Trade-off between Different Aspects of Outreach andOptimum Rates of Interest for Microcredit

Narunto Nishigaki*

Abstract
The aims or goals of microcredit are the same worldwide: to offer credit on affordable terms to
the poor and to mitigate their poverty by creating opportunities for investment. However, there
are widely divergent views on how to estimate the results of poverty alleviation efforts. One ofthese differences stems from opinions regarding interest rates for microcredit; there are those
who favor high interest rate and those that oppose them. A key point of contention revolves
around the concept of outreach. High rates proponents assess the results of poverty alleviation
efforts by observing “breadth” of outreach, that is, how many poor people have been reached. Thus,
they favor high rates so that more lenders will enter the market and more profit-led investors arewilling to provide their money to the lenders. On the other hand, opponents of high rates say that
reducing “cost” for the poor is a priority, and these costs include interest rates.
There is a trade-off between “breadth” and “cost” when it comes to interest rates: while raisingrates increases the reach of credit, the interest cost imposes a heavier burden on the poor. This
study treats the number of clients as a proxy for “breadth”; net profit (business profit minus
interest charged) as a proxy for “cost.” It takes their mathematical product as the social value ofnet gain. We then construct a framework of optimum interest rates that maximize this social
value. Using this framework, we explain the mechanism that triggered microcredit repayment
crises in developing countries at the end of 2000s, and point to future issues for microfinance inthe developed world.

Keywords: microcredit, outreach, social value, repayment crises
JEL classification: A13, G21, G28, O11*Professor, Faculty of Economics, Okayama University, 3-1-1, Tsushima-naka, Okayama, JAPAN 700-8530,
Tel: +81-86-251-7545, E-mail: nishig-n@okayama-u.ac.jp

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I．INTRODUCTION

Microcredit has emerged as a means of enabling the poor to obtain micro loans that were earlier
impossible because they lack the collateral or economic viability. Although microcredit is mostly
seen in developing countries, there are also a few instances observed in developed countries. The
aim of microcredit is to offer opportunities for the poor to borrow small amount on affordable
terms and help them mitigate their poverty by making use of these opportunities themselves.
However, opinion is divided among researchers on how the outcomes of poverty alleviation shouldbe estimated.
Some believe that high rates of interest will help micro-financiers (MFIs) cover theiroperational costs and thus ease their entry into the markets, and would also help raise more loan
from capital markets. Such views are based on the notion of “breadth” of outreach, in which theoutcome of poverty alleviation efforts is assessed by seeing how many poor clients have gained
access to credit (Helms & Reille, 2004; Armendáriz & Morduch, 2010). Meanwhile, those in the
opposite camp believe high rates of microcredit interest hurt the most vulnerable sections ofsociety, as it leaves them with little money in borrowers’ hand to better their lives after repaying
the loans and could, in some cases, even leave them worse off. Opposition to high interest rates
comes from concerns regarding both “depth”, where the outcome of poverty mitigation is expected
to equal how much the most socially vulnerable sections are better off; and “cost”, where theoutcome is reckoned in terms of the net gains after repayment (Hudom, 2007; Dale, 2012; Sinclair,2012). When raising interest rates helps more people gain access to credit, there is an increase in
welfare. Thus, the final outcome would depend on the relative strengths of these two effects ofraising interest rates.
In our study, we first construct a framework of optimal rates of interest that maximize theoutcomes of poverty alleviation efforts. We then try to analyze the causes of repayment crises from2008 to 2009 in developing countries, where, as we will show, the outreach leaned toward“breadth” and the main issue was an excess supply of loans. Next, we anatomize the case of
insufficient credit in developed countries such as New Zealand, where the outreach concept wasbiased toward “depth” and “cost.”
2

The rest of the paper is organized as follows. Section II provides a relatively long literature
review of the different definitions of outreach in microcredit to provide a baseline of theframework of optimal interest rates that we will construct in section III. Based on this framework,
we analyze issues in microcredit in both developing and developed countries in section IV. Section
V concludes the paper.

II. LITERATURE REVIEW

2.1 Different concepts of outreach and the trade-offs among them
2.1.1 Schreiner's six aspects of outreach
Although now the term Outreach is used to mean “range of aid recipients,” at first, it just meant“extending welfare hands.” We use a more broad interpretation of the term to briefly explain six
aspects of outreach—worth, cost, depth, breadth, length and scope—following Schreiner (2002),
whose work provides probably the most comprehensive literature on the meaning of outreach.
First, “worth” refers to the overall benefits to clients. In a broad sense, such benefits include
making tools of money management accessible to the poor. However, in the narrowest sense, it
refers to clients’ increased business profits earned by investing money borrowed from MFIs.
The aspect of “cost,” following Schreiner (2002), consists of two elements; first, price costs suchas direct payments of interest and charges; second, transaction costs including both indirect costs
such as travel expenses and opportunity costs. Unlike other aspects, lowering these costs resultsin higher appraisal of the outreach.
Therefore, by combining these two aspects above, we can arrive at the “net gain” of clients,
which is equal to “worth” minus “cost,” representing a rise in the economic welfare of the poor, orin other words, the social value created by microcredit.
“Depth” is an indicator of whether credit opportunities have reached appropriate targets, as
reflected in higher scores for poorest segments of the population, remote regions, and females.
According to Schreiner (2002), “breadth,” a frequently used aspect of “outreach” in a narrow
sense, simply means the number of clients reached by MFIs.
“Length” refers to timelines of credit, maturities, and the number of installments and theirintervals. If the term is used to mean the length of time for which services are offered, one must3

consider the financial sustainability of MFIs.
Lastly, the aspect of “scope” alludes to the number of services MFIs offer; its score would behigher if micro savings and micro insurance were added, or if individual lending was available inaddition to group lending.1

2.1.2 Trade-offs between different aspects of outreach
As mentioned earlier, there are trade-offs among different aspects of outreach.
For example, Hermes et al. (2011) demonstrate that MFIs with a mission to target the poorest
sections of the population and females are not cost effective. If such cost deterioration prevents asufficient lowering of interest rates on loans, it can be regarded as a trade-off between “depth” and“cost.” Meanwhile, to increase the number of clients, MFIs may be inclined to lend to wealthierpoor who may find it easier to pay higher rates of interest. In such a case, it can be regarded as atrade-off between “depth” and “breadth.”
In cases of multiple trade-offs, improving financial sustainability to extend “scope” and secure
the “length” of service may increase “cost” and decrease “depth”; for example. Embarkation uponbanking services is a case in point.
Lastly, if we assume an upward sloping supply curve for loans, marginal cost would increase
with an increase in the product amount. This implies interest rates would rise with an increase in
the loan amount, that is, an increasing “cost” caused by an expanding “breadth”. Now if “worth” isfixed, this would mean a fall in the “net profit” of borrowers. The following sections will expand on
this type of trade-off.

2.2 Outreach of “breadth” –Case for high interest rates
2.2.1 Cost structure of microloan interest
Most arguments that say microcredit’s interest rates are high focus on the peculiar cost structureof MFIs. We now delve into the literature on this topic.
Helms & Reille (2004) identify three types of costs that MFIs should cover: (1) capital cost ofraising money for lending, (2) loss-compensation cost, and (3) operational expenses. Here,
operational expenses include expenditures for identifying and screening clients, processing loan
1

Schreiner (2002), pp.592-596.

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applications, loan payments, collecting funds, and continued management of non-repayments.
Armendáriz & Morduch (2010), who authored a well-known standard textbook on microfinance,and support high rates of interest, add (4) the source of MFI profits as a component of the costs
listed by Helms & Reille (2004). However, in their view, the capital costs of raising money are themost important.2

2.2.2 MFIs’ high operational costs
Helms ＆ Reille (2004) oppose a cap on rates of microcredit interest and any institution that keep
the rates low through subsidies. Their reasons are as follows:First, they point out that MFIs’ operational costs tend to be higher than those of commercial
banks, because MFIs, which cannot rely on either collateral or credit scoring processed by acomputer, engage in face-to-face transactions in small lots and must reckon with higher supply
costs than banks. They point to two demerits of the celling from the standpoint of client benefit.
One is a possibility that the “breadth” aspect of outreach may become compromised through botha withdrawal of MFIs who find it impossible to cover their costs, and the entry of commercial
banks in a microfinance market that has become unprofitable. The other revolves around the“cost” aspect of outreach; MFIs staying and coping with a rates cap will have to charge new fees orintroduce a credit insurance to cover their high costs. This means the effective rates of interest
will not fall, making it difficult for clients to calculate the cost of their loans.
They also give three reasons for why a subsidy policy will not succeed: (1) an actual poor client
is never served because a subsidized project is likely to be a political gimmick; (2) rates of
repayment tend to decline as a subsidized interest is apt to be misunderstood as a grant; and (3)once subsidized, these costs will not be covered in the future, which means a continued
dependence on subsidies, which likely to become a fiscal problem. In particularly, they argue,
historically largely subsidized state-owned banks have borne huge fiscal losses, weeded out
players with financially sustainable rates, and excluded of competition that has hindered theevolution of the financial sector.
Therefore, they recommend the following; first, promote competition and innovation increase2

Cull, Demirguc-Kunt, & Morduch (2009) also take a similar stance on interest rates of MFIs. Incidentally, theyalso point out that “It is the operating costs, rather than capital costs or loan-loss provisions, which drive thedifferences in total costs between different kinds of microfinance institutions (p.183)”.

5

productivity; reduce operational costs, and thus realize lower rates of interest; second, use acombination of consumer education and protection to protect the poor, without placing any
restrictions on interest rates.3

2.2.3 Capital costs and commercial money
Like Helms ＆ Reille (2004), Armendáriz & Morduch (2010) too point to MFIs tending to havehigh operational costs. However, they focus the role of higher rates to cover the higher capitalcosts involved in raising money from profit-led investors in developed countries, and then improve“breadth.” In this spirit, they support Banco Compartamos in Mexico whose effective interest rate
was reportedly more than 100%.4
They echo other similar opinions on high rates. For example, Michael Chu, the founder of
ACCION, has said microfinance providers cannot meet the worldwide demand for financial
5

service without private, profit-oriented capital.” Funk (2007) has estimated that US$30 billion
per year is required to reach the world’s underprivileged effectively. Besides bank loans, he says,
capital markets could play a critical role in reaching more than 100 million poor customers.6
These views, like those of Helms & Reille (2004), justify high interest rates for advancing“breadth,” which implies a narrow definition of outreach.

2.3 Case against high rates of interest
2.3.1 Fair interest rate
Hudom (2007) put forth a concept of “fair interest rate,” and detailed four approaches to explain it.
First is the deontological approach. “In religious, Marxist, and Keynesian understanding, highinterest rates are looked upon as either intrinsically unjust and or potentially harmful,” he says.
However, he agrees with the view that limiting interest rates may threaten the financial
sustainability of MFIs.7
The second approach is the consequentialist one. According to it, whether interest rates of MFIs
are fair or not can be judged by whether the wellbeing of the clients has improved or not. Hudom
See Helms ＆ Reille (2004), pp.14-15.
Okamoto (2015) also explains why Compartamos Bank's rates are so high and their legitimacy.
5 See Armendáriz & Morduch (2010), p.240.
6 Ibid, p.241
7 We refer Hudom (2007), pp3-4.
346(2007) criticizes this approach by claiming, “If one follows a definition of fairness focusing only on
the impact of the loan on its clients in comparison with the previous situation, the 10% margin
will be fair even if it only leaves a small profit margin to the borrower.”8 This is clearly referringto the “cost” aspect of outreach and clients’ net profit as “profit margin to the borrower.” We cometo this point in a later section.
The third approach focuses on “demand for credit”, which is the view supported by almost
supporters of high interest rates. It holds that borrowers must have the ability to repay loans with
substantially high interest rates and that high rates of repayment and the presence of repeat
users indicates the fairness of credit. In addition, they stress that “access to finance is more
important than its price.”9 In contrast, Hudom (2007) holds that “As in the trade case, thedistribution of the benefits may well be unequal. The poor may also lack the bargaining power toinfluence the price or approach another lender.”10
The last approach or perspective is the “procedural one,” in which Hudom (2007) recommends
use of credit scoring by MFIs to assess the characteristics of their borrowers. In this regard,
however, it seems problematic not to consider the cost aspect of MFIs’ interest rates that isinclined to be higher than those of commercial banks for the reasons mentioned above.

2.3.2 The case of developed countries
We now look at the developed world. Here we find that the statement that “access to finance ismore important than its price” is not applicable. One of the main reasons for this revolves aroundthe use of microcredit. In many developed countries, microcredit is offered not for productive use
by poor clients, but to rebuild their consumer lives compromised by high rates of interest charged
by loan sharks or to reduce such debt burdens.
High rates of interests by MFIs should, therefore, be out of question in the developed world. The
only aspect of outreach that is relevant is “cost,” good or bad; the “breadth” aspect is secondary,matter as we point out in section IV.

8

See ibid, p.4.
Cull, Demirguc-Kunt & Morduch (2009), p.171. We can find the same sentiments in Helms ＆ Reille (2004),
pp.3-4 and in many other works supporting high interest rates.
10 See Hudom (2007), p.5.
97

2.3.3 Net profit in the hands of borrowers
Based on a practical evaluation of MFIs, Sinclair (2012) casts doubts on the effectiveness ofpoverty alleviation efforts. Notwithstanding the lack of any economic or statistical verification,
one of his critical assertions could be seen as another interpretation of the “cost” aspect ofoutreach.11
The premise of microcredit is that a poor client without any capital can get a loan from an MFI
to begin a micro enterprise and earn profits, which he can then use to repay his loan. The mostimportant part of profits in relation to poverty alleviation is retained earnings after repayment.
Yet, the poor client must spend his profits on living costs for food, clothing, housing, and otherexpenses to maintain the health of a family member, a child’s education, and so on. Whether thelife of the beneficiary's is better or worse off depends wholly on the size of this “net profit.” A
higher rate of interest obviously entails a smaller net profit. Sinclair (2012) says that “interest
rates [are] so high [that] no reasonable entrepreneur could make any genuine profit and repay the12loan; [there is] massive inefficiency and zero evidence of any widespread impact on poverty.”

2.3.4 Summary of the case against high rates
We can summarize Sinclair’s assertion as follows; interest rates of microcredit as “cost” are sohigh in comparison with business revenue or “worth” that poor clients cannot retain enough net
profit to improve their wellbeing or alleviate their poverty. Thus, it should be possible to improve
the wellbeing of the poor if microcredit’s rates of interest are low enough, which is also a
fundamental perspective of microfinance in the developed world.
Hudom (2007) expresses similar views when he says, “some public action will be necessary not
only to broaden access to credit but also to encourage to charge interest rates that do not exceed
certain limits.”13 It is clear that his words “broaden access to credit” corresponds to the “breadth”
aspect of outreach, and “interest rates that do not exceed certain limit” to the "cost" aspect.
However, it is not easy to answer what is this “certain limit” or how can we define the level if weinterpret these terms using his “procedural approach”. Nevertheless, it becomes easy if wetranslate them in line with his objections to the “consequentialist approach.” That is, he hopes to11

Sinclair (2012), pp.104-105, p.152
Ibid, pp.65–66.
13 Hudom (2007), p.7
128

encourage “net profit” by keeping the interest rate or “cost” level sufficiently low in comparison
with “worth.”
Now, let us formulate the perspective of the opponents of high interest rates by defining thebusiness profit of a borrower yb as “worth,” principal and interest to repay k as “cost,” and net
profit Gb as “net gains.” We can define a simple relationship, as given below:

Gb  yb  k （2–1）
Equation (2–1) tells us that if yb is fixed, raising interest rates must decrease Gb because of anincreasing k . Even if yb is not constant, there is a relationship between rising interest rates andthe growth of profits: the higher the rate, the lower the growth of net profit.

2.4 Section summary
The statement by the supporters of high rates that “access to finance is more important than its
price” ignores by how much the wellbeing of the poor has increased because their point of interest
is whether business profit yb exceeds “cost” k or not. As long as the cost does not exceed businessprofits, raising interest rates can be justified on grounds of expanding “breadth.” On the contrary,
the crucial point of the opponents is how much net profit Gb remains by reducing interest rates.
In this scenario, “cost” is critical, while “breadth” is secondary.

III．GROUND MODEL FOR OPTIMAL INTEREST RATES

3.1 What is an optimal rate of interest?
Each “breadth” and “cost” aspect of outreach, between which there is a precise trade-off, is justone facet of microfinance’s mission: poverty reduction. Basically, we need to estimate the effects or
impacts of all aspects of outreach, including “breadth” and “cost.”
Schreiner (2002), as mentioned in section II, where we referred to the different aspects ofoutreach, puts forth three methods to assess the social value of net gains that BancoSol, one of thelargest MFIs in Latin America, has brought to their customers, combining six aspects of outreach:worth, cost, depth, breadth, length, and scope. One of the formulas is used is as follows:14

14

He mentions this formulation “may have better theoretical support”. In addition, it appears that each of six each
aspects is most clearly reflected in other formulae.

9

T

St

N ts

Social value of net gains     t 0 . 9 /  wtsn  ctsn . （3–1）
t 1 s  1 n 1

For simplicity, he limits “scope: S ” to group lending, and indicates “depth: D ” as an average 0.9 in
first parenthesis, where  is a discount factor. The social value of net gains is calculated bysumming up the net gains (“worth: wtsn ” minus “cost: ctsn ”) of each customer “ N ts ”served in eachyear “from 1 to T .”When we introduce a “trade-off” into this formula, we notice a functional relationship between
the number of N ts and cost ctsn , the other factors being constant. Both variables should be
increasing functions of interest rates. Raising the rate would increase the number of clients ineach year by both expanding (1) the number of MFIs who find it easier to cover operational
expenditures, and (2) the amount of money from profit-seeking investors. On the other hand,raising the interest rate directly ties in with the rise in clients’ repayment costs. With regard to
the social value of net gains, from (3–1) we see that raising the interest rate is a positive factor as
to number of clients or the “breadth” aspect of outreach; it is a negative factor in terms of clients’“cost” aspect of outreach.
According to conventional wisdom, an optimal interest rate is one that maximizes the social
value of net gains (or overall effect of poverty reduction), other aspects being constant.
For further simplicity, we treat “net gain” as “net profit” per customer, as shown in (2–1). Then
we describe the social value of net gain as “the product” of net profit per client multiplied by the
number of clients at a certain level of interest rate, with other aspects of outreach being constantdespite a change in the rate. In addition, we assume that the number of clients served will
increase in proportion to a rise in the interest rate. Therefore, the social value of “net profit”
increases rapidly at first, gradually slows down, and finally turns downward. Thus, the overall
effect is that represented by an inverse U-shaped curve. If the aim is maximization of the overallsocial value, interest rates corresponding to the top of the curve would be a potential target (SeeFigure 1).

3.2 A ground model for an optimal rate of interest
Therefore, we propose a ground model for an optimal interest rate. We assume there is no risk
to borrowers’ business profits. We define  as the additional rise in interest rates and l as the10increased number of clients for each 1 percent rate increase. Thus, l indicates the expanded“breadth” (   0 ). We redefine (2–1) as borrowers’ net profit when   0 . Converting thesubscript b (meaning a general borrower) to s (implying a safe borrower), we can express net
profit when   0 as given in (3–2):

Gs    y s  k   （3–2）
At a certain level of interest rate increase, we can represent the social value of “net profit” oroverall poverty reductionW as:

W  G s     l  lGs  l 2 （3–3）
If we define the optimum interest rate rise maximizing W as  * , we can calculate it as below:

dW / d  lGs  2l  0,
Thus,  *  Gs / 2   y s  k  / 2 （3–4）
The social value of net profit realized by an optimal rise of the interest rate is as given in this next
equation:2

W  *  G s2 l / 4   y s  k  l / 4 （3–5）

Net profit per borrower (%)

ys  kys  k  ＊The optimum point ys  k  / 2

Overall poverty reduction (Social value of net profit)

Expansion of “breadth” ( l )0

 ys  k  l / 2

Social value of net profit

 ys  k 2 l / 4

Expansion of “breadth” ( l )0

 ys  k l / 2

Figure１

Ground Model for Optimum Interest Rate

11

In the upper part of Figure 1, the vertical axis indicates net profit per borrower, and thehorizontal axis, the expanded “breadth,” or more clients. The downward-sloping line traces the
combination of net profit and client numbers at each level of the raised interest rate. Thus, thearea of the rectangle represents the social value of net profit. On the lower part, while the verticalaxis represents the social value of net profit, the horizontal axis is just the same as in the upper
part, and of identical scale.
Raising the interest rate initially enlarges the social value as the horizontal effect exceeds thevertical one. However, the marginal growth rate of value decreases and it turns negative after acertain level of interest rate is reached. The turning point corresponds to the optimal interest rate,
as indicated in (3–4), where maximum social value is realized.
The implications of the model are as follows: First, while we can justify supporting raisinginterest rates until it helps realize the largest social value of net profit, we cannot rationalize
raising it above the optimum point even if the borrower is able to repay when net profit perborrower remains zero or slightly more. Meanwhile, adherence to a zero percent rate of interest or
a rate that is much lower than the optimal point would be a barrier to the maximization of social
value, even as a few fortunate customers enjoy the largest net profit. In the next section, we apply
this model to explain the microcredit case.

IV. DEVELOPING VS. DEVELOPED COUNTRIES

4.1 Excess supply of credit at high interest rates in developing nations
According to Chen (2010), the microcredit debt crises in Bosnia-Herzegovina, Nicaragua, Morocco,and Pakistan from 2008 to 2009 typically broke after several years of rapid market growth fueledby ample commercial funds from developed countries (85% in the case of Morocco). He points tothree causes of the crises: (1) multiple borrowing linked to intense competition among MFIs, (2)overstretched MFI systems and controls, and (3) erosion of MFI credit discipline. The intensecompetition made it easy for customers to repay one institution using credit from anotherinstitution, and the efficiencies of group lending or incentives based on a loyalty to one MFI werelost because of ease of borrowing from other MFIs. Although staff expansion corresponded to this
rapid growth, they had not been trained enough to screen and monitor their greater number of12clients reliably. This meant fewer group meetings and simplified customer evaluations. In brief,markets had expanded at the expense of loan discipline.15
As Chen (2010) noted: “In the first decade of this century, the focus was on expanding access toservices. As a result, millions of clients gained access to microcredit, thanks to high-growth
institutions fueled by abundant funds. In the next decade, the focus was on sustainable growth.”16
In terms of “sustainable growth,” we must take note of one point, which is related to the central
argument of supporters of high interest rates. High rates of repayment are proof that loans areaffordable. The term “repayment crises” refers to the macro level where MFI borrowers indeveloping nations lost the ability to repay their loans. This supports the argument of high-rate
supporters that poor borrowers must have lost their capacity to repay.
Why does this happen? Applying our model presented above, we show that (4–1) a situation
where a poor borrower without own capital can repay his loan, assuming there is no refunding:ys  k    0 （4–1）
That is, the loan is affordable when net profit is more than zero. In contrast, it becomes
unaffordable whenys  k    0 （4–2）
In this case, the repayment amount exceeds the borrower’s business profit. We can attribute thereasons for this to all three variables on the left-hand side. Business profit ys is likely to fallwhen the market share per borrower reduces because of intense business competition which thelending offensive launched by MFIs stimulates. The principal contained with k , if refunding ispossible, increases as a portion of the interest paid to the previous creditor increases at each
additional round of funding. Regarding the higher interest rate  , we cannot exclude thepossibility it already exceeds the optimal. As a precondition of crises, excess supply of commercial
money from profit-led investors induces a combination of more clients and a smaller amount of
net profit than that at the optimal level. Besides, an expanded principal should raise the amountto be repaid and thus reduce the net profit of borrowers at a certain level of interest. The
downward-sloping line now becomes steeper.
15

Chen (2010), pp.7-11
He proposes several solutions. For example, “MFIs should balance their growth objective with the need to
improve the quality of client service.” For this purpose, he points to roles of external audits, ratings, portfolio
testing, credit information bureaus, and financial access mapping (Chen, 2010, pp.13-15). Of course, there is no
reason to believe that these institutions are equipped and utilized sufficiently in the case of microcredit.
16

13

Net profit per borrower (%)

ys  k＊Each factor is in no particular orderys  k  ys  k   1     ＊Optimum point
Factor①：Rate rising beyond optimum point
Factor②：Increased principal & interest
Factor③：Revenue deteriorating

Expansion of “breadth”（ l ）0Social value of net profit

 ys  k 2 l / 4
Area where Crises Occur y s  k 2 l
41     Expansion of “breadth”（ l ）0

 y s  k l / 21     －Figure 2

An Explanation for Repayment Crises

Thus, we must revise equations (3–2) to (3–5) above. By defining  as the additional amountto repay, and assuming  is proportional to  for simplicity, we can express net profit perborrower as

Gs      Gs      Gs  1    （4–3）
Using a similar calculation as in section III, we arrive at a revised optimal interest rate increase
as given below: *'  Gs / 21      y s  k  / 21    （4–4）
Then, the social value of net profit with a revised optimal rise in the rate is as given here:2

W '  *'  G s2 l / 41      y s  k  l / 41    （4–5）
Comparing (3–4) and (3–5), the optimal rate falls because   0 , and consequently, themaximization of social value falls. Next, we additionally consider declining business profit fromy s . If we assume such profit declines are proportional to  , we must revise net profit as:Gs        Gs  1      （4–6）
14The optimal interest rate and, subsequently, the social value of net profit also changes, as given inequations (4–7) and (4–8).

 *' '  Gs / 21        ys  k  / 21      （4–7）02

W " *"  Gs2l / 41        ys  k  l / 41      （4–8）
We see that these values are even lower than those obtained from (4–4) and (4–5). Simultaneously,a borrower’s net profit easily becomes negative. If the net profit goes below the horizontal axis asin (4–2), we have a repayment crisis (see Figure 2).
A crisis is not only problematic because it causes chaos in the macro economy, but it is also asign of a mission drift if it is connected to an excess supply of credit that makes borrowers’ net
profits go below zero.17 Now we can redefine “sustainable growth” as growth that is in keepingwith borrowers’ net profit above zero, even if not at an optimum level.

4.2 The challenge in a developed country: Under-supply of microcredit
Even though on a far smaller scale than in developing countries, we now look at examples ofactive microcredit projects in the developed world. This paper examines the Nga Tangata
Microfinance (NTM) scheme in New Zealand.
Dale (2012) states “there are some important differences between developing countries anddeveloped countries. In the case of the former, the role of microfinance is to support or establish
micro-entrepreneurial enterprises. In addition, the lack of collateral is a more widespread
problem and therefore moral hazard is a more important concern. In the case of no interest loan
scheme (NILS) in developed countries, the role of microfinance is to provide a path to engagementwith mainstream lenders through access to financial literacy and affordable credit for asset
building.”18 She also says that the NILS loans emphasize “safe” and “fair” as well as “affordable”
as loan characteristics.19 It was a benevolent institution in Australia; the Good Shepherd Sisters,that initially started the interest-free loans program with women in domestic violence situation.
NTM is the NILS provider accredited by Good Shepherd; however, it is mainly funded by
Kiwibank, which is New Zealand’s own bank capitalized by a state-owned enterprise, New
17

The term “mission drift” is used for financial sustainability; an MFI shifts its main clients from the poorest
people to the less poor, when the amount of loan per borrower becomes bigger in general (for example, see
Armendáriz, Szafarz, 2010). In other words, it is a trade-off between “depth” and “length” or “breadth.”
18 Dale (2012), p.311
19 Ibid. p.304, for example

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Zealand Post Limited.20
NTM uses inherent devices in NILS, which is uncommon in developing countries.21 To protect
against adverse selection, budget advisers (BAs), assess clients’ compatibilities with loan products,
and if approved, introduce them to the loan commission. After payment, they not only follow up on
the repayment but also assist with improving the borrowers’ financial literacy.22 NTM has further
established methods to secure repayments: paying directly to providers of the goods andencouraging the use of automatic payments from the borrower’s income, to minimize theborrower’s discretion.23
Dale and Sabi (2017) have evaluated NTM from its start in 2011 to 2016. During this period,
NTM added a new low (not free) interest rate product, called the debt relief loan scheme (DRLS),24
for which they also assessed the efficiency. The assessment was based on large-scalequestionnaire surveys of their customers, BAs, and others, in which they expressed theirsatisfaction with the results, confirming that they corresponded to the aims of the schemes.
However, NTM’s projects are not above criticism.
The largest discontent of BAs and financial mentors who deal directly with borrowers is that itis necessary to lift the upper limit of DRLS from NZ$3000 to NZ$5000.25 There are calls to,“increase the resources available including funding and staff,” and opinions such as, “It is
important to build NTM capacity in terms of the number and size of loans, as well as ensuring
long term sustainability,” and “…NTM needs to make a stronger connection with the businesssector.”26
Since the reforms of the 1980s, income inequality has been expanding in New Zealand; issues
related with poverty, especially child poverty, have become serious. An estimated 0.3 million
children have fallen into poverty in a population of 4.7 million (Dale, 2014). Meanwhile, Dale andSabi (2017) found that “from February 2011 to November 2016, NTM loans are estimated to havesaved their 187 clients over $800,000 in credit costs and charges.”27

20

Ibid. p.306
Products offered by NTM are of only individual lending type.
22 Ibid. p.308
23 Ibid. pp.309-310
24 Its expected role is to provide relief from the debt burden caused by high interest rates by refunding former
loans with loans carrying far lower rates of interest (DRLS).
25 Dale and Sabi (2017), p.7
26 Ibid. p.31
27 Ibid. p.38
21

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Net profit per borrower (%)

ys  kRealized social value of net profit＊The optimal point ys  k  / 2

ys  k  
0Expansion of “breadth”（ l ）

 ys  k l / 2

Social value of net profit

 ys  k 2 l / 4

Expansion of “breadth”（ l ）0Figure 3 An Issue Observed in a Developed Country

Although we cannot simply compare both NILS and DRLS with microcredit projects indeveloping countries because of the difference between consumer loans and business ones, as
pointed out by Dale (2012), there is no intrinsic functional difference, as a pecuniary source ofrelief from poverty, between earnings remaining after repayment in the hands of NTM clients andnet profit of borrowers in developing countries. Although free or lowest-interest rates loans are
the best tools to reduce poverty, the “breadth” aspect of outreach poses the gravest challenge to
NTM, as is evident from the discontent seen in the questionnaire answers. Thus, we ought torecognize it as the opposite of the problem in developing countries cases where the narrow senseof outreach of NTM largely falls short of the optimal, even though it never crosses the horizontal
axis (See Figure 3).

V．CONCLUSION

We have examined the issues surrounding microcredit in both developing and developed
countries from the perspective of social value of net profit, or in other word, from the two17

points of view of the “cost” aspect of outreach and the “breadth” aspect of outreach. Lastly, we
would like to talk of the political implications of the points detailed above.
In the case of developing countries, especially in nations facing repayment crises,borrowers’ net profits Gs  ys  k  have potentially declined to near zero. Thus, the required
increase in the interest rate  ought to be negative. Our analysis shows that one-sided
expansion or growth is not necessarily a right course. Rather, the goal should be to realize an
optimal level of interest rates and the corresponding outreach in a narrow sense ought to be moredesirable.
If the main reason for a rate of interest higher than the optimal level is increased capital costs
involved in raising funds from profit-led investors, the most appropriate policy is to control themoney inflow to an optimum level, which may be different in each nation. If the chief reason ofhigh interest rate is high operational expenses of MFIs, the most suitable policy is to encourage
cost reduction by promoting market competition and restricting money inflow to avoid a mere
lending competition. If low or zero net profit results in low business profit y s of borrowers, one
promising approach may be to establish and promote social businesses to increase theirprofit-making opportunities, for which we can refer to the examples in Bangladesh where theGrameen Phone started.
However, it may not be appropriate to talk of an optimum interest rate in the case of developed
countries, where retained earnings by borrowers after repayment may be less than the net profit
of micro enterprisers in developing countries. Accordingly, as Roberts (2013) suggests, we expect
non-profit MFIs to decrease the effective rates of interest through qualitative competition. In thedeveloped world, it may be more worthwhile to examine policies to promote non-profit MFIs
rather than introduce commercial money.
It is further challenge for us to ascertain which policy would be better suited to each country inthe developed world estimating variables in equation (3–2) and the increased number of clientsfor each 1 percent rate increase in each case.

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