**5. Theoretical analysis of capital investment for handling postharvest crops**

This section presents the economic theoretical model illustrating the circumstances of capital investment for managing postharvest crops in developing countries. Because many of this chapter's readers are assumed to be unfamiliar with these constructs, a simple theoretical model was formulated. As established, the development of facilities with sufficient functions is necessary to reduce postharvest losses; however, budget constraints render many developing countries unable to afford the construction of such facilities. Subsequently, development support from foundation bodies (i.e. international organisations and investors) presents a realistic financing method. To encourage this development support, sufficient outcomes (i.e. reduction of postharvest losses) are required; however, as discussed in Section 4, some capital investments for managing postharvest crops in developing countries are not achieving the expected results (i.e. postharvest loss has not decreased as much as expected). Additionally, we also provide case studies of agricultural development support from a government organisation, a nongovernment organisation (NGO) and foreign direct investment to the developing countries. The case studies are compared to the theoretical analysis to consider the factors behind its successes.

### **5.1 Illustration of circumstances in which invested capital is not fully utilised to handle postharvest crops**

This subsection introduces a theoretical illustration of the circumstances in which invested capital is not fully utilised to reduce postharvest losses. This circumstance can be illustrated by the following setup.<sup>4</sup>

$$Y = L^a K^{1-a} \tag{1}$$

where *Y* is postharvest crops delivered to consumers without being discarded, *L* represents the number of labourers handling postharvest crops, *K* is the capital invested to handle postharvest crops and *α* measures the dependence on *L* to produce *Y*. <sup>5</sup> Eq. (1) indicates that postharvest crops are handled by *L* and *K* and a higher *Y* indicates less postharvest losses.

By differentiating *Y* with respect to *L* results in the following equation:

$$\frac{\partial Y}{\partial L} = a \left( \frac{K}{L} \right)^{1-a} \tag{2}$$

Eq. (2) measures how much *Y* increases when 1 unit of *L* is added. This equation has some notable features. According to Eq. (2), *<sup>∂</sup><sup>Y</sup> <sup>∂</sup><sup>L</sup>* is positively related with *<sup>K</sup> <sup>L</sup>*; thus, the larger the size of *K* and the smaller the size of *L* leads the larger the size of *<sup>∂</sup><sup>Y</sup> ∂L*. This implies that when there is an insufficient number of labourers and substantial capital, some capital will be unused. In such circumstances, additional labour will significantly improve productivity. In contrast, if there is insufficient capital and a large number of labourers, additional labourers will be unable to leverage capital to produce *Y*. Furthermore, if the postharvest crop handling depends excessively on labourers, *α* will be close to 1; hence, *<sup>∂</sup><sup>Y</sup> <sup>∂</sup><sup>L</sup>* becomes a larger value. Conversely, if the postharvest crop handling depends excessively on capital, *α* becomes close to 0, then *<sup>∂</sup><sup>Y</sup> <sup>∂</sup><sup>L</sup>* becomes close to 0.

By differentiating *Y* with respect to *K*, the following equation is generated.

$$\frac{\partial Y}{\partial K} = (\mathbf{1} - a) \left(\frac{L}{K}\right)^a \tag{3}$$

According to Eq. (3), *<sup>∂</sup><sup>Y</sup> <sup>∂</sup><sup>K</sup>* is positively related with *<sup>L</sup> <sup>K</sup>*; thus, a larger size of *L* and smaller size of *K* leads to a larger size of *<sup>∂</sup><sup>Y</sup> <sup>∂</sup>K*. Moreover, if *<sup>α</sup>* is close to 0, *<sup>∂</sup><sup>Y</sup> <sup>∂</sup><sup>K</sup>* becomes the larger value. Conversely, if *α* is close to 1, *<sup>∂</sup><sup>Y</sup> <sup>∂</sup><sup>K</sup>* will become close to 0.

Considering the relationship between *α*, *<sup>∂</sup><sup>Y</sup> <sup>∂</sup><sup>L</sup>* and *<sup>∂</sup><sup>Y</sup> <sup>∂</sup>K*, the production process appears to depend excessively on one input (i.e. *L* or *K*), and adding a few dependent inputs (i.e. *L* in the case of small *α* and *K* in the case of large *α*) does not increase production as expected.

Due to lack of sufficient knowledge and skills, even if high-performance equipment for managing post-harvest crops is installed, farmers are unable to fully utilise it. This circumstance reflects a case of *α* almost equalling 1. As was demonstrated, when *α*≈ 1, *<sup>∂</sup><sup>Y</sup> <sup>∂</sup><sup>K</sup>* becomes close to 0. Thus, capital investment for the management of postharvest crops does not significantly improve the situation. To improve this circumstance and sufficiently reduce the loss of postharvest crops with the capital

<sup>4</sup> Eq. (1) takes form of Cobb–Douglas production function, which is often used by economists to express output as a function of labour and capital.

<sup>5</sup> We assume that the number of crops harvested is fixed.

*Challenges and Measures to Recapitalise Handling of Postharvest Crops in Developing… DOI: http://dx.doi.org/10.5772/intechopen.101222*

investment, production must be processed with a smaller value of *α*. This is only possible when labour is capable of utilising the capital.

#### **5.2 Funding Body possible when under outcome uncertainties from development support for reducing postharvest losses**

As illustrated in Subsection 5.1, if labourers are unable to utilise the capital for handling postharvest crops, increased capital does not reduce postharvest losses. This subsection analyses the process of the funding body vest crops with the capital investments. An additional theoretical setup is introduced as a part of this analysis, partially referring to the equations in the previous subsection. The setup assumes two time periods (*t* ¼ 1 *and* 2Þ. <sup>6</sup> The funding body expects the provision of development support to increase *K*, which will cost *C*. If the support is provided at *t* ¼ 1, *K* is enhanced at *t* ¼ 2; however, improvement of postharvest management depends on how much the labour can utilise the invested capital, which is assumed by two potential values of *Y* at *t* ¼ 2, represented by *Y*<sup>1</sup> and *Y*2, which satisfy a condition of *Y*<sup>2</sup> <*C*<*Y*1. *Y*<sup>1</sup> indicates that development support can sufficiently contribute to reducing postharvest losses, whereas *Y*<sup>2</sup> indicates that the cost of development support exceeds its contribution. A chance of having *Y*<sup>1</sup> is probability *P* where 0≤*P*≤1, and *P* is inversely related to *α*. Finally, the model uses a risk-free rate *r* to discount the values at *<sup>t</sup>* <sup>¼</sup> 2 to *<sup>t</sup>* <sup>¼</sup> 1.<sup>7</sup> This is illustrated below in **Figure 1**.

A present value of expected outcome *E O*ð Þ from the development support can be calculated as follows.

$$E(O) = \frac{P \times Y\_1 + (1 - P) \times Y\_2}{1 + r} \tag{4}$$

As it is clear from Eq. (4), the size of *E O*ð Þ depends on, and *P* depends on *α*. From the funding body's perspective, development support is not worth providing unless it can contribute to sufficiently reducing postharvest losses. To investigate the decision to provide development support, this study uses the return on investment (ROI) shown in Eq. (5).

**Figure 1.** *Outcome from development support for reducing postharvest losses.*

<sup>6</sup> In this setup, Eqs (1)–(3) are assumed at *<sup>t</sup>* <sup>¼</sup> 2.

<sup>7</sup> Financial analysis generally considers that a future monetary value is lower than the corresponding current monetary value (i.e. 1 dollar at *t* ¼ 2 is valued lower than 1 dollar at *t* ¼ 1). This is because money at a current time can be invested, and an investment return can be realised at a future time.

*Postharvest Technology - Recent Advances, New Perspectives and Applications*

$$\text{ROI} = \frac{E(O) - C}{C} \tag{5}$$

The funding body decides to provide development support when *ROI* >0, and the opposite is true in the case of *ROI* < 0.<sup>8</sup> As is clear from Eq. (5), *ROI* is positively related to the size of *E O*ð Þ; hence, when *α* is sufficiently reduced, the development support is provided.

Summing up the above analysis, if labour does not have enough capacity to utilise the invested postharvest technology, the funding body forgoes development support.

#### **5.3 The case studies of capital investment for handling postharvest crops**

In Subsections 5.1 and 5.2, we theoretically demonstrated the situation where invested capital is not fully utilised to handle postharvest crops and the funding body's judgement under outcome uncertainties from development support for reducing postharvest losses. In this subsection, we analyse the three successful cases of agricultural development support from the government organisation, NGO and foreign direct investment to the developing countries. We compare the cases and the theoretical model to consider the factors behind the success of the cases.

#### *5.3.1 Post-harvest handling and storage (PHHS) project in Rwanda*

First, we try to consider the successful case of the government organisation (U.S. Agency for International Development (USAID)).<sup>9</sup> USAID is managing PHHS Project carried out between September 2009 and August 2013, which budgeted 8.3 million US dollars [17]. The PHHS project is to integrate local farmers into commercial marketing channels as a way of driving investment in postharvest technology and process improvements for maize, beans and rice in Rwanda [17]. According to the report, the agricultural products are fragmented in Rwanda due to a lack of the farmers [17]. According to the report, the agricultural products are fragmented in Rwanda due to lack of the farmers' capital and know-how to efficiency harvest, store and market their surplus yields [17]. This situation is reminiscent of the case of having a high level of *α* and low level of *K* in Eq. (1) (i.e. there is a lack of capital, however, because the production process is overly dependent on labours, increasing capital cannot be expected to reduce the postharvest loss significantly). As was demonstrated in Subsections 5.1 and 5.2, one of the measurements to overcome the situation is reducing the value of *α* in Eq. (1) by improving the skill of local farmers. The latter can be achieved by providing training for local farmers. As a part of the PHHS project, the training for technical and business practices in postharvest handling are provided [17]. The training can be considered to help the local farmers to effectively utilise the capital to manage the postharvest products.

Additionally, we also pay attention to the funding process of this program. PHHS set an objective to mobilise private investment and bank finance to develop businesses that require storage infrastructure [17]. Such funding bodies are like the one illustrated in Subsection 5.2, which dislikes uncertainty of outcomes. If there is no intervention of PHHS, the private funding bodies would be discouraged to fund

<sup>8</sup> The funding body can be considered indifferent regarding the choice to provide or not provide the development support when *ROI* ¼ 0.

<sup>9</sup> USAID is established in 1961 to lead the US government's international development and humanitarian efforts [16].

*Challenges and Measures to Recapitalise Handling of Postharvest Crops in Developing… DOI: http://dx.doi.org/10.5772/intechopen.101222*

the project, because they can hardly expect its succession. However, the intervention of PHHS helps the private funding bodies to understand the project and expect *α* in Eq. (1) to be reduced. This is to alleviate the asymmetry of information, which is a barrier to undertaking financial transactions.

As a result of this project, 104 storage centres were constructed or rehabilitated and over 60,000 farmers were trained in postharvest handling and storage best practices [17].

#### *5.3.2 Sasakawa Africa Association (SAA)'s Activity in Africa*

In this subsection, we consider the case of the NGO called SAA that provides agricultural development support in Africa.<sup>10</sup> Although SAA is an NGO, they have a large financial resource and can provide sufficient assistance for the agricultural development in African countries [18]. SAA organises its operations under five key themes, and one of them (i.e. Theme 2) is to promote postharvest handling and agro-processing in African developing countries [18]. Their activity is diversified to many countries. For example, SAA launched a project in Tanzania to promote improved grain storage, both on the farm and also in the form of communal storehouses [18]. Moreover, at several locations in Tanzania, organised farmer groups were linked to credit institutions that would provide short-term loans against grain held by the associations in bonded warehouses [18].

The projects of SAA and USAID is in common with emphasising human resource development (training) in addition to providing financial support and capital constrictions between 1989 and 1995, about 1,000 of the country's 5,000 government extension workers received crop management training from Sasakawa-Global 2000 staff. Such training leads to lowering the value of *α* in Eq. (1).

In addition, rather than providing all the financial support, SAA and USAID tries to act as a bridge for transactions with other financial institutions and makes efforts to attract further investment.

Providing funding support to farmers in developing countries is accompanied by the risk due to the lack of available information and the uncertainty of future outcomes. If a prominent NGO like SAA act as a bridge, investors' anxieties will be alleviated and the problems shown in Subsection 5.2 will be resolved.

#### *5.3.3 China's overseas investment in agriculture*

Unlike the case in Sub-subsections 5.3.1 and 5.3.2, some countries encourage private investors to provide agricultural development support to the developing countries for a purpose of meeting their own needs. For example, China has promoted to increase overseas foreign direct investment (OFDI), and a large portion of OFDI is devoted to agricultural support in developing countries [19].

China is one of the major producers of agricultural products in the world; however, the contribution of agriculture to their GDP has dropped considerably over the past three decades [19]. This is mainly due to China's remarkable economic growth that has led to industrialisation. As a result, China faces a challenge in sustaining the self-sufficiency of agricultural products and increased import of agricultural products from other countries [19]. Especially, in recent years, China has emphasised ties with ASEAN, and OFDI to Cambodia, Myanmar and Laos is increasing [19].

<sup>10</sup> SAA is the NGO established in 1986 aiming to support the development of farming productivity and the rural economic value chain [18].

In Cambodia, many Chinese firms are directly involved in the development of plantations [19]. As a result, the export of rice, cassava, sugar and cocoa from Cambodia to China has significantly increased from 2012 to 2015 [19]. Similar to the case of Cambodia, the export of maize, rice, beans and oilseeds and tea from Laos to China has significantly increased [19].11

Similar to Sub-subsections 5.3.1 and 5.3.2, in this case, a large amount of capital was injected into the agricultural industry in the developing countries through OFDI from China. However, the report also points out some challenges in local work sites. For example, communication and consultation with local people are often challenging for foreign investors, and having lack of information flows causes distrust between foreign investors and local people.

As can be seen from the case studies in this section, there are some successful trials for providing agricultural development support to farmers in developing countries. The trials are operated by many types of organisations (i.e. government organisations, NGOs and private investors). One of the reasons for the success of these trials is that they provide comprehensive support such as training local farmers through agricultural development support. Moreover, by eliminating information asymmetry between investors and local farmers causing concerns about uncertainties of investment, the organisations help local farmers to obtain loans from private financial institutions.
