# An Exploratory Pledging Framework of Crowdfunding for Utilities Tunnel Engineering Project

Authors: Feng Sun; Cheng Liu
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

This paper gives an exploratory mathematical framework for crowdfunding pledging of utilities tunnel engineering project. For two typical types of “All-or-Nothing” and “Keep-it-All” platforms, it analyzes the crowdfunding process how to operate on the platforms for the project. There are four types of crowdfunding modes, and a utilities tunnel project can flexibly choose one or several crowdfunding types analyzed in this paper to improve project construction according to the status of the project. Debt crowdfunding should design rational interest payment mechanism and Macaulay duration, and equity crowdfunding should consider the backers may get dividend and capital revenue for a utilities tunnel project. Simulation analyses of debt crowdfunding and equity crowdfunding give some cases for project fulfillment. The founder of reward crowdfunding can give free or low price energy products to the backers, while the backers of donation crowdfunding are completely philanthropic to supply the pledged capital.


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## Body

## 1. Introduction

Utilities tunnel engineering projects have been built in many countries in the world now, which make up an important part for the construction of urban underground space. For the construction of utilities tunnel, electric power, water supply and drainage, gas, telecommunication, and waste pipelines are laid inside the tunnel, which transport many types of energy for the city. Canto-Perello, Curiel-Esparza, and Calvo [1] point out that a utilities tunnel is an underground structure containing one or more utilities, permitting the installation, maintenance, and removal of the systems without the necessity of making street cuts or excavations.A utilities tunnel has many advantages comparing with traditional “open-cut” style. Under traditional “open-cut” style, electric power, water supply and drainage, gas, telecommunication, and waste pipelines are usually laid underground separately. The roads need to be dug many times to complete the construction of all kinds of pipelines. When there are obstacles for the pipeline to be maintained, the roads must be dug to find the pipeline with obstacle to repair or replace with new pipeline. So, the roads are usually dug many times for “open-cut” operation, which create traffic problem and waste of time and cost. On the contrary, all kinds of pipelines are gathered into the utilities tunnel, and the roads only need to be dug once to construct the tunnel. When there are obstacles for the pipelines, the maintenance worker will enter into the tunnel and easily find the pipelines with obstacles to repair or replace with new pipelines.To construct a utilities tunnel project, the ground is usually dug deeply to build up one-way, two-way, or multi-way tunnels to lay all kinds of pipelines [2–4]. The lighting, ventilation, and supervision devices need to be set up in the tunnel, so the construction cost for a utilities tunnel is usually high. It is very important to design rational pledging style and pledging procedure for construction funds of a utilities tunnel to successfully fulfill the project.For a utilities tunnel project, many kinds of funding modes besides traditional debt funding and equity funding should be flexibly adopted to broaden funding sources according to the character of the project. Crowdfunding is an emerging project funding mode. The utilities tunnel project can make the advantage of crowdfunding mode to strengthen funding management and construction process.In crowdfunding mode, the founder posts project introduction on the crowdfunding platform, and the backer browses and chooses suitable project on the platform and supplies pledged capital during pledged period of the project [5–7]. Mollick [8] indicates that crowdfunding refers to the efforts by entrepreneurial individuals and groups (cultural, social, and for-profit) to fund their ventures by drawing on relatively small contribution from a relatively large number of individuals using the Internet, without standard financial intermediaries.Now crowdfunding mode has been used in many countries in the world, and numerous crowdfunding platforms have been built up [9–11]. The founder can choose suitable crowdfunding platform to fulfill the crowdfunding project. Kickstarter platform in the US is the largest crowdfunding platform, which permits the founder to pose crowdfunding project to pledge the fund from 2009.Now the project categories on Kickstarter platform mainly include Games, Design, Technology, Film & Video, Music, Publishing, Fashion, Food, Art, Comics, Photography, Theater, Crafts, Journalism, and Dance. Figure1 lists the numbers of crowdfunding projects of all the categories on Kickstarter platform until December, 2021, and the mean of launched projects is 36,271. The maximum of launched projects is Film & Video projects, which arrives at 79,054. The minimum of launched projects is Dance projects, which arrives at 4,383. The maximum of successfully pledged projects is 32,958 for Music projects. The minimum of successfully pledged projects is 1,408 for Journalism projects.Figure 1
The numbers of crowdfunding projects on Kickstarter platform. Launched projects refer to all projects that have ever launched on Kickstarter.Figure2 lists the numbers of total pledged capital of all the crowdfunding categories on Kickstarter platform until December, 2021, and the mean of total pledging dollars is 419.5 million dollars. The maximum of total pledging dollars is Games projects, which arrives at 1.79 billion dollars. The minimum of total pledging dollars is Dance projects, which arrives at 15.56 million dollars.Figure 2
The numbers of total pledged capital. Total pledging dollars refer to dollars pledged to all projects. Successful pledging dollars refer to pledges to successfully pledged projects, and these pledges were collected. Unsuccessful pledging dollars refer to pledges to unsuccessfully pledged projects, and these pledges were not collected.For the management of crowdfunding project on the platform, now the mainstream modes include “All-or-Nothing” and “Keep-it-All” according to the pledged status of the founder. Under “All-or-Nothing” mode, only if the pledged fund is more than pledged goal during the regulated pledging period, the founder can get the pledged fund. If the pledged fund is less than pledged goal during the regulated pledging period, the backer need not supply the fund and the founder cannot get any pledged fund. The platform mode used by Kickstarter is “All-or-Nothing”. Under “Keep-it-All” mode, whether or not the pledged fund arrives at pledged goal during the regulated pledging period, the backer must supply the fund and the founder can get the pledged fund. The platform mode used by famous Indiegogo is “Keep-it-All”. The choice between these two platform modes may affect the result and successful rate for the crowdfunding projects. Veuger [12] uses platform size, the degree of regulation and the funding models including “All-or-Nothing” and “Keep-it-All” to analyze their effect on the overall platform success rate.Crowdfunding mode has not been used with big scale in engineering field now. But because crowdfunding mode has the character of low cost and convenience, it can be flexibly used in engineering field with big scale to broaden the construction fund source for the engineering project. The first crowdfunding engineering project (Mosaic Solar House Roof) in US was built in 2011, which had 18 MW volumes and pledged 600 thousand dollars. The first photovoltaic power station for crowdfunding in China was built in early 2014, which had 1 MW volume and pledged 1.57 million dollars.During the construction process for utilities tunnel project, the construction fund with big scale is needed to timely construct the project. To improve project construction, many kinds of funding modes can be designed and their advantages can be used. Crowdfunding mode is a new type funding mode which can be used for utilities tunnel. Now crowdfunding mode has not been used for utilities tunnel project, for example, there is not crowdfunding for utilities tunnel project among fifteen categories on Kickstarter platform. Crowdfunding mode can be used for utilities tunnel project in the future. The experience of engineering project which has used crowdfunding can be referred by utilities tunnel. The advantage of crowdfunding mode can be used to improve utilities tunnel construction. In the early stage crowdfunding mode can be used in small and middle-sized utilities tunnel project, and it can be gradually used in large utilities tunnel project in the future.This paper gives an exploratory crowdfunding pledging framework for fulfillment of utilities tunnel. It analyzes four types of crowdfunding modes for utilities tunnel including debt crowdfunding, equity crowdfunding, reward crowdfunding and donation crowdfunding. For two typical types of “All-or-Nothing” and “Keep-it-All” platforms, it analyzes the crowdfunding process how to operate on the platforms for utilities tunnel project. It gives simulation analyses of crowdfunding based on debt and crowdfunding based on equity under this framework. Existing literature papers about crowdfunding mainly analyze the influence factors of crowdfunding operation, but do not give the analysis on how to operate crowdfunding for utilities tunnel project. To the best of the authors’ knowledge, this paper is the first to create a crowdfunding framework to analyze utilities tunnel funding.Just as mentioned in this paper, every crowdfunding type has its own character, which can be used to improve the construction of utilities tunnel project. Debt crowdfunding gives some interest for the capital supply of the backer, and the founder need not give management vote right of utilities tunnel project to the backer. For equity crowdfunding, the founder does not have the duty to repay the pledged capital, while may give certain amount dividend to the backer. The founder of reward crowdfunding can give some free or low price energy products conveyed by utilities tunnel project to the backer as reward. The backer of donation crowdfunding is completely philanthropic to supply the pledged capital to the utilities tunnel project for the improvement of social welfare. The utilities tunnel project can flexibly choose one or several above crowdfunding types to acquire project fund according to the status of the project. Using the mathematical framework of four types of crowdfunding analyzed in this paper, the founder and the backer can get a full understanding for the process and procedure of a utilities tunnel funding, which will promote the construction and operation for the utilities tunnel engineering project.The rest of this paper is structured as follows: Section2 analyzes debt crowdfunding for “All-or-Nothing” and “Keep-it-All” platforms, and the duration and convexity management for the utilities tunnel project. It also gives simulation analysis of crowdfunding based on debt. Section 3 analyzes equity crowdfunding with dividend and equity crowdfunding with dividend and capital revenue for utilities tunnel, and it gives simulation analysis of crowdfunding based on equity. Crowdfunding mode based on reward and crowdfunding mode based on donation are analyzed in Section 4. Section 5 concludes this paper.


## 2. Analysis of Crowdfunding Mode Based on Debt for the Utilities Tunnel Project

For a utilities tunnel project, the corridor is built at some depth underground in which water supply and drainage, electric power, telecommunication, gas, rubbish, and other pipelines are laid. The utilities tunnel is given to pipeline using units to use after project construction. So, the utilities tunnel project is a complicated integrated engineering project [13–16]. For different utilities tunnel projects, the main differences are investment amount, project scale, pipeline kinds, engineering condition, etc. The scales of utilities tunnel projects in the world are greatly different. There are some small-scale utilities tunnel projects, such as utilities tunnel of Shanghai Taopu Science and Technology Intelligence City in China whose investment is about 7.85 million dollars. There are also some utilities tunnel projects with big scale whose investments are from several hundreds of millions dollars to several billions dollars, such as the utilities tunnel project of Tokyo in Japan whose construction capital is 3.2 billion dollars. According to construction scale, project condition, operation, and other factors, suitable crowdfunding modes can be chosen to pledge capital for the utilities tunnel project. Crowdfunding modes can be flexibly used to pledge construction capital in small- and middle-sized utilities tunnel projects now.When the utilities tunnel project uses crowdfunding to pledge capital, according to the modes given by crowdfunding backers to the project, there are mainly four types of crowdfunding that can be used for the utilities tunnel funding. Comparisons among these four types of crowdfunding using the framework can improve the funding process and fulfillment effects for the utilities tunnel project.


### 2.1. Crowdfunding Based on Debt for “All-or-Nothing” and “Keep-It-All” Platforms

The first type is crowdfunding based on debt for the utilities tunnel project. Project backers supply investment capital to utilities tunnel crowdfunding, and they can get repayment of investment with certain amount interest or without interest from project revenue after the project is delivered. In some cases, the backers are interested in not only debt interest but also reputation from the project, so they admit to receive repayment of investment without interest.The crowdfunding founders of the utilities tunnel project may be organizations or individuals, while crowdfunding backers of utilities tunnel project are usually individuals. Assume during construction period, the financial capital is fromjj=1,2,…,n individuals. No. j individual invests ISj to utilities tunnel project, and the total pledged capital is(1)IS=∑j=1nISj.For utilities tunnel crowdfunding on the platform, backers usually supply pledged capital by basic units. One basic unit of pledged capital is often from several dollars to several tens of dollars. Assume one backer suppliesQSj number of basic unit φ, and then, all the backers supply total pledged capital(2)IS=∑j=1nφQSj.For a utilities tunnel project, there is usually certain pledged period for backers to supply pledged capital. The pledged period is usually between zero and three months. When founder of utilities tunnel project poses one project on the crowdfunding platform, the backers enter into the crowdfunding platform and look at the videos, photos, and words introduction for the utilities tunnel project. Wonderful videos and photos about the utilities tunnel project will attract more backers to supply the pledged capital. At the early stage of crowdfunding posing, which is usually from several days to several weeks, many backers who are interested in the utilities tunnel project will supply pledged capital. These backers often include many Tweets friends of the founder and many people who are familiar with the utilities tunnel project or very interested in the utilities tunnel project. At the next stage of crowdfunding posing, there are not usually many backers supplying the pledged capital. At the near-end stage of pledged period, there will be many backers who supply pledged capital to the utilities tunnel project again. One reason of this phenomenon is that total pledged capital at this time is usually near pledged goal, and many backers supply pledged capital for the successful fulfillment of the utilities tunnel project. Rakesh et al. [17] analyze this phenomenon of pledged capital for crowdfunding mode based on empirical data on Kickstarter platform. Kim et al. [18] find that potential donors are more likely to donate to projects, which are closer to their funding goal.For crowdfunding platform of the utilities tunnel project with “All-or-Nothing” type, if pledged capital surpasses pledged goalK, the crowdfunding of utilities tunnel will be successful. The founder of utilities tunnel crowdfunding can get pledged capital if ∑j=1nφQSj≥K. On the contrary, the founder cannot get pledged capital if ∑j=1nφQSj<K. While for crowdfunding platform of the utilities tunnel project with “Keep-it-All” type, the founder can get pledged capital whether or not ∑j=1nφQSj surpasses pledged goal K.The crowdfunding platform for utilities tunnel project will manage the crowdfunding process and pledged fund between the founder and the backers. The crowdfunding platform usually charges usage fee from crowdfunding founder. In “All-or-Nothing” type, the usage fee rate paid to platform isη to let founder of utilities tunnel crowdfunding fulfill the project. In “Keep-it-All” type, the usage fee rate paid to platform is η1 if pledged capital does not surpass pledged goal, whereas the usage fee rate paid to platform is η2 if pledged capital surpasses pledged goal, and it is often η1<η2.The platform for utilities tunnel crowdfunding with “All-or-Nothing” type can get usage fee(3)FK≡∑j=1nφQSjη.The founder for utilities tunnel crowdfunding can get pledged capital∑j=1nφQSj1−η.The usage fee paid to platform for utilities tunnel project with “Keep-it-All” type is as follows:(4)FK≡∑j=1nφQSjη1+∑j=1nφQSjη2−η1I∑j=1nφQSj≥K.The founder for utilities tunnel crowdfunding can get pledged capital∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥K. I• is indicator function. The function value is 1 if the condition ∑j=1nφQSj≥K is satisfied, while the value is 0 if the condition is not satisfied.The backers of utilities tunnel crowdfunding give pledged capital with hope of refunding the investment with some interest or without interest. The bond founder of utilities tunnel crowdfunding is usually organizations. The total value of utilities tunnel crowdfunding atTj period with bond interest rate RTSj of continuous period for “All-or-Nothing” type is as follows:(5)Kj=∑j=1nφQSj1−ηeRTSjTj.The investment revenue rate of backers for utilities tunnel crowdfunding is as follows:(6)HSj=∑j=1nφQSj1−ηeRTSjTj∑j=1nφQSj.The investment revenue rate of backers for “Keep-it-All” type is as follows:(7)HSj=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KeRTSjTj∑j=1nφQSj.After the founder for utilities tunnel crowdfunding gets the pledged capital, the utilities tunnel project will be delivered atTγD period. The founder of utilities tunnel crowdfunding will pay bond interest based on par value U to backers according to the predetermined annual interest rate Cr. Assume term to maturity is α years, maturity revenue rate is RTγ, and RTγD is delivery date discount rate.For utilities tunnel crowdfunding with “All-or-Nothing” type, the interest discount is∀U,Cr>0,∃Φ1:(8)Φ1=Cr1−1/1+RTγαRTγ.The end value discount for utilities tunnel crowdfunding is as follows:(9)Φ2=11+RTγα.The founder can get capital from the backers of crowdfunding(10)Φ3=φQSj1−η.The delivery date discount of crowdfunding bond for utilities tunnel project is as follows:(11)FSj=∑j=1nΦ3Φ1+Φ21+RTγD.The investment revenue rate for bond crowdfunding of utilities tunnel project is as follows:(12)HSj=∑j=1nΦ3Φ1+Φ21+RTγD∑j=1nφQSj.If backers of utilities tunnel crowdfunding supply pledged capital to buy bonds without interest, the delivery date discount of crowdfunding bond becomes(13)FSj=∑j=1nΦ3Φ21+RTγD.The investment revenue rate for bond crowdfunding of utilities tunnel project becomes(14)HSj=∑j=1nΦ3Φ21+RTγD∑j=1nφQSj.For utilities tunnel crowdfunding with “Keep-it-All” type, the investment revenue rate is as follows:(15)HSj=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KΦ1+Φ2∑j=1nφQSj1+RTγD.The investment revenue rate for bond crowdfunding without interest is as follows:(16)HSj=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KΦ2∑j=1nφQSj1+RTγD.When crowdfunding founder fulfills bond crowdfunding, it is necessary to take some measures to increase the investment confidence of backers [19–22]. Because backers search the Internet platform to find suitable investment projects from many platform projects, the introduction posed by founder of bond crowdfunding for the utilities tunnel project is important. Excellent videos, photos, and words will attract more backers in short time and increase the confidence of backers to acquire Cr of bond crowdfunding for the utilities tunnel project. Zhou et al. [23] find that the length, readability, and tone from the content of project descriptions and past experience and past expertise are all significantly associated with crowdfunding success.After the delivery of the utilities tunnel project, all kinds of pipeline using units will transport energy through the tunnel, and they need pay usage fee to the project, which is the main revenue of the project. In addition, in many cases the utilities tunnel project belongs to public city infrastructure goods, and the government will give certain bonus to the project. The founder of bond crowdfunding should pay interest rateCr and guarantee the backers can get HSj from project revenue and get refund of investment ∑j=1nφQSj. Good reputation of fulfillment of bond crowdfunding for one utilities tunnel will benefit the founder more chances to fulfill other utilities tunnel crowdfunding in the future.


### 2.2. The Duration and Convexity for Crowdfunding Based on Debt

Assume bond interest for the utilities tunnel project is paidV times in one year with time period Tm, and θ is the variable to count the payment times in α years.The duration investment period discount of bond crowdfunding for par value is as follows:(17)Φ4=∑θ=1αV−1θTmUCr/V21+RTγθ.The duration investment discount at the end of bond crowdfunding for par value is as follows:(18)Φ5=αTmUCr/V+11+RTγαV.The investment period discount of bond crowdfunding is as follows:(19)Φ6=∑θ=1αV−1UCr/V/1+RTγθ.The investment discount at the end of bond crowdfunding is as follows:(20)Φ7=UCr/V+11+RTγαV.The Macaulay duration for bond crowdfunding of utilities tunnel project is as follows:(21)M=Φ4+Φ5Φ6+Φ7.The convexity investment period discount of bond crowdfunding is as follows:(22)Φ8=∑θ=1αVθθ+1UCr/V/1+RTγθ+2.The convexity investment discount at the end of bond crowdfunding is as follows:(23)Φ9=αVαV+1U1+RTγαV+2.The convexity of bond crowdfunding for utilities tunnel project is as follows:(24)Cb=Φ8+Φ9.Bond crowdfunding should optimize the Macaulay duration and convexity for the utilities tunnel project. The backers of bond crowdfunding for the project want to recycle the pledged capital∑j=1nφQSj in a relatively short time, and they need a small Macaulay duration. The founder of bond crowdfunding will fulfill the operation, maintenance, and management of utilities tunnel after the delivery of project, and he/she need to choose suitable Macaulay duration to coordinate operation revenue and cost for long running of the utilities tunnel project. Suitable convexity of bond crowdfunding is also needed to improve bond price and management for the utilities tunnel project.


### 2.3. Simulation Analysis of Crowdfunding Based on Debt for Utilities Tunnel Project

Assume the financial capital is fromn=100 backers, and one backer supplies QSj=2000 numbers of basic unit φ=5 dollars. Then, the total pledged capital IS is one million dollars for the utilities tunnel project, which surpasses the pledged goal K = 0.8 million dollars. For crowdfunding platform of the utilities tunnel project with “All-or-Nothing” type, the usage fee rate is η=5%. Then, the platform can get usage fee FK=50000, and the founder of the utilities tunnel project can get pledged capital 0.95 million dollars. For different conditions of pledged capital, the investment revenue rate HSj of the backers changes, and 13 simple cases are chosen to compute the investment revenue rate. Table 1 lists statistical description of main variables of crowdfunding based on debt.Table 1
Statistical description of main variables of crowdfunding based on debt.
VariableMean (%)Standard deviationMin (%)Max (%)Interest rateCr12.150.02882318.0017.00Maturity revenue rateRTγ4.000.01825742.008.00Investment revenue rateHSj2.790.00599311.533.78Figure3 lists the average annual investment revenue rate HSj of the backers for 13 simple cases. For same delivery period TγD and same term to maturity α, the investment revenue rate is mainly decided by maturity revenue rate RTγ and annual interest rate Cr. Case 13 has maximum investment revenue rate 3.78%, and case 6 has minimum investment revenue rate 1.53%. Comparing with maturity revenue rate curve and annual interest rate curve, investment revenue rate curve is flatter, whose mean is 2.79% and standard deviation is the smallest.Figure 3
The investment revenue rateHSj of the backers of crowdfunding based on debt. 13 simple cases are chosen to compute the investment revenue rate. Cases 1–7 are that the utilities tunnel project will be delivered at TγD=2 period. To compute investment revenue rate, the different conditions of pledged capital are as follows: Case 1: U=1000, Cr=8%, α=5, and RTγ=2%; Case 2: U=1000, Cr=11%, α=5, and RTγ=3%; Case 3: U=1000, Cr=9%, α=5, and RTγ=2%; Case 4: U=1000, Cr=12%, α=5, and RTγ=4%; Case 5: U=1000, Cr=14%, α=5, and RTγ=6%; Case 6: U=1000, Cr=17%, α=5, and RTγ=8%; Case 7: U=1000, Cr=15%, α=5, and RTγ=5%. Cases 8–10 are that the utilities tunnel project will be delivered at TγD=3 period. The different conditions of pledged capital are as follows: Case 8: U=1000, Cr=9%, α=7, and RTγ=2%; Case 9: U=1000, Cr=12%, α=7, and RTγ=4%; Case 10: U=1000, Cr=15%, α=7, and RTγ=5%. Cases 11–13 are that the utilities tunnel project will be delivered at TγD=1 period. The different conditions of pledged capital are as follows: Case 11: U=1000, Cr=9%, α=3, and RTγ=2%; Case 12: U=1000, Cr=12%, α=3, and RTγ=4%; Case 13: U=1000, Cr=15%, α=3, and RTγ=5%.


## 2.1. Crowdfunding Based on Debt for “All-or-Nothing” and “Keep-It-All” Platforms

The first type is crowdfunding based on debt for the utilities tunnel project. Project backers supply investment capital to utilities tunnel crowdfunding, and they can get repayment of investment with certain amount interest or without interest from project revenue after the project is delivered. In some cases, the backers are interested in not only debt interest but also reputation from the project, so they admit to receive repayment of investment without interest.The crowdfunding founders of the utilities tunnel project may be organizations or individuals, while crowdfunding backers of utilities tunnel project are usually individuals. Assume during construction period, the financial capital is fromjj=1,2,…,n individuals. No. j individual invests ISj to utilities tunnel project, and the total pledged capital is(1)IS=∑j=1nISj.For utilities tunnel crowdfunding on the platform, backers usually supply pledged capital by basic units. One basic unit of pledged capital is often from several dollars to several tens of dollars. Assume one backer suppliesQSj number of basic unit φ, and then, all the backers supply total pledged capital(2)IS=∑j=1nφQSj.For a utilities tunnel project, there is usually certain pledged period for backers to supply pledged capital. The pledged period is usually between zero and three months. When founder of utilities tunnel project poses one project on the crowdfunding platform, the backers enter into the crowdfunding platform and look at the videos, photos, and words introduction for the utilities tunnel project. Wonderful videos and photos about the utilities tunnel project will attract more backers to supply the pledged capital. At the early stage of crowdfunding posing, which is usually from several days to several weeks, many backers who are interested in the utilities tunnel project will supply pledged capital. These backers often include many Tweets friends of the founder and many people who are familiar with the utilities tunnel project or very interested in the utilities tunnel project. At the next stage of crowdfunding posing, there are not usually many backers supplying the pledged capital. At the near-end stage of pledged period, there will be many backers who supply pledged capital to the utilities tunnel project again. One reason of this phenomenon is that total pledged capital at this time is usually near pledged goal, and many backers supply pledged capital for the successful fulfillment of the utilities tunnel project. Rakesh et al. [17] analyze this phenomenon of pledged capital for crowdfunding mode based on empirical data on Kickstarter platform. Kim et al. [18] find that potential donors are more likely to donate to projects, which are closer to their funding goal.For crowdfunding platform of the utilities tunnel project with “All-or-Nothing” type, if pledged capital surpasses pledged goalK, the crowdfunding of utilities tunnel will be successful. The founder of utilities tunnel crowdfunding can get pledged capital if ∑j=1nφQSj≥K. On the contrary, the founder cannot get pledged capital if ∑j=1nφQSj<K. While for crowdfunding platform of the utilities tunnel project with “Keep-it-All” type, the founder can get pledged capital whether or not ∑j=1nφQSj surpasses pledged goal K.The crowdfunding platform for utilities tunnel project will manage the crowdfunding process and pledged fund between the founder and the backers. The crowdfunding platform usually charges usage fee from crowdfunding founder. In “All-or-Nothing” type, the usage fee rate paid to platform isη to let founder of utilities tunnel crowdfunding fulfill the project. In “Keep-it-All” type, the usage fee rate paid to platform is η1 if pledged capital does not surpass pledged goal, whereas the usage fee rate paid to platform is η2 if pledged capital surpasses pledged goal, and it is often η1<η2.The platform for utilities tunnel crowdfunding with “All-or-Nothing” type can get usage fee(3)FK≡∑j=1nφQSjη.The founder for utilities tunnel crowdfunding can get pledged capital∑j=1nφQSj1−η.The usage fee paid to platform for utilities tunnel project with “Keep-it-All” type is as follows:(4)FK≡∑j=1nφQSjη1+∑j=1nφQSjη2−η1I∑j=1nφQSj≥K.The founder for utilities tunnel crowdfunding can get pledged capital∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥K. I• is indicator function. The function value is 1 if the condition ∑j=1nφQSj≥K is satisfied, while the value is 0 if the condition is not satisfied.The backers of utilities tunnel crowdfunding give pledged capital with hope of refunding the investment with some interest or without interest. The bond founder of utilities tunnel crowdfunding is usually organizations. The total value of utilities tunnel crowdfunding atTj period with bond interest rate RTSj of continuous period for “All-or-Nothing” type is as follows:(5)Kj=∑j=1nφQSj1−ηeRTSjTj.The investment revenue rate of backers for utilities tunnel crowdfunding is as follows:(6)HSj=∑j=1nφQSj1−ηeRTSjTj∑j=1nφQSj.The investment revenue rate of backers for “Keep-it-All” type is as follows:(7)HSj=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KeRTSjTj∑j=1nφQSj.After the founder for utilities tunnel crowdfunding gets the pledged capital, the utilities tunnel project will be delivered atTγD period. The founder of utilities tunnel crowdfunding will pay bond interest based on par value U to backers according to the predetermined annual interest rate Cr. Assume term to maturity is α years, maturity revenue rate is RTγ, and RTγD is delivery date discount rate.For utilities tunnel crowdfunding with “All-or-Nothing” type, the interest discount is∀U,Cr>0,∃Φ1:(8)Φ1=Cr1−1/1+RTγαRTγ.The end value discount for utilities tunnel crowdfunding is as follows:(9)Φ2=11+RTγα.The founder can get capital from the backers of crowdfunding(10)Φ3=φQSj1−η.The delivery date discount of crowdfunding bond for utilities tunnel project is as follows:(11)FSj=∑j=1nΦ3Φ1+Φ21+RTγD.The investment revenue rate for bond crowdfunding of utilities tunnel project is as follows:(12)HSj=∑j=1nΦ3Φ1+Φ21+RTγD∑j=1nφQSj.If backers of utilities tunnel crowdfunding supply pledged capital to buy bonds without interest, the delivery date discount of crowdfunding bond becomes(13)FSj=∑j=1nΦ3Φ21+RTγD.The investment revenue rate for bond crowdfunding of utilities tunnel project becomes(14)HSj=∑j=1nΦ3Φ21+RTγD∑j=1nφQSj.For utilities tunnel crowdfunding with “Keep-it-All” type, the investment revenue rate is as follows:(15)HSj=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KΦ1+Φ2∑j=1nφQSj1+RTγD.The investment revenue rate for bond crowdfunding without interest is as follows:(16)HSj=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KΦ2∑j=1nφQSj1+RTγD.When crowdfunding founder fulfills bond crowdfunding, it is necessary to take some measures to increase the investment confidence of backers [19–22]. Because backers search the Internet platform to find suitable investment projects from many platform projects, the introduction posed by founder of bond crowdfunding for the utilities tunnel project is important. Excellent videos, photos, and words will attract more backers in short time and increase the confidence of backers to acquire Cr of bond crowdfunding for the utilities tunnel project. Zhou et al. [23] find that the length, readability, and tone from the content of project descriptions and past experience and past expertise are all significantly associated with crowdfunding success.After the delivery of the utilities tunnel project, all kinds of pipeline using units will transport energy through the tunnel, and they need pay usage fee to the project, which is the main revenue of the project. In addition, in many cases the utilities tunnel project belongs to public city infrastructure goods, and the government will give certain bonus to the project. The founder of bond crowdfunding should pay interest rateCr and guarantee the backers can get HSj from project revenue and get refund of investment ∑j=1nφQSj. Good reputation of fulfillment of bond crowdfunding for one utilities tunnel will benefit the founder more chances to fulfill other utilities tunnel crowdfunding in the future.


## 2.2. The Duration and Convexity for Crowdfunding Based on Debt

Assume bond interest for the utilities tunnel project is paidV times in one year with time period Tm, and θ is the variable to count the payment times in α years.The duration investment period discount of bond crowdfunding for par value is as follows:(17)Φ4=∑θ=1αV−1θTmUCr/V21+RTγθ.The duration investment discount at the end of bond crowdfunding for par value is as follows:(18)Φ5=αTmUCr/V+11+RTγαV.The investment period discount of bond crowdfunding is as follows:(19)Φ6=∑θ=1αV−1UCr/V/1+RTγθ.The investment discount at the end of bond crowdfunding is as follows:(20)Φ7=UCr/V+11+RTγαV.The Macaulay duration for bond crowdfunding of utilities tunnel project is as follows:(21)M=Φ4+Φ5Φ6+Φ7.The convexity investment period discount of bond crowdfunding is as follows:(22)Φ8=∑θ=1αVθθ+1UCr/V/1+RTγθ+2.The convexity investment discount at the end of bond crowdfunding is as follows:(23)Φ9=αVαV+1U1+RTγαV+2.The convexity of bond crowdfunding for utilities tunnel project is as follows:(24)Cb=Φ8+Φ9.Bond crowdfunding should optimize the Macaulay duration and convexity for the utilities tunnel project. The backers of bond crowdfunding for the project want to recycle the pledged capital∑j=1nφQSj in a relatively short time, and they need a small Macaulay duration. The founder of bond crowdfunding will fulfill the operation, maintenance, and management of utilities tunnel after the delivery of project, and he/she need to choose suitable Macaulay duration to coordinate operation revenue and cost for long running of the utilities tunnel project. Suitable convexity of bond crowdfunding is also needed to improve bond price and management for the utilities tunnel project.


## 2.3. Simulation Analysis of Crowdfunding Based on Debt for Utilities Tunnel Project

Assume the financial capital is fromn=100 backers, and one backer supplies QSj=2000 numbers of basic unit φ=5 dollars. Then, the total pledged capital IS is one million dollars for the utilities tunnel project, which surpasses the pledged goal K = 0.8 million dollars. For crowdfunding platform of the utilities tunnel project with “All-or-Nothing” type, the usage fee rate is η=5%. Then, the platform can get usage fee FK=50000, and the founder of the utilities tunnel project can get pledged capital 0.95 million dollars. For different conditions of pledged capital, the investment revenue rate HSj of the backers changes, and 13 simple cases are chosen to compute the investment revenue rate. Table 1 lists statistical description of main variables of crowdfunding based on debt.Table 1
Statistical description of main variables of crowdfunding based on debt.
VariableMean (%)Standard deviationMin (%)Max (%)Interest rateCr12.150.02882318.0017.00Maturity revenue rateRTγ4.000.01825742.008.00Investment revenue rateHSj2.790.00599311.533.78Figure3 lists the average annual investment revenue rate HSj of the backers for 13 simple cases. For same delivery period TγD and same term to maturity α, the investment revenue rate is mainly decided by maturity revenue rate RTγ and annual interest rate Cr. Case 13 has maximum investment revenue rate 3.78%, and case 6 has minimum investment revenue rate 1.53%. Comparing with maturity revenue rate curve and annual interest rate curve, investment revenue rate curve is flatter, whose mean is 2.79% and standard deviation is the smallest.Figure 3
The investment revenue rateHSj of the backers of crowdfunding based on debt. 13 simple cases are chosen to compute the investment revenue rate. Cases 1–7 are that the utilities tunnel project will be delivered at TγD=2 period. To compute investment revenue rate, the different conditions of pledged capital are as follows: Case 1: U=1000, Cr=8%, α=5, and RTγ=2%; Case 2: U=1000, Cr=11%, α=5, and RTγ=3%; Case 3: U=1000, Cr=9%, α=5, and RTγ=2%; Case 4: U=1000, Cr=12%, α=5, and RTγ=4%; Case 5: U=1000, Cr=14%, α=5, and RTγ=6%; Case 6: U=1000, Cr=17%, α=5, and RTγ=8%; Case 7: U=1000, Cr=15%, α=5, and RTγ=5%. Cases 8–10 are that the utilities tunnel project will be delivered at TγD=3 period. The different conditions of pledged capital are as follows: Case 8: U=1000, Cr=9%, α=7, and RTγ=2%; Case 9: U=1000, Cr=12%, α=7, and RTγ=4%; Case 10: U=1000, Cr=15%, α=7, and RTγ=5%. Cases 11–13 are that the utilities tunnel project will be delivered at TγD=1 period. The different conditions of pledged capital are as follows: Case 11: U=1000, Cr=9%, α=3, and RTγ=2%; Case 12: U=1000, Cr=12%, α=3, and RTγ=4%; Case 13: U=1000, Cr=15%, α=3, and RTγ=5%.


## 3. Analysis of Crowdfunding Mode Based on Equity for the Utilities Tunnel Project

The second type is crowdfunding based on stock. Project backers for utilities tunnel as investors supply equity investment to crowdfunding project, and project founder does not have the duty to repay the pledged capital, while it may give certain amount dividend to backers, which comes from the profit after the delivery of project. The backers of debt crowdfunding mainly acquire fixed interest revenue from crowdfunding investment, while the backers of equity crowdfunding mainly acquire changeable dividend, capital revenue, and management vote right. The founder of equity crowdfunding for utilities tunnel is organizations, while the backers of utilities tunnel crowdfunding are usually individuals. This kind of crowdfunding company is usually not listed company.Ahlers et al. [24] give a definition that equity crowdfunding is a method of financing whereby an entrepreneur sells equity or equity-like shares in a company to a group of small investors through an open call for funding on Internet-based platforms. Walker [25] points out that equity crowdfunding is the process whereby people invest in an early-stage, unlisted company in exchange for shares in that company. Butticè and Vismara [26] compare equity crowdfunding with traditional sources of entrepreneurial finance and find that the online dimension of equity crowdfunding offerings reduces the costs for entrepreneurial ventures to raise funds.Because of the special character of equity crowdfunding, the cases for equity crowdfunding fulfillment are different in different countries. Some countries permit to operate equity crowdfunding projects on crowdfunding platform, while other countries do not permit to operate equity crowdfunding projects on crowdfunding platform now. There are still some countries that permit to give profit shares to the backers of equity crowdfunding project, but prohibit giving vote rights to the backers of equity crowdfunding project. Pekmezovic and Walker [27] point out that business angels refrain from buying common shares without voting rights, which tend to be common in crowdfunding. Crowdfunding investors do not participate on the boards of crowdfunded firms, and owing to small equity stakes, they may lack the necessary incentives to participate in the monitoring of the internal governance of the invested firms.The tendency of equity crowdfunding is that it grows rapidly as legal barriers are being relaxed in many countries [24]. In 2015, Malaysia became the first Asia-Pacific country legislating equity crowdfunding, with six platforms approved [25].


### 3.1. Equity Crowdfunding with Dividend for the Utilities Tunnel Project

The backers of equity crowdfunding for the utilities tunnel project supply pledged stock capital without the aim of refunding this investment capital. They can get dividend from project revenue according to dividend rategD for stock par value U and can take part in the management decisions for utilities tunnel crowdfunding. If founder of equity crowdfunding for utilities tunnel project believes this project will have good prospect and strong profit acquiring ability, the founder can regulate the issuing price Sp>U. If founder of equity crowdfunding for utilities tunnel project thinks it is better to give certain discount to the backers of equity crowdfunding to acquire pledged goal K timely, the founder can regulate the issuing price Sp<U. Assume the founder regulates the issuing price Sp=U for simplicity of analysis.The dividend discount at delivery date for par value of equity crowdfunding is as follows:(25)DSj=UgDRTγ1+RTγD.The dividend paid toSj backer of equity crowdfunding for utilities tunnel project with “All-or-Nothing” type is as follows:(26)Φ10=φQSj1−ηgD.The discount rate at delivery date of equity crowdfunding is as follows:(27)Φ11=RTγ1+RTγD.The backers of equity crowdfunding for the utilities tunnel project can get dividend(28)DS=∑j=1nΦ10Φ11.The revenue rate of equity crowdfunding backers for the utilities tunnel project is as follows:(29)HS=∑j=1nΦ10Φ11∑j=1nφQSj.The backers of equity crowdfunding for the utilities tunnel project with “Keep-it-All” type can get dividend(30)DS=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KgDΦ11.The revenue rate of equity crowdfunding backers for utilities tunnel project becomes(31)HS=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KgD∑j=1nφQSjΦ11.If the utilities tunnel project has strong profit acquiring ability, the dividend is assumed to increase atgl rate. The dividend discount at delivery date for par value of equity crowdfunding becomes(32)DSj=UgDRTγ−gl1+RTγD.The dividend discount rate of equity crowdfunding is as follows:(33)Φ12=RTγ−gl1+RTγD.The dividend acquired by the backers of equity crowdfunding for the utilities tunnel project with “All-or-Nothing” type becomes(34)DS=∑j=1nΦ10Φ12.The investment revenue rate of the backers of equity crowdfunding for the utilities tunnel project becomes(35)HS=∑j=1nΦ10Φ12∑j=1nφQSj.The dividend acquired by the backers of equity crowdfunding for the utilities tunnel project with “Keep-it-All” type becomes(36)DS=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KgDΦ12.The investment revenue rate of the backers of equity crowdfunding becomes(37)HS=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KgD∑j=1nφQSjΦ12.


### 3.2. Equity Crowdfunding with Dividend and Capital Revenue for the Utilities Tunnel Project

If the backers of equity crowdfunding for the utilities tunnel project sell the stocks at priceSt at π period, they will get capital revenue for equity crowdfunding. The dividend at delivery date for par value of j backer is (πSj is the period j backer sells the stocks) as follows:(38)DSj=UgD1−1/1+RTγπSjΦ11.The backers of equity crowdfunding for the utilities tunnel project with “All-or-Nothing” type can get dividend(39)DS=∑j=1nΦ101−1/1+RTγπSjΦ11.The discount rate of capital revenue of par value for equity crowdfunding is as follows:(40)Φ13=1+RTγπSj1+RTγD.The capital revenue of backers for equity crowdfunding is (Stj is stock price that j backer sells the stocks) as follows:(41)CS=∑j=1nΦ3Stj−UUΦ13.The investment revenue rate of the backers of equity crowdfunding is as follows:(42)HS=DS+CS∑j=1nφQSj.The backers of equity crowdfunding for the utilities tunnel project with “Keep-it-All” type can get dividend(43)DS=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥K1−1/1+RTγπSjgDΦ11.The capital revenue of backers for equity crowdfunding becomes(44)CS=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KStj−UUΦ13.The investment revenue rate of backers for equity crowdfunding becomes(45)HS=DS+CS∑j=1nφQSj.If the utilities tunnel project has strong profit acquiring ability, the dividend is assumed to increase atgl rate. The j backer of equity crowdfunding can get dividend(46)DSj=UgD1−1+gl/1+RTγπSjΦ12.The total dividend of the backers for equity crowdfunding with “All-or-Nothing” type becomes(47)DS1=∑j=1nΦ101−1+gl/1+RTγπSjΦ12.The capital revenue of the backers for equity crowdfunding is as follows:(48)CS=∑j=1nΦ3Stj−UUΦ13.The investment revenue rate of the backers for equity crowdfunding becomes(49)HS=DS1+CS∑j=1nφQSj.The total dividend of the backers for equity crowdfunding with “Keep-it-All” type becomes(50)DS1=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥K1−1+gl/1+RTγπSjgDΦ12.The capital revenue of the backers for equity crowdfunding becomes(51)CS=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KStj−UUΦ13.The investment revenue rate of the backers for equity crowdfunding becomes(52)HS=DS1+CS∑j=1nφQSj.Whether “All-or-Nothing” type or “Keep-it-All” type for equity crowdfunding of the utilities tunnel project, the founder should pay dividendDSDS1 to backers from project revenue, which can increase the confidence of backers for the utilities tunnel project. If the utilities tunnel project has good revenue at operation period, the founder can increase the dividend rate gD to backers [28–30].


### 3.3. Simulation Analysis of Crowdfunding Based on Equity for the Utilities Tunnel Project

Assume the financial capital is fromn=100 backers, and one backer supplies QSj=2000 numbers of basic unit φ=5 dollars. Then, the total pledged capital IS is one million dollars for the utilities tunnel project, which surpasses the pledged goal K=0.8 million dollars. For crowdfunding platform of the utilities tunnel project with “All-or-Nothing” type, the usage fee rate is η=5%. Then, the platform can get usage fee FK=50000, and the founder of utilities tunnel project can get pledged capital 0.95 million dollars. Assume the backers hold the stock of the utilities tunnel project for unlimited period and no consideration of capital revenue, and the project gives dividend to the backers according to fixed dividend rate gD. 12 simple cases are chosen to compute the investment revenue rate HS. Table 2 lists statistical description of main variables of crowdfunding based on equity.Table 2
Statistical description of main variables of crowdfunding based on equity.
VariableMeanStandard deviationMinMaxDividend rategD7.00%0.01651455.00%9.00%Maturity revenue rateRTγ3.75%0.01544792.00%6.00%Investment revenue rateHS1.8540.68121451.0642.767Figure4 lists the total investment revenue rate HS of the backers in holding period for 12 simple cases. For same delivery period RTγD, the investment revenue rate is mainly decided by maturity revenue rate RTγ and dividend rate gD. Case 10 has maximum investment revenue rate 2.767 times, and Case 8 has minimum investment revenue rate 1.064 times. Comparing with maturity revenue rate curve and dividend rate curve, investment revenue rate curve is steeper, whose mean is 1.854 times and standard deviation is the biggest.Figure 4
The investment revenue rateHS of the backers of crowdfunding based on equity. 12 simple cases are chosen to compute the investment revenue rate. Cases 1–4 are that the utilities tunnel project will be delivered at RTγD=2 period. To compute investment revenue rate, the different conditions of pledged capital are as follows: Case 1: U=10, gD=5%, and RTγ=2%; Case 2: U=10, gD=8%, and RTγ=6%; Case 3: U=10, gD=6%, and RTγ=4%; Case 4: U=10, gD=9%, and RTγ=3%. Cases 5–8 are that the utilities tunnel project will be delivered at RTγD=3 period. The different conditions of pledged capital are as follows: Case 5: U=10, gD=6%, and RTγ=4%; Case 6: U=10, gD=5%, and RTγ=2%; Case 7: U=10, gD=9%, and RTγ=3%; Case 8: U=10, gD=8%, and RTγ=6%. Cases 9–12 are that the utilities tunnel project will be delivered at RTγD=1 period. The different conditions of pledged capital are as follows: Case 9: U=10, gD=6%, and RTγ=4%; Case 10: U=10, gD=9%, and RTγ=3%; Case 11: U=10, gD=8%, and RTγ=6%; Case 12: U=10, gD=5%, and RTγ=2%.


## 3.1. Equity Crowdfunding with Dividend for the Utilities Tunnel Project

The backers of equity crowdfunding for the utilities tunnel project supply pledged stock capital without the aim of refunding this investment capital. They can get dividend from project revenue according to dividend rategD for stock par value U and can take part in the management decisions for utilities tunnel crowdfunding. If founder of equity crowdfunding for utilities tunnel project believes this project will have good prospect and strong profit acquiring ability, the founder can regulate the issuing price Sp>U. If founder of equity crowdfunding for utilities tunnel project thinks it is better to give certain discount to the backers of equity crowdfunding to acquire pledged goal K timely, the founder can regulate the issuing price Sp<U. Assume the founder regulates the issuing price Sp=U for simplicity of analysis.The dividend discount at delivery date for par value of equity crowdfunding is as follows:(25)DSj=UgDRTγ1+RTγD.The dividend paid toSj backer of equity crowdfunding for utilities tunnel project with “All-or-Nothing” type is as follows:(26)Φ10=φQSj1−ηgD.The discount rate at delivery date of equity crowdfunding is as follows:(27)Φ11=RTγ1+RTγD.The backers of equity crowdfunding for the utilities tunnel project can get dividend(28)DS=∑j=1nΦ10Φ11.The revenue rate of equity crowdfunding backers for the utilities tunnel project is as follows:(29)HS=∑j=1nΦ10Φ11∑j=1nφQSj.The backers of equity crowdfunding for the utilities tunnel project with “Keep-it-All” type can get dividend(30)DS=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KgDΦ11.The revenue rate of equity crowdfunding backers for utilities tunnel project becomes(31)HS=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KgD∑j=1nφQSjΦ11.If the utilities tunnel project has strong profit acquiring ability, the dividend is assumed to increase atgl rate. The dividend discount at delivery date for par value of equity crowdfunding becomes(32)DSj=UgDRTγ−gl1+RTγD.The dividend discount rate of equity crowdfunding is as follows:(33)Φ12=RTγ−gl1+RTγD.The dividend acquired by the backers of equity crowdfunding for the utilities tunnel project with “All-or-Nothing” type becomes(34)DS=∑j=1nΦ10Φ12.The investment revenue rate of the backers of equity crowdfunding for the utilities tunnel project becomes(35)HS=∑j=1nΦ10Φ12∑j=1nφQSj.The dividend acquired by the backers of equity crowdfunding for the utilities tunnel project with “Keep-it-All” type becomes(36)DS=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KgDΦ12.The investment revenue rate of the backers of equity crowdfunding becomes(37)HS=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KgD∑j=1nφQSjΦ12.


## 3.2. Equity Crowdfunding with Dividend and Capital Revenue for the Utilities Tunnel Project

If the backers of equity crowdfunding for the utilities tunnel project sell the stocks at priceSt at π period, they will get capital revenue for equity crowdfunding. The dividend at delivery date for par value of j backer is (πSj is the period j backer sells the stocks) as follows:(38)DSj=UgD1−1/1+RTγπSjΦ11.The backers of equity crowdfunding for the utilities tunnel project with “All-or-Nothing” type can get dividend(39)DS=∑j=1nΦ101−1/1+RTγπSjΦ11.The discount rate of capital revenue of par value for equity crowdfunding is as follows:(40)Φ13=1+RTγπSj1+RTγD.The capital revenue of backers for equity crowdfunding is (Stj is stock price that j backer sells the stocks) as follows:(41)CS=∑j=1nΦ3Stj−UUΦ13.The investment revenue rate of the backers of equity crowdfunding is as follows:(42)HS=DS+CS∑j=1nφQSj.The backers of equity crowdfunding for the utilities tunnel project with “Keep-it-All” type can get dividend(43)DS=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥K1−1/1+RTγπSjgDΦ11.The capital revenue of backers for equity crowdfunding becomes(44)CS=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KStj−UUΦ13.The investment revenue rate of backers for equity crowdfunding becomes(45)HS=DS+CS∑j=1nφQSj.If the utilities tunnel project has strong profit acquiring ability, the dividend is assumed to increase atgl rate. The j backer of equity crowdfunding can get dividend(46)DSj=UgD1−1+gl/1+RTγπSjΦ12.The total dividend of the backers for equity crowdfunding with “All-or-Nothing” type becomes(47)DS1=∑j=1nΦ101−1+gl/1+RTγπSjΦ12.The capital revenue of the backers for equity crowdfunding is as follows:(48)CS=∑j=1nΦ3Stj−UUΦ13.The investment revenue rate of the backers for equity crowdfunding becomes(49)HS=DS1+CS∑j=1nφQSj.The total dividend of the backers for equity crowdfunding with “Keep-it-All” type becomes(50)DS1=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥K1−1+gl/1+RTγπSjgDΦ12.The capital revenue of the backers for equity crowdfunding becomes(51)CS=∑j=1nφQSj1−η1+∑j=1nφQSjη1−η2I∑j=1nφQSj≥KStj−UUΦ13.The investment revenue rate of the backers for equity crowdfunding becomes(52)HS=DS1+CS∑j=1nφQSj.Whether “All-or-Nothing” type or “Keep-it-All” type for equity crowdfunding of the utilities tunnel project, the founder should pay dividendDSDS1 to backers from project revenue, which can increase the confidence of backers for the utilities tunnel project. If the utilities tunnel project has good revenue at operation period, the founder can increase the dividend rate gD to backers [28–30].


## 3.3. Simulation Analysis of Crowdfunding Based on Equity for the Utilities Tunnel Project

Assume the financial capital is fromn=100 backers, and one backer supplies QSj=2000 numbers of basic unit φ=5 dollars. Then, the total pledged capital IS is one million dollars for the utilities tunnel project, which surpasses the pledged goal K=0.8 million dollars. For crowdfunding platform of the utilities tunnel project with “All-or-Nothing” type, the usage fee rate is η=5%. Then, the platform can get usage fee FK=50000, and the founder of utilities tunnel project can get pledged capital 0.95 million dollars. Assume the backers hold the stock of the utilities tunnel project for unlimited period and no consideration of capital revenue, and the project gives dividend to the backers according to fixed dividend rate gD. 12 simple cases are chosen to compute the investment revenue rate HS. Table 2 lists statistical description of main variables of crowdfunding based on equity.Table 2
Statistical description of main variables of crowdfunding based on equity.
VariableMeanStandard deviationMinMaxDividend rategD7.00%0.01651455.00%9.00%Maturity revenue rateRTγ3.75%0.01544792.00%6.00%Investment revenue rateHS1.8540.68121451.0642.767Figure4 lists the total investment revenue rate HS of the backers in holding period for 12 simple cases. For same delivery period RTγD, the investment revenue rate is mainly decided by maturity revenue rate RTγ and dividend rate gD. Case 10 has maximum investment revenue rate 2.767 times, and Case 8 has minimum investment revenue rate 1.064 times. Comparing with maturity revenue rate curve and dividend rate curve, investment revenue rate curve is steeper, whose mean is 1.854 times and standard deviation is the biggest.Figure 4
The investment revenue rateHS of the backers of crowdfunding based on equity. 12 simple cases are chosen to compute the investment revenue rate. Cases 1–4 are that the utilities tunnel project will be delivered at RTγD=2 period. To compute investment revenue rate, the different conditions of pledged capital are as follows: Case 1: U=10, gD=5%, and RTγ=2%; Case 2: U=10, gD=8%, and RTγ=6%; Case 3: U=10, gD=6%, and RTγ=4%; Case 4: U=10, gD=9%, and RTγ=3%. Cases 5–8 are that the utilities tunnel project will be delivered at RTγD=3 period. The different conditions of pledged capital are as follows: Case 5: U=10, gD=6%, and RTγ=4%; Case 6: U=10, gD=5%, and RTγ=2%; Case 7: U=10, gD=9%, and RTγ=3%; Case 8: U=10, gD=8%, and RTγ=6%. Cases 9–12 are that the utilities tunnel project will be delivered at RTγD=1 period. The different conditions of pledged capital are as follows: Case 9: U=10, gD=6%, and RTγ=4%; Case 10: U=10, gD=9%, and RTγ=3%; Case 11: U=10, gD=8%, and RTγ=6%; Case 12: U=10, gD=5%, and RTγ=2%.


## 4. Analysis of Crowdfunding Mode Based on Reward and Crowdfunding Mode Based on Donation for the Utilities Tunnel Project

Debt crowdfunding and equity crowdfunding are two typical crowdfunding modes for the utilities tunnel project. In addition to these two types, there are other two types of crowdfunding for the utilities tunnel project.


### 4.1. Crowdfunding Mode Based on Reward for the Utilities Tunnel Project

The third type is crowdfunding based on reward for the utilities tunnel project. The project backers supply pledged capital∑j=1nφQSj to the project with the requirement of some noncash rewards after the delivery of project. In some cases, this reward may be a project product, which is supplied to backers after the delivery of project. In other cases, this reward may be reputation compensated to backer; for example, the backer’s name is listed in the crowdfunding film. When the utilities tunnel project uses crowdfunding mode to pledge the capital, the founder of crowdfunding for utilities tunnel project can give some products to the backers of crowdfunding. Read [31] explains nonprofits (no cash return) is more successful than other crowdfunding styles and nonprofits could do better by using physical rewards to express how the funds were allocated.Utilities tunnel project is a complicated large-scale engineering, and many pipelines are laid inside the corridors. These infrastructure pipelines are necessary for people to live and work in cities, and the important role of utilities tunnel is to transport energy to the people in cities. The main users of utilities tunnel are pipeline using units. To arrive at pledged goalK through crowdfunding mode, pipeline using units can give free energy products or low price energy products to backers of crowdfunding after the delivery of the utilities tunnel project. The backers of reward crowdfunding for the utilities tunnel project supply pledged capital ∑j=1nφQSj to the crowdfunding project, and the founder has not the duty to refund the pledged capital to backers. The crowdfunding founder of the utilities tunnel project can give future products to backers as reward.Assume pipeline using units giveςς=1,2…m free energy products or low price energy products to backers for reward crowdfunding. The energy product price Pς is continuous function of utilities tunnel demand QT:(53)Pς=fςQT.The discount rate of energy product isdςφ;Pς for ς energy product price Pςdςφ;Pς∈0,1. dςφ;Pς=1 means pipeline using units give free ς energy product to backers of reward crowdfunding.The energy product pricePς is satisfied with(54)dPςQT≡μςtPςQTdt+δςtPςQTdBWS.μςt and δςt are mean and standard deviation of energy product price PςQT at time t. BWS is satisfied with stochastic process of standard Brown motion.The variation of energy product pricePς is usually not independent, and energy product prices of stochastic time series among different periods are autocorrelated. The autoregressive time series for energy product price ARp is satisfied with(55)PςQTt=β0+β1PςQTt−1+β2PςQTt−2+⋯+βpPςQTt−p+ες,t.Energy product pricePς is usually a process of martingale, and stochastic error term ες,t is not white noise.(56)EPςQTt|PςQTt−1,PςQTt−2,…PςQTt−p=PςQTt−1.The first-order lag term of energy product pricePς is as follows:(57)PςQTt−1=β0+β1PςQTt−2+β2PςQTt−3+⋯+βpPςQTt−p−1+ες,t−1.The first differentiation term of energy product pricePς is as follows:(58)ΔPςQTt=β1ΔPςQTt−1+β2ΔPςQTt−2+β3ΔPςQTt−3+⋯+βPΔPςQT+t−pΔες,t.The first differentiation term of energy product pricePς is usually without unit root and becomes stationary time series, and this differentiation makes Pς be a stationary martingale process.Assume pipeline using units give free or low price energy products to backers of reward crowdfunding forλλ=1,2,…q years. The reward for backers of crowdfunding at λ year with “All-or-Nothing” type is as follows:(59)DEλ=∑j=1n∑ς=1mEPςQTdςφ;PςQSj1−η|λ.For∀Pς, ∃f1• probability density function, which produces the expectation of energy product price Pς for utilities tunnel at λ year, is as follows:(60)EPςQTλ=∫0PUPςQTf1PςQTdPςQT|λ.The variance of energy product pricePς for utilities tunnel at λ year is as follows:(61)VPςQTλ=EPςQT−∫0PUPςQTf1PςQTdPςQT2|.λThe reward for backers of crowdfunding for utilities tunnel project is as follows:(62)Φ14=∑λ=1qDEλ1+RTγλ1+RTγD.The reward divided by investment for crowdfunding backers is as follows:(63)RE=Φ14∑j=1nφQSj.The reward for backers of crowdfunding atλ year with “Keep-it-All” type is as follows:(64)DEλ′=∑ς=1mEPςQTdςφ;Pς∑j=1nQSj1−η1+∑j=1nQSjη1−η2I∑j=1nφQSj≥K|λ.The reward for crowdfunding backers of the utilities tunnel project becomes(65)Φ15=∑λ=1qDEλ′1+RTγλ1+RTγD.The reward divided by investment for crowdfunding backers becomes(66)RE=Φ15∑j=1nφQSj.


### 4.2. Crowdfunding Mode Based on Donation for the Utilities Tunnel Project

The fourth type is crowdfunding based on donation for the utilities tunnel project. The backers of this kind of crowdfunding are completely philanthropic to supply the pledged capital to the utilities tunnel project. They need not any reward for the supply of pledged capital. Because the utilities tunnel project transports important energy to the people in the cities, the fulfillment of utilities tunnel project will be beneficial for people to live and work in cities. Many backers supply free pledged capital to crowdfunding for the utilities tunnel project based on this point.Assume there arej1j1=1,2,…,n1 donation backers and j2j2=1,2,…,n2 bond backers of crowdfunding for utilities tunnel project. The total pledged capital for donation backers and bond backers is as follows:(67)Φ16=∑j1=1n1φQSj1+∑j2=1n2φQSj2.For crowdfunding with “All-or-Nothing” type, the founder of crowdfunding can get pledged capital(68)ID=Φ161−η.The ratio of bond revenue with interest divided by pledged capital for utilities tunnel project is as follows:(69)RB=∑j2=1n2φQSj21−ηΦ1+Φ21+RTγDΦ16.The ratio of bond revenue without interest divided by pledged capital is as follows:(70)RB=∑j2=1n2φQSj21−ηΦ21+RTγDΦ16.For crowdfunding with “Keep-it-All” type, the founder of crowdfunding can get pledged capital(71)ID=Φ161−η1+Φ16η1−η2IΦ16≥K.The ratio of bond revenue with interest divided by pledged capital becomes(72)RB=∑j2=1n2φQSj21−η1+∑j2=1n2φQSj2η1−η2IΦ16≥KΦ1+Φ21+RTγDΦ16.The ratio of bond revenue without interest divided by pledged capital becomes(73)RB=∑j2=1n2φQSj21−η1+∑j2=1n2φQSj2η1−η2IΦ16≥KΦ21+RTγDΦ16.


## 4.1. Crowdfunding Mode Based on Reward for the Utilities Tunnel Project

The third type is crowdfunding based on reward for the utilities tunnel project. The project backers supply pledged capital∑j=1nφQSj to the project with the requirement of some noncash rewards after the delivery of project. In some cases, this reward may be a project product, which is supplied to backers after the delivery of project. In other cases, this reward may be reputation compensated to backer; for example, the backer’s name is listed in the crowdfunding film. When the utilities tunnel project uses crowdfunding mode to pledge the capital, the founder of crowdfunding for utilities tunnel project can give some products to the backers of crowdfunding. Read [31] explains nonprofits (no cash return) is more successful than other crowdfunding styles and nonprofits could do better by using physical rewards to express how the funds were allocated.Utilities tunnel project is a complicated large-scale engineering, and many pipelines are laid inside the corridors. These infrastructure pipelines are necessary for people to live and work in cities, and the important role of utilities tunnel is to transport energy to the people in cities. The main users of utilities tunnel are pipeline using units. To arrive at pledged goalK through crowdfunding mode, pipeline using units can give free energy products or low price energy products to backers of crowdfunding after the delivery of the utilities tunnel project. The backers of reward crowdfunding for the utilities tunnel project supply pledged capital ∑j=1nφQSj to the crowdfunding project, and the founder has not the duty to refund the pledged capital to backers. The crowdfunding founder of the utilities tunnel project can give future products to backers as reward.Assume pipeline using units giveςς=1,2…m free energy products or low price energy products to backers for reward crowdfunding. The energy product price Pς is continuous function of utilities tunnel demand QT:(53)Pς=fςQT.The discount rate of energy product isdςφ;Pς for ς energy product price Pςdςφ;Pς∈0,1. dςφ;Pς=1 means pipeline using units give free ς energy product to backers of reward crowdfunding.The energy product pricePς is satisfied with(54)dPςQT≡μςtPςQTdt+δςtPςQTdBWS.μςt and δςt are mean and standard deviation of energy product price PςQT at time t. BWS is satisfied with stochastic process of standard Brown motion.The variation of energy product pricePς is usually not independent, and energy product prices of stochastic time series among different periods are autocorrelated. The autoregressive time series for energy product price ARp is satisfied with(55)PςQTt=β0+β1PςQTt−1+β2PςQTt−2+⋯+βpPςQTt−p+ες,t.Energy product pricePς is usually a process of martingale, and stochastic error term ες,t is not white noise.(56)EPςQTt|PςQTt−1,PςQTt−2,…PςQTt−p=PςQTt−1.The first-order lag term of energy product pricePς is as follows:(57)PςQTt−1=β0+β1PςQTt−2+β2PςQTt−3+⋯+βpPςQTt−p−1+ες,t−1.The first differentiation term of energy product pricePς is as follows:(58)ΔPςQTt=β1ΔPςQTt−1+β2ΔPςQTt−2+β3ΔPςQTt−3+⋯+βPΔPςQT+t−pΔες,t.The first differentiation term of energy product pricePς is usually without unit root and becomes stationary time series, and this differentiation makes Pς be a stationary martingale process.Assume pipeline using units give free or low price energy products to backers of reward crowdfunding forλλ=1,2,…q years. The reward for backers of crowdfunding at λ year with “All-or-Nothing” type is as follows:(59)DEλ=∑j=1n∑ς=1mEPςQTdςφ;PςQSj1−η|λ.For∀Pς, ∃f1• probability density function, which produces the expectation of energy product price Pς for utilities tunnel at λ year, is as follows:(60)EPςQTλ=∫0PUPςQTf1PςQTdPςQT|λ.The variance of energy product pricePς for utilities tunnel at λ year is as follows:(61)VPςQTλ=EPςQT−∫0PUPςQTf1PςQTdPςQT2|.λThe reward for backers of crowdfunding for utilities tunnel project is as follows:(62)Φ14=∑λ=1qDEλ1+RTγλ1+RTγD.The reward divided by investment for crowdfunding backers is as follows:(63)RE=Φ14∑j=1nφQSj.The reward for backers of crowdfunding atλ year with “Keep-it-All” type is as follows:(64)DEλ′=∑ς=1mEPςQTdςφ;Pς∑j=1nQSj1−η1+∑j=1nQSjη1−η2I∑j=1nφQSj≥K|λ.The reward for crowdfunding backers of the utilities tunnel project becomes(65)Φ15=∑λ=1qDEλ′1+RTγλ1+RTγD.The reward divided by investment for crowdfunding backers becomes(66)RE=Φ15∑j=1nφQSj.


## 4.2. Crowdfunding Mode Based on Donation for the Utilities Tunnel Project

The fourth type is crowdfunding based on donation for the utilities tunnel project. The backers of this kind of crowdfunding are completely philanthropic to supply the pledged capital to the utilities tunnel project. They need not any reward for the supply of pledged capital. Because the utilities tunnel project transports important energy to the people in the cities, the fulfillment of utilities tunnel project will be beneficial for people to live and work in cities. Many backers supply free pledged capital to crowdfunding for the utilities tunnel project based on this point.Assume there arej1j1=1,2,…,n1 donation backers and j2j2=1,2,…,n2 bond backers of crowdfunding for utilities tunnel project. The total pledged capital for donation backers and bond backers is as follows:(67)Φ16=∑j1=1n1φQSj1+∑j2=1n2φQSj2.For crowdfunding with “All-or-Nothing” type, the founder of crowdfunding can get pledged capital(68)ID=Φ161−η.The ratio of bond revenue with interest divided by pledged capital for utilities tunnel project is as follows:(69)RB=∑j2=1n2φQSj21−ηΦ1+Φ21+RTγDΦ16.The ratio of bond revenue without interest divided by pledged capital is as follows:(70)RB=∑j2=1n2φQSj21−ηΦ21+RTγDΦ16.For crowdfunding with “Keep-it-All” type, the founder of crowdfunding can get pledged capital(71)ID=Φ161−η1+Φ16η1−η2IΦ16≥K.The ratio of bond revenue with interest divided by pledged capital becomes(72)RB=∑j2=1n2φQSj21−η1+∑j2=1n2φQSj2η1−η2IΦ16≥KΦ1+Φ21+RTγDΦ16.The ratio of bond revenue without interest divided by pledged capital becomes(73)RB=∑j2=1n2φQSj21−η1+∑j2=1n2φQSj2η1−η2IΦ16≥KΦ21+RTγDΦ16.


## 5. Conclusions

This paper uses an exploratory pledging framework of crowdfunding to analyze the mode, procedure, and management for the utilities tunnel project. For Kickstarter as the largest crowdfunding platform in the world, this paper analyzes the status of 15 categories for crowdfunding projects. To the number of launched projects on the platform, the maximum is Film & Video projects, while the minimum is Dance projects. For the two types of “All-or-Nothing” and “Keep-it-All” crowdfunding platforms, the process and management among debt crowdfunding, equity crowdfunding, reward crowdfunding, and donation crowdfunding should be differentiated. Simulation analysis of crowdfunding based on debt shows that comparing with maturity revenue rate curve and annual interest rate curve, average annual investment revenue rate curve is flatter. Simulation analysis of crowdfunding based on equity shows that comparing with maturity revenue rate curve and dividend rate curve, the total investment revenue rate curve is steeper.Flexible choice and usage of these four types of crowdfunding modes will decrease pledged time and increase pledged efficiency for the utilities tunnel project. Because there are not empirical crowdfunding data for utilities tunnel, quantitative empirical analysis on crowdfunding for utilities tunnel is impossible now. The future research can consider quantitative analysis after acquiring crowdfunding data for utilities tunnel, such as the analysis on the influence factors for the success rate of utilities tunnel crowdfunding.



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*Source: 4658454-2022-04-18.xml*