10) $2,200
Assume that this project can be abandoned at the end of the first year for $200.
What is the project worth?
(0.20) $1,200
(0.60) $1,200 1
(0.30) $ 900
(0.35) $ 900
(0.60) $450
(0.40) $ 600
–$900 2
(0.25) $ 300
(0.10) $ 500
(0.20) –$600
(0.50)–$ 100 3
(0.40)–$ 700
Year 1
Year 2

41. Project Abandonment Node 3:
(0.10) $2,200
Node 3:
(500/1.05)(0.1)+ (–100/1.05)(0.5)+ (–700/1.05)(0.4)=
($476.19)(0.1)+ –($ )(0.5)+ –($666.67)(0.4)=
–($266.67)
(0.20) $1,200
(0.60) $1,200 1
(0.30) $ 900
(0.35) $ 900
(0.60) $450
(0.40) $ 600
–$900 2
(0.25) $ 300
(0.10) $ 500
(0.20) –$600
(0.50) –$ 100 3
(0.40) –$ 700
Year 1
Year 2

42. What is the “new” project value?
Project Abandonment
(0.10) $2,200
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?
(0.20) $1,200
(0.60) $1,200 1
(0.30) $ 900
(0.35) $ 900
(0.60) $450
(0.40) $ 600
–$900 2
(0.25) $ 300
(0.10) $ 500
(0.20) –$600
(0.50) –$ 100 3
(0.40) –$ 700
Year 1
Year 2

43. Project Abandonment $ 2,238.32 $ 1,331.29 $ 1,059.18 $ 344.90 $ 72.79
(0.10) $2,200
$ 2,238.32
$ 1,331.29
$ 1,059.18 $ $ –$
–$ 1,280.95
(0.20) $1,200
(0.60) $1,200 1
(0.30) $ 900
(0.35) $ 900
(0.60) $450
(0.40) $ 600
–$900 2
(0.25) $ 300
(0.20) –$400*
(1.0) $ 3
*–$600 + $200 abandonment
Year 1
Year 2

44. Summary of the Addition of the Abandonment Option
The standard deviation* = SQRT (740,326) = $857.56
The expected NPV* = $
NPV* = Original NPV Abandonment Option
Thus, $ = –$ Option
Abandonment Option = $
* For “True” Project considering abandonment option