The difference between risk and uncertainty

Risk - when the decision maker knows the probability of each and every state of nature and thus each and every outcome. An expected value of each alternative action can be determined

Uncertainty - when a decision maker has information that is not complete and therefore cannot determine the expected value of each alternative

Incorporating risk into project analysis through adjustments to the discount rate, and by the certainty equivalent factor.

Project Analysis Under Risk

What is Risk?Risk is the variation of future

expectations around an expected value.

Risk is measured as the range of variation around an expected value.

Risk and uncertainty are interchangeable words.

Handling RiskRisk may be accounted for by (1)

applying a discount rate commensurate with the riskiness of the cash flows, and (2), by using a certainty equivalent factor

Risk may be accounted for by evaluating the project using sensitivity and breakeven analysis.

Risk may be accounted for by evaluating the project under simulated cash flow and discount rate scenarios.

Risk is the variation in future cash flows around a central expected value.

Risk can be accounted for by adjusting the NPV calculation discount rate: there are two methods – either the WACC, or the CAPM

Analysis Under Risk

Risk can also be accommodated via the Certainty Equivalent Method.

All methods require management judgment and experience.

Simulation is a flexible methodology we can use to analyze the behavior of a present or proposed business activity, new product, manufacturing line or plant expansion, and so on (analysts call this the 'system' under study).

Simulation

By performing simulations and analyzing the results, we can gain an understanding of how a present system operates, and what would happen if we changed it -- or we can estimate how a proposed new system would behave

Often -- but not always -- a simulation deals with uncertainty, in the system itself, or in the world around it.

A technique used to determine how different values of an independent variable will impact a particular dependent variable under a given set of assumptions.

Sensitivity Analysis

This technique is used within specific boundaries that will depend on one or more input variables, such as the effect that changes in interest rates will have on a bond's price.

Scenario Analysis

The process of estimating the expected value of a portfolio after a given period of time, assuming specific changes in the values of the portfolio's securities or key factors that would affect security values, such as changes in the interest rate.

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Using a Risky Discount Rate

The structure of the cash flow discounting mechanism for risk is:-

layInitialOutriskyrate

lowRiskycashf

riskyrate

lowRiskycashfNPV

......

)1()1( 22

1

1

The $ amount used for a ‘risky cash flow’ is the expected dollar value for that time period.

A ‘risky rate’ is a discount rate calculated to include a risk premium. This rate is known as the RADR, the Risk Adjusted Discount Rate.

Decision Trees

A decision tree is a chronological representation of the decision problem.

Each decision tree has two types of nodes; round nodes correspond to the states of nature while square nodes correspond to the decision alternatives.

Decision Tree Analysis

A graphical tool for describing

(1) the actions available to the decision-maker,

(2) the events that can occur, and (3) the relationship between the actions and events.

ConditionalProfit

Decision Points

Events

( ) Probability

Do not market

MarketCompetitiveProduct (0.7)

No CompetitiveProduct (0.3)

High

Low

High

Low

High

Low

High

Low

$60

-$20

$40

$10

$100

$30

(0.5)

(0.5)

(0.2)

(0.8)

$0

Our Price

Competitor’s price

First Decision Point Second Decision Point