07. Project Appraisal Under Risk

Question 1

Distinguish between risk and uncertainty.

Answer 1

Risk - a condition in which several possible outcomes exist, the probabilities of which can be quantified from historical data.

Uncertainty - the inability to predict possible outcomes dies to a lack of historical data (ie information) being available for quantification.

Question 2

What is sensitivity analysis?

Answer 2

The analysis of changes made to significant variables in order to determine their effect on a planned course of action.

Sensitive analysis can also be referred to as “what if?” analysis.

Question 3

State a formula for calculating Sensitivity. Does a lower or higher % indicate more sensitivity?

Answer 3

Sensitivity = (NPV / PV of relevant cash flow) * 100

The lower the %, the more sensitive the NPV is to that project variable, as the variable would need to change by a smaller amount to make the project non-viable.

Question 4

What is the relevant cash flow for a change in sales volume?

Answer 4

The relevant cash flow is contribution.

Question 5

What are four advantages of sensitivity analysis?

Answer 5

1. It gives an idea of how sensitive the project is to changes in any of the original estimates.
2. It directs management attention to checking the quality of data for the most sensitive variables.
3. It identifies the critical success factors for the project and directs project management.
4. It can easily be adapted for use in spreadsheet packages.

Question 6

What are five limitations of sensitivity analysis?

Answer 6

1. Although it can be adapted to deal with multiple—variable changes, sensitivity analysis is normally used to examine what happens when one variable changes and others remain constant. Variables are often interdependent, however.
2. It assumes data for all other variables is accurate.
3. Without a computer, it can be time-consuming.
4. Probability of change in a variable is not considered.
5. Sensitivity analysis does not provide a decision rule. Management must decide the level of sensitivity that is acceptable.

Question 7

What is simulation?

Answer 7

A technique which allows more than one variable to change at the same time.

Question 8

What are the 6 stages in a Monte Carlo simulation?

Answer 8

1. Specify the major variables (e.g. revenue and costs).
2. Specify the relationship between the variables (eg revenue minus costs equals profit).
3. Attach probability distributions to each variable and assign random numbers to reflect the distribution (eg a 10% probability that costs are $1,000, a 50% probability that they are $10,000 and a 40% probability that they are $12,000).
4. Simulate the environment by generating random numbers for revenue and costs. For example, using random numbers from 00 to 99:
   - assign 00 to 09 to $1,000 cost with 10% probability
   - assign 10 to 59 to $10,000 with 50% probability assigned to it, and so on.
5. Record the outcome of each simulation (eg the profit based on the revenue and costs levels randomly selected are recorded).
6. Repeat the simulation many times to obtain a probability distribution of the possible outcomes (eg the simulation will show the probabilities of various profit levels being achieved).

Question 9

What are two advantages of simulation?

Answer 9

1. Monte Carlo simulation provides more information about the possible outcomes and their relative probabilities.
2. This data can be used to calculate an expected NPV (and the standard deviation of the expected NPV).

Question 10

What are four limitations of simulation?

Answer 10

1. Monte Carlo simulation is not a technique for making a decision, only for obtaining more information about the possible outcomes.
2. It can be very time-consuming without a computer.
3. It could prove expensive in designing and running the simulation, even on a computer.
4. Simulations are only as good as the probabilities, assumptions and estimates used.

Question 11

What are the benefits of using expected values for risk measurement?

Answer 11

1. Expected value reduces the information to one value for each choice.
2. The idea of an average is readily understood.

Question 12

What are the disadvantages of using expected values for risk measurement?

Answer 12

1. The probabilities of the different possible outcomes may be difficult to estimate.
2. The average may not correspond to any of the possible outcomes.
3. Unless the same decision has to be made many times, the average will not be achieved; therefore, it is not a valid way of making a decision in “one-off” situations.
4. The average gives no indication of the spread of possible results (ie it ignores risk).

Question 13

What are five methods of keeping project risk within acceptable levels?

Answer 13

1. Setting maximum adjusted payback period in the initial screening process of potential projects.
2. Using risk-adjusted discount rates for both NPV and adjusted payback. A higher discount rate should be applied to projects with higher risk, thereby reducing the influence of more distant cash flows. In addition, investors prefer cash now to later and so require a higher return for longer time periods. Project-specific discount rates can be found using the CAPM.
3. Using conservative forecasts, such as reducing the forecast returns downwards to reflect the guaranteed mimim inflows from a project (certainty equivalents). Then discount these lower cash flows at the risk-free interest rate (ie risk is removed from the cash flows rather than adjusted for in the discount rate).
4. Selecting projects with a combination of an acceptable expected NPV and a relativity low standard deviation of NPV.
5. Focusing attention on the critical success factors indicated by sensitivity analysis.