Chapter 7 Flashcards
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 due to a lack of historical data (i.e. information) being available for quantification
What is the major risk to an investment
The major risk to the success of an investment project will be the variability of future cash flows. This could be the variability of income streams or the variability of cost cash flows, or a combination of both.
Sensitivity analysis
the analysis of changes made to significant variables in order to determine their effect on a planned course of action.
sensitivity analysis is used to analyse the effect of changes in the value of an input variable (occasionally more than one input variable), assuming other inputs are kept constant.
Key point
For a change in sales volume, the relevant cash flow is contribution. This may involve combining a number of cash flows (i.e. revenue and variable costs).
Advantages of sensitivity analysis
It gives an idea of how sensitive the project is to changes in any of the original estimates.
It directs management attention to checking the quality of data for the most sensitive variables.
It identifies the critical success factors for the project and directs project management.
It can be easily adapted for use in spreadsheet packages.
Limitations of sensitivity analysis
Although it can be adapted to deal with multi-variable changes, sensitivity analysis is normally used to examine what happens when one variable changes and others remain constant. Variables are often interdependent, however.
It assumes data for all other variables is accurate.
Without a computer, it can be time-consuming.
Probability of change in a variable is not considered.
Sensitivity analysis does not provide a decision rule. Management must decide the level of sensitivity that is acceptable.
Simulation
a technique which allows more than one variable to change at the same time.
Stages in a Monte Carlo Simulation
Specify the major variables (e.g. revenue and costs).
Specify the relationship between the variables (e.g. revenue minus costs equals profit).
Attach probability distributions to each variable and assign random numbers to reflect the distribution (e.g. 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).
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.
Record the outcome of each simulation (e.g. the profit based on the revenue and costs levels randomly selected are recorded).
Repeat the simulation many times to obtain a probability distribution of the possible outcomes (e.g. the simulation will show the probabilities of various profit levels being achieved).
Advantages of simulation
Monte Carlo simulation provides more information about the possible outcomes and their relative probabilities.
This data can be used to calculate an expected NPV (and the standard deviation of the expected NPV).
Limitation of a simulation
Monte Carlo simulation is not a technique for making a decision, only for obtaining more information about the possible outcomes.
It can be very time-consuming without a computer.
It could prove expensive in designing and running the simulation, even on a computer.
Simulations are only as good as the probabilities, assumptions and estimates used.
Expected value
the quantitative result of weighting uncertain events by the probability of their occurrence.
Advantages of expected values
Expected value reduces the information to one value for each choice.
The idea of an average is readily understood
Disadvantages of expected values
The probabilities of the different possible outcomes may be difficult to estimate.
The average may not correspond to any of the possible outcomes.
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.
The average gives no indication of the spread of possible results (i.e. it ignores risk).
Methods of keeping project risk within acceptable levels include
Setting a maximum adjusted payback period in the initial screening process of potential projects.
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 capital asset pricing model (see Chapter 12).
Using conservative forecasts, such as reducing the forecast returns downwards to reflect the guaranteed minimum inflows from a project (certainty equivalents). Then discount these lower cash flows at the risk-free interest rate (i.e. risk is removed from the cash flows rather than adjusted for in the discount rate).
Selecting projects with a combination of an acceptable expected NPV and a relatively low standard deviation of NPV.
Focusing attention on the critical success factors indicated by sensitivity analysis.
