Financing and Farm-Gate Pricing Strategies for Agricultural Cooperatives With Cash-Constrained Farmers

Abstract

Equity investment in agricultural cooperatives (co-ops) is typically limited to farmer-members; yet farmers are usually cash-constrained. In addition to the common stock that is held by farmer-members, many co-ops are changing their financial structure by raising equity from external investors. This helps co-ops to collect capital, but also brings to the fore the conflicting benefits of farmers and external investors. In this paper, we develop a two-stage game-theoretic model to examine a start-up co-op’s farm-gate pricing and financing strategies, considering two types of external fund: preferred stock that bears a fixed return rate and outside stock that shares the net profit (in proportion to equity) with common stock. We characterize the co-op’s strategies in different scenarios and generate the following insights. First, while both types of external equity outperform the case with common stock only, the preferred stock generally outperforms outside stock due to its lower financial cost, higher tolerance for fund size limits, and flexibility in setting farm-gate prices. However, outside stock can outperform preferred stock if it allows a higher fund size limit. Second, the co-op’s financial strategy exhibits a similar structure in equilibrium regardless of whether it is preferred stock or outside stock, despite their distinct financial terms. Finally, farm-gate pricing has a unique role in co-ops affecting the returns to farmers and external investors, which also highlights the conflicting roles of farmers as both patrons and investors when external equity is used.

1. Introduction

Sustainable agriculture is widely recognized as a key challenge for the world, where sustainability is broadly defined both in terms of land and resource use and also in the financial sense for the farmer (Glover, 2020). Agriculture is moving from being an exploitative and extractive industry to a more collaborative and sophisticated undertaking. This is particularly the case for agricultural marketing cooperatives (co-ops), where farmer-owners see financial and resource-use sustainability as critical to their long-term success. This requires the co-op to not only operate efficiently, but also to design effective financial strategies to ensure sufficient funds for its operations and development. However, this is not easily achieved due to the unique features of agricultural co-ops, especially for co-ops with smallholder farmers, who are often trapped in a vicious cycle of insufficient capital, low-intensity farming, low yields, and limited market access (Meemken and Bellemare, 2020).

As a member-owned organization, a co-op differs from other business structures and needs to follow user-owned, user-controlled, and user-benefit ¹ principles. These member-focused principles of co-ops do not lend themselves to raising capital from non-member investors (Royerk and Karantininis, 2007). Thus, a co-op’s capital typically comes from its farmer-members, whose equity contribution is tied to the patronage ² they provide. This causes shortages in funds when co-ops increasingly require more capital investment for sustainable development, such as novel marketing initiatives and processing technologies, especially when farmer members are small-scale and cash-constrained. As a result, many co-ops are looking to diverge from traditional financial structures (Chaddad and Cook, 2004) and seek external, non-member investment while still keeping the key principles of a co-op. For example, U.S. Premium Beef (USPB) restructured in 2004 by introducing external equity, allowing both beef producers and non-producer investors to own USPB units. Similarly, the Fonterra Co-operative Group restructured in 2009 to raise capital from outside investors by selling investment units (Qian and Olsen, 2021).

A co-op is like other businesses in some but not all aspects of its operations. As with a typical agricultural business, a co-op pool harvests from farmers and pays farmers at the farm gate. Furthermore, when selling processed products, a co-op faces an uncertain market. However, unlike other businesses, the relationship between the co-op and farmers is not simply that of customer and supplier. Since a co-op is owned and primarily financed by its farmer members, farmers bear the mixed roles of owners, patrons, and investors. The co-op therefore needs to work for the farmers’ interests, in both its operations and financing. As such, the farm-gate price a co-op pays to farmers is not simply a payment to suppliers, but can be used as a tool to adjust the profit distribution and thus the return to farmers and investors, which in turn influences their decisions regarding participation and investment. Therefore, the co-op’s operations, particularly the farm-gate pricing strategy in this case, are naturally intertwined with its strategy in terms of financing sources and capital structure, especially when external financing is involved. To aid the reader’s understanding, we explain co-op financing in the following subsection.

1.1. The Financing of a Co-op

Like other businesses, co-ops require capital to buy equipment and plant, pay staff, and cover other operating expenses. To start up a co-op business, the co-op can raise capital through both equity and debt. In this paper, we focus on equity financing because we are interested in how the emerging shift to non-member equity impacts farmers’ participation behavior and the co-op’s financial strategies. Considering both equity and debt financing is left for future research. Equity provides a key channel to raise capital to cover business costs. When co-ops diverge from traditional member-equity-only financing, more than one type of equity may be issued, to both members and non-members. Though they may appear in different forms, three types of equity are commonly observed in practice: (a) the common stock that farmers are required to purchase to join the co-op, which entitles them to membership and ownership rights; (b) preferred stock, which provides a fixed return to equity holders; and (c) outside stock, which entitles the equity holder to share the net profit (in proportion to equity) with common stock. However, for co-ops, any change in equity financing is often accompanied by a change in ownership structure, residual claim rights, and/or profit distribution. Next, we explain the specific features of each equity type.

Common Stock is tied to patronage, and individual farmers are generally expected to provide common stock in proportion to their patronage (the proportionality principle). Although some co-ops allow variations, most still subscribe to the proportionality principle. For example, each Class A unit in the USPB co-op requires each farmer to deliver one finished animal per year, and each share in Fonterra corresponds to one kilogram of milk solids.

Preferred Stock provides a way for co-ops to raise additional capital from investors while raising only modest concerns over their co-op status. The terms of preferred stock are flexible and dividend provisions vary. In this paper, we specifically consider a preferred stock that provides an expected fixed rate of return but does not confer control rights. For example, CHS co-op in the United States announced an offering of $50 million in preferred stock in 2001 with an 8% effective net annual yield. Furthermore, in 2003, Friesland Foods in the Netherlands issued subordinate notes with a total value of 125 million EUR, which generated a fixed interest of 7.125%. However, due to the limited liability of the co-op (Fee, 1984), the return on preferred stock is not guaranteed in the sense that investors can get a return lower than the committed rate if the co-op ends up with a low profit.

Outside Stock is another way for co-ops to acquire additional equity. The main distinction between preferred stock and outside stock lies in the rights to residual claim (van Bekkum and Bijman, 2006). Outside stock is on a par with, rather than senior to common stock for dividend payments. To provide financial incentives to outside investors, co-ops may switch to distributing net profit in proportion to equity. Therefore, outside stock will rarely have a fixed return rate, and the actual return on investment will depend on profitability. However, wary of turning into investor-owned firms (IOFs), many co-ops limit control rights to farmer-members when introducing outside stock. For example, Fonterra claims that it is still a 100% farmer-owned organization and outside investors only enjoy the economic rights of shareholders. Saskatchewan Wheat Pool (SWP), a Canadian grain marketing co-op, converted members’ equity stock to nonvoting stock (B shares) for outside investors (Chaddad and Cook, 2004). Therefore, although outside stock shares the benefits of common stock, it conveys no or very limited control rights. In this paper, we will focus on the case with no control rights.

In contrast to common stock that is tied to patronage and control rights, both preferred stock and outside stock bear no patronage obligation nor control rights and thus can be issued to any investors for additional capital investment. These are therefore referred to as “external” equity. Note that such external equity stock is also open to farmer-members: those who wish to contribute more than their compulsory common stock share may purchase preferred stock and outside stock; this allows them to earn interest or dividends, but with no additional voting privileges.

As farmer-owned organizations, co-ops are subject to some restrictions when raising capital from external funds. This is because issuing external equity is a diversion from the traditional user-owned, user-controlled, and user-benefit principles of co-ops. In response to this problem, many co-ops, in practice, take measures to control the size of external equity. For example, Fonterra specifies that the equity from external investors shall be no more than 12% of the total equity (Qian and Olsen, 2021). In some countries, co-ops also have to comply with federal and state securities law in connection with the external equity offering. For example, the Law of Agricultural Co-ops in China stipulates that non-farmer members should be no more than 20% of all farmer-members. ³

1.2. Research Questions and Contribution

We consider a co-op initiator planning to set up a co-op business with multiple farmers who are cash-constrained. To cover the capital needed, the co-op first raises member equity through common stock and then chooses to raise additional funds through preferred stock or outside stock, both of which are subject to certain fund size limits. In particular, we examine three scenarios for the capital structure, based on (a) pure common stock; (b) common stock and preferred stock; and (c) common stock and outside stock.

This paper seeks to answer the following questions. Considering different sources of funds for equity: (a) What are the equilibrium financial strategies in each scenario? (b) How is the farm-gate pricing linked to the co-op’s financial decisions? (c) Which type of funds should the co-op choose and under what conditions? To answer these questions, it is necessary to explore the interaction between the co-op’s financing and its operations, which are naturally intertwined. In particular, we study the financing decisions regarding the capital structure associated with each fund type, and the tactical decision on farm-gate pricing under an uncertain market. As discussed, co-ops need to follow certain key principles to maintain their co-operative status. These requirements and restrictions create a regulatory friction, which is identified as one primary category of capital market frictions (DeGennaro and Robotti, 2007).

In essence, co-ops are owned by and should be mainly invested in by farmer-members. Our model captures the essence and most salient features unique to agricultural co-ops that introduce regulatory market frictions. First, following co-op principles, the co-op typically aims to maximize the farmer-members’ profit. This is at odds with the objective of maximizing business value as expected by external investors and also provides an opportunity to manipulate the farm-gate price to adjust the profit distribution between farmers and investors. Second, co-ops usually limit the capital obtained from external funds. In the model, this is captured through fund-size constraints, where the external funds cannot exceed certain limits based on the size of common stock raised from farmer-members. This creates liquidity constraints; that is, co-ops’ financing activities are constrained by members’ equity, and thus co-ops are prevented from fully optimizing the capital from external funds.

We find that both preferred stock and outside stock, compared to the scenario with common stock only, contribute to the formation of a co-op and improve the total profit. This provides support for using external equity and is consistent with co-ops’ practice of seeking to issue external equity when possible in order to capture a higher value. Furthermore, the pooling effect, a key driver for co-op formation, enables the co-op to accommodate a higher proportion of external funds, though this positive effect is only present when the fixed cost is not too high.

Comparing the two types of external equity, we demonstrate that preferred stock is likely to (weakly) dominate outside stock in certain practical situations. This is consistent with financial theory (e.g., Houston and Houston, 1990), which emphasizes the lower financial costs of preferred stock. However, our research complements the theory by highlighting additional advantages of preferred stock in its higher flexibility for setting the farm-gate price and/or higher tolerance on the fund size limit, which are unique to co-ops. This provides corroboration for our observation that in practice many co-ops prefer to issue preferred stock when seeking external equity. Furthermore, it is important to note that outside stock could still become the favored option if it allows a larger size limit than preferred stock.

Despite the distinct features of preferred stock and outside stock, we find that the co-op’s equilibrium financial strategy exhibits a similar structure regardless of the type of external equity being raised. This similarity arises from the comparable financial requirements faced by the co-op when raising external equity. Specifically, the co-op utilizes preferred stock or outside stock solely to address capital shortfalls beyond common stock and makes the expected return to external investors at their anticipated premium rate so that external funds are fairly priced.

Furthermore, our results uncover the unique role of farm-gate pricing in co-ops and show that the co-op’s farm-gate pricing with preferred stock can exhibit greater flexibility compared to outside stock. This flexibility stems from the concurrent determination of the farm-gate price and the face value of preferred stock. Essentially, the co-op can offer a higher face value, incorporating a risk premium, to offset the influence if a higher farm-gate price increases the default risk. In contrast, the farm-gate price under outside stock is uniquely set in equilibrium as it directly determines the return to external investors. Meanwhile, the farm-gate price influences the co-op’s financial decisions only when external funds are involved, but not when equity is restricted to farmers. This arises from the conflicting interests of farmers and investors: while farmers as patrons prefer a higher farm-gate price, investors typically favor a lower farm-gate price. As such, our analysis sheds light on the conflicting roles of farmers as both patrons and investors when external equity is used.

The remainder of this paper is organized as follows. In Section 2, we review the relevant literature. Section 3 develops the model and Section 4 characterizes the equilibria in the three scenarios. In Section 5, we discuss managerial insights under our specific financing types, and Section 6 compares the performance of the three types of equity. Finally, Section 7 summarizes the results and discusses future research. Sensitivity analysis, numerical experiments, and the extension considering farmers’ opportunity cost and all proofs are available in the E-Companion.

2. Literature Review

Our work contributes to quantitative research analyzing both the financial and operational decisions of agricultural co-ops, as there is a general lack of such studies. Existing quantitative analysis of co-ops tends to focus on just one aspect, either financing or operations, and most of the relevant studies are qualitative or empirical (e.g., Rebelo et al., 2017; Russell et al., 2017). Among quantitative studies that limit their analysis to co-ops’ financial decisions, VanSickle and George (1983) present a theoretical model for co-op capital structure optimization, calculating the optimal cash patronage refund rate and the members’ after-tax total profit. In another example, Wang (2016) constructs a maximization model for a co-op adopting an equity management program of revolving funds, and derives the optimal decisions of the dividend rate, the cash patronage refund rate, and the length of the revolving fund cycle. There is also a rich set of quantitative studies on co-ops’ operational decisions, including with regard to co-op formation, contractual coordination, and quality management (e.g., An et al., 2015; Ayvaz-Çavdaroğlu et al., 2021; Bontems and Fulton, 2009; Mu et al., 2019; Qian and Olsen, 2022). However, in these studies, the financial aspect receives only minimal if any consideration.

Only a few studies consider both financing and operations in agricultural co-ops. Qian and Olsen (2020) examine the coordination of operational and financial decisions by co-ops. In their paper, the co-op limits its equity to farmers and does not allow investment from external investors. Removing this restriction, we study financing strategies that allow external investment through preferred stock and outside stock, as already adopted by many current co-ops. Similar capital structure innovations for co-ops have been modeled by Qian and Olsen (2021). Through a case study, they numerically demonstrated that a higher tolerance on the external fund size limit can enhance equity holders’ returns and that raising capital from outside investors could alleviate financial constraints. We find similar results using an analytical approach, and further derive the equilibrium decisions, providing additional insights such as the unique role of the farm-gate price in co-op financing. Moreover, we model two types of external equity and compare their performance, while Qian and Olsen (2021) considered only one type of external equity resembling the outside stock in our paper.

Our work also contributes to the growing literature on supply chain finance that connects operational and financial decisions (e.g., Alan and Gaur, 2018; Boyabatlı and Toktay, 2011; Kouvelis and Dong, 2023; Li et al., 2013). This research stream has derived a rich set of results on how a firm’s financial constraints affect its operational decisions. For example, in an agricultural setting, Yi et al. (2021) consider a supply chain with a capital-constrained smallholder farmer and an intermediary platform that can help solve the bottleneck of capital through debt financing and guarantor financing. However, no studies in this literature consider agricultural co-ops, which have unique operational and financial features.

Our work also relates to the literature on agricultural operations. Dong (2021) and Gupta et al. (2023) review agricultural research from the operations management perspective, and identify challenges and trends in agricultural supply chains. Studies have examined the incentives and interventions to adopt innovations in farm practices such as organic and sustainable farming (e.g., Akkaya et al., 2021; Acs et al., 2009), and the interaction of procurement, processing, and distribution decisions (e.g., Azoury and Miyaoka, 2013; Boyabatlı et al., 2011; Kazaz and Webster, 2011). While these studies mainly focus on agricultural operations, we also take financial decisions into consideration and look at how agricultural co-ops’ operations influence innovation in their financing.

3. Model Description

We propose a two-stage game theoretic model to study the financing and farm-gate pricing problem for a start-up co-op seeking to raise equity from both farmers and external investors. As illustrated in Figure 1, the first stage is to raise common stock through interaction between the co-op initiator and the farmers, and the second stage is to raise external equity from investors. The equity raised from both stages is used to fund the co-op’s establishment and operations if feasible. We model both stages as a Stackelberg game in which the co-op takes the leader position. Specifically, the co-op proposes terms for common stock share to farmers in the first stage and then offers financial contracts to competitive external investors, as is standard in the finance literature. This is in line with the observation that a co-op is usually initiated by several leading members who determine a common need and develop an idea of how to fulfill it (Rapp and Ely, 2010). These leading members, who we group together as the co-op initiator, propose co-op terms, such as common stock share, to other farmers who then decide whether to participate accordingly. Most smallholder farmers (as assumed in this paper) just make their individual decisions on whether to participate, rather than operational and financial decisions at the organizational level. Thus, we do not differentiate between the roles of the co-op initiator and the start-up co-op, and simply use the term the co-op to refer to the entity that makes organizational decisions for the co-op in the rest of the paper. A summary of all notation and parameters can be found in Table 1.

Figure 1.

The timing of events.

Table 1.

Summary of notation.

Notation	Description
$n$	The total number of farmers
$s$	The share price of common stock (Decision)
$m$	The cooperative size (Decision)
$e^c$ , $e^p$ , $e^o$	The equity size of common stock, preferred stock, and outside equity, respectively
$f^p$ , $f^o$	The proportion of preferred stock and outside equity, respectively (Decision)
$p_0$	The farm-gate price to farmers (Decision)
$k^p$	The face value of preferred stock (Decision)
${\hat{f}}^p$ , ${\hat{f}}^o$	The size limits on preferred stock and outside stock, respectively
$r^p$ , $r^o$	The premium rate expected by investors for preferred stock and outside stock
$c_v$ , $c_f$ , $\beta c_f$	Variable cost, fixed cost of the co-op, and fixed cost of the individual business
$X^p$ , $X^o$ $x^p$ , $x^o$	The return to external investors (random variable) and their realizations
$W$ , $\overline{w}$	The wealth of farmers (random variable) and its maximum value
$P$ , $p$ , ${\mu }_p$	The market price (random variable), its realization, and its mean value
$\pi$ , ${\pi }^{*}$	The total profit of farmers and its equilibrium value

As in other businesses, establishing a co-op requires a large amount of capital upfront. As described in a report of United States Department of Agriculture (Rapp and Ely, 2010), the co-op needs to cover both the cost of facilities and operating costs. Required facilities may include land, buildings, and equipment, whose cost is largely dependent on the expected business volume. Operating costs may include raw material costs, employee salaries, office and utilities, transportation, etc., with the per-unit operating costs tending to decline as the volume increases. In line with this, we assume that the total cost for the co-op to get established and operate is $c_{v}m+c_f$ , where $c_f$ is the fixed cost and $c_v$ is the variable cost related to the co-op size $m$ , which is collectively determined by the farmers and will be discussed and formulated in Subsection 3.1. The per-unit cost $c_v+c_f/m$ , which is decreasing with the co-op size $m$ , captures the economies of scale of co-op businesses. In other words, as more farmers participate in the co-op, they can enjoy more cost savings. However, the co-op can only be established if the equity raised from the farmers and the external investors is sufficient to cover the required capital.

Once established, the co-op can start its operations and process the products collected from farmers. When selling the processed product, the co-op is subject to an uncertain market price. Let $P$ denote the random market price, which can be drawn from the cumulative distribution function (CDF) $G(\cdot )$ , with a compact support $[0,\overline{p}]$ , a mean of ${\mu }_p$ , and its realization $p$ . We assume that the co-op is a price-taker as we consider a start-up co-op. This is in line with the practical observation that except for some highly successful co-ops, most existing co-ops, especially start-up co-ops in developing countries, are price-takers. Furthermore, this assumption allows us to focus on the co-op’s farm-gate price decision to investigate the ways in which co-ops finance their business. Thus, while considering a price-maker may be relevant in some other cases, this is left for future research.

As explained in Section 1.1, we consider three types of equity: common stock, preferred stock, and outside stock. To separate the effects, we assume the co-op can only combine common stock with one other financing source, and accordingly examine three scenarios as described below. Recall that both farmer-members and non-members can purchase preferred stock or outside stock. This does not challenge the rule of profit distribution because in each scenario the profit is distributed based on how the co-op raises the capital, rather than on who finances the co-op.

1. 1.

Scenario 1 (Pure Common Stock): The co-op limits its equity to common stock and distributes the profit by patronage.

2.

Scenario 2 (Common Stock + Preferred Stock): In addition to common stock, the co-op determines the size of preferred stock and the financial return to preferred stockholders. After the realization of market revenue, the co-op first pays farmers at the farm-gate price, then meets its obligation to the preferred stockholders, and finally distributes the remaining value by patronage.

3.

Scenario 3 (Common Stock + Outside Stock): In addition to common stock, the co-op determines the size of outside stock, which enjoys the same economic benefit as common stock. In this case, the co-op distributes the profit by equity after making the product payment to farmers.

We use $e^c$ , $e^p$ , and $e^o$ to denote the size of common stock, preferred stock, and outside stock, respectively, with the decisions on fund size based on other related decision variables. Let $s$ denote the share price of common stock, and then the common stock size $e^c$ can be determined through the decision on the common stock price $s$ and the equilibrium co-op size $m$ , with $e^c=sm$ . The external fund size is represented as a portion of the common stock size, denoted by $f^i$ where $i=\{p,o\}$ . The size of external funds is thus expressed as $e^i=f^i{e}^c$ , with $f^i$ being a decision for the co-op. As introduced earlier, there is a size limit for each external fund, which is denoted by ${\hat{f}}^i$ , and hence $f^i\le {\hat{f}}^i$ . As well as ensuring the user-owned principle, the fund size limits also capture the resource-pooling benefit associated with external financing; that is, raising more money from farmers through common stock allows the co-op to attract more external funds. In principle, the external fund limits ${\hat{f}}^i$ may constitute another decision for the co-op. However, given that the co-op is a member-owned organization and therefore mainly invested in by members, it has limited latitude in choosing ${\hat{f}}^p$ and ${\hat{f}}^o$ ; thus, we make them exogenous in our model.

In addition to the size of preferred stock, $e^p$ , the co-op also determines the face value of preferred stock $k^p$ , which incorporates the risk premium to investors with the uncertain market revenue. However, the face value $k^p$ may be defaulted if the realized market revenue is not sufficiently high due to the limited liability. Different from preferred stock, there is no face value decision for outside stock because outside stock investors share the net profit according to their equity contributions, so the return is determined by the dividend payments after the product payments. For both preferred and outside stock, the expected return to external investors, which is denoted by $E[X^i]$ , depends on the realization of market revenue as well as the farm-gate price.

To motivate external investors to invest in a co-op, the expected return should at least meet their expectations. In the current supply chain finance literature (see de Véricourt and Gromb, 2018), the investors, on expectation, usually earn a rate equal to the risk-free interest rate (generally assumed to be zero). However, considering the fact that external investors in a co-op rarely enjoy control rights or voting rights, we assume external investors expect a premium rate $r^i>0$ with $i=\{p,o\}$ , which is added on top of the risk-free interest rate (zero under our assumption). Our current model explicitly accounts for the unique principles of co-ops (i.e., user-owned, user-controlled, and user-benefit) and the implications for the premium charged by external investors. Since we consider two different types of external funds, the premium expected by preferred stock investors $r^p$ may differ from that expected by outside stock investors $r^o$ . In Section 6, we compare the performance of these two types of stock when their premiums are the same or different.

As discussed, one critical decision that influences the expected return to external investors is the farm-gate price $p_0$ , particularly when raising capital from external equity. Considering the fact that external investors will not invest in a co-op business without knowing the farm-gate price, and also to fully capture the farmers’ risk as owners, we assume that the farm-gate price is committed upfront before the realization of market revenue and before external investors make decisions, but is fulfilled after revenue realization. The co-op will not be able to fully pay farmers at the committed price if the market realization is particularly low. The assumed $p_0$ to be paid after revenue is an approximation of reality as co-ops usually make progressive payments to farmers after the realization of market revenue, though an advance payment is paid upon delivery of the product (Qian and Olsen, 2022).

3.1. The Farmers’ Problem

Farmers need to decide whether to participate in the co-op based upon the co-op’s decision on the common stock price (the first stage as shown in Figure 1). We consider $n$ small-scale farmers who are potential members. For simplicity, the yield of each farmer is assumed to be deterministic and is normalized to 1. This is reasonable for small-scale farmers in developing countries, and a similar assumption can be found in Liao et al. (2019). Considering uncertain yield, which brings supply risk, is left for future research. We further assume that if a farmer chooses to participate, he/she is obligated to deliver all products to the co-op. This follows from the marketing agreement between members and the co-op and also implies that each farmer contributes a single unit of patronage, which leads to equal allocation of the profit among the co-op members. Thus, the co-op size in equilibrium $m$ , which is formally presented in equation (1), is exactly the number of farmers who participate in the co-op.

There are two conditions for farmer participation. First, a farmer will expect an adequate profit to be willing to join and stay with the co-op. This involves comparing a farmer’s expected profit from the co-op with a reservation profit that can be earned without joining the co-op. When participating in the co-op, the individual farmer’s profit is the co-op’s average profit, that is, ${\pi }^i/m$ , where ${\pi }^i$ with $i\in \{p,o\}$ is the total expected profit of all participating farmers; its expression will be made concrete in the next subsection. Meanwhile, farmers can have outside options; that is, a farmer can choose not to join the co-op but operate individually (if it is affordable). We assume that the fixed cost for a farmer to process individually is $\beta c_f$ , with $0<\beta <1$ , which is smaller than the fixed cost of the co-op. This is because individual farmers with a limited production volume would require a smaller processing facility than the co-op.

Thus, the participation constraint depends on whether a farmer can afford the individual processing cost. Denote the wealth of farmer $k$ as $w_k$ . For farmers with sufficient capital, that is, $w_k\ge c_v+\beta c_f$ , the expected profit from selling directly to the market is $E[P]-(c_v+\beta c_f)>0$ . So, for farmers with $w_k>c_v+\beta c_f$ , the participation constraint is ${\pi }^i/m\ge E[P]-(c_v+\beta c_f)$ ; that is, the expected payoff when participating in the co-op shall be no less than the expected payoff under the status quo. Note that although the individual farmer can get the same (uncertain) market price as the co-op in a competitive market, he/she will not enjoy the reduced average cost as the co-op farmers. In reality, the co-op may leverage its collective bargaining power to negotiate a higher market price (in an expected value). In such a case, our model can easily accommodate this adjustment by incorporating the increased market price into the reduced cost, which would not change the main results. For farmers who cannot afford to process by themselves, that is, $w_k<c_v+\beta c_f$ , we normalize their profit from the outside option to be zero. So, for $w_k<c_v+\beta c_f$ , the participation constraint is ${\pi }^i/m\ge 0$ .

Second, a farmer needs to have sufficient wealth to cover the required common stock for membership. This requires $w_k\ge s$ , which may not hold given small-scale farmers, as we consider in this paper, are usually cash-constrained. In our model, we assume that the information about $w_k$ is private; that is, it is unknown to the co-op and other farmers, but known to farmer $k$ . However, the co-op can estimate the distribution of farmers’ wealth based on the available information regarding a region. We use $W$ to denote the stochastic counterpart of the wealth and assume $W$ follows a uniform distribution within the support $[0,\overline{w}]$ . The upper bound $\overline{w}$ indicates the wealth condition of farmers and plays a critical role in determining the financial strategies in equilibrium.

The decisions of other farmers (regarding whether they will join or not) affect the benefits of all participating members. We assume that co-op membership is observable to the co-op and to all the other farmers. Potential farmer-members must form beliefs about their equilibrium values when deciding whether to join the co-op. In turn, these beliefs must be confirmed in equilibrium; that is, farmers should act rationally with respect to information and correctly predict the equilibrium values as a result. As in all definitions of equilibrium, farmers’ choices and beliefs are simultaneously determined. Taking these into consideration, together with the fact that any farmer will only join the co-op if the common stock share is affordable and if he/she expects to receive a high expected payoff, we can write the following recursive relationships:

$$\begin{array}{rl}m& =n*\mathbb{P}[W\ge s]*1_{\{{\pi }^i/m\ge E[P]-(c_v+\beta c_f)\}}\\ & =n\frac{\overline{w}-s}{\overline{w}}{1}_{\{{\pi }^i/m\ge E[P]-(c_v+\beta c_f)\}},\end{array}$$

(1)

where $1_{\{\}}$ is the indicator function. Note the condition of the indicator function, ${\pi }^i/m\ge E[P]-(c_v+\beta c_f)$ , indicates that the co-op business needs to be more profitable than individual businesses. Theoretically, there could be another possibility that the expected profit of the co-op is lower than that of the individual businesses such that $0\le {\pi }^i/m<E[P]-(c_v+\beta c_f)$ ; however, this makes a less interesting case in reality. As shown in EC.1 in the E-Companion, if $0\le {\pi }^i/m<E[P]-(c_v+\beta c_f)$ , then the co-op cannot be established when the equity is restricted to farmer members, and participation is limited to farmers who do not afford to process independently, that is, with $s\le w_k<c_v+\beta c_f$ , if external equity is introduced. So, we focus on the case where ${\pi }^i/m\ge E[P]-(c_v+\beta c_f)$ . In addition, we treat farmers as non-atomic (infinitesimal) and hence $m$ as a continuous parameter. To ensure valid formation of the co-op, we constrain $1\le m\le n$ .

3.2. The Co-op’s Problem

As described in Figure 1, the co-op’s problem is a two-stage problem when external equity is used: deciding the share price for common stock in the first stage and considering variables related to raising capital from external funds in the second stage. Note that the second stage is only relevant for Scenarios 2 and 3, since external funds are not considered in Scenario 1. To capture the user-benefit principle, we assume that the co-op aims to maximize the total farmer-members’ profit in all scenarios, as is standard in the co-op literature (Soboh et al., 2009). This objective combined with the fund-size constraint applied in the model ensures the co-op can protect the control rights of farmers in Scenario 3, where outside stockholders share the net profit with farmers.

For all scenarios, the construction of the co-op’s problem follows a similar structure, though the formulated expressions could differ, as will be analyzed in Section 4. In the first stage, the co-op makes a decision on the share price of common stock $s$ subject to farmers’ participation constraints. In the second stage, the co-op makes decisions on how to raise capital from external funds, given the co-op size in equilibrium $m$ and the share price of common stock $s$ . We use ${\delta }^p$ , ${\delta }^o$ to denote the second-stage decisions with preferred/outside stock; ${\delta }^p=\{p_0,f^p,k^p\}$ and ${\delta }^o=\{p_0,f^o\}$ .

With the objective of maximizing total farmer-members’ payoff, the second-stage objective is written as in equation (2). After the market revenue is realized and financial returns are paid to external investors, the payoff for all farmers includes several elements: any leftover funds after setting up the co-op ( $sm+f^{i}sm-c_{v}m-c_f$ ) and the revenue from selling the product in the market ( $pm$ ), minus the actual return to external investors ( $x^i$ ) and the investment cost ( $sm$ ). Recall that as the expected return to investors $E[X^i]$ depends on the realization of market price and the farm-gate price $p_0$ , its exact expression varies in different scenarios.

$${\pi }^i(s)=\underset{{\delta }^i\ge 0}{max}E[Pm-X^i+f^{i}sm-c_{v}m-c_f].$$

(2)

The co-op makes second-stage decisions subject to several constraints. First, the funds raised from both common stock and external equity should cover the cost; that is, the following funding constraint must hold:

$$(1+f^i)sm\ge c_{v}m+c_f.$$

(3)

Second, the investors should be willing to accept the contract; that is, the expected payoff should at least meet their expectations. Hence, the following investor participation constraint must hold:

$$E[X^i]\ge (1+r^i)f^{i}sm.$$

(4)

Also, the size of external equity should be no more than its limit:

$$0\le f^i\le {\hat{f}}^i.$$

(5)

Thus the two-stage problem can be summarized as below. When the co-op and farmers participate in the first-stage game, they must anticipate the equilibrium of the second-stage game and base their decisions on this anticipation. Therefore, the problem is solved backward, beginning with solving the second-stage model followed by the first-stage model. Consequently, the solutions presented in Section 4 represent a subgame perfect equilibrium.

Stage 1: Maximizing the expected total profit of all farmers:

$$\begin{array}{rl}{\pi }^{i*}=& \underset{0\le s\le \overline{w}}{max}{\pi }^i(s)\\ \text{s.t.}& \frac{{\pi }^i(s)}{m}\ge E[P]-(c_v+\beta c_f),m=n\frac{\overline{w}-s}{\overline{w}},1\le m\le n.\end{array}$$

Note the expression of co-op size $m$ as in equation (1) has been split into two constraints; specifically, $m=n[(\overline{w}-s)/\overline{w}]$ and the condition of the indicator function ${\pi }^i/m\ge E[P]-(c_v+\beta c_f)$ .

Stage 2: Given $s$ and the realization of $m$ , the co-op aims to maximize the expected payoff for all farmers:

$$\begin{array}{rl}{\pi }^i(s)& =\underset{{\delta }^i\ge 0}{max}E[Pm-X^i+f^{i}sm-c_{v}m-c_f],\\ & s.t.equations(3),(4),(5).\end{array}$$

In the next section, we analyze the equilibrium decisions for each scenario. For the problem to be nontrivial, we make the following assumptions on the model parameters. First, we assume $r^i\le [({\mu }_p-c_v)/c_v]$ for $i\in \{p,o\}$ . This assumption implies that the premium charged by the external investors should not be too high; otherwise, it might be never profitable for the co-op to raise external funds. Second, to ensure a non-negative reservation profit for farmers, we assume ${\mu }_p\ge c_v+\beta c_f$ . Third, to focus on the most relevant cases, for some of our results, we require that $n\ge max\{2/\beta ,[2(1+r^o)c_f]/[{\mu }_p-(1+r^o)c_v],[(2\beta c_f+2c_v-{\mu }_p)c_f]/[({\mu }_p-c_v-\beta c_f)c_v]\}$ . This implies that the pool of potential farmer members for the co-op is sufficiently large, which is likely to be the case with small-scale farmers; otherwise, a co-op may not be established because a very small farm base cannot cover the cost.

4. Model Analysis

We start our analysis with Scenario 1 in Subsection 4.1, where the co-op limits its equity to common stock. We continue in Subsection 4.2 with Scenario 2, where the co-op issues preferred stock and common stock, and in Subsection 4.3 we consider Scenario 3, where the co-op issues outside stock and common stock.

4.1. Scenario 1: Pure Common Stock

We first present Scenario 1 where no external funds are raised. This serves as a benchmark to compare with the other scenarios. Recall that the co-op’s problem is a one-stage problem in Scenario 1, with no external equity. Setting $f^i=0$ and $E[X^i]=0$ , the farmers’ participation constraint becomes $[E(Pm-c_{v}m-c_f)]/m\ge E[P]-(c_v+\beta c_f)$ , that is, $m\ge 1/\beta$ . In other words, only when the co-op size is larger than a certain value, that is, $1/\beta$ , farmers can enjoy a larger profit than that when they process by themselves. Thus, the co-op’s problem can be written as:

$$\begin{array}{rl}{\pi }^{c*}\equiv & \underset{0\le s\le \overline{w}}{max}[{\mu }_p-c_v]m-c_f\\ \text{s.t.}& sm\ge c_{v}m+c_f,1/\beta \le m\le n,m=n\frac{\overline{w}-s}{\overline{w}}.\end{array}$$

(P1)

Proposition 1

(Scenario 1) Suppose $n\ge 4\overline{w}{c}_f/(\overline{w}-c_v{)}^2$ , there exists a threshold ${\underset{\_}{w}}^c$ such that if $\overline{w}\ge {\underset{\_}{w}}^c$ , then in equilibrium the share price is $s^{c*}={\underset{\_}{s}}^c$ , where ${\underset{\_}{s}}^c\equiv min\{s:(s-c_v)m-c_f\ge 0\}$ and the co-op size is $m^{c*}=n[(\overline{w}-{\underset{\_}{s}}^c)/\overline{w}]$ . Furthermore, $m^{c*}$ and ${\pi }^{c*}$ are decreasing in $c_f$ .

Table 2.

The profit distribution with preferred stock after the realization of market revenue.

	Product payment	Return to investors $x^p$	Farmers’ profit
if $p\ge k^p/m+p_0$	$p_{0}m$	$k^p$	$pm-k^p+f^{p}sm-c_{v}m-c_f$
if $p_0\le p<k^p/m+p_0$	$p_{0}m$	$pm-p_{0}m$	$p_{0}m+f^{p}sm-c_{v}m-c_f$
if $p<p_0$	$pm$	$0$	$pm+f^{p}sm-c_{v}m-c_f$

The existence of equilibrium as in Proposition 1 requires that the number of farmers shall be larger than a certain value. This is because a small farm base may mean insufficient farmers to participate and hence make it not profitable to establish a co-op business. The establishment of a co-op also requires farmers to have enough money to pay the share price required to cover the cost, that is, $\overline{w}\ge {\underset{\_}{w}}^c$ . If farmers can afford it, one might notice that in equilibrium, the liquidity constraint is always binding, that is, $sm=c_{v}m+c_f$ . In other words, the co-op will not require more money than needed because the co-op size is decreasing in share price. Furthermore,with the increase of fixed cost $c_f$ , the co-op requires more equity investment from farmers to cover the cost, hence decreasing the co-op size. A higher cost also leaves less margin for the co-op and thus farmers.

Note that the farm-gate price is muted when the equity is limited to farmers. This is because both the farm-gate price and the profit after the product payment belong to the farmers. In other words, the farm-gate price does not change farmers’ payoff and thus does not influence their participation behavior. This is consistent with our observations for start-up co-ops. In particular, the co-op would not guarantee a farm-gate price when raising equity from farmer-members due to the uncertain market price (Co-op Farming, 2023). Nevertheless, benefits such as economies of scale, democratic control, or ownership rights continue to serve as incentives for farmers to participate in the co-op.

4.2. Scenario 2: Common Stock and Preferred Stock

In this scenario, the co-op can issue preferred stock in addition to common stock. Recall that $f^p$ is the proportion of preferred stock with its stock size being $e^p=f^p{e}^c=f^{p}sm$ , and that $k^p$ is the face value of preferred stock. The profit distribution after the realization of market revenue is illustrated in Table 2. Note that the cash available for distribution should be the realized market revenue plus any leftover funds. However, given that it is costly to raise external equity, there is no reason for the co-op to prioritize external equity over common stock. Therefore, the leftover fund should be zero (as is formally presented in Lemma 1) and the market revenue is used for distribution. If the market revenue is sufficiently high, the co-op can fulfill both the product payment at the promised farm-gate price $p_0$ and the repayment of preferred stock face value $k^p$ and then distribute the rest to farmers. If the realized market revenue is in the medium range, the co-op will first make the product payment to farmers and then distribute the rest to investors. If the market revenue is sufficiently low, the co-op will pay all available cash to farmers and distribute nothing to investors. Because of the limited liability of the co-op, claims by the preferred stock and product payment are capped at the co-op’s revenue.

From Table 2, we can get the expected return to investors from the preferred stock $E[X^p]\dot{=}{k}^p-m{\int }_{p_{0}m/m}^{(k^p+p_{0}m)/m}G(p)\mathrm{d}p$ . Then, the co-op’s second-stage problem is as follows:

$$\begin{array}{rl}{\pi }^p(s)=& \underset{p_0,f^p,k^p}{max}E[Pm-X^p+f^{p}sm-c_{v}m-c_f]\\ \text{s.t.}& (1+f^p)sm\ge c_{v}m+c_f,\\ & E[X^p]\ge (1+r^p)f^{p}sm,\\ & 0\le f^p\le {\hat{f}}^p,k^p\ge 0,p_0\ge 0.\end{array}$$

Lemma 1

In the second stage, with given $s$ and $m$ , the optimal financial strategy is to use preferred stock to fund any shortfall on top of the farmers’ investment $sm$ , that is, $f^{p}sm=(c_v-s)m+c_f$ , while the face value $k^p$ and farm-gate price $p_0$ shall satisfy

$$k^p-m{\int }_{p_0}^{k^p/m+p_0}G(p)\mathrm{d}p=(1+r^p)[(c_v-s)m+c_f].$$

(6)

Let $k_o^p$ denote the value of $k^p$ that satisfies equation (6), then $k_o^p$ increases with $p_0$ .

Lemma 1 shows that the co-op will never issue more preferred stock than needed, so all equity raised is used to cover the required cost; this is because of the financial cost implied by $r^p$ . Equation (6) illustrates how a risk premium is incorporated into the face value $k^p$ for investors in preferred stock. The right-hand side of equation (6) is the expected return to external investors, which equals the return evaluated at their expected premium rate $r^p$ , and the left-hand side is the face value $k^p$ minus the extra return required by investors to compensate for their risk. Note that ${\int }_{p_0}^{k^p/m+p_0}G(p)\mathrm{d}p$ represents the risk of default, which shall be zero if there is no uncertainty in the market price. It is easy to show that the default risk is increasing in $p_0$ ; that is, with uncertain market prices, a higher farm-gate price committed to by the co-op will pose a higher default risk on the preferred stockholders. Therefore, the co-op should increase the extra return and thus offer a higher face value $k^p$ to compensate for the increasing default risk when the farm-gate price $p_0$ increases. This also reflects the conflict between farmers and external investors: a higher product payment, which can benefit farmers as patrons, could increase the risk for external investors.

Put the second-stage decisions into the co-op’s first-stage problem and it can be written as:

$$\begin{array}{rl}{\pi }^{p*}=& \underset{s}{max}{\pi }^p(s)=\underset{s}{max}[{\mu }_p-(1+r^p)c_v+r^{p}s]m-(1+r^p)c_f\\ \text{s.t.}& g_1^p(s)\equiv c_{v}m+c_f-sm\ge 0,\\ & g_2^p(s)\equiv (1+{\hat{f}}^p)sm-[c_{v}m+c_f]\ge 0,\\ & g_3^p(s)\equiv (m\beta -1)c_f-r^p[c_{v}m+c_f-sm]\ge 0,\\ & m=n\frac{\overline{w}-s}{\overline{w}},1/\beta \le m\le n,0\le s\le \overline{w}.\end{array}$$

(P2)

The first constraint is $f^p\ge 0$ , while the second represents $f^p\le {\hat{f}}^p$ with $f^{p}sm=(c_v-s)m+c_f$ . The third constraint is the individual farmer’s participation constraint, where the first item is the reduced cost when joining the co-op and the second is the financing cost of preferred stock. This implies that when the co-op decides to issue preferred stock, the total financing cost should be no more than the cost-savings from the co-op business.

Regarding the constraints, we can show $g_1^p(s)$ is convex, while $g_2^p(s)$ and $g_3^p(s)$ are concave (see the proof of Theorem 1). Thus, we define ${\underset{\_}{s}}_1^p\equiv min\{ss.t.g_1^p(s)\ge 0\}$ , ${\underset{\_}{s}}_2^p\equiv min\{ss.t.g_2^p(s)\ge 0\}$ , and ${\underset{\_}{s}}_3^p\equiv min\{ss.t.g_3^p(s)\ge 0\}$ . Since the objective is concave in $s$ , we let ${\hat{s}}^p\equiv \arg \max [{\mu }_p-(1+r^p)c_v+r^{p}s]m(s)-(1+r^p)c_f=[(\overline{w}+c_v)/2]-[({\mu }_p-c_v)/2r^p]$ . Next, Theorem 1 characterizes the equilibrium financial strategies with preferred stock.

Theorem 1

(Scenario 2) Assume $n\ge max\{4\overline{w}{c}_f/(\overline{w}-c_v{)}^2,4\overline{w}{c}_f(1+r^p)/[r^p(\overline{w}-c_v+c_f/r^p{)}^2],(2\beta c_f+2c_v-{\mu }_p)c_f/[({\mu }_p-c_v-\beta c_f)c_v]\}$ , there exist several thresholds ${\hat{w}}_1^p$ , ${\hat{w}}_2^p$ , ${\hat{w}}_3^p$ , ${\underset{\_}{w}}^p$ (with ${\underset{\_}{w}}^p<{\hat{w}}_2^p/{\hat{w}}_3^p<{\hat{w}}_1^p$ ), and ${\tilde{r}}^p$ , such that in equilibrium the share price $s^{p*}$ and the size of preferred stock $f^{p*}$ are characterized as follows:

1. 1.

No business is established if $\overline{w}<{\underset{\_}{w}}^p$ .

2.

Not include preferred stock, that is, $f^{p*}=0$ , and $s^{p*}={\underset{\_}{s}}_1^p$ , if $\overline{w}>max\{{\hat{w}}_1^p,{\underset{\_}{w}}^c\}$ .

3.

Include the preferred stock but not to the limit, $0<f^{p*}<{\hat{f}}^p$ , and

• (a)

$s^{p*}={\hat{s}}^p$ if $max\{{\hat{w}}_2^p,{\hat{w}}_3^p\}\le \overline{w}\le max\{{\hat{w}}_1^p,{\underset{\_}{w}}^c\}$ and

(b)

$s^{p*}={\underset{\_}{s}}_3^p$ if $r^p>{\tilde{r}}^p$ and ${\underset{\_}{w}}^p\le \overline{w}<{\hat{w}}_3^p$ .

4.

Issue preferred stock up to the limit; that is, $f^{p*}={\hat{f}}^p$ , and $s^{p*}={\underset{\_}{s}}_2^p$ , if $r^p\le {\tilde{r}}^p$ and ${\underset{\_}{w}}^p\le \overline{w}<{\hat{w}}_2^p$ .

With the share price $s^{p*}$ , the farm-gate price $p_0^{p*}$ and the face value $k^{p*}$ are determined by equation (6).

Theorem 1 provides insights into the three key decisions regarding the co-op’s capital structure. The first decision is whether to establish a co-op business; the second is whether to completely exclude external funds (exclusive system) or access external funds (inclusive system); and the third is whether the existing limit on external funds should be fully used (full) or intentionally kept underused (not full) at the profit-maximizing co-op size. To follow the discussion, the reader may find it helpful to refer to Figure 2.

Figure 2.

Structure of the financing policy in equilibrium with preferred stock. Notes: ${\mu }_p=400$ , $c_v=200$ , ${\hat{f}}^p=0.8$ , $n=50$ , $c_f=100$ , $\beta =0.5$ .

Theorem 1 Part (1) answers the first question, stating that if the wealth of farmers is sufficiently low, that is, lower than a certain threshold ( ${\underset{\_}{w}}^p$ ), the co-op cannot be established. This conclusion is similar to the benchmark case (Scenario 1). However, compared to Scenario 1, the threshold for business establishment is reduced, that is, ${\underset{\_}{w}}^p<{\underset{\_}{w}}^c$ . This implies that access to preferred stock lowers the wealth requirement for farmers to participate, and thus promotes the establishment of co-ops.

Part (2) answers the second question by characterizing whether to issue preferred stock. In particular, there exists a threshold between an inclusive and an exclusive system, $max\{{\hat{w}}_1^p,{\underset{\_}{w}}^c\}$ . If the farmer’s wealth is sufficiently high, the co-op is better off leaving the preferred stock out of the system; then the co-op can start issuing preferred stock as the wealth becomes lower. This is consistent with reality because issuing preferred stock incurs financing costs, so is used as a supplementary source of funds when farmers are financially constrained. Furthermore, the threshold ${\hat{w}}_1^p$ is decreasing with $r^p$ . In other words, with an increasing financing cost, the wealth threshold between an inclusive and an exclusive system becomes lower because the co-op is less likely to issue preferred stock when the financing cost becomes high.

Parts (3) and (4) answer the third question by characterizing the financial structure when the system is inclusive. If $r^p$ is low (lower than a threshold ${\tilde{r}}^p$ ), there exists a wealth threshold ${\hat{w}}_2^p$ between the full and not full systems. With a given financial cost $r^p$ and starting from a not full system, the co-op will increase the amount of preferred stock as the relative wealth decreases, until it reaches the limit ${\hat{f}}^p$ (i.e., full system). Note ${\hat{w}}_2^p$ decreases with $r^p$ ; this means the co-op is less likely to issue to the external funds limit as the financial cost gets higher. If $r^p$ is high (higher than a threshold ${\tilde{r}}^p$ ), then the level of preferred stock in equilibrium is always lower than the limit ${\hat{f}}^p$ ; that is, a decrease in the wealth can never result in the co-op moving from not full to full. This is because when the financial cost becomes sufficiently large, the size of the preferred stock is constrained by the farmers’ participation constraint before it reaches the size limit. Recall that the farmers’ participation constraint requires the cost of raising preferred stock to be no more than the cost savings from the co-op. Therefore, when investors expect a high return, the co-op has to reduce the size of preferred stock to control the total financial cost, so it will not issue to the limit even when the wealth level is low. A high financial cost coupled with a low wealth level will prevent the co-op from being established, rather than the co-op issuing a high amount of preferred stock.

Note that when issuing preferred stock, both the farm-gate price and the face value of preferred stock $(p_0^{p*},k^{p*})$ are determined concurrently by equation (6). This suggests that the co-op possesses the flexibility to select a farm-gate price (within a certain range) and set the face value accordingly, as long as these choices align with investors’ expectations. Given that the co-op can assume multiple values of the farm-gate price in equilibrium, an interesting question arises regarding how the farm-gate price influences other equilibrium decisions. From Theorem 1, we observe that $p_0$ does not affect the equilibrium share price $s^{p*}$ , the co-op size $m^{p*}$ , the external financing portion $f^{p*}$ , or the farmers’ profit, as its influence is offset by $k^{p*}$ in the objective (see Problem P2). Lemma 1 shows $k^{p*}$ increases with $p_0$ ; however, our numerical analysis reveals that the face value $k^{p*}$ is not sensitive to the farm-gate price (refer to Figure EC.1 in the E-Companion). That is, although the farm-gate price influences the financial returns of the preferred stock, its impact is not significant.

4.3. Scenario 3: Common Stock and Outside Stock

In this scenario, the co-op raises equity from both common stock and outside stock. Recall that $f^o$ is the proportion of outside stock and the equity size $e^o=f^{o}sm$ . The profit distribution is presented in Table 3. Similar to Scenario 2, it is easy to prove that there will be no leftover fund with outside stock, so the market revenue is used for distribution. If the realized market revenue is sufficiently high, the co-op distributes the surplus by equity after product payment; otherwise, the co-op pays farmers as much as possible and returns nothing to investors. Because of the limited liability, the payment to farmers shall be no more than the realized market revenue. Comparing Table 3 with Table 2, we observe that for a given $s$ , $m$ , and $p_0$ , outside stockholders do not necessarily receive a higher portion of the profit than preferred stockholders, and indeed receive a smaller portion when $p_0\le p<(k^p/m)+p_0$ . Consequently, it is not immediately clear which type of external stock yields a higher return for investors.

Table 3.

The profit distribution with outside stock after the realization of market revenue.

	Product	Return to	Farmers’
	payment	investors $x^o$	profit
if $p\ge p_0$	$p_{0}m$	$\frac{f^o}{1+f^o}[pm-p_{0}m]$	$\frac{1}{1+f^o}[pm-p_{0}m]+p_{0}m-sm$
if $p<p_0$	$pm$	$0$	$pm-sm$

Following Table 3, the expected return to investors is $E[X^o]\dot{=}[f^o/(1+f^o)]E[P-min(p_0,P)]m$ . Then, the co-op’s second-stage problem can be written as:

$$\begin{array}{rl}{\pi }^o(s)=& \underset{p_0,f^o}{max}E[Pm-X^o+f^{o}sm-c_{v}m-c_f]\\ \text{s.t.}& (1+f^o)sm\ge c_{v}m+c_f,\\ & E[X^o]\ge (1+r^o)f^{o}sm,\\ & 0\le f^o\le {\hat{f}}^o,p_0\ge 0.\end{array}$$

Analyzing this problem, we see that the objective is increasing with $p_0$ while the expected return to outside investors $E[X^o]$ is decreasing with $p_0$ . In other words, the farmers want higher product payments while the external investors want the opposite. Therefore, the co-op determines a farm-gate price $p_0$ up to a level beyond which investors will no longer invest, that is, $E[X^o]=(1+r^o)f^{o}sm$ . This is because a high product payment, which is paid out before the dividends, can lead to insufficient returns to investors and make them unwilling to invest.

Lemma 2

In the second stage, with given $s$ and $m$ , the optimal strategy is to use outside stock to fund any shortfall on top of the farmers’ investment $sm$ , that is, $f^{o}sm=(c_v-s)m+c_f$ ; and when $f^o>0$ , the optimal farm-gate price $p_0$ satisfies

$$E[min(p_0,P)]m={\mu }_{p}m-(1+r^o)(c_{v}m+c_f),$$

(7)

which requires ${\mu }_p-(1+r^o)[c_v+(c_f/m)]\ge 0$ .

As equation (7) sets the optimal farm-gate price given a certain co-op size, it also highlights the conflicting interests of farmers as patrons and investors. The left-hand side of equation (7) is the expected product payment, while the right-hand side is the expected market revenue minus the financial return. Since the co-op’s total cost $c_{v}m+c_f$ is funded by both common stock and outside stock, the financial return should be repaid to both farmers who hold common stock and external investors who hold outside stock. Also, because the participation constraint for external investors is binding with an expected premium of $r^o$ , the total financial return for all equity investments is $(1+r^o)(c_{v}m+c_f)$ . Thus, Equation (7) confirms that the co-op’s market revenue is paid out as the product payment to farmers and the financial return to all investors. So, from the revenue, if more is paid for the product payment, then less is left for investors, and vice versa. This not only reflects the conflicting benefits between farmers and external investors, but also the conflicting roles of farmers: recall that farmers are both patrons who receive product payment and investors who receive dividends.

Furthermore, ensuring a non-negative product payment requires ${\mu }_{p}m\ge (1+r^o)(c_{v}m+c_f)$ . This implies that the co-op size in equilibrium should not be too small, that is, $m\ge [(1+r^o)c_f]/[{\mu }_p-(1+r^o)c_v]$ . Only when the co-op size is larger than a certain value, is the expected market revenue able to cover the expected financial cost. Note that if the premium rate expected by investors is sufficiently high, for example, $r^o\ge ({\mu }_p-c_v)/c_v$ , it is never affordable to raise outside stock.

With Lemma 2, the first-stage problem is:

$$\begin{array}{rl}{\pi }^{o*}=& \underset{s}{max}{\pi }^o(s)=\underset{s}{max}[{\mu }_p-(1+r^o)c_v+r^{o}s]m-(1+r^o)c_f\\ \text{s.t.}& g_1^o(s)\equiv c_{v}m+c_f-sm\ge 0,\\ & g_2^o(s)\equiv (1+{\hat{f}}^o)sm-[c_{v}m+c_f]\ge 0,\\ & g_3^o(s)\equiv (\beta m-1)c_f-r^o[c_{v}m+c_f-sm]\ge 0,\\ & [{\mu }_p-(1+r^o)(c_v+\frac{c_f}{m})]f^o\ge 0,\\ & m=n\frac{\overline{w}-s}{\overline{w}},1/\beta \le m\le n,0\le s\le \overline{w}.\end{array}$$

(P3)

When comparing Problems (P2) and (P3), it is interesting to observe that the first-stage problem with outside stock is highly similar to that with preferred stock, except that the parameters $r^i$ and ${\hat{f}}^i$ can have different values under the two scenarios. This is because of the similar financial requirements for the co-op; that is, no matter whether outside stock or preferred stock, the co-op will only use external equity to fund any capital shortfalls on top of the common stock and repay external investors, in expectation, at their expected premium rate, as suggested by solving the second-stage problem. There is one difference between (P2) and (P3), however, regarding the co-op size constraint: on top of $m\ge 1/\beta$ , which is required for the preferred stock case, the outside stock case further requires $m\ge (1+r^o)c_f/[{\mu }_p-(1+r^o)c_v]$ to ensure a non-negative farm-gate price $p_0$ . Note that if $(1+r^o)c_f/[{\mu }_p-(1+r^o)c_v]\le 1/\beta$ , that is, $r^o\le [{\mu }_p-(c_v+\beta c_f)]/(c_v+\beta c_f)$ , then Problem (P3) becomes equivalent to Problem (P2) as they both require $m\ge 1/\beta$ . However, if $r^o>[{\mu }_p-(c_v+\beta c_f)]/(c_v+\beta c_f)$ , the lower bound for the co-op size with outside stock is larger than that with preferred stock, that is, $(1+r^o)c_f/[{\mu }_p-(1+r^o)c_v]>1/\beta$ . This will lead to different thresholds for the co-op’s establishment, as is illustrated in Figure 3.

Figure 3.

Structure of the financing policy with outside stock in equilibrium. Note: We use the same parameters as in Figure 2.

Similarly, define ${\underset{\_}{s}}_1^o\equiv min\{ss.t.g_1^o(s)\ge 0\}$ , ${\underset{\_}{s}}_2^o\equiv min\{ss.t.g_2^o(s)\ge 0\}$ , ${\underset{\_}{s}}_3^o\equiv min\{ss.t.g_3^o(s)\ge 0\}$ , and ${\hat{s}}^o=[(\overline{w}+c_v)/2]-[({\mu }_p-c_v)/2r^o]$ .

Theorem 2

(Scenario 3) Suppose $n\ge max\{4\overline{w}{c}_f/(\overline{w}-c_v{)}^2,4\overline{w}{c}_f(1+r^o)/[r^o(\overline{w}-c_v+c_f/r^o{)}^2],(2c_v+2\beta c_f-{\mu }_p)c_f/[({\mu }_p-c_v-\beta c_f)c_v],2c_f(1+r^o)/[{\mu }_p-(1+r^o)c_v]\}$ , there exist several thresholds ${\hat{w}}_1^o,{\hat{w}}_2^o,{\hat{w}}_3^o$ , ${\underset{\_}{w}}^o$ (with ${\underset{\_}{w}}^o<{\hat{w}}_2^o/{\hat{w}}_3^o<{\hat{w}}_1^o$ ) which are functions of $r^o$ , and ${\tilde{r}}^o$ , such that in equilibrium the share price $s^{o*}$ and the size of outside stock $f^{o*}$ are characterized as follows:

No business is established if $\overline{w}<{\underset{\_}{w}}^o$ .

Not to include outside stock, that is, $f^{o*}=0$ and $s^{o*}={\underset{\_}{s}}_1^o$ if $\overline{w}\ge max\{{\hat{w}}_1^o,{\underset{\_}{w}}^c\}$ .

Include the outside stock but not to the limit, $0<f^{o*}<{\hat{f}}^o$ and

$s^{o*}={\hat{s}}^o$ if $max\{{\hat{w}}_2^o,{\hat{w}}_3^o\}\le \overline{w}\le max\{{\hat{w}}_1^o,{\underset{\_}{w}}^c\}$ ;

$s^{o*}={\underset{\_}{s}}_3^o$ if $r^o>{\tilde{r}}^o$ and ${\underset{\_}{w}}^o\le \overline{w}\le {\hat{w}}_3^o$ .

Issue outside stock up to the limit, that is, $f^{o*}={\hat{f}}^o$ and $s^{o*}={\underset{\_}{s}}_2^o$ if $r^o\le {\tilde{r}}^o$ and ${\underset{\_}{w}}^o\le \overline{w}\le {\hat{w}}_2^o$ .

With the co-op’s decision on $s^{o*}$ , the farm-gate price $p_0^{o*}$ is determined by equation (7).

Each statement in Theorem 2 corresponds to an analogous statement in Theorem 1, with the statements also providing insights into the three key decisions (see Figure 3). As explained above, there exists a watershed in terms of $r^o$ . If $r^o\le ({\mu }_p-c_v-\beta c_f)/(c_v+\beta c_f)$ , the structure of the equilibrium financial strategy with outside stock is the same as that with preferred stock, as evidenced by the comparison between Figures 2 and 3. This may seem counterintuitive, as one would expect distinct structures for the financial strategy given the significant differences between these two types of equity in terms of residual claim rights and profit distribution, as explained in the Introduction. However, this similarity is not coincidental but rather stems from the similar formulation of the first-stage problem. As explained, the co-op utilizes external equity to address any capital shortfall and repays external investors at their expected premium rate. If  $r^o>({\mu }_p-c_v-\beta c_f)/(c_v+\beta c_f)$ , the outside stock case has different thresholds for the co-op’s establishment than the preferred stock case, though this does not change the equilibrium decisions. In Section 6, we will further demonstrate that the thresholds with outside stock actually increase compared to Scenario 2 if $r^o=r^p$ and ${\hat{f}}^o={\hat{f}}^p$ .

While preferred stock and outside stock may exhibit similar structures in the co-op’s equilibrium financial decisions, they are priced differently through the farm-gate price $p_0$ (and the face value $k^{p*}$ for preferred stock). Recall that the farm-gate price and the face value of preferred stock $(p_0^{p*},k^{p*})$ are determined concurrently by equation (6). In contrast, when issuing outside stock, the farm-gate price is determined by equation (7) and is therefore uniquely determined by the co-op’s decision on the share price. This distinction stems from the different financial terms associated with preferred and outside stock. Preferred stock bears a fixed return (the face value $k^{p*}$ ), which is determined simultaneously with the decision on the size of preferred stock. Consequently, the influence of the farm-gate price on the risk of preferred stock can be moderated by adjusting the face value. Conversely, there is no fixed return attached to the outside stock as it shares the net profit with common stock by equity contributions. Therefore, the financial return to investors is directly influenced by the amount paid to farmers as product payments, leading to the farm-gate price being uniquely determined in equilibrium. This highlights the different approaches for the co-op to manage the farm-gate price when proposing financial contracts for the two types of equity. With outside stock, tight control over the farm-gate price is necessary due to its significant impact on financial returns, and this should be factored in early on when proposing financial terms. In contrast, with preferred stock, the control over the farm-gate price can be more relaxed, allowing the co-op to commit to different farm-gate prices without significantly altering other equilibrium decisions.

5. Managerial Insights

In this section, we provide managerial insights under our specific financing types. Recommendations regarding financing types will be investigated in the following section.

5.1. The Role of Farm-Gate Pricing in Agricultural Co-ops

The first insight from our analysis is the unique role of the farm-gate price in agricultural co-ops. To start with, our model indicates that the influence of the farm-gate price in a co-op supply chain is not as significant as in a typical buyer–supplier chain. Typically, the purchasing price set by a buying company will play a critical role in motivating suppliers’ behavior (Ayvaz-Çavdaroğlu et al., 2021). However, this role of farm-gate price is muted in a co-op, particularly when the equity is limited to farmers only. As discussed in the Introduction, one feature that distinguishes the co-op is that it is owned by farmers and thus obliged to return all profit to its farmer-members. This feature makes the farm-gate price in a co-op less critical in motivating farmers’ participation. As such, a co-op does not need to commit to a farm-gate price when farmers make participation decisions.

However, the farm-gate price influences the investors’ returns and hence the co-op’s financial decisions when the equity is extended to external investors. As discussed with Lemmas 1 and 2, the farm-gate price reflects the conflicting benefits between farmers and external investors for both preferred stock and outside stock. This is consistent with the literature (Chaddad and Cook, 2004) that non-common stock can create conflicts with the interests of patron members.

Interestingly, our analysis also highlights the conflicting roles of farmers as patrons who care about product payments and as investors (or owners) who enjoy the residual claim. When the equity is limited to farmers, this conflict is not apparent because both product payments and the after-product payments residual claim belong to the farmers. However, when the equity is open to external investors, this conflict becomes apparent. Naturally, farmers as patrons expect a high farm-gate price while they as investors would prefer a low farm-gate price so the residual claim can be high. In this sense, the farm-gate price serves as a tool for reconciling the conflict in farmers’ dual roles through different approaches for preferred stock and outside stock.

5.2. Fixed Cost and the Value of Pooling

As per our analysis, the average cost of the co-op decreases as the co-op size increases, which demonstrates a pooling benefit and forms a motivation for farmers to participate. In our model, the pooling benefit is associated with the fixed cost $c_f$ : usually, a higher fixed cost suggests a larger pooling benefit, because the cost-savings for individual farmers joining the co-op are in proportion to $c_f$ . Thus, the value of pooling can be manifested by analyzing the impact of the fixed cost $c_f$ . The fixed cost can generate competing effects. On the one hand, a higher fixed cost, which indicates larger cost-savings and pooling benefits, will motivate more farmers to participate. On the other hand, a higher fixed cost increases the total cost and thus poses a higher requirement for raising capital through equity. This could discourage farmers from participating, since it could force the co-op to raise more from common stock and thus make it harder for farmers. So, how the co-op size and the financial decisions change with the fixed cost is not straightforward.

Before visualizing the impact, we first characterize the financial strategies in equilibrium in terms of the farmers’ wealth and the fixed cost $c_f$ (presented in Proposition EC.1 in the E-Companion). Recall that when $r^o\le ({\mu }_p-c_v-\beta c_f)/(c_v+c_f)$ , the structure of the equilibrium decisions with outside stock is the same as that with preferred stock. To make Figure 4 applicable to both preferred and outside stock, we constrain $c_f\le [{\mu }_p-(1+r^i)c_v]/(\beta +r^i)$ .

Figure 4.

The influence of the fixed cost and the pooling benefit. Note: We set ${\mu }_p=400$ , $c_v=200$ , ${\hat{f}}^i=0.8$ , $n=50$ , $r^i=0.2$ , $\overline{w}=800$ . Furthermore, the profit has been scaled down by 100, $s^{i*}$ by 5, while the proportion $f^{i*}$ scaled up by 25.

Figures 4(a) and 4 (b) illustrate how the co-op size $m^{i*}$ , the profit ${\pi }^{i*}$ , and various financial variables change with different levels of fixed cost; and the financial aspect includes share price $s^{i*}$ , the portion of external funds $f^{i*}$ , and the amount of internal funds $s^{i*}{m}^{i*}$ and external funds $f^{i*}{s}^{i*}{m}^{i*}$ . A clear turning point is evident (at $c_f={\tilde{c}}_f^i$ ) where the plots of all variables change directions. This is due to the varying effects of the fixed cost on farmers’ participation. When the fixed cost is very low, the pooling benefit that motivates farmers to participate is not prominent, thus constraining the co-op size significantly. It further constrains the size of external equity, as the farmers’ participation constraint requires the financial cost to be no more than the cost-saving of joining the co-op. Thus, internal funds (common stock shares collected from farmer members) provide a main source of capital to cover the total cost when the fixed cost is low (see Figure 4(b)). As the fixed cost increases, the pooling benefit becomes more prominent and the increased pooling benefit allows the co-op to issue more equity from external funds, both of which greatly increase the co-op size and the total profit despite the higher total cost; accordingly, the co-op increases external funds and decreases internal funds. However, when the fixed cost becomes large, for example, $c_f>{\tilde{c}}_f^i$ , the farmers’ participation constraint becomes relaxed so the capacity for external equity stops increasing with the fixed cost, and the pooling benefit no longer contributes to the co-op size. Instead, the fixed cost increases the total cost, demanding a higher share price for the common stock. Hence, when the fixed cost continues to increase, both the co-op size and the farmers’ total profit slowly decrease while the proportion of external funds stabilizes at the limit.

The results confirm that pooling benefit is a key driver for farmers to participate and so increases the co-op size and the total profit. Yet these benefits can only be enjoyed until the fixed cost reaches a certain level. The pooling effect does not always help expand the co-op size or increase the profit, and a high fixed cost could lead to side effects, where the co-op size and the total profit start decreasing with the fixed cost.

6. Policy Comparison

In this section, we focus on another important aspect of the co-op’s decision, that is, which type of funding is better. We first compare external equity with the benchmark case and then compare performance between the two types of external equity. As preferred stock and outside stock have a similar policy structure and thus lead to the same performance in several cases, the term “dominate” is used to indicate “weakly dominate” throughout this section.

Proposition 2 presents the comparison between common stock and external equity in terms of co-op size, farmers’ total profit, and the individual farmer’s profit. In the earlier analysis, we have shown that the equilibrium share price with preferred stock or outside stock is less than that in the benchmark case, that is, $s^{i*}\le {\underset{\_}{s}}^{c*}$ . Therefore, issuing preferred stock or outside stock (if it is optimal to do so) contributes to the co-op size, and also contributes to farmers’ total profit because excluding external funds is always one option for the co-op. This is consistent with the practice followed by many co-ops raising funds from either preferred stock or outside stock to increase the co-op size and/or profit.

Proposition 2

In comparison with the financial structure limited to common stock,

The financial structure with either preferred stock or outside stock increases the co-op size and the total farmers’ profit, i.e., ${\pi }^{i*}\ge {\pi }^{c*}$ and $m^{i*}\ge m^{c*}$ .

If $c_f(m^{i*}-m^{c*})/(m^{i*}{m}^{c*})\ge r^i[c_v+(c_f/m^{i*})-s^{i*}]$ , the financial structure with either preferred stock or outside stock increases the individual farmer’s profit; otherwise not.

An interesting observation from Proposition 2 is that issuing external equity does not guarantee an improvement in the individual farmer’s profit, which equals the average profit. This is because of the two opposing effects of external equity. On the one hand, introducing external equity increases the co-op size and can lead to a cost reduction through the pooling effect. On the other hand, issuing external equity increases the financial cost of the co-op. So, the individual farmer’s profit is increased only if the cost-saving is larger than the financial cost of raising external equity (as expressed in the inequity condition in Proposition 2), and not otherwise. A specific example of the individual farmer’s profit being reduced compared to the benchmark case is when $s^{i*}={\underset{\_}{s}}_3^{i*}$ where the farmers’ participation constraint becomes binding. This leads to the average profit ${\pi }^{i*}/m^{i*}={\mu }_p-c_v-\beta c_f$ (note that $r^i$ is high in this case), which is reduced because ${\pi }^{c*}/m^{c*}>{\mu }_p-c_v-\beta c_f$ . Note, although issuing preferred or outside stock may decrease the average profit, farmers are still willing to participate as long as their profit from the co-op is higher than that from their outside option.

This also suggests maximizing the total profit of all farmer-members is not always consistent with maximizing the individual farmer’s profit. With the objective of maximizing the total profit, the co-op may expand the co-op size at the cost of a decreased average profit. As such, the equilibrium co-op size can differ when the co-op applies different objectives. Specifically, when maximizing the total profit, the co-op will choose a co-op size where the marginal utility of $m$ to the total profit is zero, that is, $\mathrm{\partial }{\pi }^i/\mathrm{\partial }m=0$ (when all constraints are relaxed). In contrast, when the objective is maximizing the individual farmer’s profit, the co-op will choose a co-op size where the marginal profit equals the average profit, that is, $\mathrm{\partial }{\pi }^i/\mathrm{\partial }m={\pi }^i/m>0$ . Therefore, the equilibrium co-op size when maximizing the total profit is no smaller than that when maximizing the individual farmer’s profit.

With this result, we are also interested in how the co-op and its external financial strategies impact the profit of the whole farmer population. To explore this, we first examine the profit of farmers before a co-op is established. In the absence of a co-op, only farmers who can afford to process independently, that is, those with $w_k>c_v+\beta c_f$ , realize a positive profit. However, with the formation of a co-op, all farmers who can afford to join the co-op, that is, those with $w_k\ge s$ , get a positive profit. Furthermore, it is evident that the share price in equilibrium is less than the cost of individual businesses, that is, $s^{i*}<c_v+\beta c_f$ , due to the cost reduction achieved by the co-op through the pooling effect. Consequently, the co-op enables more farmers to participate in the business, thereby increasing their total profit, particularly for farmers with $s^{i*}<w_k<c_v+\beta c_f$ who cannot engage in processing independently. Meanwhile, other farmers who choose not to join the co-op are not adversely affected. Hence, the co-op enhances the overall profit of all farmers in the system, as we assume the individual farmers get the same market price as the co-op does. This improvement would be more significant if the co-op can secure a higher market price than individual farmers. Moreover, as demonstrated in Proposition 3, when the co-op raises external funds through preferred or outside stock, the size of the co-op is further expanded. This implies that external financing contributes to further enhancing the overall profit of the entire farmer population.

Next, we compare the performance of preferred stock versus outside stock. The comparison between the two is more complicated because each scenario could lead to a different financial structure in equilibrium. To produce meaningful comparisons, we make assumptions about whether external equity-related parameters, such as the size limits of external funds ${\hat{f}}^i$ and the premium rate $r^i$ , are equal for preferred stock and outside stock. Accordingly, Theorem 3 presents the results when the size limits of external funds are equal, and Theorem 4 when the size limits are different.

Theorem 3

For both the co-op size and the farmers’ total profit,

Suppose $r^p=r^o$ and ${\hat{f}}^p={\hat{f}}^o$ , the profit and the co-op size in equilibrium are the same with preferred and outside stock when $r^i\le ({\mu }_p-c_v-\beta c_f)/(c_v+\beta c_f)$ or $\overline{w}\ge {\underset{\_}{w}}^c$ ; otherwise, preferred stock dominates.

Suppose $r^p<r^o$ and ${\hat{f}}^p={\hat{f}}^o$ , preferred stock dominates.

When both preferred stock and outside stock have the same size limit and investors’ premium rate, that is, ${\hat{f}}^p={\hat{f}}^o$ and $r^p=r^o$ , preferred stock dominates if the premium rate is high or farmers’ wealth is low; otherwise, the two types of external equity are equal (which has been explained earlier). Note that the dominance of preferred stock is only due to its larger contribution to the co-op’s establishment, rather than the profit perspective. Indeed, if the co-op can be established by both, the total profit with preferred stock is the same as that with outside stock. However, recall that the co-op has higher flexibility in making decisions on the farm-gate price when issuing preferred stock, and this is an advantage of preferred stock over outside stock, even when both can achieve the same total profit and co-op size.

In practice, investors can demand different premium rates for preferred stock and outside stock. In particular, investors are likely to demand a return higher from outside stock than from preferred stock, that is, $r^p<r^o$ , because outside stock is generally regarded as having less potential for regular dividends, given outside stock does not enjoy a fixed dividend and is not senior to common stock. In this case, we show that if $r^p<r^o$ , preferred stock dominates in terms of both the co-op size and total profit because of its lower financial cost.

The above results are derived when the size limits of preferred stock and outside stock are the same, which may not always be the case. Recall that outside stock raises concerns over the co-op status of the business, because it shares the net surplus with common stock. In some co-ops, outside stock may even bear limited control and voting rights, which further increases concerns about demutualization. Therefore, it is likely that the size limit of outside stock is less than that of preferred stock, that is, ${\hat{f}}^o<{\hat{f}}^p$ . However, in the analysis, we do not exclude the possibility ${\hat{f}}^o>{\hat{f}}^p$ . For tractability, we limit our analysis to the most relevant case when $\overline{w}\ge {\underset{\_}{w}}^c$ , where the co-op can be established in the benchmark case.

Theorem 4

When $\overline{w}\ge {\underset{\_}{w}}^c$ , in terms of the farmers’ profit: (i) with ${\hat{f}}^p>{\hat{f}}^o$ , preferred stock dominates if $r^p\le r^o$ ; (ii) with ${\hat{f}}^p<{\hat{f}}^o$ , outside stock dominates if $r^p=r^o$ .

Theorem 4 shows that preferred stock dominates in terms of the total profit if it has a larger size limit ( ${\hat{f}}^o<{\hat{f}}^p$ ) and/or a smaller financing cost ( $r^p\le r^o$ ), which is likely to be the case in the practice, as discussed earlier. In this case, preferred stock bears the advantages of a lower cost and larger size limit compared to the outside stock. However, if ${\hat{f}}^p<{\hat{f}}^o$ , then outside stock may dominate if the two types of equity have the same financial cost. This observation may appear to deviate from financial theory, which typically expects preferred stock to dominate. However, the unique feature of agricultural co-ops, particularly the size limit of external financing ${\hat{f}}^i$ , also plays a crucial role in this comparison and contributes to the overall profit. With a larger size limit, the co-op can raise more capital from external investors, especially when farmers face significant cash constraints. This increased external financing capacity can significantly contribute to the profit, potentially favoring outside stock over preferred stock. However, it is worth noting that outside stock may not dominate if ${\hat{f}}^p<{\hat{f}}^o$ along with $r^p<r^o$ , as illustrated in Figure EC.8 in the E-Companion. Particularly, preferred stock could still outperform if its financial cost is sufficiently low, despite the higher size limit of the outside stock.

In summary, preferred stock can be attractive for the co-op due to its relatively low financial cost, higher tolerance on the fund size limit, as well as greater flexibility in the farm-gate price. In this regard, our analysis provides corroboration for our observation that many co-ops prefer to issue preferred stock when seeking external equity (Pitman, 2020). However, from the perspective of investors, preferred stock with a fixed return rate may not provide sufficient return, depending on the interest rate environment and the perceived risk of the co-op. While preferred stock can be attractive to external investors when interest rates are low, investors will quickly switch to alternative investment choices, particularly those that provide a higher rate of return and that are considered to be of a lower risk, when the interest rate rises. Therefore, when preferred stock is unattractive, outside stock could be a good option.

7. Conclusions and Future Research

This work is motivated by the increasing number of co-ops restructuring their financial structures and the growing number of co-ops being established with cash-constrained farmers in developing countries. In addition to members’ equity, co-ops have options for seeking external funds, including preferred stock and outside stock. To control the risk and maintain the control rights of farmers, co-ops usually constrain the size of external funds based on how much they can raise from farmers through common stock. Despite the prevalence of such strategies in practice, they have received limited attention in the literature. Thus, one of the important contributions of this paper is developing a stylized framework that helps when building new models to investigate various research questions on related financing and operations problems in co-ops.

Key results from analyzing the model are briefly summarized as follows. First, we have characterized the equilibrium financial strategies when raising external funds and answered questions concerning whether and how much to issue, and under what conditions. Furthermore, our analysis finds that financial strategies in relation to the farm-gate pricing differ when issuing preferred stock compared to outside stock. Second, we have investigated the effect of the pooling benefit on the farmers’ participation decision and show that the pooling benefit is able to motivate farmers to participate while also allowing the co-op to raise more external equity. Third, by comparing the performance of the two types of external funds, we have provided important insights into the co-op’s choice of financing options.

Several limitations arise due to our specific modeling assumptions, and further research is needed to validate the relevance of our insights when these assumptions are relaxed. First, we only consider uncertain market price and assume deterministic yields in this paper. However, there are other uncertainties in agricultural operations that can bring financial risks to investors, such as uncertain yield or uncertain demand. Therefore, considering multiple uncertainties including uncertain and/or heterogeneous yield is worthwhile for future research. Second, we assume that outside stock does not convey any control or voting rights. However, in some co-ops, outside stock may bear limited control and voting rights. In this case, the external investors could challenge the co-op’s objective of maximizing the farmers’ profit and more trade-offs will be considered. Third, we assume that the market price is exogenous. However, it would be interesting to examine a situation in which the market price is determined by the total supply of all farmers and each farmer determines an equilibrium output. Fourth, our model assumes that all farmers are risk-neutral. However, in reality, farmers could be risk-averse, especially toward equity investment. This is interesting but left for future research. Fifth, we consider pure equity financing; but it could be worthwhile considering both equity and debt financing. Last, it would be helpful to examine our model’s predictions regarding priorities for financing strategies using empirical data.

Supplemental Material

sj-pdf-1-pao-10.1177_10591478241262279 - Supplemental material for Financing and Farm-Gate Pricing Strategies for Agricultural Cooperatives With Cash-Constrained Farmers

Supplemental material, sj-pdf-1-pao-10.1177_10591478241262279 for Financing and Farm-Gate Pricing Strategies for Agricultural Cooperatives With Cash-Constrained Farmers by Xiaoyan Qian, Quan Zhou and Tava Lennon Olsen in Production and Operations Management