Risk Analysis ppt

© Harry Campbell & Richard BrownSchool of Economics The University of Queensland BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets Chapter 9: Risk Analysis... The

© Harry Campbell & Richard Brown

School of Economics The University of Queensland

BENEFIT-COST ANALYSIS

Financial and Economic

Appraisal using Spreadsheets

Chapter 9: Risk Analysis

In the preceding chapters we assumed all costs and benefits are

known with certainty.

The future is uncertain:

• factors internal to the project

• factors external to the project

Risk and Uncertainty

Where the possible values could have significant impact on project’s profitability, a decision will involve taking a risk

In some situations, degree of risk can be objectively determined

Estimating probability of an event usually involves subjectivity

Risk and Uncertainty

In risk analysis different forms of subjectivity need to be addressed

in deciding:

• what the degree of uncertainty is;

• whether the uncertainty constitutes a significant risk;

• whether the risk is acceptable

Establishing the extent to which the outcome is sensitive to the

assumed values of the inputs:

• it tells how sensitive the outcome is to changes in input values;

• it doesn’t tell us what the likelihood of an outcome is

Sensitivity Analysis

Table 9.1: Sensitivity Analysis Results: NPVs for Hypothetical Road Project

($ millions at 10% discount rate)

Construction Costs

Road Usage

Risk modeling is the use of discrete probability distributions to compute expected value of variable rather than point estimate

Risk Modeling

Table 9.3: Calculating the Expected Value from a Discrete Probability Distribution

($ millions)

Road Construction Cost (C) Probability (P) E(C)=P x C NPV E(NPV)

The expected cost of road construction can be derived as:

E(C) = $10 + $60 + $25 = $95

And the expected NPV as:

E(NPV) = 17.2 + 21.6 + 2.2 = $41

Table 9.2: A Discrete Probability Distribution of Road Construction Costs

($ millions)

Road Construction Cost (C) Probability (P)

• Usually uncertainty about more than one input or output;

• The probability distribution for NPV depends on aggregation of probability distributions for individual variables;

• Joint probability distributions for correlated and uncorrelated variables

Joint Probability Distributions

Assume that if road usage increases, so to do road maintenance costs

There is a 20% chance of road maintenance costs being $50 and

road user benefits being $70; a 60% chance of road maintenance costs

being $100 and road user benefits being $125, and so on.

Correlated and Uncorrelated Variables

Table 9.4: Joint Probability Distribution: Correlated Variables

($ millions)

Probability (P) Cost ($) Benefits ($) Net Benefits ($)

(Expected

Table 9.5: Joint Probability Distribution: Uncorrelated Variables

($ millions)

Probability (P) Probability(P) Cost ($) Benefits ($)

Low (L) 20% 50 70 Best Guess (M) 60% 100 125 High (H) 20% 125 205

Combination Joint Probability Net Benefit ($)

LC-HB 0.2 x 0.2 = 0.04 155(6.2) LC-MB 0.2 x 0.6 = 0.12 75(9.0) LC-LB 0.2 x 0.2 = 0.04 20(0.8) MC-HB 0.6 x 0.2 = 0.12 105(12.6) MC-MB 0.6 x 0.6 = 0.36 25(9.0) MC-LB 0.6 x 0.2 = 0.12 30(3.6) HC-HB 0.2 x 0.2 = 0.04 80(3.2) HC-MB 0.2 x 0.6 = 0.12 0(0.0) HC-LB 0.2 x 0.2 = 0.04 -55(-2.2)

E(NPV) = 42.2

An example is the normal distribution represented as a bell-shaped curve

This distribution is completely described by two parameters:

• the mean

• the standard deviation

Degree of dispersion of the possible values around the mean is measured by the variance (s2) or, the square root of the variance – the standard deviation (s)

Continuous Probability Distributions

Figure 9.1: Triangular probability distribution

100

80

60

40

20

0 -20

20

40

60

NPV ($ millions) Frequency (%)

• triangular or ‘three-point’ distribution offers a more formal risk modeling exercise than a sensitivity analysis;

• the distribution is described by a high (H), low (L) and

best-guess (B) estimate;

• provide the maximum, minimum and modal values of the

distribution respectively

Figure 9.2: Cumulative Probability Distribution

Cumulative Frequency

40 48 60 80 100

20 28

0 -20

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

NPV ($ millions)

• The cumulative distribution indicates what the probability is of the NPV lying below (or above) a certain value;

• There is a 50% chance that the NPV will be below $28 million, and

a 50% chance it will above it;

• There is an 80% chance that the NPV will be less than $48 million

Figure 9.3: Projects with different degrees of risk

NPV

B

A

Project B

Project A Probability

Using Risk Analysis in Decision Making

• Choice depends on decision-maker’s attitude towards risk;

• B has higher expected NPV, but is riskier than A;

• final choice depends on how much the decision-maker is risk averse

or is a risk taker

Figure 9.5: A Risk Averse Individual's Indifference Map between Mean and Variance of Wealth

R0

R1

R2

G

H

F

D E(WF) E(WH) E(WG)

VAR(W) VAR(WG)

VAR(WH)

• Shape of indifference map shows how the decision-maker perceives risk;

• Slope shows amount by which E(W) needs to increase to offset any given increase in risk;

• The larger this amount is, the more risk averse the individual is at the

• Add-on for spreadsheet allowing for Monte Carlo simulations;

• Instead of entering single point estimate in each input cell, analyst enters information about the probability distribution of variable;

• Program then re-calculates NPV or IRR many times over, using a random sample of input data;

• Output results (NPVs or IRRs) are then compiled and presented in form of a probability distribution in:

- statistical tables

- graphical format