Investment Appraisal, Part IV: Project Risk and Sensitivity Analysis

Risk is an unavoidable nuisance that if not treated with care and delicacy, can topple even the most wealthy and profitable companies. However, get it right, and you could be sitting pretty and a pile of cash and capital wealth. Companies undertake projects with risk because it the risk that generates additional wealth for not only the company, but primarily the shareholders.

According to the Oxford English Dictionary, risk is “a chance or probability of danger, loss, injury, or other adverse consequences”. Probably the only certainty in project appraisal is the initial cost of the project, as start up costs and equipment can often be costed up. It is often the future costs and estimated cash flows that create risk due to often uncontrollable uncertainties. However, even that can change between the decision being made and the money being spent. As projects deal with future events, no one knows with certainty what will happen, thus there is always some risk present.

In order to try and deal with project risk, there are a number of different techniques available to managers, three of which I will look at in more detail: probability analysis, simulation analysis and sensitivity analysis.

Probability Analysis

Because of the uncertain nature of project risk, there is more often than not more than one possible outcome, and probabilities can be attached to these outcomes.

Example. – Probabilities

What will the economy be like in the next financial year?

30% chance of economic boom / 20% chance of economic downturn / 50% chance of economic stability – the company’s cash flows will be dependent on the economic climate that prevails.

Expected Cash Flows and NPV

Expected cash flows can be calculated using probabilities, and then these can be used to work out an expected NPV (ENPV). The simple calculation of working out an expected cash flow, is to multiply the different cash flows by the assigned probabilities and to total the new amounts.

Worked Example. – Expected cash flows and NPV

Andersons Ltd. is considering a one-year project with an initial investment cost of £50,000. The year one cash flow will depend on how well the project is received. If the project is well received, the cash flows are expected to be £100,000, and if they are badly received it is expected to achieve £30,000. The probabilities of each occurring are 60% and 40% respectively. The company’s cost of capital is 12%.

Expected year one cash flow:

Well received                               £100,000   x      60% =                £60,000

Badly received                             £ 30,000    x      40% =                £12,000

Expected NPV:   (£50,000) + (£72,000 / 1.12) = £14,286 – positive, thus accept the project.

Problems with ENPV

The problem with using an ENPV is that the ENPV value will never be the actual cash flow. The actual cash flow will usually be one of the expected probability values e.g. either £100,000 or £30,000 using figures from the example above. The risk is that no one knows what the outcome will actually be. Similarly, because of this risk, neither of the expected cash flows may be achieved.

ENPV is only good for projects that take place repeatedly. This is because ENPV shows the average NPV if the project is taken many times. If the NPV of projects is close, it may help to calculate the standard deviation, and this too gives an indication about the risk.

Example. – Standard deviation

Economic State                            Probability                             Return

Boom                                                 30%                                          20%

Stable                                                 50%                                          12%

Decline                                              20%                                             5%


Expected return:        (0.3 x 20) + (0.5 x 12) + (0.2 x 5) = 13%


Standard deviation:      √0.3(13 – 20)² + 0.5(13 – 12)² + 0.2(13 – 5)²   =   5.29%

Simulation Analysis

Simulation analysis is only suitable for large investment projects. The process sees all possible project cash flows and their probabilities put into a computer simulation software program, and then the computer selects (at random) a cash flow for each variable and calculates an NPV. The resulting NPV’s will give a good indication of the spread of results and thus the risk. It also allows mangers to better understand the interdependencies of the components within the cash flows.

For more information on the simulation analysis process, click here.

Sensitivity Analysis

Sensitivity analysis looks at how sensitive the NPV (or ARR, IRR etc.) is to changes in the cash flows from which it is derived. If sensitivity analysis is carried out on all components of the cash flow, then it can be seen which items the project is most sensitive to. This enables managers to focus on these items.

A simple sensitivity analysis uses a random percentage deviation both plus and minus to create two points that can be used to plot a line on a graph. The steepness of the line dictates the sensitivity of a cash flow component, thus the steeper the line, the stronger the sensitivity to changes. For example, the graph below shows sales price to be the most sensitive component as it has the steepest gradient, showing that NPV decreases the most for small changes in sales prices.


Sensitivity Analysis Graph

Limitations of Sensitivity Analysis

One of the drawbacks of sensitivity analysis is that it doesn’t give the likelihood of these items changing. The project may be very sensitive to changes in selling price, but if a contract has been signed, the likelihood of prices changing on the contract is nil. This shows that viewing the figures without considering the likelihood of them changing can be misleading.

Sensitivity analysis views changes to components of the cash flow in isolation i.e. one figure changes at a time. However, in reality this is rarely the case, for example, generally when material costs increase, selling price increases to make up for the loss in profit margin.

Click here to download a sensitivity analysis question.

Click here for the answer.


Featured image courtesy of


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