Sensitivity analysis

Sensitivity analysis involves calculating cash flows under the best estimate of input variables, and then calculating the consequences of limited changes in the value of these inputs. It assists the evaluator to identify the variables that significantly affect the outcome and correspondingly needs more information and investigation. Sensitivity analysis is carried out during practically every financial and economic evaluation of projects; it is simple and informative. It is a review of the impact that changes in selected project inputs, costs or benefits, or a combination of these, can have on the project’s net present value or IRR. In this case one or more variables are changed independently or collectively, within reasonable limits (say, 10–20 per cent) to see the likely effect of the change on the net present value of the project and its likely IRR. Alternatively the aim may be to calculate the change in one variable, like the selling price per unit or project cost that will reduce the net present value of project benefits to zero. This will indicate the selling price per unit or project cost below or above which, respectively, it is not worthwhile pursuing the project. Another alternative may be break-even analysis, to work out values of inputs and outputs that will reduce the project benefits to below the cut-off rate, which is a rate established as a ‘threshold’ below which projects should not be accepted. The cut-off rate depends to a large extent on the riskiness of the project. A project with a high volatility in some inputs will therefore need a much higher acceptable cut-off rate than a project with almost sure estimates.

One of the most important exercises in sensitivity analysis is to review the impact of the discount rate on the project’s net present value and its profitability. In this case, and if there is no single firm discount rate, more than one discount rate is tried and the outcome with each discount rate is described. The UNIPEDE/EURELECTIC study into the projected cost of generating electricity considers two discount rates, 5 per cent and 10 per cent, each applied with different outcomes [6].

Sensitivity analysis is therefore an essential and easy means of evaluating the vulnerability of the project to likely future deviation from best-input estimates. It can also greatly help in assessing the extent of risk in the project, and the particular inputs that significantly affect the project outcome. Once these are identified, then a more careful study should be undertaken of these particular items to enable better estimates and a firmer calculation of the net present value and the project’s IRR. For the electrical power industry the most important items affecting a project’s financial performance are the electrical tariff and fuel prices. With the increasing availability of electronic calculating facilities it has become much easier to undertake many sensitivity analysis scenarios and to analyse the effect of various parameters on the project’s financial and economic feasibility.

One of the major weaknesses of sensitivity analysis is that the changes are, most of the time, ad hoc (10 per cent change in price of fuel or 10 per cent change in demand, etc.), without regard to the expectancy and probability of these happening. Such ad hoc assumptions do not assist decision makers to examine the likelihood of the event. Fuel price changes, in the future, may be much more likely to occur than other operational costs, therefore dealing with these two on equal terms can lead to

wrong impressions and conclusions. So also can the effect of a change of one input on other inputs; a significant change in fuel prices will not only affect the NPV and IRR, but will also affect demand, prices and merit order and can cause significant implications, which are not captured by sensitivity analysis. What is important is not only the prospect of change of a fundamental input assumption but also the probability of this happening and its extent, and also the interrelationship between variation in one variable and other inputs. Such prospects can only be adequately evaluated by proper risk analysis.

To demonstrate this, consider a 100 MW CCGT set, firing LNG, that consumes 6000 BTU per kWh generated, at a cost of £2.60 per million BTU. The set will cost £50 million at commissioning and is expected to act as a base-load generating unit at full load for 7000 hours annually. There is a fixed annual cost of £1 million.

With a 10 per cent discount rate, over 20 years, the equivalent annual cost of investment is equal to

investment 20-year annuity factor=

£50 million

8.514 = £5.87 million. The fixed annual cost of capital and operation will equal

5.87 million+ 1 million = £6.87 million, with an annual generation of

100 MW× 7000 h = 700 GWh. The fixed annual cost per kWh will be

£6.87 million÷ 700 GWh = 0.98p. Fuel cost per kWh is

(£2.6× 6000)/106= 1.56p. Total cost of generation is

0.98+ 1.56 = 2.54p kWh−1.

Consider the case of a sensitivity analysis of a possible increase in fuel cost by 20 per cent, then the fuel cost will become 1.872p kWh−1and total cost of generation 2.85p kWh−1.

With such a fuel price and operational cost, the set most likely will not remain a base-load set and correspondingly the energy output of the set and its cost per kWh will be higher (depending on the position of the set in the merit order). Sensitivity analysis fails to capture such correlation between fuel cost, energy contribution of the set and correspondingly system cost. It is only simulation that can give the generation cost, capture the system effect and evaluate the true economics of investing in such a plant compared with other alternatives firing other fuels.