Chapter 9: Risk Analysis

Question 1

When will a decision involve risk?

Answer 1

A decision will involve risk where the possible values could have a significant impact on a project’s profitability

Question 2

The estimation of the probability of an event usually involves…

Answer 2

Subjectivity

Question 3

In risk analysis, different forms of subjectivity need to be addressed, in deciding:

Answer 3

• What the degree of uncertainty is;
• Whether the uncertainty constitutes a “significant risk”;
• Whether the risk is acceptable

Question 4

Sensitivity Analysis

Answer 4

Estimating the extent to which the outcome is sensitive to the assumed values of the inputs

Question 5

Two steps in performing a sensitivity analysis

Answer 5

1. Establish which of the various input variables impact most on the outcome (NPV or BCR)
2. Undertake and report the range of results allowing each of these to vary between low and high (pessimistic and optimistic) - individually and in combination

Question 6

Rule of thumb for variation

Answer 6

There is no golden rule about how much variation around the “best guess” estimation should be allowed, but 20% is a good rule of thumb

Question 7

Important information learned from a sensitivity analysis

Answer 7

Whether or not the NPV or BCR of the policy option could be negative under some scenarios within a reasonable range of assumed input values
However, does not tell us the likelihood of this happening

Question 8

Applied risk analysis

Answer 8

Use of discrete probability distributions to compute expected value or variable rather than a point estimate

Question 9

Applied risk analysis: joint probability distributions

Answer 9

We are usually uncertain about more than one input/output
The probability distribution for NPV depends on aggregation of probability distributions for individual variables
Joint probability distributions can be for correlated and uncorrelated variables

Question 10

Continuous probability distribution: e.g. the normal distribution

Answer 10

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 (s^2) or the standard deviation (s)

Question 11

Expected Wealth

Answer 11

(W1 x p1) + (W2 x p2)

Question 12

Expected Utility

Answer 12

p1 x U(W1) + p2 x U(W2)

Question 13

Risk modelling in Excel: Monte Carlo simulations

Answer 13

In Monte Carlo simulations we use additional software to perform a formal risk analysis
In the simulation the project’s net benefits are recalculated thousands of time using random values for input variables from a given distribution
It assembles the results and presents them in the form of a probability distribution, showing the likelihood of achieving a given outcome

Question 14

Suppose NPV>0. Is there any reason (other than budget constraint) why you would recommend that the project should not go ahead immediately?

Answer 14

Uncertainty and the value of information
Might be uncertainty about the values of some of the variables used to calculate the NPV (e.g. future prices)
Delaying the project might resolve these uncertainties

Question 15

How to investigate the value of delaying the project

Answer 15

Compare the NPV of undertaking the project immediately at time 0 with the NPV of delaying the project until time 1

Question 16

The expected value of information

Answer 16

The expected project NPV if we delay the project for one year minus the expected project nPV if we undertake the project at time 0

Question 17

The value of information rises as…

Answer 17

• the initial capital cost (K) rises;
• the return in the low price environment (Pl) falls
• the probability of a high price (q) falls
• the return in the current period (R0) falls
• the interest rate rises

Question 18

The bad news principle

Answer 18

The level of the return in the high price environment (Rh) does not affect the value of information