10. Risk and Uncertainty

Question 1

What is sensitivity analysis?

Answer 1

Seeing how much the estimates used to make the original decision can change before the decision becomes incorrect

Question 2

What is the equation for sensitivity?

Answer 2

Project NPV / PV of variable

Question 3

When calculating the sensitivity of selling prices, what does care need to be taken over?

Answer 3

Reducing the sales price by tax charges

Question 4

How do you calculate sensitivity for cost of capital?

Answer 4

(IRR - Existing Cost of Capital) / Existing Cost of Capital

How much does can the cost of capital change before NPV is zero?

Question 5

How do organisations measure the likelihood of risks?

Answer 5

By probabilities

Question 6

How do organisations measure the impact of risks?

Answer 6

Estimating monetary amounts or using a scale of 1 to 100

Question 7

What is Value at Risk?

Answer 7

A measure that quantifies the maximum loss that is acceptable to a company over a period of time, given normal market movements and a given level of probability

Question 8

What is the formula for value at risk?

Answer 8

Confidence interval value x standard deviation

Where the confidence interval value is the Z score at Confidence % - 0.5

Question 9

Given a 1 period Value at Risk, how would you calculate the X period Value at Risk?

Answer 9

Value at risk * Sqrt(X)

Question 10

What is the expected value? E(V)

Answer 10

The weighted average payoff: Sum (Probability x Payoff)

Question 11

What risk preference investor would use E(V) to base their decisions on?

Answer 11

Risk neutral

Question 12

What are the 3 key limitations of E(V)?

Answer 12

1. Not relevant in one offs as they represent a long run average
2. Ignores the spread of possible returns
3. Relies on the accuracy of probabilities

Question 13

What is the equation for the value of perfect information?

Answer 13

VOPI = EV (with perfect information) - EV (without)

Where EV (with perfect information) comes from the expected values as if we know what the outcome scenario will be

Question 14

What is the equation of the coefficient of variation?

Answer 14

SD / E(V)

Question 15

What do we use the coefficient of variation for?

Answer 15

To compare relative risks of projects

Question 16

What is a decision tree?

Answer 16

A pictorial method of showing a sequence of interrelated decisions and their expected outcomes

Question 17

From what direction do you draw / read decision trees?

Answer 17

From the left / from the right

Question 18

What is the EV at a decision point?

Answer 18

The of lower of all cost or higher of all return options to the right

Question 19

What is maximax?

Answer 19

Maximising the maximum achievable profit - selecting the option with the best outcome possible

Question 20

Who favours maximax criteria?

Answer 20

Risk seekers

Question 21

What is maximin?

Answer 21

Maximising the minimum achievable profit - selecting the option with the best worst possible outcome

Question 22

Who favours maximin criteria?

Answer 22

Risk averse investors

Question 23

What is minimax regret?

Answer 23

Minimising the maximum regret of making the wrong decision

Question 24

What is the payback period approach to assessing risk?

Answer 24

Projects with faster paybacks are less risky

Question 25

What is the risk adjusted discount rate approach to assessing risk?

Answer 25

Adding a premium to the cost of capital when appraising higher risk projects - setting a higher hurdle rate

Question 26

What is the certainty equivalent approach to assessing risk?

Answer 26

Multiplying each years cash flow by a ‘certainty equivalent factor’ to give a ‘risk free’ cash flow, before discounting to find an NPV

Question 27

What are simulation techniques?

Answer 27

Statistical techniques, often using computers and random numbers, for simulating potential outcomes are useful in situations where they are multiple uncertain variables

Question 28

What is stress testing?

Answer 28

Simulation designed to determine the ability of a project to deal with worse case situations