Investment compensation mechanism for affordable housing construction project based on decision function

Abstract

With continuously accelerated development of China’s urbanization, the price of commercial housing is also rising and the housing problem has become a hot issue in China’s social development at current stage. The affordable housing, as a means to guarantee the housing rights of medium- and low-income groups, has seriously insufficient attractiveness to the returns on project investment due to its non-profit nature. The social capital is unwilling to enter this field and thus leads to inadequate supply of affordable housing. Therefore, it is very necessary to establish an investment compensation mechanism for affordable housing construction. Based on decision theory and reasonable return principle, this study constructs an investment compensation model for construction of rental-type affordable housing based on satisficing decision. Finally, it uses the data of a public rental housing project in Beijing, China to conduct empirical analysis, quantifies all government subsidies and actually calculates the government compensation amount with the net present value of project as the decision goal. The results show that: (1) determining the reasonable profit rate of affordable housing developers is the key point to promote the investment and development of affordable housing; (2) investment compensation model for affordable housing construction based on satisficing decision can be used to objectively calculate the compensation amount payable to the affordable housing developer; (3) the private sector that invests in affordable housing should not passively wait for subsidies and preferential policies and measures of the government; instead, they should actively innovate in the profit model of affordable housing and promote the construction of affordable housing. The study shows that the investment compensation model for affordable housing based on decision function is good to judge the project feasibility. Compared with other models, it improves the model’s interpretation and prediction ability and provides new decision ideas and methods for the government and enterprises to develop and construct affordable housing.

Keywords

Affordable housing construction investment decision function net present value of project compensation mechanism

1 Introduction

With continuously accelerated development of China’s urbanization, the price of commercial housing is also rising. The 2015 Ranking of House Price-Income Ratio in 35 Large and Medium-sized Cities of China issued by E-house China R&D Institute shows that, in 2015, Shenzhen, China ranks ranked first in terms of the house price-income ratio excluding the salable affordable housing, with the ratio as high as 27.7, and the house price-income ratio including the salable affordable housing was 23.2. This means that Shenzhen residents need an average of 23.2 months’ disposable income to afford one-square-meter house, which is obviously not commensurate with the residents’ income level. For this reason, the China’s government has been vigorously developing affordable housing in recent years. The affordable housing refers to the specific housing provided by the government to the specific group. The specific group refers to the medium- and low-income group and the specific housing refers to the housing with price, service objects and standards being of social security nature. Affordable housing plays a role in redistribution and security of social wealth and ensures the regional economic and social stability.

In March 2011, the Department of Household of National Bureau of Statistics released a report on the income and expenditure and life quality of urban and rural residents. The report shows that, by the end of 2010, 89.3% of China’s urban residents have their own houses, indicating that the proportion of private housing gets higher and higher and the proportion of public housing becomes smaller. This reflects that there is an inadequate supply of affordable housing and the people are forced to buy houses with private property rights in the commercial housing market. There are many reasons for the insufficient construction of affordable housing. Non-profit nature of affordable housing operation is one important reason. In contrast with the commercial housing, affordable housing is to guarantee the housing needs of medium- and low-income families but not to make profits. For instance, according to experts’ estimates, even if the occupancy rate of rental-type affordable housing is as high as 70% to 90%, it still requires 20 to 35 years to cover the principal and interest of the project loan after taking into account the investment-income ratio of the project, namely the project construction cost, the project operation and management cost, the various tax reduction and exemption as well as financial subsidies from the government. The non-profit nature of affordable housing operations leads to seriously inadequate attractiveness of affordable housing to the investment returns and the current government-led development model has led to complicated market environment and multiple administration of the project. The social capital is not enthusiastic in investing in the construction of affordable housing. Hence, it is necessary to establish an investment compensation mechanism for affordable housing construction. However, previous studies on compensation mechanism mainly focused on ecology, urban infrastructure construction, and construction of road traffic facilities. The income of the medium- and low-income residents, target of the affordable housing, is insufficient to pay for the high-margin commercial housing, and it is difficult for the private sector which undertakes the construction of and investment in affordable housing to recover the cost and obtain the profits, resulting in little research on investment compensation mechanism for affordable housing construction in the real economic life and academic theories. From the perspective of rational decision-making theory, the private sector will choose the optimal solution according to the preference relationship after mastering all the information on the decision-making behavior in affordable housing construction and investment. However, it is often inconsistent with the actual investment behavior of the private sector, leading to insufficient investment in affordable housing. Therefore, it is of great practical significance to comprehensively analyze the quasi-public product nature of affordable housing, the low-income characteristics of users, and the bounded rationality of private sector in affordable housing construction and investment, provide scientific and reasonable compensation methods and standards to the investors and construct a satisficing decision model to improve the enthusiasm of the private sectors in affordable housing construction. Currently, BOT model has been widely applied in construction projects of infrastructure, such as power plants, roads, and urban rail transit. The affordable housing construction in developed countries and some cities in China show that the BOT model is also applicable in construction of public rental housing. In the BOT model, the enterprises finance for the rental-type affordable housing construction and, after formation of the rental affordable housing, obtains the right to operate the housing and a certain amount of return through collection of rent and charges over the commercial facilities during the franchise period authorized by the government. The enterprises bear the corresponding responsibility of maintaining the habitability of the housing and hand it over to the government upon expiration of the franchise period [1]. This model not only fundamentally solves the contradiction between the government’s financial shortage and the urgent need for funds in construction of rental-type affordable housing but also greatly reduces the construction cost of rental-type affordable housing because of the flexible mechanism of private enterprises, thus achieving the efficient and rapid development of rental-type affordable housing and the win-win between the government and the enterprises. In addition, during the BOT financing period, the government can supervise the leasing, investment, operation and rent collection of the enterprises to avoid the nature of affordable housing from changing. This study studies the investment compensation for rental-type affordable housing and adopts the data of a public rental housing project in Beijing, China for empirical research.

2 Research status

Von Neumann and Morgenstern [2] established the axiom system of rational behavior which is a cornerstone of classic normative decision-making theory. The expected utility theory proposed by Von Neumann and Morgenstern and the Bayesian decision-making theory put forward by Savage [3] are the foundation of the development of rational decision-making theory. Allais [4] and Ellsberg [5] took the lead in experimental research and found that people’s actual decision-making behaviors are not consistent with rational decision theory. Due to the bounded rationality, deterministic effect and inconsistent preference of decision-makers in real life, Simon [6] and others thought that decision-makers can not follow the principle of utility maximization, but only follow the principle of “satisfaction” when making decisions. That is, the decision-makers in real life follow the “satisficing heuristic” principle.

Scholars have studied on the compensation mechanism in the construction of social welfare projects by private sector and the government compensation calculation model based on the game theory, risk preference, performance evaluation, and system dynamics. Akintayo et al. [7] studied the compensation mechanism for minimizing the risks of private sector in concession-based public-private partnerships. Hans-Peter et al. [8] studied the compensation mechanism in farmland acquisition for flood response. Estelle et al. [9] studied such three factors as choice overload, coordination and inequality which affect the effectiveness of compensation mechanism. With affordable housing PPP project as an example, Oxley believed that subsidies can be provided in many forms, such as government payments, tax reduction and exemption, low-interest loans, and cross-subsidies during development [10]. Chowdhury et al. [11] believed that appropriate government compensation has an important impact on the success of PPP projects. Jaebum Jun studied the revenue guarantees in government compensation mechanisms [12]. Androcec et al. [13] studied the TSO compensation mechanism cost within the EU and the path to maximize the benefits. Candel-Sánchez [14] studied the principle of continuous pollution treatment based on system dynamics, and the research showed that the balance tax and Pigovian taxes in the Varian compensation mechanism are not always consistent. Kim [15] studied the location of indivisible public goods. In the traditional literature, the compensation mechanism is basically based on Bayesian equilibrium. Few literature pays attention to the implementable strategic dominance of compensation mechanism. This study proposes a strategic implementation mechanism, “almost ideal mechanism (AIM)”, which is superior to other mechanism. Such mechanism has the characteristics of incentive compatibility, individual rationality, efficiency and dominance. Sarvašová et al. [16] adopted econometric Heckman selection model to evaluate the implementation of Natura 2000 ecological network policy on compensation mechanism of private forest. Saijo et al. [17] compared and analyzed the advantages and disadvantages of the Varian compensation mechanism and the approval system in solving the prisoner’s dilemma. Yang [18] constructed a government compensation model for rental-type affordable housing based on system dynamics mechanism, studied the basic government compensation, evaluated the performance of social capital, and tested the feasibility and rationality of government compensation for rental-type affordable housing. Liu et al. [19] established a Stackelberg dynamic game model for urban rail transit projects based on different risk preference combinations, and studied the government compensation mechanism on this basis. They obtained the optimal investment scale of private investors and the optimal subsidy strategy of government through empirical research. Du et al. [20] studied the compensation mechanism in PPP projects from the perspective of coordination between centralized decision-making and decentralized decision-making. Zhang et al. [21] analyzed the reasons for government compensation mechanism in PPP projects from the perspective of incomplete contract, and established a bargaining game model between government and enterprises in government compensation for PPP projects. Li [22] adopted the principal-agent model in game theory to construct a two-stage game model based on performance implementation compensation and designed an economic and policy compensation scheme for PPP projects on such basis. Chen et al. [23] introduced the real options and employed the pricing model of real option to defer investment to study the incentives for private enterprises in three ways: investment subsidies, income subsidies and demand guarantees. Qi et al. [24] analyzed the interrelationships among main stakeholders in the project construction, employed economic mechanism design theory and incentive theory to design the government compensation mechanism, and applied the game theory model to study the reasonable compensation intensity of government. From the perspective of social capital interest structure, Shen et al. [25] constructed a system dynamics model of government compensation and designed, through model simulation and sensitivity analysis, the government compensation mechanism from the aspects of public interest, social capital income, and fiscal expenditure of government. Most of the previous studies on project compensation mechanism employed the mathematical research methods such as game theory, system dynamics, and performance evaluation. Of which, the game theory method considered more about the game relationship between government and enterprises. However, in the research on affordable housing, the game theory relationship often exists between the central government and local governments. The performance evaluation on the enterprises constructing and investing the affordable housing and the fuzzy comprehensive evaluation, analytic hierarchy process and gray clustering methods applied in the evaluation are not applicable to the studies on investment in affordable housing construction. In view of this, based on the fact that the private sector seeks economic profits and follows satisficing decision theory during its investment, this study starts with the net present value of project to construct a government compensation model for rental-type affordable housing. Meanwhile, it measures whether the government should subsidize and the reasonable subsidy amount in the construction of affordable housing through analysis of the relevant data of a public rental housing project in Beijing, China and proposes relevant suggestions to facilitate the construction and development of affordable housing.

3 Research methods

The satisficing decision concept was put forward on the basis of bounded rationality. To the mind of proposer, the essence of satisficing decision is that the decision-maker only needs to exceed the determined minimum satisfaction criterion in making choice. In the actual decision-making, the decision-maker does not have to search all possible alternatives nor have to order all the plans before choosing a plan. He/she only needs to find a solution that fits or exceeds the target value, which greatly improves the efficiency of decision-making. Therefore, it can more effectively guide the decision-making in real life.

3.1 Analysis of satisfaction behavior of investors of affordable housing

As mentioned earlier, because of the existence of bounded rationality, the “satisfying” standard pursued by investors is not the optimal standard. Investors do not pursue profit maximization but follow the satisficing heuristic. Namely, the investors will consider investing when they find the satisfactory profits from investment. Net present value (NPV) of project is a basic indicator in project evaluation, and refers to the difference between the present value of future capital (cash) inflows (income) and the present value of future capital (cash) outflows (expenses). The net present value of future capital inflows and outflows is determined after they are converted into the present value according to the present value coefficient of each period of the estimated discount rate. The net present value method is a method of evaluating a scheme according to the size of net present value. The scheme is feasible if the net present value is greater than zero, and the larger the net present value, the better the scheme and the higher the investment returns. Therefore, for the developers of affordable housing projects, it would be better if the net present value is greater and their basic requirement is that the project’s net present value should be greater than or equal to zero. The developer’s behavior model is as follows:

$\begin{matrix} max NPV = & \sum_{j = 1}^{n} \frac{R_{j} + Y_{j} - D_{j} - M D_{j} - B T_{j}}{{(1 + a)}^{m + j}} \\ - \sum_{i = 1}^{m} \frac{C_{i} + M C_{i} + O T_{i} - X_{i}}{{(1 + a)}^{i}} \end{matrix}$ (1)

Where, C_i is the development and construction cost (market average level) in the i year and it mainly includes the land cost, upfront cost, infrastructure construction cost and management cost; D_j is the project operation cost (excluding taxes) in the j year and it mainly includes the management cost and maintenance cost; MC_i is the loan interest in the i year of the construction period; MD_j is the loan interest in the j year of the franchise period; OT_i is the taxes of the i year; BT_j is the taxes of the j year; X_i is the government’s subsidies on the investment in the i year; Y_j is the government’s subsidies on the operation in the j year; R_j is the total income of the project (rent and others) in the j year; m is the years of construction period; n is the years of franchise period (excluding the construction period). Affected by the service life and maintenance cost of the buildings, the franchise period n should be shorter than the average service life of the buildings T_max. Namely 0≤n≤T_max. a is the discount rate which is usually the average rate of return on investment of the private enterprises and can be obtained with reference to the industry level.

Specifically, the construction and investment cost of affordable housing mainly includes two aspects: the construction cost and the loan interest and taxes in the construction period; and the operation cost and the loan interest and taxes in the operation period. More specifically, the construction cost is mainly comprised of land cost, upfront cost, construction and installation cost, infrastructure construction cost and management cost and so on [26] and the operation cost mainly consists of the management cost and maintenance cost and so on. (1) Land cost. It mainly refers to the cost of land acquisition, demolition and resettlement at the earliest stage and the compensation according to the laws and regulations. (2) Upfront cost. It mainly refers to the cost of survey, planning, design, water, electricity and gas supply, road leveling and engineering at the earlier stage of the housing project [27]. (3) Construction and installation cost. It mainly covers the cost of water supply, heating and electrical appliances, pile foundations and a series of ancillary works. (4) Infrastructure construction cost. It refers to the cost of facilities built together with the housing in the community and includes non-business public facility expenses that cannot be transferred for compensation according to government standards. (5) Management cost. The management cost should not exceed 3% of the sum of the land cost, upfront cost, construction and installation cost and infrastructure construction cost. (6) Loan interest. Loan interest refers to the bank’s loan interest expenses incurred by the investor in raising funds for construction. (7) Taxes. It refers to the taxes and administrative charges during the development process. (8) Operation cost.

The developers of affordable housing projects will also take into account economic benefits while undertaking social responsibilities. Their returns on construction and investment not only include the current direct income but also the indirect income. The direct income from construction and investment of affordable housing includes: (1) the rent of rental-type affordable housing, the sales profits of salable affordable housing like economically affordable housing, charges over commercial facilities and services and the operation and management cost; (2) tax reduction and exemption by the governmental departments, the government’s direct subsidies and the income from corresponding cost reduction [28]. The indirect income from construction and investment of affordable housing includes: (1) the purchase of commercial land at a relatively lower price: the enterprises can invest the commercial facilities construction in the community while constructing the affordable housing and then lease or sell them to obtain returns; (2) the income from conversion of the industrial land into residential land: the enterprises constructing the affordable housing can transform their own industrial land into residential land; (3) the improvement of social impact ability and market share of the enterprises’ product. The enterprises can increase their market share and improve their brands’ social impact while undertaking the social responsibilities [29], and thus improve their popularity; (4) rapid administrative approval of the projects; (5) financing preferences: local governments or banks can provide preferential policies on financing; (6) obtainment of land development right through primary and secondary linkages: in the development process, the enterprises can obtain development rights without the need to go through bidding and auctioning procedures and can get profits from sales; (7) the income from sales of the supporting commercial buildings: the enterprises are allowed to construct a certain proportion of commercial housing in the affordable housing construction and can obtain profits through sales of the commercial housing; (8) obtainment of lower-cost land through participation in the construction of affordable housing: this reduces the land cost to a certain extent and reduces the losses of investment profits at the earlier stage.

Formula (1) is a linear programming problem. Its feasible solution requires the lowest construction cost of affordable housing. However, affordable housing is a product provided by the government to meet the housing needs of some special groups that cannot be satisfied by the market. Since it has certain public product attributes, it is impossible for the developers to infinitely reduce the construction cost and increase the sales profit. One of the basic requirements of the developers is that the net present value of the project is equal to or greater than zero (NPV≥0). Then whether a development project needs subsidies or not is decided by the final benefits: if the NPV is greater than zero (NPV > 0), then compensation is not necessary; if the NPV is smaller than zero (NPV < 0), obviously the compensation is required and the government plays the main role in compensation.

3.2 Calculation of compensation for affordable housing projects investment

In principle, the project developers should be able to recover the costs and get a reasonable return. In other words, the minimum criteria we need to meet is that NPV is equal to zero (NPV = 0). On this basis, we regarded the criteria that NPV = 0 as the target of compensation. Then we obtained the formula on compensation:

It is assumed that the rent in the j year is r_j RMB/m²*year, the annual average occupancy rate is ρ _j and the total area of the affordable housing is S, then the rent income is ρ_jr_jS. If other income is expressed as a percentage β of the rent income, then the income of the j year is R_j = (1 +β)ρ_jr_jS. In the real estate market, considering the use efficiency of the government’s financial funds, it is also required that the rent r_j in the j year should be lower than the market rent z_j, namely 0≤r_j≤z_j. The annual operating expenses of this project can be divided into two parts: the annual fixed operating expenses D_j and the annual variable operating expenses V_j. We assumed that the annual variable operating expenses are proportional to the annual occupancy rate and the proportionality coefficient is α, then the annual expenses calculation formula is: Dj = F_j + V_j = F_j +αρ_jr_jS. And the formula for calculating the government compensation is:

$\begin{matrix} \sum_{i = 1}^{m} \frac{X_{i}}{{(1 + a)}^{i}} + \sum_{j = 1}^{n} \frac{Y_{j}}{{(1 + a)}^{m + j}} \\ = \sum_{i = 1}^{m} \frac{C_{i} + M C_{i} + O T_{i}}{{(1 + a)}^{i}} - \sum_{j = 1}^{n} \frac{R_{j} - D_{j} - M D_{j} - B T_{j}}{{(1 + a)}^{m + j}} \\ = \sum_{i = 1}^{m} \frac{C_{i} + M C_{i} + O T_{i}}{{(1 + a)}^{i}} + \sum_{j = 1}^{n} \frac{B T_{j} + M D_{j} + F_{j}}{{(1 + a)}^{m + j}} \\ - \sum_{j = 1}^{n} \frac{(1 + β - α) ρ_{j} r_{j} S}{{(1 + a)}^{m + j}} \\ 0 ⩽ n ⩽ T_{max}, 0 ⩽ r_{j} ⩽ z_{j} \end{matrix}$ (3)

We can conclude from Formula (3) that the amount of government compensation is associated with C_i, MC_i, MD_j, OT_i, BT_j, ρ _j , β, α, F_j, n after determining the rent r_j. (1) In the reality, the construction cost of residential housing is directly proportional to the design plan, and the amount of government subsidies is directly proportional to the construction cost of residential housing. Therefore, the estimation of construction costs is the key for the government to subsidize the housing project. Based on the general situation, it is planned to use the average level in the market to estimate its data. (2) It can be concluded from simple analysis that the amount of government subsidies will increase with the increase of tax revenue. Conversely, the less the tax revenue is, the less the government subsidies. (3) The higher the occupancy rate, the less the government subsidies. The occupancy rate is greatly associated with the location of affordable housing, which requires the government to make a long-term plan for the development of affordable housing. However, due to the uncertainty of occupancy rate, the corresponding compensation value is also uncertain. This form of risk brought about by uncertainty can be solely borne by the developer or shared by the government. (4) The higher the other non-rent income, the less the government subsidies. β reflects the income other than rent, such as the income from sales of supporting commercial facilities. (5) The value of α measures the work efficiency and management level of the developers. For the purpose of encouraging these two abilities of the developers to the greatest extent, F_j and α should adopt the market average level when calculating the subsidies. (6) The government subsidies are inversely proportional to the franchise period. The shorter the franchise period, the more the government subsidies, and the greater the government’s financial burden. However, the enterprises can recover the investment as soon as possible, and bear smaller risks. In the case of longer franchise period, the government can make use of the business experiences of housing developers to operate the affordable housing more efficiently during this period while the enterprises face greater risks at the same time [30].

If the lessee rents the affordable housing at the actual rent and the government directly subsidizes the enterprise with the difference between the actual rent r_j and the profit rent r_sj of the enterprise, a rent subsidy mechanism is formed. Assuming that NPV = 0, then the profit rent r_sj of the enterprise can be calculated by formula 4.

$\begin{matrix} \sum_{j = 1}^{n} \frac{(1 + β - α) ρ_{j} r_{s j} S}{{(1 + a)}^{m + j}} = \sum_{i = 1}^{m} \frac{C_{i} + M C_{i} + O T_{i}}{{(1 + a)}^{i}} \\ + \sum_{j = 1}^{n} \frac{B T_{j} + M D_{j} + F_{j}}{{(1 + a)}^{m + j}} - A \end{matrix}$ (4)

It can be calculated with formula (4) that the government subsidies (A) are:

$\begin{matrix} A = \sum_{j = 1}^{n} \frac{(1 + β - α) ρ_{j} (r_{s j} - r_{j}) S}{{(1 + a)}^{m + j}} \\ = \sum_{i = 1}^{m} \frac{C_{i} + M C_{i} + O T_{i}}{{(1 + a)}^{i}} + \sum_{j = 1}^{n} \frac{B T_{j} + M D_{j} + F_{j}}{{(1 + a)}^{m + j}} \\ - \sum_{j = 1}^{n} \frac{(1 + β - α) ρ_{j} r_{j} S}{{(1 + a)}^{m + j}} \end{matrix}$ (5)

Based on the principle of reasonable returns, this study establishes an investment compensation model, quantifies all government subsidies that were difficult to calculate, and calculates the actual amount of government subsidies.

4 Results analysis and discussion

According to China’s economic development environment and industry standards, this study makes the following general settings in the calculation process of the model:

(1) The investor already has 35% of the total investment amount (description of loan conditions), and the remaining 65% is generated by the loan;

(2) The three-year loan from the bank is: 80% of the loan in the first year, 10% in the second year, and 10% in the third year.

(3) In terms of the annual interest rate, the unified rate issued by the People’s Bank of China is adopted. It is 6.15% in 2014 for the first year, 6% in 2015 for the second year and 5% in 2016 for the third year respectively.

(4) As what the developer constructs and commercially uses is public rental housing (including low-rent housing), the basic taxes except for farmland occupation tax is exempted.

(5) The loan period is three year and there is no extension of the period (and the principal is returned when the construction period expires).

(6) The loan principal will be repaid in one lump after the three-year construction period expires, and no loan interest will be incurred thereafter.

(7) The interest will be repaid every year during the construction period.

(8) Operating expenses are temporarily excluded.

(9) After completion of the construction, the occupancy rate of the residential houses and the shops will all be 100%.

(10) Except for rent, there are no other incomes from housing sales.

(11) With regard to the discount rate (return rate), it plans to adopt the average long-term lease return rate of 4.4% in Beijing.

(12) The project construction period is 3 years and the franchise period is 30 years.

The data involved in the model calculations in this study are shown in Table 1:

Table 1
Construction cost of a public rental housing project in Beijing, China

Items Cost Unit

Land cost 33698 Ten thousand RMB

Upfront cost 2610 Ten thousand RMB

Construction and installation cost 38280 Ten thousand RMB

Total land area 23176.82 Square meter

Total construction area 86953.64 Square meter

Above-ground construction area 57942.17 Square meter

Underground construction area 29011.47 Square meter

Area per household 44.68 Square meter

Total houses 1046 House

Plot ratio 2.50 %

Greening rate 30 %

Construction period 3 year

Actual rent 32 RMB/square meter

Rental of ordinary housing in the surrounding area 37 RMB/square meter

Area of supporting commercial facilities 8578.37 Square meter

Rental of supporting commercial facilities 1.77 RMB/square meter · day

Items	Cost	Unit
Land cost	33698	Ten thousand RMB
Upfront cost	2610	Ten thousand RMB
Construction and installation cost	38280	Ten thousand RMB
Total land area	23176.82	Square meter
Total construction area	86953.64	Square meter
Above-ground construction area	57942.17	Square meter
Underground construction area	29011.47	Square meter
Area per household	44.68	Square meter
Total houses	1046	House
Plot ratio	2.50	%
Greening rate	30	%
Construction period	3	year
Actual rent	32	RMB/square meter
Rental of ordinary housing in the surrounding area	37	RMB/square meter
Area of supporting commercial facilities	8578.37	Square meter
Rental of supporting commercial facilities	1.77	RMB/square meter · day

This study divides the government subsidy formula A into three parts (calculated with EXCLE and MATLAB, and the results are shown in Table 2). The three parts are the expenditure in the construction period, the expenditure in the operation period and the revenue in the operation period respectively.

Table 2

Calculation results

Description of calculation items	Value (unit: 10,000 RMB)
Part I Expenditure in the construction period	81559.22
Taxes in the construction period	53.3
First-year interest in the construction period	2385.3
Second-year interest in the construction period	2618
Third-year interest in the construction period	2424.1
Part II Expenditure in the operation period	0
Part III Revenue in the operation period	34022.14
Annual income of leased residential houses during the operation period	1794.6
Annual income of leased shops during the operation period	554.2
House sales income during the operation period	0
Total amount of subsidy A	47537.08

The calculation result of Part I $\sum_{i = 1}^{m} \frac{C_{i} + M C_{i} + O T_{i}}{{(1 + a)}^{i}} = 815, 592, 200$

The land cost, upfront cost, and construction and installation cost were regarded as the first-year cost of the construction period and thus calculated.

The construction cost during the next two years was reduced to only loan interest. The loan interest is 23,853,000 in the first year, 26,180,000 in the second year and 24,241,000 in the third year.

The calculation result of Part II $\sum_{j = 1}^{n} \frac{B T_{j} + M D_{j} + F_{j}}{{(1 + a)}^{m + j}} = 0$

Note that the operating cost has not been incurred for the time being. There is no interest calculation after the loan principal is repaid and there is no tax incurred in the case of separate rent accounting of the standard public rental housing or low-rent housing.

The calculation result of Part III $\sum_{j = 1}^{n} \frac{(1 + β - α) ρ_{j} r_{j} S}{{(1 + a)}^{m + j}} = 340, 221, 400$

In the case of assuming that the occupancy rate in general situation is 100%, the annual rent of residential public rental housing or low-rent housing is 17,946,000 RMB and the annual rent of shops is 5,542,000 RMB.

Note that only the rent of residential public rental housing (including low-rent housing) and general shops was considered when calculating the income and any form of sales was not considered.

On this basis, this study obtains that the total government subsidy amount A for the project in construction period and franchise period (totally 33 years) is 475,370,800 RMB and the annual average subsidy is 14,405,000 RMB.

Based on the realities in China, some idealized treatment was conducted in the empirical analysis. It can be observed from the calculation results that the government subsidy A is large. In general, in the development of public rental housing (including low-rent housing), there will be a series of supporting commercial properties (commercial housing, villas) for sales and other profitable supporting projects [31]. This part of income can fill the gap of government subsidies to a certain extent, thus significantly reducing the amount of government subsidies and achieving the goal of win-win between the enterprises and the government.

5 Conclusion

In the process of investing in affordable housing construction, the private sector faces the risks such as low profits and changes in supporting policies of local governments. To guarantee the benefits of the private sector during its investment in affordable housing and improve its enthusiasm in affordable housing investment, this study applies the NPV model to make up for the deficiencies of traditional research methods, and employs the data of a public rental housing in Beijing, China to verify the scientific of the model. This study draws the following conclusions:

(1) The investment behavior of affordable housing investors other than the central government, local governments, and non-profit organizations is centered on economic benefits. However, the quasi-public product attribute of affordable housing determines its low profit margin. Therefore, determining the reasonable profit rate of affordable housing developers is the key point to promote the investment in and development of affordable housing.

(2) The investment compensation model for affordable housing based on satisficing decision can objectively calculate the amount of compensation to be paid to the affordable housing developers.

(3) The private sector that invests in the affordable housing should not passively wait for the subsidies and preferential policies and measures of the government. It should actively innovate in the profit model of affordable housing so as to promote the construction and development of affordable housing.

Investment compensation mechanism for affordable housing construction is a multi-angle and multi-level complex system. This study conducts related research from the perspective of net present value of the project and is of practical significance. However, there are many issues requiring further in-depth analysis and discussion, for example, there is a stable profit model for the salable affordable housing and the investor’s capital flow can be guaranteed in this model. In order to improve the effectiveness of the research, this study only builds an investment compensation model for rental-type affordable housing. With further advancement of shanty town renovation and development of common property right, it is required to further improve the investment compensation model for affordable housing so that such model covers all types of affordable housing. This is also the future research direction so that the theoretical significance of the research fits more effectively with its practical significance.

References

Zhang

S.M.

and Lei

L.H.

, Application of BOT model in the construction of low-rent housing, Finance & Economy8 (2013), 42–54.

Von Neumann

and Morgenstern

, Theory of games and economic behavior, Princeton: Princeton University Press, (1944).

Savage

L.J.

, The foundations of statistics, New York: John Wiley & Sons, (1954).

Allais

and Hagen

, Expected utility hypotheses and the Allais paradox: contemporary discussions of decisions under uncertainty with Allais’ rejoinder, Holland: D. Reidel Publishing Company, (1979).

Ellsberg

, Risk, ambiguity and the savage axioms, Quarterly Journal of Economics75 (1961), 643–660.

Papi

, Satisficing choice procedures, Journal of Economic Behavior & Organization84 (2012), 451–462.

Akintayo

and Jagboro

G.O.

, Compensation mechanisms for minimizing private party risks in concession-based public-private partnership contracts, International Journal of Building Pathology and Adaptation36 (2018), 93–120.

Hans-Peter

, András

and Gábor

, A simple compensation mechanism for flood protection services on farmland, Land Use Policy65 (2017), 128–134.

Estelle

, Charles

and Willinger

, Choice overload, coordination and inequality: three hurdles to the effectiveness of the compensation mechanism?, Social Choice and Welfare45 (2015), 513–535.

10.

Oxley

, Supply-side subsidies for affordable rental housing, International Encyclopedia of Housing & Home81 (2012), 75–80.

11.

Chowdury

A.N.

and Charoenngam

, Factors influencing finance on IPP projects in Asia: A legal framework to reach the goal, International Journal of Project Management27 (2009), 51–58.

12.

Jaebum

, Appraisal of combined agreements in BOT project finance: Focused on minimum revenue guarantee and revenue cap agreements, International Journal of Strategic Property Management14 (2010), 139–155.

13.

Androcec

, Krajcar

and Wangensteen

, Optimization of costs and benefits in Inter TSO Compensation Mechanism. In 2011 8th International Conference on the European Energy Market (EEM), 647–652.

14.

Candel-Sánchez

, Pigouvian taxes and the Varian’s mechanism in dynamic settings, Journal of Regulatory Economics42 (2012), 39–51.

15.

Kim

, An almost Ideal Solution to the Siting Problem of Publicly Provided Indivisible Goods, International Tax and Public Finance10 (2003), 357–375.

16.

Sarvašová

, Quiroga

, Suárez

, Ali

, Lukmine

and Hrib

, Understanding the drivers for Natura payments in forests: A Heckman selection analysis, Journal for Nature Conservation46 (2018), 28–37.

17.

Saijo

, Masuda

and Yamakawa

, Approval mechanism to solve prisoner’s dilemma: comparison with Varian’s compensation mechanism, Social Choice and Welfare51 (2018), 65–77.

18.

Yang

, Government compensation mechanism of rent-type affordable housing based on PPP model. Master Dissertation, Xi’an University of Architecture and Technology, (2018).

19.

Liu

, Yuan

J.F.

and Guo

, Compensation mechanism of urban rail transit PPP project based on risk preference, Project Management Technology16 (2018), 19–25.

20.

and Feng

J.C.

, Government’s compensation mechanism for PPP project based on risk preference, Operations Research and Management Science26 (2017), 190–199.

21.

Zhang

S.Y.

, Ren

Z.T.

and Hu

, Government compensation mechanism of PPP project from the perspective of incomplete contract, Project Management Technology15 (2017), 15–19.

22.

L.Y.

, Compensation mechanism of sponge city PPP project based on performance evaluation. Master Dissertation, Chongqing Jiaotong University, (2018).

23.

Chen

X.H.

and Guo

P.H.

, The Model of government subsidies of PPP project on real option method, Soft Science30 (2016), 26–29.

24.

B.K.

, Jin

L.C.

, Wang

and Zhang

, Research of design of government compensation mechanism of assembly building based on game theory, Architecture Technology48 (2017), 835–837.

25.

Shen

J.X.

and Wang

X.H.

, The government compensation mechanism of pension PPP project based on system dynamics, Journal of Engineering Management33 (2019), 61–66.

26.

Dai

L.M.

, Xi’an JH, affordable house project’s market development pattern research, Master Dissertation, Central South University, (2012).

27.

Zhou

J.C.

, Benefits and risks of real estate enterprises’ participating in the construction of affordable housing, Shanghai Real Estate8 (2011), 20–22.

28.

Zhang

Y.Y.

and Xie

F.Q.

, The interest and main risk of real estate enterprises for their participation into the indemnificatory apartment construction project, Scientific Development11 (2011), 63–967.

29.

Jiang

R.L.

, Research of PPP model in affordable housing construction of China, Master Dissertation, Yunnan University, (2013).

30.

Zhang

, Analysis and evaluation of public rental housing policy, China Real Estate Finance7 (2011), 11–16.

31.

Cerezo-Narvaez

, Otero-Mateo

and Pastor-Fernandez

, From requirements agreement to changes integration: keys for not failing in construction projects, Dyna92 (2017), 254–254.