1. The meaning of shadow price

Shadow price is also called "optimal planned price". It is artificially determined to achieve certain economic development goals, and it can better reflect the efficiency price of rational utilization of resources than the exchange price. From the pricing principle, it can not only reflect the product value more reasonably, but also reflect the social labor consumption, the market supply and demand relationship and the scarcity of resources. Judging from its effect, it is beneficial to the optimal allocation of resources. Therefore, the shadow price is an evaluation of the resources people use, not the real commodity price. Because China's market economy is incomplete and insufficient, the prices of some commodities cannot reflect the real social value, so shadow prices must be adopted in the national economic evaluation of the project.

2. Theoretical calculation of shadow price

The dual solution of static and discrete optimal linear programming can get the ideal shadow price; For dynamic and continuous, Lagrange multiplier can be used to calculate.

Using the dual solution of linear programming to calculate the "optimal planned price" From a mathematical point of view, shadow price is the optimal solution of linear dual programming, the first-order partial derivative of the extreme value of objective function to the constant term of constraint conditions, or the marginal value of resources. Some foreign experts use linear programming to prove that the optimal utilization of resources is closely related to the shadow price. That is, any linear programming problem that maximizes the objective function has a unique dual linear programming problem that minimizes the objective function; or vice versa, Dallas to the auditorium

Of course, the shadow price calculated by the mathematical method of linear programming is a quasi-price reflecting the optimal utilization of resources. In the economic evaluation of the project, it is not necessary and impossible to calculate the shadow price of resources in this way, and the approximate calculation method of shadow price is adopted. See related contents below for details.

(2) Adjustment and calculation of shadow price

1. Classification of goods types

In order to correctly calculate the economic value (shadow price) of input and output of investment projects, it is necessary to divide input and output into three categories: foreign trade goods, non-foreign trade goods and special inputs.

(1) foreign trade commodities

Foreign trade goods refer to goods whose production and use will directly or indirectly affect the import and export of the country. Including: direct export (increase export), indirect export (increase export instead of other project products), import substitution (reduce import by production); Direct import (increasing imports), indirect import (increasing imports by occupying inputs of other projects) and reducing exports (occupying domestic products that can be used for export) among project inputs.

(2) Non-foreign trade goods

Non-foreign trade goods refer to goods whose production and use will not affect the import and export of the country. In addition to the so-called "natural" non-foreign trade goods, such as construction, domestic transportation, domestic telecommunications, commercial and other infrastructure products and services. There are also commodities that cannot be used for foreign trade because of high transportation costs or restrictions of domestic and foreign trade policies.

(3) Special investment

Special inputs include labor, land and natural resources.

Since the calculation methods of shadow costs such as labor and land have already been introduced, the following only explains the calculation and determination methods of shadow prices of foreign trade goods and non-foreign trade goods.

2. Calculation of shadow price of foreign trade goods

The calculation of shadow price of foreign trade goods is based on the actual possible port price, and the specific pricing method is as follows.

The output of (1) is generally required to be adjusted to the ex-factory price on the basis of FOB.

(a) Shadow price (SP) of direct export products: FOB price multiplied by shadow exchange rate (SER), minus domestic transportation cost (T 1) and trade cost (Tr 1). Its expression is:

SP=FOB×SER-(T 1+Tr 1)

If the project output is a direct export product, the FOB price is USD 20/set. The project is 200km away from the port, the shadow freight is 0.20 yuan (unit km), the trade cost is 6% of the goods price, and the official foreign exchange rate is 8.27 (the same below). The shadow price of the output is:

20× 8.27×1.08-200× 0.20-20× 8.27×1.08× 6% =127.95438+0 (yuan/unit)

(b) Shadow price (SP) of indirect export products (domestic products, replacing other commodities to increase exports): FOB price multiplied by shadow exchange rate, minus transportation cost (T2) and trade cost (Tr2) from the original supplier to the port, plus transportation cost (T3) and trade cost (Tr3) from the original supplier to the user, minus transportation cost (T4) from the proposed project to the new supplier. Its expression is:

SP = FOB× SER-(T2+TR2)+(T3+TR3)-(T4+TR4)

When the original supplier and user are difficult to determine, direct export can be considered.

For example, some of the raw materials needed by similar users in the proposed project in Zhejiang were originally supplied by a factory in Jiangsu, and now a new supply factory is built in the original user's place in Zhejiang to meet the local supply, so that a factory in Jiangsu can increase its exports. The FOB price of this raw material is USD 300/ton, and the shadow freight is RMB 0.20/(t km). Jiangsu is 300km away from the port, 200km away from the original user's location, and the new supply factory in Zhejiang is 150km away from the project location. The trade cost is 6% of the commodity price, so the shadow price of raw materials is:

300×8.27× 1.08-(300×0.20 +300×8.27× 1.08×6%)+200×0.20

+300× 8.27×1.08× 6%-(150× 0.20+300× 8.27×1.08× 6%) = 2468.438+0 (yuan/ton).

(c) The shadow price (SP) of substituting imported products (domestic products, with production at the top to reduce imports): the CIF price of the original imported goods is multiplied by the shadow exchange rate, the transportation cost (T5) and trade cost (Tr5) from the port to the user, and then the transportation cost and trade cost (Tr4) from the proposed project to the user (T4) are deducted (see Figure 5-3b). Its expression is:

SP=CIF×SER+(T5+Tr5)-(T4+Tr4)

When the specific user is difficult to determine, it can be calculated according to the CIF price.

For example, a factory (user) needs imported raw materials, and now a new project somewhere produces this raw material, which is supplied by the new project. The import cif price of this raw material is 100 USD/unit, and the shadow freight is 0.20 yuan/(unit kilometer). The distance from the original factory (user) to the port is 200km, the distance from the new project is 100km, and the trade cost is 6% of the price of the goods. The shadow price of raw materials produced by the new project is:

100× 8.27× 1.08+200× 0.20+ 100× 8.27× 1.08× 6% ( 100× 0.20+ 100×

(2) Inputs are generally required to be adjusted to the ex-factory price on the basis of CIF.

(a) Shadow price of directly imported products: CIF times the shadow exchange rate, plus domestic transportation cost (T 1) and trade cost (Tr 1). Its expression is:

SP=CIF×SER+(T 1+Tr 1)

If the raw materials used in the project are imported goods, the CIF price is 100 USD/unit, and the project is 500 kilometers away from the port. The shadow freight of this material is 0.20 yuan/(unit kilometer), the trade cost is 6% of the price of goods, and the official foreign exchange rate is 8.27. The shadow price of inputs (raw materials) is:

100× 8.27×1.08+500× 0.2+100× 8.28×1.08× 6% =1046.75 (yuan/set)

(b) Shadow price of indirect imported products (domestic products that have been imported before are now imported in large quantities, but other original users need to import to meet the demand due to the construction of this project): CIF price is multiplied by shadow exchange rate, transportation cost and trade cost from port to original users, minus transportation cost and trade cost from suppliers to users, plus transportation cost (T6) and trade cost (Tr6) from suppliers to the proposed project. Its expression is:

SP = cif×SER+(T6+Tr6)-(T3+Tr3)+(T5+Tr5)

If suppliers and users are difficult to determine, direct import can be considered.

For example, the wood used by a timber factory in Zhejiang was originally supplied by a forest farm in Jiangxi. Now it is planned to build a new timber factory in Jiangxi, and the timber will be supplied by Jiangxi Forest Farm. The wood used by a timber factory in Zhejiang can only be imported and supplied through Shanghai. The CIF timber import price is 180 USD/m3. Shanghai is 200 kilometers away from Zhejiang, Jiangxi Forest Farm is 500 kilometers away from Zhejiang and 200 kilometers away from the location of the proposed project. The shadow freight of wood is 0.20 yuan/(m3 km), and the trade cost is 6% of the goods price. Therefore, the shadow price of wood consumed by the proposed project is:

180× 8.27× 1.08+200× 0.20+ 180× 8.27× 1.08× 6%-(500× 0.20+ 180× 8.27×

(c) Shadow price of self-use export products: the FOB price is multiplied by the shadow exchange rate, minus the transportation cost and trade cost from the supplier to the port, plus the transportation cost and trade cost from the supplier to the proposed project (see Figure 5-3d). Its expression is:

SP = FOB× SER-(T2+TR2)+(T6+TR6)

Figure 5-3 Schematic Diagram of Shadow Price Calculation of Foreign Trade Goods

When the supplier is difficult to determine, it can be calculated according to FOB price.

For example, a proposed project in Shanghai consumes raw coal from Huainan Coal Mine, which can be exported. Its FOB price is $40/ton. Huainan Coal Mine is 200 kilometers away from the port and 500 kilometers away from Shanghai. The shadow freight of raw coal is 0.20 yuan/(t km), and the trade cost is 6% of the price of goods. The shadow price of raw coal consumed by the proposed project is:

40× 8.27× 1.08-(200× 0.20+40× 8.27× 1.08× 6%)+500× 0.20+40× 8.27× 1.08× 6% = 465438.

3. Adjustment and determination of shadow prices of non-foreign trade goods

(1) Principles for Determining Shadow Price Adjustment of Non-foreign Trade Goods

(1) Output, including three aspects: First, increase output supply to meet domestic consumption. Supply and demand balance, according to the property price pricing; If the demand exceeds the supply, it shall be formulated with reference to the domestic market price and considering the price change trend, but it shall not be higher than the import price of products of the same quality; If it is impossible to judge the supply and demand situation, the lower of the above two prices shall be taken. Second, only replace the products of other identical or similar enterprises without increasing domestic supply, and if the replaced enterprises stop production or reduce production, the quality is the same as that of the replaced products, they should be priced according to the variable cost of the corresponding products of the replaced enterprises; To improve the quality, in principle, the price should be set according to the variable cost of the replaced product plus the national economic benefits brought by improving the product quality. Among them, the benefits brought by improving product quality can be approximately determined by the difference between the international market price and the price of the replaced product. Third, after the output is priced according to the above principles, it is calculated as ex-factory price.

(2) inputs, including four aspects: first, if the supply can be increased by tapping the potential of the original enterprise (that is, without increasing investment), it will be priced at variable cost. Second, in the calculation period of the proposed project, in order to meet the needs of the proposed project, it is necessary to increase investment and expand the production scale, and the price shall be subdivided according to the total cost (including variable cost and fixed cost). When it is difficult to obtain the information needed to break down the cost, we can refer to the domestic market price for pricing. Third, if the supply cannot be increased by expanding the production scale (reducing the supply of original users) during the calculation period of the project, the price shall be set with reference to the higher of the domestic market price, the national unified price and the subsidy (if any). Fourthly, after the inputs are priced according to the above principles, they are calculated as ex-factory prices.

(2) the cost decomposition of non-foreign trade goods

It is an important method to determine the shadow price of non-foreign trade goods by decomposing a certain kind of goods with cost decomposition method to get the decomposition cost of the goods. In principle, cost decomposition should decompose marginal cost instead of average cost, but if there is no information, average cost can also be decomposed. Of course, in the cost decomposition, it should be noted that the shadow prices of some non-foreign trade commodities (such as water, electricity, transportation and construction projects) can be determined directly according to the conversion coefficient determined by the state. If it is necessary to increase the supply of required inputs with new investment, it should be decomposed according to its full cost; If the production capacity of the original enterprise can be brought into play, it should be decomposed according to its variable cost. The steps are as follows:

The first step is to list the financial cost of a non-foreign trade commodity, the fixed assets investment and working capital of a unit commodity, and list the construction period of commodity manufacturers and the investment ratio of each year during the construction period.

The second step is to eliminate the taxes contained in the above data.

The third step is to adjust the input of raw materials, fuel and power. Among them, some of them can directly use the given shadow price or conversion coefficient, while important non-foreign trade commodities can be left to the second round of decomposition. If conditions permit, we should also adjust some large cost elements in the investment.

Fourth, adjust the depreciation expense to the unit fixed assets investment recovery expense.

Firstly, according to the requirements of national economic evaluation, the fixed assets investment in each year under financial evaluation is adjusted, and then it is converted into the final value at the end of construction by social discount rate. Its expression is:

Technical and economic evaluation method and application of oil and gas industry (third edition)

Where: IF is the investment in fixed assets from the beginning of production to the end of construction; For the adjusted investment in each year during the construction period; M is the number of years of the construction period; Is is the social discount rate;

Secondly, the depreciation expense in financial evaluation is replaced by the recovery expense of fixed assets fund.

First, the residual value of fixed assets should be converted into the present value at the beginning of production, namely:

Pc=Pυ(P/F，is，t)

Where: Pc is the present value calculated from the residual value of fixed assets to the initial stage of production; Pυ is the residual value of fixed assets (residual value); T is the production period of the project.

Then, calculate the value of fixed assets that should be recovered every year during the production period, namely:

MA=(IF-Pc)×(A/P，is，t)

Finally, the annual recovery cost of fixed assets investment per unit product can be obtained by dividing the annual recovery value of fixed assets calculated above by the annual production capacity of the project.

For example, the initial investment in fixed assets of a project is 6,543,800,000 yuan, the expected service life is 654.38+02 years, the expected residual rate is 4%, the social discount rate is 654.38+02%, and the annual designed production capacity is 6,543,800,000 pieces, so the investment cost of fixed assets per unit product is:

M = [ 1000-40× (P/F， 12%， 12)]×(A/P， 12%， 12)/ 100 = 65430。

Of course, in practical work, the following formula can also be adopted approximately:

Investment cost of unit product assets = value of fixed assets occupied by unit product × capital recovery coefficient

Value of fixed assets occupied by unit product = depreciation expense of unit product/estimated annual depreciation rate.

In addition, the investment recovery cost of intangible assets per unit product can also refer to the calculation method of investment recovery cost of fixed assets per unit product.

Thirdly, the working capital interest in financial expenses is replaced by the working capital recovery fee (Mw). The calculation formula of working capital recovery cost is:

Mw=W×is

Where: W is the amount of liquidity occupied by the unit commodity.