Flashcards in Chapter 9: Risk Analysis Deck (18):

1

## When will a decision involve risk?

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

2

## The estimation of the probability of an event usually involves...

### Subjectivity

3

## 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

4

## Sensitivity Analysis

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

5

## Two steps in performing a sensitivity analysis

###
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

6

## Rule of thumb for variation

### 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

7

## Important information learned from a sensitivity analysis

###
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

8

## Applied risk analysis

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

9

## Applied risk analysis: joint probability distributions

###
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

10

## Continuous probability distribution: e.g. 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 (s^2) or the standard deviation (s)

11

## Expected Wealth

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

12

## Expected Utility

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

13

## Risk modelling in Excel: Monte Carlo simulations

###
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

14

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

###
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

15

## How to investigate the value of delaying the project

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

16

## The expected value of information

### 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

17

## The value of information rises as...

###
- 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

18