Investment Timing Analysis of Hydrogen-Refueling Stations and the Case of China: Independent or Co-Operative Investment?

Abstract

The investment in hydrogen-refueling stations (HRS) is key to the development of a hydrogen economy. This paper focuses on the decision-making for potential investors faced with the thought-provoking question of when the optimal timing to invest in HRS is. To fill the gap that exists due to the fact that few studies explain why HRS investment timing is critical, we expound that earlier investment in HRS could induce the first mover advantages of the technology diffusion theory. Additionally, differently from the previous research that only considered that HRS investment is just made by one individual firm, we innovatively examine the HRS co-investment made by two different firms. Accordingly, we compare these two optional investment modes and determine which is better considering either independent investment or co-operative investment. We then explore how the optimal HRS investment timing could be figured out under conditions of uncertainty with the real options approach. Given the Chinese HRS case under the condition of demand uncertainty, the hydrogen demand required for triggering investment is viewed as the proxy for investment timing. Based on analytical and numerical results, we conclude that one-firm independent investment is better than two-firm cooperative investment to develop HRS, not only in terms of the earlier investment timing but also in terms of the attribute for dealing with the uncertainty. Finally, we offer recommendations including stabilizing the hydrogen demand for decreasing uncertainty, and accelerating firms’ innovation from both technological and strategic perspectives in order to ensure firms can make HRS investments on their own.

1. Introduction

As a clean and efficient energy carrier, hydrogen can be widely used in the transportation sector [1,2]. The utilization of fuel cell vehicles (FCVs) is the key to the future decarbonization of the automobile industry, an alternative option to reduce externalities related to fossil fuels [3]. A major bottleneck in the wide adoption and market attractiveness of hydrogen vehicles is the low availability of hydrogen-refueling stations (HRSs) [4], which will lead to “hydrogenation anxiety” [5]. FCVs and HRSs are like complementary goods, depicting a causal loop relationship with a reinforcing feedback impact. This loop now is running in a negative direction, represented by the “chicken-and-egg” dilemma; without sufficient HRS, no one invests in hydrogen vehicles using the new fuel, and without sufficient FCV customers for the fuel, no one invests in hydrogen infrastructure [6]. Fortunately, the negative causal loop due to the “chicken-and-egg” problem could be reversed to a positive direction [7,8].

Available infrastructure is crucial in the early technology life cycle of hydrogen vehicles, as infrastructure is the first element of each historical transport system to have for obtaining a new alternative transportation fuel [9]. Therefore, to address this hurdle, a supporting network of HRS is required for commercializing FCVs, which calls for large-scale investment in HRS [10]. Efforts for accelerating HRS investment are ongoing towards greater economies of scale and reaching a self-sustaining business case [11]. The investment in new technologies is a significant component for firms’ strategies, because the adoption of new technologies is generally irreversible and the timing of acquiring a new technology is critical for a firm. It can be risky for early investment, but noteworthy comparative advantages also accompany this [12]. Nevertheless, firms are unwilling to commit to the investment in HRS because of the immature industry standards, high costs and uncertain payoffs [13]. It is risky for firms to invest huge capital in HRS without the expected growth of hydrogen demands and assured profits [14]. Potential investors face the dilemma of investing now, or waiting until a better thenvestment condition comes [15].

When firms consider the appropriate investment appraisal, classic evaluation techniques of discounted cash flows (DCF), represented by net present value (NPV) criterion, are usually used. Nevertheless, without considering extra uncertainties associated with future payoffs, the NPV approach sees the investment as a now-or-never chance [16]. This would underestimate the value of the real asset due to the neglect of the option to postpone an investment for the sake of acquiring more information on how market and technological conditions develop [17]. Therefore, the rule of NPV of “invest as the value per unit of capital is at or larger than its installation cost” should be adjusted [18]. As a result, the integration of uncertainty and irreversibility into energy project investments calls for sophisticated wait-and-see strategies [19]. Facing the uncertain circumstance, investment decision-making can be viewed as an option to exercise now, or to delay for better opportunities. That is, firms have the right to invest but are not obligated, making it feasible to find out the optimal investment timing [20]. The real options approach allows the estimation of the optimal investment timing and enables the integration of uncertain factors [21], which is the analogy between financial and real asset investments, providing the firm with the ability to hold an option [22]. Specifically, the real options approach considers a sequence of decision timings over an investment horizon. The decision-maker determines whether to invest, or to delay and hold the option to invest later at each decision timing [23]. In terms of energy investments, once the investment is initiated, it exercises the option and the investment cost sunk. The real options framework is a viable tool for dealing with managerial flexibilities in the presence of uncertainties and is widely acknowledged in evaluations for the energy projects [24]. Empirical evidence also indicates that actual investment decisions are consistent with the real option theory [25,26].

With regard to the investment strategy to be studied in this paper, we explore the timing of HRS installation. According to the technological diffusion theory [27], the diffusion and adoption of HRS projects by energy firms take time. The timing evaluation of HRS investment is critical as climate targets are explicitly tied to given time scales [28]. Firstly, the earlier roll-out in a HRS project takes place, the larger the impact on decarbonization in the transportation sector [9]. Secondly, the achievement of the hydrogen economy target depends on enough early investment in infrastructure for technological development and market creation [29]. Additionally, earlier roll-out in HRS will offer the first mover and competitive advantages to relevant actors and implies an advanced emission peak [30]. The ambition of being a technological precursor, showing environmental awareness, and pursuing competitive first-mover advantages over other competitors would make firms interested in being early adopters of investment in HRS. Additionally, social benefits are derived from network externalities associated with the increased in HRS [31]. Under such conditions, adopters higher in the adoption order receive greater returns than do firms lower in the order of adoption [32]. Further, greater economies of scale achieved through capacity expansion can internalize the external costs of fuel purchase hence offering a higher profit to the first mover [30,33].

The investment appraisal of a HRS project roughly fits the real options application because HRS investment involves several uncertainties, such as the dynamic hydrogen demand [34], a changeable hydrogen price [35], unclear governmental incentives [8,36], etc. These factors which can impact profitability are intertwined, making it difficult for firms to make optimal investment decisions [37]. Moreover, there will be a possibility of co-operation between firms in terms of HRS investment [38,39]. That is, HRS investment can be achieved whether through independent investment or co-operative investment between different actors (e.g., fuel suppliers and technology providers), generating more managerial flexibilities [40]. Therefore, the real options approach is suitable for HRS investment evaluation. A strand of the literature is focused on the project appraisal of hydrogen production projects through real options. From the perspective of wind-to-hydrogen, Biggins et al. [41] evaluated the values of investing in green hydrogen production on wind farms. The authors depicted the evolution of future hydrogen prices and found that considering options to delay could increase the expected value of electrolyzer investment. Kroniger and Madlener [42] explored the economics of wind power generation integrated into hydrogen storage projects by converting excess electricity into hydrogen through electrolyzers. They calculated the impacts of uncertain wind speeds, spot market electricity prices and uncertainty in the minute reserve capacity on investment value. Schmitz and Madlener [43] also calculated the real option value of a wind-to-hydrogen project considering the uncertainties of compressed air price, hydrogen price and storage cost. Xue et al. [44] evaluated wind–hydrogen storage projects from the perspective of compound real options, proving that operational flexibility would increase the economic value. Yang et al. [45] deduced the optimal investment timing and corresponding optimal investment capacity of a power-to-hydrogen (P2G) project. The results showed that the impact of electricity price fluctuations on the value of P2G projects was greater. When the uncertainty of operating costs was high, choosing to delay the investment was a better choice. Botterud et al. [46] simulated the fluctuation of hydrogen and electricity prices and evaluated the investment feasibility of different nuclear hydrogen production technologies. Gharieh et al. [47] appraised hydrogen tri-generation for wastewater treatment plants, determined the optimal investment timing through a compound real option approach, and analyzed the sensitivity of investment decisions to random variable parameters. The results showed that delayed investment became more valuable as the volatility of the variable increased.

As for the project appraisal of hydrogen infrastructure, Boomen et al. [48] used compound real options to evaluate the hydrogen pipeline network, and determined the optimal expansion strategy under uncertain demand conditions. The authors found that phased pipeline expansion that considered option value minimized risks. Benthem [49] adopted real options theory to calculate the investment value and optimal timing of the commercialization of FCVs. The authors viewed the project as a call option, and found that the optimal investment timing depended on the maturity of the technology. Li et al. [50] evaluated the optimal investment strategy for HRS. The authors integrated the generalized Bass model from technology diffusion theory into an N-phase compound real options framework to conduct a case study of the deployment of HRS. They concluded that the interaction between HRS availability and the speed of adoption needed to be considered to avoid suboptimal decisions. Engelen et al. [51] used knock-out barrier options to study investment in HRS by considering the sudden ceasing of investment due to uncertainties such as the sudden termination of governmental incentives.

In summary, the investment appraisal of hydrogen-based projects has been studied using the real options approach. To the best of our knowledge, however, there is scant research investigating HRS investment timing building upon real options frameworks. Additionally, the previous literature has another two main knowledge gaps. First, in addition to independent investment by one firm, inter-firm co-operation in HRS investment is the case. However, the previous literature has not distinguished different characteristics between these two investment models. No study has considered this type of co-operation model in HRS investment and the entry timing of a cooperative investment was ignored. Second, our recent research [13] explored the development of HRS based on the case of China and found that the potential investors would finally invest, but did not provide the specific timing for triggering investment.

Accordingly, the main contribution of this study is threefold; (i) we explain why it is critical to prompt potential investors to invest in HRS earlier from perspectives of technology diffusion theory. Differently from our recent study on HRS development [13] that failed to present when the appropriate time to kickstart HRS investment was, this paper improves it by concentrating on potential investors’ decision-making on their investment entry timing. (ii) Additionally, since co-operation is not reflected in the standard real options approach, this is accordingly the first study to explore HRS investment in the co-operative mode in addition to the commonly independent mode, and determine which the optimal investment mode for earlier HRS investment is. (iii) The present study is the first to use the Chinese case to provide firms with the answer to which the better investment model is and when the optimal investment timing is, by considering the hydrogen demand required for triggering HRS investment as the indicator.

This paper tries to answer two highly pertinent questions: (i) When do firms optimally invest in HRS given the uncertainties on the demand side? (ii) How is entry timing affected by the investment mode considering either independent or co-operative investment? Based on the above research questions, the aim of this paper is to develop a feasible decision-making framework of HRS investment; that is, a framework for how to determine the optimal HRS investment timing for decision-makers. In addition to figuring out the demand threshold triggering investment, two investment models of either independent investment or co-operative investment are analyzed, and we compare these two feasible investment modes and find out which is the better one in terms of the timing of the exercise of the investment option. Additionally, we use the real Chinese case for numerical analysis, in order to present how the real options framework works. We expect to assist potential investors with better decisions on HRS investment.

The remainder of this paper is organized as follows. Section 2 presents the real options framework. Section 3 describes a case study. Section 4 presents the conclusions.

2. Methods

2.1. The Basic Set-Up

Hydrogen demand at the pump from HRS is modeled as the uncertainty. The reasons why the demand instead of the price is chosen as the uncertainty are threefold: (i) It is consistent with real cases in China (http://www.gov.cn/zhengce/zhengceku/2020-10/22/content_5553246.htm, accessed on 16 September 2020), where the hydrogen price set by the local government of Chinese hydrogen pilot cites is seen as relatively stable. (ii) The hydrogen fuel market is in its infancy, and the unstable end user demand would cause the uncertainty [8]. (iii) The demand factor has been set as the uncertainty in previous research [52,53,54,55]. Additionally, on the one hand, there are not so many FCVs now on the road and the hydrogen demand can increase as the industry progresses. On the other hand, with a possible hydrogen shortage in one region, the demand for hydrogen may also show a downward trend (https://www.yicai.com/news/100990916.html, accessed on 16 September 2020). Therefore, HRS investment evaluation needs to reflect a change in hydrogen demand over time as it is shortsighted to invest in HRSs by merely building upon the current demand and it is also inefficient to instantly construct enough HRSs to meet the expected long-run demand [56].

Accordingly, the threshold of hydrogen demand at the pump is chosen to be the indicator of the trigger for HRS investment [57]. Specifically, in the terminology of options theory, the option value of waiting to invest implies an action threshold where the expected value from investing exceeds the cost. That is, at the threshold, the cost of waiting outweighs the benefit of waiting, and it becomes optimal to exercise the investment option, and thereby acquire the value of the project by incurring the sunk cost of investment. Hence, HRS investment decision-making is viewed as an optimal stopping time problem, whereby the optimal timing of incurring a sunk investment cost needs to be determined in order to maximize the expected net payoff of HRS investment. The decision rule is that the investment will not be triggered until the hydrogen demand is higher than its threshold as influenced by the option value of waiting, with the first passage time when the actual demand is above the threshold, this being the optimal investment timing [58]. In this section, we explore the threshold of hydrogen demand for the optimal investment timing under two different scenarios; that is, the independent investment scenario and co-operative investment scenario. We can determine the demand threshold from our following dynamic programming analysis using the value-matching and smooth-pasting conditions. Moreover, we use the data from Chinese hydrogen pilot cities to form a case study.

By allowing for uncertainty, the demand $Q_t$ is assumed to follow a continuous stochastic process called geometric Brownian motion (GBM) which is the standard setting widely used in real options models as a good approximation for uncertainty [21]. The GBM process of demand is as follows:

$$d{Q}_t=\mu Q_{t}dt+\sigma Q_{t}d{z}_t$$

(1)

where $\mu$ is the drift of the hydrogen demand reflecting the expected growth rate, $\sigma$ is the volatility of the hydrogen demand, and $d{z}_t$ is the standard increment of a Wiener process.

Once the investment in HRS is activated, the project cash flow is generated as follows [13]:

$$V_t=(p+s-c)Q_t$$

(2)

where $p$ is the hydrogen retail price per unit (kg), $s$ is the operation subsidy per kg, and c is the operation cost per kg. The profit flow of the HRS project is certain initially at time zero, but its future path becomes uncertain over time. We assume that the potential investor is risk-neutral, and the expected present value of the investment at the generic time t > 0 is as follows (we assume infinite operations for simplicity):

$$\Pi (Q_t)=E\left[{\int }_t^{\infty }V\left(s\right)e^{-r\left(s-t\right)}ds\right]=\frac{V_t}{r-\mu }$$

(3)

where $E[\dots ]$ denotes the expectations operator, and $r$ is the discount rate.

2.2. Independent Investment from One Firm

Under this scenario, we assume that one energy firm can independently complete the whole investment in HRS on its own. Suppose that the firm solely holds the investment option and will obtain the value of $\Pi$ through expending the investment cost $I$. Building upon the rule of real options approach, the firm needs to decide when to invest. That is, it should postpone the investment until the demand is greater than its optimal threshold, $Q_1^{*}$, where we define the corresponding optimal investment timing as ${\tau }_1^{*}=inf\left(t\ge 0\mid Q_t\ge Q_1^{*}\right)$ [59].

The value of the option to invest in HRS is as follows:

$$F\left(Q\right)=\underset{\tau \ge \mathrm{t}}{\max }E\left[\left(\Pi \left(Q_{\tau }\right)-I\right)e^{-r\left(\tau -t\right)}\right]$$

(4)

According to the Ito’s Lemma,

$$\frac{1}{2}{\sigma }^2{Q}^2{F}^{″}\left(Q\right)+\mu Q{F}^{\prime }\left(Q\right)-rF=0$$

(5)

Additionally, $F\left(Q\right)$ also satisfies the following boundary conditions [57]:

$$F\left(0\right)=0$$

(6)

$$F\left(Q_1^{*}\right)=\frac{(p+s-c)Q_1^{*}}{r-\mu }-I$$

(7)

$$F^{\prime }\left(Q_1^{*}\right)=\frac{p+s-c}{r-\mu }$$

(8)

If the demand is zero, then the value of operating the HRS is negative. Hence, the value of the option to invest is supposed to be zero because this would be optimal for waiting. This accounts for Equation (6). Equation (7) means that the value of the investment option must equal the net value obtained by exercising it, which is called the value-matching condition. Equation (8) is called the smooth-pasting condition which is obtained by calculating the derivative of Equation (7).

The general solution to Equation (5) is as follows:

$$F\left(Q_t\right)=A_1{Q}_t^{{\beta }_1}+A_2{Q}_t^{{\beta }_2}$$

(9)

where $A_1$ and $A_2$ are constants to be determined, and ${\beta }_1$ and ${\beta }_2$ are the roots of the the so-called quadratic equation shown as follows [60]:

$$\frac{1}{2}{\sigma }^2\beta \left(\beta -1\right)+\mu \beta -r=0$$

(10)

where ${\beta }_1=\frac{1}{2}-\frac{\mu }{{\sigma }^2}+\sqrt{{\left(\frac{\mu }{{\sigma }^2}-\frac{1}{2}\right)}^2+\frac{2r}{{\sigma }^2}}>1,{\beta }_2=\frac{1}{2}-\frac{\mu }{{\sigma }^2}-\sqrt{{\left(\frac{\mu }{{\sigma }^2}-\frac{1}{2}\right)}^2+\frac{2r}{{\sigma }^2}}<0$. In our problem, the boundary condition (6) implies that $A_2=0$. Thus, $F\left(Q_t\right)=A_1{Q}_t^{{\beta }_1}$.

At last, the $A_1$ and the threshold $Q_1^{*}$ can be obtained by substituting $F\left(Q_t\right)=A_1{Q}_t^{{\beta }_1}$ into Equations (7) and (8):

$$Q_1^{*}=\frac{{\beta }_1}{{\beta }_1-1}\frac{\left(r-\mu \right)I}{p+s-c}$$

(11)

and $A_1=\frac{\frac{(p+s-c)Q_1^{*}}{r-\mu }-I}{{Q_1^{*}}^{{\beta }_1}}$.

To sum up, the value of the option to invest is as follows:

$$F\left(Q_t\right)=\left\{\begin{array}{c}\left(\frac{I}{\beta -1}\right){\left(\frac{Q_t}{Q_1^{*}}\right)}^{{\beta }_1}{Q}_t<Q_1^{*}\\ \frac{(p+s-c)Q_1^{*}}{r-\mu }-I{Q}_t\ge Q_1^{*}\end{array}\right.$$

(12)

When the threshold of the demand is not reached, and the hydrogen demand is so low that it is disadvantageous to invest immediately; that is when $Q_t<Q_1^{*}$ [61]. Further, the positivity of $F\left(Q_t\right)=\left(\frac{I}{\beta -1}\right){\left(\frac{Q_t}{Q_1^{*}}\right)}^{{\beta }_1}$ guarantees that the firm will indeed undertake the investment once $Q_1^{*}$ is reached [62].

2.3. Co-Operative Investment by Two Firms

The managerial decisions on investing in new technologies are characterized by risk and irreversibility, which are often beyond the resources a single firm possesses [63]. Accordingly, an investment partner is frequently sought as partnerships would reduce investment costs and risks to some extent. In this scenario, we assume that the investment in HRS has to depend on the co-operation between two firms for technological reasons [64]. For example, the energy firm is the hydrogen fuel supplier, and the equipment firm is the dispenser provider. This setting fits real-life examples. Specifically, the energy firms are actively prompted to pursue having a leading role in the hydrogen industry (for instance, the China Petrochemical Corporation is striving to become the biggest HRS operator in China; see http://www.sinopecgroup.com.cn/group/xwzx/gsyw/20210426/news_20210426_371789179787.shtml, accessed on 26 April 2021). However, it might be insufficient for energy firms alone to commence HRS investment as they do not possess all indispensable resources such as the equipment of a hydrogen fuel dispenser (for instance, the Censtar is a company specially engaged in providing complete equipment solutions and provided hydrogen fuel dispensers for the new HRS invested in by the China Petrochemical Corporation; see https://mp.weixin.qq.com/s/8z0K5uITIQ_68kHL97tYcg (accessed on 26 April 2021) and https://news.bjx.com.cn/html/20211118/1188876.shtml (accessed on 26 April 2021)), so they need to cooperate with equipment providers in order to construct HRS. Another possible case is that energy firms plan to install hydrogen dispensers in existing gasoline stations [65]. This kind of hybrid gasoline–hydrogen refueling station has the benefits of saving unnecessarily additional costs of land and labor and unreasonable site selection [66]. Thus, if energy firms want to construct but do not possess their own gasoline stations, they need to seek co-operation by reaching an agreement with gasoline station operators [29]. Therefore, as for one energy firm that decides to invest in HRS but cannot accomplish it independently, a feasible solution required is to rely on another firm for co-operation [36].

Considering that HRS investment involves the co-operation between two participants, we assume firm $\mathcal{A}$ to be the HRS promoter that undertakes the investment and generates direct benefits from the investment, while firm $\mathcal{B}$ is the one with complementary resources for HRS construction that reaches joint agreements (such as cost-sharing and profit-sharing contracts [67,68]) with firm $\mathcal{A}$. Assume that $\mathcal{B}$ cooperates by sharing a portion of investment cost for $\mathcal{A}$, with the coefficient being $\omega \in \left(0,1\right)$. In return. $\mathcal{B}$ claims a share of investment benefits from $\mathcal{A}$, with the coefficient being $\delta \in \left(0,1\right)$. Therefore, the investment value at time $\tau$ of the two firms are as follows:

$${\mathcal{H}}_{\mathcal{A}}\left(\tau \right)=(1-\delta )\frac{(p+s-c)Q_{\tau }}{r-\mu }-(1-\omega )I$$

(13)

$${\mathcal{H}}_{\mathcal{B}}\left(\tau \right)=\delta \frac{(p+s-c)Q_{\tau }}{r-\mu }-\omega I$$

(14)

In this co-operative setting, we consider that $\mathcal{A}$ decides the optimal timing to exercise the option to invest, and the rule of benefit sharing is decided by $\mathcal{B}$. The threshold of the hydrogen demand and the benefit sharing coefficient can be obtained via backward induction. For any profit sharing coefficient, $\delta$, that $\mathcal{B}$ may claim, the investment threshold chosen by $\mathcal{A}$ is obtained through an analogy of Equation (11) which is as follows:

$$Q_2^{*}(\delta )=\frac{{\beta }_1}{{\beta }_1-1}\frac{1-\delta }{1-\omega }\frac{\left(r-\mu \right)I}{p+s-c}$$

(15)

thee optimal investment timing for $\mathcal{A}$ is ${\tau }_2^{*}=inf\left\{t\ge 0\mid Q_t\ge Q_2^{*}\left(\delta \right)\right\}$.

After $\mathcal{A}$ exercises the investment option, $\mathcal{B}$ will choose ${\delta }^{*}$ for maximizing its expected present value by solving the following problem,

$$\underset{\delta \in \left(\mathrm{0,1}\right)}{\max }E\left[\left(\frac{\delta (p+s-c)Q_2^{*}\left(\delta \right)}{r-\alpha }-\omega I\right)e^{-r{{\tau }_2}^{*}}\right]$$

(16)

which can be rewritten as follows [69]:

$$\underset{\delta \in \left(\mathrm{0,1}\right)}{\mathit{max}}\left[\frac{\delta (p+s-c)Q_2^{*}\left(\delta \right)}{r-\alpha }-\omega I\right]{\left[\frac{Q_t}{Q_2^{*}\left(\delta \right)}\right]}^{{\beta }_1}$$

(17)

By solving the first-order condition of Equation (17), that is,

$$\frac{\partial }{\partial {\delta }^{*}}\left[\frac{{\delta }^{*}(p+s-c)Q_2^{*}\left({\delta }^{*}\right)}{r-\alpha }-\omega I\right]{\left[\frac{Q_t}{Q_2^{*}\left({\delta }^{*}\right)}\right]}^{{\beta }_1}=0$$

(18)

we can obtain ${\delta }^{*}=\frac{\beta \omega -2\omega +1}{\beta -\omega }$. By substituting the value of ${\delta }^{*}$ into Equation (15), we obtain the threshold of the hydrogen demand in the case of co-operative investment:

$$Q_2^{*}=\frac{{\beta }_1}{{\beta }_1-1}\frac{{\beta }_1-\omega }{{\beta }_1-1}\frac{\left(r-\mu \right)I}{p+s-c}$$

(19)

In other words, there is an optimum investment rule for HRS: invest instantly if the hydrogen demand at the pump is at or beyond the threshold value $Q_1^{*}$ under an independent scenario or $Q_2^{*}$ under a co-operative scenario, and wait otherwise. Considering the fact that investment co-operation between firms might be more complex than the that in the two-firm case, we also extend the benchmark two-firm cooperative scenario to a more general case, an n-firm co-operation case, which is shown in Appendix A for interested readers.

3. Case Study

3.1. Numerical Example of One Chinese Hydrogen Pilot City

In this subsection, numerical examples are presented based on the analytical solutions derived above. We derive the real case and relevant data from Ref. [13] to present the optimal investment timing of HRS in one Chinese hydrogen pilot city, Foshan, Guangdong province. In addition to its available data, Foshan is the city in China with the largest-scale hydrogen industry and relatively good financial incentives. We assume one energy firm in Foshan City will build a HRS with a filling capacity of 350 kg/day [70]. Additionally, the HRS is assumed to operate at full capacity daily and to be used 300 days per year (https://www.china5e.com/news/news-1053982-1.html, accessed on 26 April 2021). According to the current policy, the hydrogen price, $p$, at the pump needs to be set at 35 CNY/kg (http://www.gov.cn/zhengce/zhengceku/2020-10/22/content_5553246.htm, accessed on 26 April 2021), the operation subsidy, $s$, is 18 CNY/kg (http://www.china-hydrogen.org/?newslist-bzjqz/12390.html, accessed on 26 April 2021), the operation cost, $c$, is 19 CNY/kg (https://www.in-en.com/article/html/energy-2304402.shtml, accessed on 26 April 2021), and the investment cost, $I$, for each HRS is 15.5 million CNY (http://www.china-h2.org/details.aspx?newsId=44302&firtCatgoryId=9&newsCatgoeyId=17, accessed on 26 April 2021). The cost sharing coefficient, $\omega$, under the condition of co-operative investment by two firms can be set according to the actual situation; that is, how much of the cost that each firm contributes to the total cost considering their respective resources. We set $\omega$ to be 0.8 to reflect that firm $\mathcal{B}$ provides core resources such as dispenser equipment or station land. As the relevant data of the hydrogen demand are not accessible (the drift and volatility rate of hydrogen demand can be calculated based on the historical demand data with the technique in [71] (see p. 1063).), we set the drift rate, $\mu$, of demand as 5%, and the volatility rate, $\sigma$, as 20% based on Ref. [72]. The discount rate, $r$, is set as 8% [41].

Building on the data abovementioned, we can see that hydrogen demand threshold $Q_1^{*}$ under the independent scenario is 163.69 kg/day, and that $Q_2^{*}$ under the co-operative scenario is 248.51 kg/day. From Equation (19), indeed, $Q_2^{*}=\frac{{\beta }_1-\omega }{{\beta }_1-1}{Q}_1^{*}>Q_1^{*}$. This means, given that the investment timing is chosen by firm $\mathcal{A}$ and the profit sharing rule is chosen by firm $\mathcal{B}$, the optimal timing of HRS investment in the case of co-operation between two firms is always later than that in the case of autonomy of one firm. The inclusion of $\mathcal{B}$ in co-operative investment accounts for the postponement of the exercise of the investment option for $\mathcal{A}$ compared to the case of $\mathcal{A}$’s independent investment. Although cooperative investment has the advantages of shared resources, the additional participant for the HRS project would delay the investment. This is attributed to the fact that the time-deciding firm $\mathcal{A}$ receives only a share of the project value as the rest is the compensation that firm $\mathcal{B}$ claims for contributing $\omega$. Since the presence of $\mathcal{B}$ reduces $\mathcal{A}$’s share of the project value, $\mathcal{A}$ requires the total profits to be larger before investing and consequently chooses investment threshold $Q_2^{*}$ in the cooperative scenario which is higher than $Q_1^{*}$ in the independent scenario. Additionally, note that ${\delta }^{*}-\omega =\frac{{\left(\omega -1\right)}^2}{\beta -\omega }>0$. This means that $\mathcal{B}$ always wants a greater proportion of the profits that it contributes to the investment cost. $\mathcal{B}$’s involvement squeezes the benefit from $\mathcal{A}$, which makes $\mathcal{A}$ have to wait for a higher demand threshold to exercise the investment option, causing a delay in investment.

3.2. Sensitivity Analysis

Sensitivity analyses are performed in this subsection to assess the effects of several key parameters on the investment timing of HRS [73]. Note that, the following sensitivity analyses present the key parameters changing from −20% to +20% building on parameter settings in the benchmark scenario abovementioned.

From Equations (11) and (19), it is obvious to show that under both scenarios, the lower the installation and operation cost, the lower the demand threshold triggering the investment option. On the contrary, a reduction in the hydrogen price and operation subsidy would delay HRS investment. On the one hand, due to learning effects and economies of scale, the hydrogen price and relevant subsidy would show a downward trend, which makes the investment threshold for demand higher. This creates room for improvement in technological innovations in order to avoid a longer delay in investment. Due to the assurance of returns for potential investors against the expected downside of declining hydrogen prices and subsidies, technological innovations regarding the installation and operation of HRS are required for cost reduction. On the other hand, the declining hydrogen price would also decrease vehicle running costs and increase the value proposition of hydrogen fuel in terms of climate benefits for consumers, hence stimulating the demand side in turn.

The sensitivity of volatility, $\sigma$, under different investment scenarios is shown in

Table 1. Sensitivity results for volatility under different scenarios.

	Volatility Rate (%)	16	18	20	22	24
Independent scenario	Demand thresholds (kg)	149.55	156.32	163.69	171.64	180.16
	Rates of change (%)	−8.64	−4.50	0	4.86	10.06
Cooperative scenario	Demand thresholds (kg)	217.76	232.26	248.51	266.56	286.52
	Rates of change (%)	−12.37	−6.54	0	7.27	15.3

and Figure 1. Apparently, whichever the investment model is, the lower the demand volatility, the lower the demand threshold triggering the investment option. This indicates that the exercise of an investment option would be hampered by a larger uncertainty represented by higher volatility. Additionally, the investment timing under the co-operative scenario is more sensitive to demand volatility than thatunder the independent scenario. This indicates that when the investment is undertaken in the co-operative mode, firm $\mathcal{A}$ should pay more attention to the demand volatility in order to ideally seize the optimal entry time, because a higher volatile demand makes future payoffs more difficult to expect [55]. Hence, the independent one-firm model is better for dealing with the volatile hydrogen demand uncertainty.

From

Table 2. Sensitivity results for the drift rate under different scenarios.

	Drift Rate (%)	4	4.5	5	5.5	6
Independent scenario	Thresholds (kg)	169.03	166.26	163.69	161.32	159.14
	Rates of change (%)	3.26	1.57	0	−1.45	−2.78
Cooperative scenario	Thresholds (kg)	229.23	236.95	248.51	266.07	293.96
	Rates of change (%)	−7.76	−4.65	0	7.07	18.29

and Figure 2, nevertheless, the demand threshold shows an opposite trend for the change in the drift rate, $\mu$, under different scenarios. That is, the investment timing is earlier as the drift in demand grows under the independent scenario, but this occurs the other way around under the cooperative scenario. As the drift reflects the expected growth rate, firm $\mathcal{A}$ would be accelerated due to the larger growth rate of the demand if it invests independently. In the cooperative case, however, when the growth trend of the demand becomes lower, the investment timing for $\mathcal{A}$ is advanced. This means that the lower the expected hydrogen demand is, the better the co-operative investment shows its advantage of risk sharing, though its investment timing is still later than that under the independent scenario. Another reason is since the expected growth rate of demand becomes higher, $\mathcal{B}$ wants to claim greater benefit from $\mathcal{A}$. Accordingly, $\mathcal{A}$ requires its payoff to be greater and has to wait more until choosing a higher investment threshold. Additionally, the sensitivity for the investment threshold is bigger under the cooperative scenario than that under the independent scenario, which means when the hydrogen market becomes more promising, potential investors have to delay their investment much later than usual if they depend on another actor to cooperate. Given that the hydrogen industry is developing rapidly, the optimal mode for firms is independent investment.

From

Table 3. Sensitivity results for the cost sharing coefficient under the cooperative scenario.

Cost Sharing Coefficient under Co-Operation Model	0.64	0.72	0.8	0.88	0.96
Thresholds under cooperative scenario (kg)	316.36	282.43	248.51	214.58	180.66
Rates of threshold change (%)	27.3	13.65	0	−13.65	−27.3

and Figure 3, in the case of the co-operation model, the cost sharing coefficient is negatively correlated with the demand threshold. This finding can be attributed to the fact that ${\delta }^{*}>\omega$. That is, $\mathcal{B}$ decides the profit sharing rule and always requests a greater portion of payoffs from $\mathcal{A}$ than of the investment cost it shares for $\mathcal{A}$. For this reason, $\mathcal{A}$ requires $\mathcal{B}$ to bear the cost as much as possible to wait for a lower demand threshold to trigger the investment. However, although $\mathcal{B}$ would bear almost all of the investment cost (0.96) in the extreme case, the demand threshold for $\mathcal{A}$ is still higher than that in the case of the independent model.

4. Conclusions

This paper presents a real options framework for the optimal entry timing of when to initiate HRS investment considering co-operation. From the results, it is obvious that the lower the installation and operation cost, the lower the demand threshold triggering the investment option. On the contrary, increasing the amount of net cash flow due to the investment will accelerate investment. The main contribution to the previous research is that both independent and cooperative investment models are considered. Based on analytical and numerical results, the one-firm independent model is the better way than a the two-firm cooperative model to develop HRS for earlier investment timing, indicating that the HRS will be invested in later with an increasing number of stakeholders of the investment project.

This paper also explores the effects of the expected growth rate and the volatility of an uncertain demand on investment timing. It indicates that for both independent and cooperative models, the volatility of demand has an adverse impact on the investment timing. Greater volatility requires a higher current threshold to bring forth investment. Furthermore, the independent investment mode is better for dealing with the volatile hydrogen demand uncertainty. However, the growth rate of demand has different effects on investment timing for independent and cooperative models. That is, for the independent model, the increase in expected growth rate will prompt the potential investor to invest, but it will be the other way around for the cooperative model. Additionally, the growth rate sensitivity for the threshold is bigger under the cooperative scenario than that under the independent scenario, meaning that if the hydrogen industry becomes more promising, firms have to delay their investment until much later than usual if they depend on another investment partner. Although growth rate and volatility play various roles in investment timing, this shows that independent investment is the optimal model for HRS development. The government should play an important role in stabilizing the demand side for minimizing uncertainty for potential investors.

In the short term, the construction of HRS might rely on co-investment by different actors to share their own resources. However, considering earlier investment is key to entering the self-sustaining stage of HRS diffusion, it is better that one firm undertakes the HRS independently instead of finding a partner to cooperate. For the case that the potential investor cannot independently invest in HRS without technological support from another actor such as the dispenser provider, it is critical to accelerate the firm’s innovation for grasping the core technology in the area of HRS. For the case that the potential investor wants to develop a hybrid gasoline–hydrogen-refueling station, the solution can be to combine the firm that possesses an existing gasoline station with the firm that possesses the necessary equipment for HRS and plans to develop HRS with one firm using the mergers and acquisitions model instead of mere co-operation model with profit and cost sharing rules.

Although in this paper we obtained original findings, the limitation still remains. In this work, we focused on studying alternative HRS investment modes only considering the option of co-operation. In reality, however, HRS investment does not just involve one single energy firm, but a number of contenders given the diffusion of the HRS network. There should be more factors to be considered as the investment in HRS also involves competition that would significantly prompt potential investors to bring forward their decisions, but this is not captured by the methodology presented in the paper. This issue needs to be explored in a future study. One direction in which this work could be extended is to mix concepts from both game theoretic analysis and real options theory. That is, an investment decision in a competitive market can be seen as a game between firms, as firms implicitly take into account other firms’ reactions to their own investment actions, which is called a “real options game” in the terminology.