Accounting & Finance
Financial Analysis, Information and Markets
Sensitivity and Probability Analysis
Definitions
Return refers to the expected outcome of an investment (the NPV or IRR of a capital
investment project).
Risk refers to:
The extent to which the actual outcome may vary from the expected outcome.
The likelihood or probability that the aforementioned variance will occur.
Risk Considerations
Financial managers should consider to firstly identify and understand the risks. Risks
should then be evaluated in terms of the extent of potential risks and the likelihood of
them occurring (where extent refers to the financial impact and likelihood refers to the
probability of an occurrence, as per the definitions above).
Once risks have been identified, understood and evaluated, appropriate action should
be taken, which will consist of one of the following:
Accept the necessary risks
Reduce or minimise the risk
Avoid or eliminate the unnecessary risks
Risk is evaluated using a number of methodologies, one of which being sensitivity
analysis and one of which being probability analysis. Other methodologies include
Portfolio Theory and the Capital Asset Pricing Model which will be discussed separately.
Sensitivity Analysis
The rationale of sensitivity analysis is to ascertain the riskiness of a project to changes
in its forecast input variables (selling price, sales volumes, project life etc.) which could
change during the course of the project (due to the fact that forecasts are inherently
inaccurate).
The sensitivity of each input variable is known as the safety margin. The safety margin
refers to how much each input variable can vary before the investment decision
changes from accept to reject or vice versa, i.e. when the NPV of the project passes
, zero. The riskiest input variables have the lowest absolute safety margin and are
nearest to zero.
N.B. It may not be possible to calculate the sensitivity of every input variable of a
project.
Process
To calculate sensitivity analysis for a project with annuity cash flows, the following steps
should be followed:
1. Calculate the NPV of the project using forecasts of the input variables and the
below formula (this will never exactly match the overall NPV of the project,
because annual averages are used in the sensitivity calculation):
NPV = (Annual Contribution x Annuity Factor) – Initial Investment
Where Annual contribution = (Price per unit – cost per unit) x volume p.a;
and the annuity factor gives the present value for a series of identical cash
flows and can be found using present value tables (Appendix item 1) and
the discount factor/project life. The project should be accepted if NPV is
greater than zero and rejected if it’s less than zero.
2. Calculate the value of each input variable in turn which would result in a project
NPV of zero. The sensitivity of each input variable is the percentage change from
its forecast to the value which would result in a project NPV of zero Using the
formula for NPV stated above, set the NPV to zero and rearrange the formula to
solve for each input variable, as follows:
For initial investment:
Original Formula
0 (NPV) = (Annual Contribution x Annuity Factor) – Initial Investment
1. Rearrange
Initial Investment = Annual Contribution x Annuity Factor
2. Sensitivity (percentage change)
% = (Initial Investment at 0 NPV – actual initial investment) / actual initial
investment
N.B. The initial investment as 0 NPV is always equal to the actual NPV
For annual contribution:
1. Rearrange
Financial Analysis, Information and Markets
Sensitivity and Probability Analysis
Definitions
Return refers to the expected outcome of an investment (the NPV or IRR of a capital
investment project).
Risk refers to:
The extent to which the actual outcome may vary from the expected outcome.
The likelihood or probability that the aforementioned variance will occur.
Risk Considerations
Financial managers should consider to firstly identify and understand the risks. Risks
should then be evaluated in terms of the extent of potential risks and the likelihood of
them occurring (where extent refers to the financial impact and likelihood refers to the
probability of an occurrence, as per the definitions above).
Once risks have been identified, understood and evaluated, appropriate action should
be taken, which will consist of one of the following:
Accept the necessary risks
Reduce or minimise the risk
Avoid or eliminate the unnecessary risks
Risk is evaluated using a number of methodologies, one of which being sensitivity
analysis and one of which being probability analysis. Other methodologies include
Portfolio Theory and the Capital Asset Pricing Model which will be discussed separately.
Sensitivity Analysis
The rationale of sensitivity analysis is to ascertain the riskiness of a project to changes
in its forecast input variables (selling price, sales volumes, project life etc.) which could
change during the course of the project (due to the fact that forecasts are inherently
inaccurate).
The sensitivity of each input variable is known as the safety margin. The safety margin
refers to how much each input variable can vary before the investment decision
changes from accept to reject or vice versa, i.e. when the NPV of the project passes
, zero. The riskiest input variables have the lowest absolute safety margin and are
nearest to zero.
N.B. It may not be possible to calculate the sensitivity of every input variable of a
project.
Process
To calculate sensitivity analysis for a project with annuity cash flows, the following steps
should be followed:
1. Calculate the NPV of the project using forecasts of the input variables and the
below formula (this will never exactly match the overall NPV of the project,
because annual averages are used in the sensitivity calculation):
NPV = (Annual Contribution x Annuity Factor) – Initial Investment
Where Annual contribution = (Price per unit – cost per unit) x volume p.a;
and the annuity factor gives the present value for a series of identical cash
flows and can be found using present value tables (Appendix item 1) and
the discount factor/project life. The project should be accepted if NPV is
greater than zero and rejected if it’s less than zero.
2. Calculate the value of each input variable in turn which would result in a project
NPV of zero. The sensitivity of each input variable is the percentage change from
its forecast to the value which would result in a project NPV of zero Using the
formula for NPV stated above, set the NPV to zero and rearrange the formula to
solve for each input variable, as follows:
For initial investment:
Original Formula
0 (NPV) = (Annual Contribution x Annuity Factor) – Initial Investment
1. Rearrange
Initial Investment = Annual Contribution x Annuity Factor
2. Sensitivity (percentage change)
% = (Initial Investment at 0 NPV – actual initial investment) / actual initial
investment
N.B. The initial investment as 0 NPV is always equal to the actual NPV
For annual contribution:
1. Rearrange
