Sensitivity analysis

Sensitivity analysis is a going back to the economics methodology that can be evaluated how sensitive economic indicators to small changes of input parameters.

Definition

The term sensitivity was Germanized from the English (English sensitivity ) and has the original label sensitivity largely replaced in the field of economics. The term can also be equated with sensitivity. In metrology, the change of displayed by the meter values ​​relative is referred to the changes of the measured quantity, for example, as the sensitivity. The sensitivity is expressed in how sensitively reacts to display a meter. The sensitivity analysis provides general statements about how changes in the input conditions influence the result, so how sensitive, sensitive, or sensitive to a system.

Applications

The sensitivity analysis is often applied in the field of investment analysis ( calculation of profitability, profitability analysis ). The investment analysis provides this key indicators for the profitability of investments. For several forward-looking assumptions are usually taken. For example, can often only be determined with a remaining uncertainty, the expected investment costs. This is true during the useful life for revenue and expenditure. In Mietprojekten the rental income from the rental market and the rental rate was achieved for example, are dependent and the maintenance costs of actually occurring damage and the development of prices for repairs. For wind power projects, the current revenues of the duration and strength of the wind, the feed-in tariff and the availability of the system are dependent, while there is a more or less well-known development also in operating costs. Thus, these uncertainties affect the results of decisive investment calculations, ie whether an investment will prove to be economically or not. The sensitivity analysis can indicate how much the economy is influenced by the factors - that is how sensitive it reacts to influences.

Sequence of the method

In the investment account are as a basis initially recurring and current income and expenditure to determine. As these amounts are listed in annual tranches as subtotal ( revenue minus expenses) by year in ascending order, one obtains a series of investments. If the net present value method applied to the investment series as process, the investment account returns the net present value and payback period. In addition, can be determined as a further measure on this basis, the internal rate of return. Only one characteristic value for the net present value, payback period and internal rate of return ( IRR ) is calculated for each series of investments.

In the sensitivity analysis is now considered how these metrics are affected by changes in the investment series, ie changes in the one-time and ongoing revenues and expenditures. These individual parameters are changed and calculated the results of capital budgeting new. If the changes are made ​​in percentage for individual parameters over a whole range of variation, the results can be displayed in a sensitivity diagram (see Figure 1).

Figure 1 was applied as a sensitivity diagram, Internal rate of return. 80 % done - Investment cost variations in a range of /: In the series of investments were in the Parameter 1. In a change from 0 % in the example the investment account would still result in an internal rate of return of 6.90 %. Rising investment costs by a percentage, this has a decreasing internal rate of return result. The sensitivity chart illustrates how much can be influence the internal rate of return of changes in investment costs, ie reacts how sensitive this. In the investment analysis is of particular importance, how much must change the input parameters, thus the cost is just given. In Figure 1, this is still present when the investment costs increase by a maximum of 23.22 %. At this value, the graph intersects the expected interest rate (in the example default interest 5.00%).

In this way, all the other parameters for revenue and expenditure can be represented as graphs in sensitivity charts. All parameters are as in Example varied over a certain percentage range of values ​​and the result is output in the diagram as a graph.

In addition to the internal rate of return and the net present value can be output in the sensitivity chart. The efficiency is achieved when the NPV = zero ( see Figure 2). Basically, can also be applied in the technical sector representation as sensitivity chart. Here, for example, to think of the measurement and control technology, which is usually non-electrical input variables converted into electrical quantities and thus an electronic display or computational exploitation is made available.

For all these processes is indicative of how much influence physical input variables such as temperature, pressure, relative humidity, or level on the measuring system and bring to electrical output signals ( transfer function ). Here, too, plays a central role, react as sensitively the outputs to changes in the physical input variables.