Summary of Previous Lecture Understand why ranking project proposals on the basis of IRR, NPV, and...
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Transcript of Summary of Previous Lecture Understand why ranking project proposals on the basis of IRR, NPV, and...
Summary of Previous Lecture
• Understand why ranking project proposals on the basis of IRR, NPV, and PI methods “may” lead to conflicts in ranking.
• Describe the situations where ranking projects may be necessary and justify when to use either IRR, NPV, or PI rankings.
• Understand how “sensitivity analysis” allows us to challenge the single-point input estimates used in traditional capital budgeting analysis.
• Explain the role and process of project monitoring, including “progress reviews” and “post-completion audits.”
Chapter 14 (I)
Risk and Managerial (Real) Options in Capital
Budgeting
Learning OutcomesAfter 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.
Risk and Managerial (Real)Options in Capital Budgeting
• The Problem of Project Risk• Total Project Risk• Contribution to Total Firm Risk: Firm-
Portfolio Approach• Managerial (Real) Options
Expectation and Measurement of Dispersion
Probability distribution can be explained in two parameters of distribution; (1) The expected Value, (2) the standard deviation.Expected value is the weighted average of possible outcomes, with weights being probabilities of occurrence.Standard deviation is the statistical measurement of the variability of a distribution around its mean.
Coefficient of Variation (CV)
SD sometime can be misleading in comparing the risk or uncertainty. CV is the ratio of the SD of a distribution to the mean of that distribution. It is a measure of relative risk. Smaller the CV, the lesser the risk. A project with lower CV is better.
Discrete and Continuous DistributionIn the discrete case, one can easily assign a probability to each possible outcome: when throwing a die, each of the six values 1 to 6 has the probability 1/6. a continuous random variable is the one which can take a continuous range of values — as opposed to a discrete distribution, where the set of possible values for the random variable is at most countable. While for a discrete distribution an event with probability zero is impossible (e.g. rolling 3½ on a standard die is impossible, and has probability zero), this is not so in the case of a continuous random variable. For example, if one measures the width of an oak leaf, the result of 3½ cm is possible
http://en.wikipedia.org/wiki/Probability_distribution
An Illustration of Total Risk (Discrete Distribution)
ANNUAL CASH FLOWS: YEAR 1PROPOSAL A
State Probability Cash Flow
Deep Recession .10 $ 3,000Mild Recession .20 3,500Normal .40 4,000Minor Boom .20 4,500Major Boom .10 5,000
Probability Distribution of Year 1 Cash Flows
.1Prob
abili
ty
3,000 3,500 4,000 4,500 5,000
Cash Flow ($)
Proposal A
.2
.3
.4
Expected Value of Year 1 Cash Flows (Proposal A)
CF1 P1 (CF1)(P1)3000 0.1 3003500 0.2 7004000 0.4 16004500 0.2 9005000 0.1 500
Σ = 1 4000CF =
(CF1)(P1) (CF1 - CF1)2(P1)
$ 300 (3,000 - 4,000)2 (.01) 700 (3,500 - 4,000)2 (.20) 1,600 (4,000 - 4,000)2 (.40) 9,000 (4,500 - 4,000)2 (.20) 500 (5,000 - 4,000)2 (.01)
$4,000
Variance of Year 1 Cash Flows (Proposal A)
(CF1)(P1) (CF1 - CF1)2(P1)
$ 300 100000 700 50,000 1,600 0 9,000 50,000 500 100,000
$4,000 300,000
Variance of Year 1 Cash Flows (Proposal A)
Summary of Proposal A
The standard deviation = SQRT (300,000) = $548
The expected cash flow = $4,000
Coefficient of Variation (CV) = $548 / $4,000 = 0.14
CV is a measure of relative risk and is the ratio of standard deviation to the mean of the distribution.
An Illustration of Total Risk (Discrete Distribution)
ANNUAL CASH FLOWS: YEAR 1PROPOSAL B
State Probability Cash Flow
Deep Recession .01 $ 2,000Mild Recession .20 3,000Normal .40 4,000Minor Boom .20 5,000Major Boom .01 6,000
Probability Distribution of Year 1 Cash Flows
.1Prob
abili
ty
2,000 3,000 4,000 5,000 6,000
Cash Flow ($)
Proposal B
.2
.3
.4
Expected Value of Year 1 Cash Flows (Proposal B)
CF1 P1 (CF1)(P1)2000 0.1 2003000 0.2 6004000 0.4 16005000 0.2 10006000 0.1 600
Σ = 1 4000CF1 =
(CF1)(P1) (CF1 - CF1)2(P1)
$ 200 (2,000 - 4,000)2 (.10)
600 (3,000 - 4,000)2 (.20) 1,600 (4,000 - 4,000)2 (.40) 1,000 (5,000 - 4,000)2 (.20) 600 (6,000 - 4,000)2 (.10)
$4,000
Variance of Year 1 Cash Flows (Proposal B)
(CF1)(P1) (CF1 - CF1)2(P1)
$ 200 400,000
600 200,000 1,600 0 1,000 200,000 600 400,000
$4,000 1,200,000
Variance of Year 1 Cash Flows (Proposal B)
Summary of Proposal B
The standard deviation of A < B ($548< $1,095), so “A” is less risky than “B”.The coefficient of variation of A < B (0.14<0.27), so “A” has less relative risk than “B”.
The standard deviation = SQRT (1,200,000)= $1,095
The expected cash flow = $4,000Coefficient of Variation (CV) = $1,095 / $4,000
= 0.27
Total Project Risk
Projects have risk that may change from period to period.
Projects are more likely to have continuous, rather than discrete distributions.
Cash
Flo
w ($
)
1 2 3 Year
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.
Probability Tree ApproachA project that has an initial cost today of $240. Uncertainty surrounding the first year cash flows creates three possible cash-flow scenarios in Year 1.
Probability Tree Approach
Node 1: 25% chance of a $500 cash-flow.
Node 2: 50% chance of a $200 cash-flow.
Node 3: 25% chance of a -$100 cash-flow.
-$240
(.25) $500
(.25) -$100
(.50) $200
Year 1
1
2
3
Probability Tree Approach
Each node in Year 2 represents a branch of our probability tree.
The probabilities are said to be conditional probabilities.
-$240
(.25) $500
(.25) -$100
(.50) $200
Year 1
1
2
3
(.40) $500
(.20) $200
(.40) $800
(.20) $500
(.60) $200
(.20) -$100
(.20) $200
(.40) -$100
(.40) -$400
Year 2
Joint Probabilities [P(1,2)]
.01 Branch 1
.01 Branch 2
.05 Branch 3
.10 Branch 4
.30 Branch 5
.10 Branch 6
.05 Branch 7
.10 Branch 8
.10 Branch 9
-$240
(.25) $500
(.25) -$100
(.50) $200
Year 1
1
2
3
(.40) $500
(.20) $200
(.40) $800
(.20) $500
(.60) $200
(.20) -$100
(.20) $200
(.40) -$100
(.40) -$400
Year 2
Project NPV Based on Probability Tree Usage
The probability tree accounts for the distribution of cash flows. Therefore, discount all cash flows at only the risk-free rate of return.
The NPV for branch i of the probability tree for two years of cash flows is
NPV = S (NPVi)(Pi)
NPVi = CF1
(1 + Rf )1 (1 + Rf )2
CF2 - ICO+
i = 1
z
NPV for Each Cash-Flow Stream at 8% Risk-Free Rate
$ 909 $ 652 $ 394
$ 374 $ 117-$ 141
-$ 161-$ 418-$ 676
-$240
(.25) $500
(.25) -$100
(.50) $200
Year 1
1
2
3
(.40) $500
(.20) $200
(.40) $800
(.20) $500
(.60) $200
(.20) -$100
(.20) $200
(.40) -$100
(.40) -$400
Year 2
Calculating the Expected Net Present Value (NPV)
Branch NPVi
Branch 1 $ 909Branch 2 $ 652Branch 3 $ 394Branch 4 $ 374Branch 5 $ 117Branch 6 -$ 141Branch 7 -$ 161Branch 8 -$ 418Branch 9 -$ 676
P(1,2) NPVi x P(1,2) .10 $ 91 .10 $ 65 .05 $ 20 .10 $ 37 .30 $ 35 .10 -$ 14 .05 -$ 08 .10 -$ 42 .10 -$ 68
Weighted Average = $ 116=NPV
Calculating the Variance of the Net Present Value
P(1,2) (NPVi - NPV )2[P(1,2)] .10 $ 62,885 .10 $ 28,730 .05 $ 3,864 .10 $ 6,656 .30 $ 0.30 .10 $ 6,605 .05 $ 3,836 .10 $ 28,516 .10 $ 62,726
Variance = $203,819
NPVi $ 909 $ 652 $ 394 $ 374 $ 117 -$ 141 -$ 161 -$ 418 -$ 676
Summary of the Decision Tree Analysis
The standard deviation = SQRT($20,3819) = $451
The expected NPV = $ 116
Summary
We covered following topics in today’s lecture;
• 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.