Ba microfinance

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
debalinaroyster@gmail.com
2
Department of Mathematics, University Institute of Technology, University of Burdwan
Golapbag (North), Burdwan-713 104, INDIA
koushikg123@yahoo.co.uk

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 [1]. 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:


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 [2] 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 [3] 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 [1] 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


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 [4] 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 [5] 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 [6] 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 [7] 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


measuring social impact.
Kadoic and Kopic [8] 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 [9] reported the origin and development of microfinance
institutions in Papua New Guinea and other Pacific Island countries. Shah [10]
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
[11]. Mkpado and Arene [12] described the good and sustained effects of
democratization of group administration on the agricultural microcredit groups
in Nigeria. Wenner, Navajas, Trivelli and Tarazona [13] communicated the
development and functions of different rural financial institutions of Latin
America. Grezov [14] presented different developments programme for
poverty eradication in Tajikistan. Qayyum and Ahmad [15] 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


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) [16].
Mahmoud, Khalily and Wadood [17] 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.


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 [18]. 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 [16]. 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


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.


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


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 [22].
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 [22].
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


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 [8] 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


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 world's richest countries, the USA, where
37 million people (12.6%) live below the poverty line. The US business
magazine Forbes ranked the world's 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-


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


(2008).
15. Qayyum, A. and Ahmad, M.: Efficiency and Sustainability of Micro Finance Institutions in South
Asia, Pakistan Institute of Development Economics (PIDE), Pakistan.
16. Yunus, M.: Banker to the Poor: The Story of the Grameen Bank, Penguin Books India (2007).
17. Mahmoud, C.S., Khalily, M.A.B. and Wadood, S.N.: Dynamics of Market Share in The Microfinance
Industry in Bangladesh, MPRA Paper No. 16172, http://mpra.ub.uni-muenchen.de/16172/ (2009).
18. Nidheesh, K.B.: Rural Women’s Empowerment is the Best Strategy for Poverty Eradication in Rural
Areas, International Journal of Rural Studies, 15 (2), Article 9, 1 (2008).
19. Singh, Y.K., Kaushal, S.K. and Gautam, S.S.: Performance of Women’s Self Help Groups (SHGs) in
District Moradabad, U.P., International Journal of Rural Studies, 14 (2), Article 4, 1 (2007).
20. Westover, J.: The Record of Microfinance: The effectiveness & ineffectiveness of microfinance as a
means of alleviating poverty, Electronic Journal of Sociology (2008).
21. Waterfield, C.: Why we need transparent pricing in microfinance: Microfinance Transparency.org
(2008).
22. Satish, P. and Gopalakrishna, C.K.: Viability of Rural Banking, Economic and Political weekly, 2711
(1997).

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