Investment Appraisal – Risk & Uncertainty


Definition of Risk

  • Risk occurs where it is not known what the future outcome will be but where the likelihood of various possible future outcomes may be assessed with some degree of confidence, probably based on a knowledge of past or existing events.  In other words, probabilities of alternative outcomes can be estimated.
  • Uncertainty occurs where the future outcome cannot be predicted with a degree of confidence from a knowledge of past or existing events, so that no probability estimates are available.

Risk and uncertainty are the business risk of an investment.

  • Business risk can be defined as the potential volatility of profits caused by the nature and types of business operations.

There are three elements of business risk:

  • The inherent risk of the industry or market itself
  • The stage of the product life-cycle
  • The proportion of fixed costs in total costs


  • Adjust The Discount Rate

This method requires that risky projects should earn a higher return than that required for ongoing operations.  By adding a safety margin into the discount rate, what were marginally profitable projects, i.e. the riskier projects, are less likely to have a positive NPV.

If, for example, the company’s cost of capital is 10% a premium of say, 5% might be added for risk and the project evaluated using a discount rate of 15%.  If the project still produces a positive NPV at 15% it would be considered acceptable, even allowing for its risk.

The main advantage of this method is that it recognises that risky projects should earn a higher return to compensate for the additional risk.

The main drawback is in deciding the size of the premium to be added.  Thus, it is subjective and some may regard the method as unreliable.

  • Payback Period – Applying A Time Limit

In addition to requiring projects to yield a positive NPV when discounted at the cost of capital, management may apply a payback period as a means of limiting risk.  Thus, projects may be required to:

Provide a positive NPV when discounted at, say 10%                                  and

Have a Payback Period of, say, 5 years or less

One of the drawbacks to this approach is that projects with very good long-term prospects may be rejected because they do not offer the required return in the shortterm.

  • Sensitivity Analysis

The impact of changes in individual variables is measured to see the extent of the leeway before a project would only just breakeven.  What would have to happen to the variable for the NPV to change to zero?

In this way the key variables are highlighted so that management is aware of the dangers of incorrect estimating and can perhaps make contingency plans in the event of this happening.

If asked how sensitive the project is to changes in the cost of capital this can be found by calculating the Internal Rate of Return (IRR).  In the above example, the IRR is 12.5%.  Thus, the cost of capital could increase by 25%, from the existing level of 10%, before the NPV is just zero.

The conclusion is that savings are the most sensitive and particular attention must be paid by management to the estimates of these as the margin for error is only 2.8%.  They could take measures in advance to ensure that they will be achieved – e.g. by insisting on fixed price contracts.

Some of the drawbacks to Sensitivity Analysis are:

  • It treats variables as if they are independent and does not consider the interrelationships that might exist between variables.
  • There is no measure of the probability of changes in any of the variables occurring.
  • There is no automatic decision rule for managers. Managers do not know whether their decisions should be altered because of the level of sensitivity of a variable.


  • Certainty Equivalent

The expected cash flows of the project are converted to riskless equivalent amounts.  The greater the risk of an expected cash flow, the smaller the certainty equivalent value (for receipts) or the larger the certainty equivalent value (for payments).

  • Expected Values

Instead of just estimating individual cash flows for a project, probabilities could be assigned to various outcomes and these could be used to find expected values.

  • Standard Deviation of the NPV

It is unlikely that you will be expected to calculate the standard deviation of a project, but you must be able to:

  • Understand how a standard deviation might be used for risk analysis of individual investment projects.
  • Understand the relevance of standard deviations to risk measurement.


  • Simulation

The Monte Carlo simulation technique is most appropriate for modelling cash flow forecasting problems where there are several independent uncertain cash flows for which discrete probability distributions can be estimated.  The more independent cash flows there are, the more likely it is that simulation will be the only practical method available to model the system.

Random numbers are allocated to the cash flows in proportion to their relative probabilities.  A stream of random numbers is then fed into the system to simulate actual cash flows during a number of periods.

The numerical output from the application of simulation techniques is a range of possible cash flow outcomes with an indication of the likelihood of each outcome – i.e. a probability distribution of possible outcomes.  This can be used to assess the probabilities of particular events occurring during the review period.


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