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.