Chapter 7 - Risk And Uncertainty

Question 0

Sensitivity analysis

Answer 0

Takes each uncertain factor in turn and calculates the change that would be necessary in that factor before the original decision is reversed.

The process is as follows:-

1. Best estimates for variables are made and a decision arrived at.
2. Each variable is analysed in turn to see how much the original estimate can change before being reversed.
3. Estimates for each variable can then be reconsidered to assess the likelihood of the estimate being wrong.
4. The maximum possible change is often expressed as a %. This formula only works for cash flows.

Question 1

Risk and Uncertainty

Answer 1

Risk - There are a number of possible outcomes and the probability of each outcome is known.

Uncertainty - There are a number of possible outcomes but the probability of each outcome is not known.

Question 2

Simulation

Answer 2

Simulation is a modelling technique that shows the effect of more than one variable changing at the same time.

Drawbacks:

1. It is not a technique for making a decision, only for obtaining more information about the possible outcomes.
2. Models can become extremely complex.
3. The time and costs can be more than is gained from the improved decisions.
4. Probability distributions may be difficult to formulate.

Question 3

Expected Value (EV)

Answer 3

EV = Sum px

x is the value of each possible outcome.
p is the probability of that outcome.

Question 4

Maximax, maximin and minimax regret

Answer 4

Maximax (optimist or risk seeking investor):
Involves selecting the alternative that maximises the maximum pay-off achievable.
The investor would look at the best possible outcome at each supply level then select the highest one of these.

Maximin (pessimist):
Involves selecting the alternative that maximises the minimum pay-off achievable.
The investor would look at the worst possible outcome at each supply level then selects the highest one of these.
The decision maker chooses to minimise his losses.

Minimax regret (risk neutral decision maker)
A strategy which minimises the maximum regret.
Need to find the biggest pay-off for each demand row then subtract all other numbers in this row from the largest number.

Question 5

Decision trees

Answer 5

A decision tree is a diagrammatic representation of a multi-decision problem.

Three step method -
Step 1: Draw the tree from left to right showing appropriate decisions and events/ outcomes.
A square is used to represent a decision point.
A circle is used to represent a chance point. The branches coming away from a circle will have probabilities attached to them.
Label the tree and relevant cash inflows/outflows and probabilities associated with outcomes.

Step 2: Evaluate the tree from right to left and
A. Calculate an EV at each outcome point.
B. Choose the best option at each decision point.

Step 3: Recommend a course of action to management.

Question 6

The value of perfect information

Answer 6

In many questions, the decision makers receive a forecast of a future outcome. The question often requires to calculate the value of the forecast.

Perfect information: The forecast of the future outcome is always a correct prediction. If the firm can obtain a 100% prediction , they will always be able to undertake the most beneficial course of action got that prediction.

Imperfect information: The forecast is usually correct but can be incorrect. Not as valuable as perfect information.

The value of information can be calculated as follows:-

Expected profit (Outcome) WITH the information LESS expected profit (Outcome) WITHOUT the information.