Sensitivity analysis can be divided into single factor sensitivity analysis and multi-factor sensitivity analysis according to the number of uncertain factors in each change.
The so-called single factor sensitivity analysis method refers to the analysis of the influence of the change of a single uncertain factor on the economic effect of the scheme. The analysis method is similar to the partial derivative of multivariate function in mathematics, that is, when calculating the influence of the change of one factor on the economic effect index, it is assumed that other factors remain unchanged. [ 1]
Single factor sensitivity analysis steps [1]
1. Select the uncertain factors to be analyzed and determine the range of these factors.
Sensitive factors:
Investment includes investment in fixed assets and occupation of working capital, and can also be divided into equipment costs and construction and installation costs according to needs;
The production capacity of the project during the construction period, production period and put into production, and the time required to reach the designed production capacity;
Product output and sales volume;
Product price;
Operating costs, especially variable costs;
Project life cycle; Residual value of assets at the end of project life;
Discount rate; Exchange rate.
2. Determine analysis indicators: various economic effect evaluation indicators, such as net present value, net annual value, internal rate of return, investment payback period, etc. , which can be used as an index of sensitivity analysis.
Because sensitivity analysis is based on deterministic economic analysis, in general, the indicators of sensitivity analysis should be consistent with those used in deterministic economic analysis, and other indicators cannot be established outside the scope of indicators used in deterministic analysis. When there are many indicators used in deterministic economic analysis, sensitivity analysis can focus on one or several of the most important indicators.
3. Within the possible range of change, calculate the change results of the economic effect index of the scheme caused by the different amplitude changes of various uncertain factors, and establish a one-to-one quantitative relationship.
4. Determine the sensitive factors and judge the risk factors of the scheme. Methods include relative determination and absolute determination.
1) Relative measurement method: it is to set all the factors to be analyzed to change from the values used in deterministic economic analysis, and the range of each factor change is the same, and compare the influence of each factor change on the economic effect index under the same range of change, so as to judge the sensitivity of the economic effect of the scheme to each factor change.
2) Absolute determination method: assume that all factors change in the direction that is unfavorable to the scheme, take the most unfavorable value that may appear, and then calculate the economic effect index of the scheme to see if it can reach an unacceptable level. If the worst possible value of a factor can make the scheme unacceptable, it means that the factor is the sensitive factor of the scheme.
Example of single factor sensitivity analysis [1]
For example, the cash flow of an investment scheme is shown in the table, and the data is estimated according to the forecast. There are uncertainties in some factors in the future, and investment, operating costs and product prices may all change within 20%. I0= 10%, regardless of income tax, sensitivity analysis of three uncertain factors (unit: ten thousand yuan).
Year 012-1011
Investment 15000
Sales revenue 19800
Operating cost 15200 15200
The residual value of assets at the end of the period is 2000.
Net cash flow-15000 0 4600 4600+2000
Solution: Let the investment amount be K, the annual sales income be B, the annual operating cost be C, and the residual value of assets at the end of the period be L, and evaluate the economic effect of this scheme with the net present value index. As can be seen from the meaning of the question, the calculation formula of NPV is:
NPV =-k+(b-c) (P/A， 10%， 10) (P/F， 10%， 1)+L (P/F， 10%， 10%)。
Sensitivity analysis with NPV index;
Let the percentage of investment change be x, and the calculation formula for analyzing the influence of investment change on the net present value of the scheme is:
NPV=-K( 1+x)+(B-C)(P/A， 10%， 10)(P/F， 10%， 1)+L(P/F， 10%， 1 1)
Let the percentage of operating cost change be y, and the calculation formula for analyzing the influence of operating cost change on the net present value of the scheme is as follows:
NPV=-K+[B-C( 1+y)](P/A， 10%， 10)(P/F， 10%， 1)+L(P/F， 10%， 1 1)
Let the percentage of product price change be z, which will lead to the change of sales revenue and sales tax, and the proportion of sales revenue change is the same as that of product price change, so the calculation formula for analyzing the influence of product price change on the net present value of the scheme can be written as follows:
NPV=-K+[B( 1+z)-C](P/A， 10%， 10)(P/F， 10%， 1)+L(P/F， 10%， 1 1)
Take different values of x, y and z, and calculate the net present value of the scheme under different uncertain factors. The calculation results are shown in the following table.
Change rate -20%- 15%- 10%-5% 0
Investment amount (k)143941364412894121441394.
Operating cost (c) 283742412919884156391394.
Product price (b)-10725-5195335 586411394
The change rate is 5% 10% 15% 20%
Investment amount (k)10644989491448394
Operating cost (c) 7149 2904-1341-5586
Product price (b)16924 22453 27983 33918
As can be seen from the table, when the change rate (x, y, z) is the same, the change of B has the greatest influence on NPV, followed by the change of C, and the change of K has the least influence.
Using the calculation formula of the influence of sensitive factors on net present value, the
NPV =0，
It can be calculated as follows: x =76.0%, y = 13.4%, z =- 10.3%.
Result analysis:
From the results of x =76.0%, y = 13.4% and z =- 10.3%, we can draw the following conclusions:
If the investment and product price remain unchanged, the annual operating cost is higher than the expected value 13.4%, or the investment and operating cost remain unchanged, and the product price is lower than the expected value 10.3%, the scheme will become unacceptable. However, if the operating cost and product price remain unchanged and the investment increases by more than 76.0%, the scheme will become unacceptable, as shown in the figure.
From the analysis, we can see that the product price and operating cost of the scheme are sensitive factors. Before deciding whether to adopt this scheme, we should make a more accurate prediction of the future product price, operating cost and the scope of possible changes. If the investment and operating cost remain unchanged, the product price is lower than 10.3% of the original estimated value, or the investment and price remain unchanged, and the operating cost is higher than 13.4% of the original estimated value, then the scheme is unacceptable. However, under the condition of constant operating cost and price, the scheme of increasing investment by more than 76.0% is unacceptable, and the investment amount is obviously not the sensitive factor of the scheme.
Evaluation of single factor sensitivity analysis method
This single factor analysis method is not comprehensive, which tends to underestimate the risk consequences of economic evaluation and will bring losses to investors.
Single factor sensitivity analysis must assume that other factors remain unchanged when calculating the impact of specific uncertain factors on the economic benefits of the project. In fact, this assumption is difficult to establish. There may be two or more uncertain factors changing at the same time. At this time, it is difficult for single factor sensitivity analysis to accurately reflect the risk-taking situation of the project, so multi-factor sensitivity analysis is necessary.
refer to
= 1.0 1. 1.2 Shandong Jiaotong University. Technical economics [M]. Chapter IV Basic Methods of Technical and Economic Analysis
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