Sensitivity analysis is often performed to assess the likely impact on a project of cert ain estimates being inaccurate. When undertaking an NPV analysis of a project, the accuracy of the NPV depends o n the accuracy of the input factors in the calculation (e.g. estimates of cost of capital , sales, expenses, tax rates). After computing the NPV of a project, sensitivity analysis can be used: •to identify which of the input variables of the project could have the most adverse im pact on the NPV of the project if they were to change. • to assess the impact on the NPV of a certain change in a particular input factor. •to consider by how much each input variable could change before the NPV of the pr oject became zero (and hence the project became unacceptable). Interpretation of sensitivity analysis results A company has calculated the NPV of a project, and has subsequently identified the following sensitivities: Sales can fall by 10% or costs may rise by 20%, or the discount rate can increase by 1% before the NPV becomes zero. In this case we would conclude that the project NPV is very sensitive to changes in d iscount rate (small percentage sensitivity) but not very sensitive to changes in costs ( if costs were to change, unless they changed by more than 20% the NPV would still be positive. Limitations of sensitivity analysis The major problem is that we normally consider the impact of only one variable at a ti me. Management may be more interested in the risk of some key factors changing at the same time. For example, if the selling price changes, there is likely to be an imp act on sales volume too. Sensitivity analysis can only deal with one of these variable s changing at a time. Also, sensitivity analysis does not include any assessment of the probability of certai n variables changing. It is therefore useful as an aid to decision making, rather than a decision rule in itself. Two basic approaches to Both approaches will be shown in the Illustration below. sensitivity analysis (1) An analysis can be made of all the key input factors to ascertain by how much each factor must change before the NPV reaches zero, the indifference point. (2) Alternatively, specific changes can be calculated, such as the sales decreasin g by 5%, in order to determine the effect on NPV. Illustration 1 – Sensitivity A project has an NPV of $1m. The PV of material costs (included in the NPV calc ulation) are $5m. Sensitivity = (NPV / PV of cashflows affected by the estimate) × 100% = 1m / 5m = 0.2 (20%) i.e. the material costs could rise by up to 20% and the project remains viable. A ri se of greater than 20% will produce a negative NPV and the project would not be worthwhile. Alternatively, sensitivity analysis could be used to assess the impact of a given p ercentage change in a variable. To continue with the above example, if the material costs were to change by 10% (from a PV of $5m to $5.5m a change of $0.5m) the NPV would reduce by $0.5m from $1m to $0.5m (a fall of 50%). Question 1 – Rock (Practice Question) Rock Ltd invests £100,000, and proposes to make exclusive rocking chairs for 10 years. The company will plan to make 250 chairs per annum, earning a contribution of £151 per chair. Fixed costs are expected to be £17,500 per annum and the scrap value of machinery after 10 years is forecast at £10,000. Ignore tax and writing down allowances, and use a discount rate of 15%. Calculate the NPV and the sensitivity to the: • initial investmen • contribution • fixed costs • scrap. Evaluation of sensitivity analysis Sensitivity analysis attempts to identify those variables in which a small change in the estimate would lead to the decision-maker changing their mind. This might mean turning a positive NPV to a negative one, or the ranking of investments changing. Those estimates, which are crucial, can then be re-examined to ensure we are confident about them before deciding to invest. To calculate the change needed in each variable, we alter one at a time to see how far it must move to give a negative NPV or to change the ranking. Those in which the change needed is small (say less than 10%) will be the crucial estimates. Advanced Investment Appraisal Techniques 191 There are two main limitations of the method. Firstly, only one input is altered at a time even though there might be a much more dramatic impact if a number of estimates proved incorrect at the same time. Secondly, the method gives information on the impact of a change in estimate, but does not attempt to predict how likely this might be.
