Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010)Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia 524 A Proposed Model of a Microcredit Institution: Break-Even Analysis, Borrowing Group Creditworthiness and Risk Analysis Debalina Roy1 and Koushik Ghosh2 1 Department of HR, Reliance Communications Ltd., Reliance House Kolkata, 34, Chowringhee Road, Kolkata-700071, INDIA email@example.com 2 Department of Mathematics, University Institute of Technology, University of Burdwan Golapbag (North), Burdwan-713 104, INDIA firstname.lastname@example.org Abstract. Co-operation is ubiquitous in social life. Here we try to explore how the mechanism of co-operation can generate income among the high-risk, low-income clients. In this paper we have suggested a model of the operation of microcredit institution by analyzing both borrowings & delinquency in the microcredit groups. The paper starts with a brief definition of microcredit and its history in Indian context, the difference of microcredit and general banking, microcredit and microfinance, role of Grameen Bank, women’s empowerment, concept of Self-Help Group, loan schemes, process of loan repayment and types of costs associated and afterwards a plan model is demonstrated on target group and organization building. A mathematical model is proposed to understand the break-even point related to loan size and interest rates. We have also proposed a mathematical model of borrowing group creditworthiness. Corresponding risk coefficient is also measured for the entire process. 1. Introduction Microcredit is defined as provision of credit of very small amount to the poor in rural areas for enabling them to raise their income levels, improve living standards. It is a process of pure improvement in the credit market that opens up self-employment options to some agents who otherwise could only work for wages or subsist. Micro-credit can either raise or lower long-run GDP, since it can lower use of both subsistence and full-scale industrial technologies. It typically lowers long-run inequality and poverty, by making subsistence payoffs less widespread . Now with more than 10,000 microcredit lending institutions worldwide, an estimated 16 million people are borrowing loans on this burgeoning system. Microfinance addresses a full range of banking needs of poor people. It includes Microcredit, micro- savings, insurance & also fund transfers. Microcredit, in characteristics is significantly different from general banking and the distinguishing features between them are tabulated below:
Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010)Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia 525 Microcredit General Banking 1. No collateral required 1. Collateral are required 2. Normally disbursed to the individual 2. Disbursed to an individual in a formal group 3. Given to the poor people 3. Generally disbursed after proper credit check 4. Service tax is collected 4. Interest is collected The necessities of microcredit can be listed as: 1. Organization Building 2. Women Empowerment 3. Poverty alleviation 4. Human development & human rights 5. Employment & income generation 6. Peace & prosperity. Pelligra  introduced the concept of trust responsiveness in the lender- borrower relationship and formalized it in a psychological game-theoretical model aimed at explaining the unusually high rate of repayment experienced in micro-credit programs. Three well-known psychological effects were introduced to discuss the factors that may positively or negatively affect borrowers’ trustworthiness. Pelligra’s model provides important normative implications for institutional design. Gine, Jakiela, Karlan and Morduch  developed an experimental economics laboratory in a large urban market in Lima, Peru and over seven months conducted eleven different games that allow them to unpack microfinance mechanisms in a systematic way. They found that risk-taking broadly conforms to predicted patterns, but that behavior is safer than optimal. The results helped to explain why pioneering microfinance institutions have been moving away from group-based contracts. The work also provides an example of how to use framed field experiments as a methodological bridge between laboratory and field experiments. Ahlin and Jiang  pointed that the key to microcredit’s long-run effects is found to be the “graduation rate”: the rate at which the self-employed build up enough wealth to start full-scale firms and distinguished between two avenues for graduation: “winner” graduation (due to supernormal returns) and “saver” graduation (due to accumulation of normal returns). They found that “winner” graduation, however high its rate, cannot bring long-run
Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010)Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia 526 development. In contrast, if the saving rate and normal returns in self- employment are jointly high enough, then micro-credit can bring an economy from stagnation to full development via “saver” graduation. The lasting effects of micro-credit may thus partially depend on simultaneous facilitation of micro-saving. Eyo  in a communication assessed farmers’ liquidity value for un- used credit reserves and examines how the microfinance schemes can attain self sustainability. The results showed that the farmers’ liquidity value for un- used credit reserve was generally low, indicating that farmers generally allocate more credit to reserve than to loans. Consequently, micro finance schemes that can lure farmers to allocate more credit to loans than to reserve can increase the liquidity value of the farmers credit, increase outreach and attain self- sustainability; provided, their package of financial services include efforts to improve farmers knowledge of sources as well as lending practices of lenders, farmers attitude towards the use of external finance; and their managerial know-how. An article of Skees and Barnett  reviews how innovative Index- based Risk-Transfer Products (IBRTPs) can be used to transfer the correlated natural disaster risks that often hamper the development of farm-level microcredit. By linking lending to IBRTPs, access to microcredit can be enhanced while also providing opportunities to offer mutual sharing of the basis risk that remains after correlated risks are transferred into global markets. This opens the way for new thinking about developing agricultural insurance in low-income countries. Swain and Floro  developed a theoretical framework to examine the mechanisms through which the pecuniary and non-pecuniary effects of the Self Help Group program on the beneficiaries’ earnings and empowerment influence their households’ ability to manage risk. Going beyond the traditional poverty estimates, they used vulnerability measure which quantifies the welfare loss associated with poverty as well as different types of risks like aggregate and idiosyncratic risks. Applying this measure to an Indian panel survey data for 2000 and 2003, they found that SHG members have lower vulnerability as compared to a group of non-SHG (control) members. Furthermore, they found that the poverty contributes to about 80 percent of the vulnerability faced by the household followed by aggregate risk. Ghalib’s  communication reflects on the concept and practice of Social Impact Assessment (SIA), by looking at the social dimension of the relevant development theory and practice, the key components of analyses, the conceptual framework of SIA and the principles the underlie the entire process regarding microfinance. His paper identifies the variables and indicators of an impact assessment and builds a generic model of the process. It goes on to develop a social impact measurement index (SIMI) to act as a framework for
Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010)Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia 527 measuring social impact. Kadoic and Kopic  in their work attempted to incorporate particularities of a transitional economy into the original microcrediting principles. As a solution to problems afflicting the domestic economy, the authors defined a global microcrediting system framework on the macroeconomic level, assuming at the same time that microcrediting of socially vulnerable groups can resolve many problems of modern transitional societies. Arising from the authors primary intention – to consider in depth the functionality of microcrediting in general transition conditions – a transitional microcrediting system was defined in general terms, and a corresponding financial and mathematical model was developed. Bablis  reported the origin and development of microfinance institutions in Papua New Guinea and other Pacific Island countries. Shah  reported mapping strategies for rural credit disbursement through different cooperatives in the rural sectors of Maharashtra, India. A report on the growth of microfinance units in Vietnam has been placed by Nghiem, Koelli and Rao . Mkpado and Arene  described the good and sustained effects of democratization of group administration on the agricultural microcredit groups in Nigeria. Wenner, Navajas, Trivelli and Tarazona  communicated the development and functions of different rural financial institutions of Latin America. Grezov  presented different developments programme for poverty eradication in Tajikistan. Qayyum and Ahmad  reported the sustainability and efficiency of microfinance institutions in Pakistan, India and Bangladesh. In the present work a model of microcredit organization building is placed. Brief informative discussions are placed on the history of microcredit, role of Grameen Bank, women’s empowerment, Self-Help Groups, loan schemes, loan repayments and types of cost associated. A plan model is proposed on target group and organization building. A mathematical model is proposed to understand the break-even point related to loan size & interest rates. We have also proposed a viable mathematical model of borrowing group creditworthiness and a measurement of the corresponding risk coefficient for the entire process. 2. History of Microcredit The Grameen Bank of Bangladesh is often considered to be the first organization to have put contemporary microcredit into practice. In fact, it only began its activities in 1976, whilst Opportunity International, a not-for-profit organization of Christian origin, had already begun to make small-scale loans
Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010)Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia 528 available in Colombia in 1971 and the NGO Accion International made its first credits available in Brazil in 1973. The concept existed as early as the 19th century, in different forms in social economy organisations in the North (cooperatives, savings and credit mutuals, mutual guarantee societies, etc.). In Indian history also this concept has a significant signature. In 1793, history reports cases of disbursement of small-size loans to the farmers (‘Takabilon’). In 1883 Land Improvement Loan Act was passed and in the year 1904 Co- operative Act was passed. There was one prominent landmark in the history of development of microcredit: Rabindranath Tagore after getting the Nobel Prize contributed the huge amount of sum as prize money for the development of the poor people residing in the neighbouring domains of his ‘Shantiniketan’. A project was initiated by him and one of his sons to disburse small-scale loan to them. Although eventually it became a failure as a huge amount of disbursed money as loan was not repaid back but still this event is considered to be a landmark in the process of eradication of poverty. 3. Role of Grameen Bank Grameen Bank is a Bangladesh-based microfinance institution that provides collateral-free loans to poor entrepreneurs in rural areas. It was founded in the late 1970’s by Muhammad Yunus, who, along with Grameen Bank, won the 2006 Nobel Peace Prize for their work in developing a model aimed at lifting millions of people from poverty. As of February 2010, it reports 8 million borrowers. With 2,563 branches, Grameen Bank provides services to 81,343 villages. Grameen Bank has the equivalent of USD 1.2 billion in assets. Total amount of loan disbursed by Grameen Bank, since inception, is Tk 513.70 billion (US $ 8.96 billion). Out of this, Tk 456.19 billion (US $ 7.95 billion) has been repaid. Current amount of outstanding loans stands at TK 57.51 billion (US $ 831.01 million) . Mahmoud, Khalily and Wadood  discussed evidence that the microcredit industry in Bangladesh had seen emergence of large variations in the size of the microfinance institutions operating in the market-- on the one hand, there are large national-level MFIs, while on the other hand, small localized MFIs operating only within the confines of a small area. Data revealed that there is market segmentation where some borrowers and MFIs opt for a package of low interest rates tied with low amount of loan disbursed and some other borrowers and MFIs settle for a package of high interest rates tied with high amount of loan disbursed.
Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010)Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia 529 4. Women’s Empowerment Women are the victims of deprivation and destitution and therefore any poverty eradication programs must aim at improving the standard of living of women’s communities. It is through creating livelihood opportunities for women that they can be archived, and microcredit and self help groups are better sources for improving the standard of living of people . Yunus initiated the Grameen Bank project with disbursing small-scale loans mainly to the women. It is reported that among the borrowers of Grameen Bank 97 percent are women . There are reports of functioning of microcredit institutions targeting poor women in provinces like Tamilnadu, Pondicherry and Uttar Pradesh in India [18, 19]. 5. What is a Self-Help Group (SHG)? A Self-Help Group (SHG) is a registered or unregistered group of micro entrepreneurs having homogenous social and economic background voluntarily, coming together to save small amounts regularly, to mutually agree to contribute to a common fund and to meet their emergency needs on mutual help basis. The group members use collective wisdom and peer pressure to ensure proper end-use of credit and timely repayment thereof. In fact, peer pressure has been recognized as an effective substitute for collaterals [20, 21]. 5 members make a group, 1 being the leader of the group and 5 groups make a centre. Generally all the micro credit institutions are also encouraging micro savings at a same time. In India as per as the record of the year 2008 any amount up to INR 500 comes under micro-saving scheme. So all the borrowers are normally saving something as well as borrowing sum. Micro savings can be done on weekly basis, monthly basis & once in a year basis also. 6. Loan Schemes Generally loan schemes are started after 12-15 weeks of starting savings scheme. The loan scheme can be started on a yearly basis i.e. at first very minimum amount of loan will be disbursed & then when the entire amount is recovered within 1 year then the ceiling will be raised to the double for the next year & so on. 7. Loan repayment Repayment of loan is done on a weekly basis. First two weeks will remain as a grace period & then the installment starts. (Installments start after 7
Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010)Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia 530 days & before 15 days) Example: If a person has taken a loan of INR 1000 & the service tax is 15% for 1 year then he/she has to pay INR 1150 in 50 equal installments. So, each week he has to pay back INR (1150/50) = INR 23. This way it does not become a burden on the borrower. Loan Amount is also getting increased based on the performance of the borrower on year on year basis. 8. Types of costs associated 8.1. Borrowing Costs (Cost of Funds) According to a study on transaction cost in three microfinance institutions by Institute for Financial Management & Research, the largest contributor to direct transaction cost is collection charges (28-37%), followed by Group Formation Cost (19-23%). Salary structure, conveyance costs and number of groups per field worker are some of the other key factors of operational costs. 8.2. Risk of Recovery: Willful and Non-willful Default The formal banking sector has, in general, been wary of lending to the poor because of the fear of loan losses or inability to recover the loans, especially when the poor have hardly any asset to pledge as ‘collateral’. This issue has been taken care of both in the case of bank – SHG linkage where the group guarantees the loan on behalf of the individual loanee. 8.3. Financial Cost The other credit lending institutions like the credit co-operatives and the MFIs may not have sufficient deposits, as the commercial banks (& LABs) to undertake credit activity on their own. They are, therefore, dependent either on refinancing facility from agencies or borrowings from the commercial banks.
Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010)Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia 531 8. Target Group & Organization Building (A proposed model) Pre- Survey ↓ Planning ↓ Area selection & posting ↓ Socio – economic survey ↓ Selection of initiators ↓ Motivation of Initiators ↓ Area/ Village meeting ↓ List of pre-members ↓ Group training ↓ Group Formation ↓ Centre formation ↓ Group Recognition ↓ Form fill-up ↓ Final membership
Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010)Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia 532 10. Viability and Break-even Analysis A financial institution is said to be viable when its assets exceed the different liabilities excluding share capital and reserve fund that is in other words, it is said to be viable if it can generate surplus over its expenses . Agricultural Credit Review Committee (ACRC) states profitability as a function of the spread available to the microcredit institutions between the rates of income and expenses. This spread depends upon i) the cost of raising resources comprising deposits and borrowings and ii) the income earned on the investment and loans from the resources. In addition to this profitability is also a function of the internal efficiency of the institution and volume of the business handled. Transaction cost is also an important issue in this context. Any financial institution must cover the administrative costs (particularly salaries and establishment expenditure), taxes, and the cost of capital and loses from default. This is performed by charging interest on the loan products . It is evident that the break-even condition for any financial institution over a period of time is that the net income must be at least equal to the total expenditure. In other words, Income from loans + other income ≥ cost of borrowing (principal and interest) + interest paid against savings + other expenditures. We have, N M L ∑ (ai + r )(1 − Pi ) xi + I ≥ ∑ (b j + s + c j ) y j + ∑ (e + d k )Z k + F j =1 k =1 (1) i =1 where N = total number of loans disbursed xi = size of i-th loan disbursed Pi = expected default rate on i-th loan ai = share of principal of i-th loan that has to be paid back per time period to the financial institution r = lending interest rate I = non-loan income M = total number of loans taken yj = size of j-th loan taken bj = share of principal of j-th loan that has to be paid back per time period by the financial institution s = borrowing interest rate cj = administrative cost per unit of the principal for the j-th loan taken L =total number of different savings taken care of Zk = size of k-th savings e = interest rate gifted to the account holder for the savings dk = administrative cost per unit of the principal for the k-th savings
Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010)Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia 533 F = other expenditure. It is to be noted that while modelling the dynamics a microcredit institution L=0, e=0 and dk=0 for all k as a purely microcredit institution do not take care of any savings. 11. Borrowing Group Creditworthiness Kadoic and Kopic  introduced the concept of borrowing group creditworthiness which represents the ability of group of clients to return loan. We noticed a serious drawback in that model as this value of creditworthiness according to their model can become sometimes negative which is not at all desirable in reality. We have developed an alternative model of borrowing group creditworthiness in the following manner (keeping in mind that the tenure of loan repayment is 50 weeks): i (1 − α ) i CW = 1 − exp[− ] (2) i 50 for i=0,1,2,3,…. where CWi= borrowing group creditworthiness at i-th week αi= (amount not paid in i weeks)/ (amount pre-scheduled to be paid in i weeks) This model justifies that CW0=0 i.e. since the moment of disbursement of loan up to the grace period creditworthiness is considered to be zero. If loan is repaid regularly without any default we have αi=0 at all possible i and in that case creditworthiness continuously increases and at the end of 50-th week after repayment of the last installment creditworthiness becomes (1-e-1) =0.632 (approx.) and further completing the tenure if the group does not borrow any further money the creditworthiness shows a theoretical increase approaching asymptotically to 1. We introduce the concept of Progressive Creditworthiness (PCW) which is calculated by taking the average of all the CW’s within the tenure and for the case when loan is repaid regularly without any default we have 50 1 i 1 1 1 − exp(−1) PCW = 1 − ∑exp(− 50) = 1 − 50 exp(− 50)[ 50 i=1 1 ] = 0.374(approx .) (3) 1 − exp(− ) 50 The above expression gives the maximum value of PCW under normal circumstances. If there is any case of default then
Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010)Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia 534 1 50 i (1 − α ) PCW = 1 − ∑ exp[− 50 i ] 50 i =1 (4) At the end of tenure a satisfactory score of PCW will of course help the group to borrow an enhanced amount of next loan. On the other hand, depending up on this PCW value the methodology of recovery of the defaulting amount can be planned by the concerned microcredit institution. 12. Risk Analysis It is quite justified to say that the corresponding risk coefficient increases with the size of the installment. On the other hand risk will be lower if loan is disbursed to a group whose loan repayment record is satisfactory and this loan repayment record can be mapped by PCW. Considering these factors we determine the risk coefficient by the following way: Risk Coefficient= size of the installment x (1-PCW) (5) For example, if the loan amount is ‘a’ unit and the rate of interest is ‘r’ per 100 units per year and the amount is to be repaid in 50 equal installments ar (a + ) then installment size = 100 and in that case the corresponding risk 50 coefficient is given by ar (a + )(1 − PCW ) Risk Coefficient = 100 (6) 50 If for a group there is no previous record of borrowing money PCW is considered to be 0. 13. Conclusions In view of the high economic growth and an expanding domestic economy, micro-credit has a good future in India. Moreover, as the institutional sector dealing in micro-credit expands, it reduces the need of the poor to approach the informal sector for credit. Microcredit is not only provided in poor countries, but also in one of the worlds richest countries, the USA, where 37 million people (12.6%) live below the poverty line. The US business magazine Forbes ranked the worlds top 50 microfinance institutions. Forbes made the ranking of MRIs by using data available from the Microfinance Information Exchange and the analysis from rating firms Micro-
Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010)Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia 535 Credit Ratings International Limited and Micro-Rate. The ranking was based on six key variables: gross loan portfolio, operating expense, operating expense divided by the average number of active borrowers as a proportion of gross national income per capita, outstanding balance of loans overdue by more than 30 days as a proportion of gross loan portfolio, return on assets, and return on equity. India and Bangladesh together are home to the most MFIs. Seven of the 50 were little-known institutions from India. Those in other countries included five from Bosnia and Herzegovina, four each from Morocco and Peru, three from Colombia, two each from Ecuador, Ethiopia and Serbia, and one each from 15 other countries, including Russia, Pakistan, Mexico and Brazil. To conclude we quote: "microfinance has become a buzzword of the decade, raising the provocative notion that even philanthropy aimed at alleviating poverty can be profitable to institutional and individual investors." (Forbes Magazine) References 1. Ahlin, C. and Jiang, N.: Can Micro-Credit Bring Development? Working Paper No. 05-W19, http:// www.vanderbilt.edu/econ/ (2005). 2. Pelligra, V.: Banking with Sentiments: A Model of Fiduciary Interactions in Micro- Credit Programs, Contributi Di Ricera Crenos, Working Papers, CUEC, 2005/03 (2005). 3. Gine, X., Jakiela, P., Karlan, D. and Morduch, J.: Microfinance Games, NEUDC 2005, University of Groningen (2005). 4. Eyo, E.O.: Farmers Liquidity Value for Unused Credit and the Sustainability of Microfinance Schemes in Akwa Ibom State, Nigeria, Journal of Agriculture & Social Sciences, 2 (2), 79 (2006). 5. Skees, J.R. and Barnett, B.J.: Enhancing Microfinance Using Index-based Risk-Transfer Products, Agricultural Finance Review (2006). 6. Swain, R.B. and Floro, M.: Effect of Microfinance on Vulnerability, Poverty and Risk in Low Income Households, S-WoPEC, http://swopec.hhs.se/uunewp/ (2007). 7. Ghalib, A.K.: Measuring the Impact of Microfinance Intervention: A Conceptual Framework of Social Impact Assessment, The Singapore Economic Review Conference (2007). 8. Kadoic, N. And Kopic, M.: Theory of Microcrediting in Transitional Economies, Journal of Information and Organizational Sciences, 33(1), 13 (2009). 9. Bablis, F.G.: The lessons and potential for sustainability and outreach of microfinance institutions in Papua New Guinea and other Pacific Island countries, Development Bulletin, 50, 19 (1999). 10. Shah, D.: Mapping Strategies for Efficient Rural Credit Delivery System through Cooperatives in Maharashtra. 11. Nghiem, H.S., Koelli, T. and Rao, P.: The Welfare Effects of Microfinance in Vietnam: Empirical Results from A Quasi-Experiment Survey, 51st Annual Conference of the Australian Agriculture and Resources Economics Society, 13-16 February 2007, Queenstown, New Zealand (2007). 12. Mkpado, M. and Arene, C.J.: Effects of Democratization of Group Administration on the Sustainability of Agricultural Micro Credit Groups in Nigeria, International Journal of Rural Studies, 14 (2), Article 7, 1 (2007). 13. Wenner, M., Navajas, S., Trivelli, C. and Tarazona, A.: Managing Credit Risk in Rural Financial Institutions in Latin America, Inter-American Development Bank, Washington, D.C., Sustainable Development Department, Best Practices Series (2007). 14. Grezov, R.: Development Programs for Poverty Alleviation: Comparative Study of Microfinance Program in Two Areas of Tajikistan, A thesis presented to the faculty of the Centre for International Studies of Ohio University In partial fulfillment of the requirements for the degree Master of Arts
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