Dr. P.V. Viswanath
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## Assignments, Spring 2013

#### Problem assignments from: The Economics of Microfinance, Armendariz and Morduch (AM), 2nd edition

• Chapter 1 -- Probs: 1-1, 1-2, 1-5, 1-7, 1-10.
• Chapter 2 -- Prob: 2-7.
• Chapter 4 -- Prob: 4-8.
• Chapter 5 -- Prob. 5-6 and 5-7.

Solutions:

Problem 2:7

1. It is socially efficient for both types to access loans. Since the social cost of the loan is \$1.45 per dollar of loan, we need 0.9(230)-145 > 52, and 0.5(420)-145>55, both of which are true.
2. If the bank can observe types, then it would charge the first type 0.9R = 1.45 or R=1.6111. At this interest rate, the entrepreneur would accept the loan because 0.9(230-161.11) > 52. The second type would be charged an interest rate of 0.5R = 1.45 or R = 2.9. At this rate, the entrepreneur would accept the loan because 0.5(420-290) > 55.
3. If the bank couldn't observe the types, then it would be repaid (0.9(0.6) + 0.4(0.5)) or 74% of the time. Hence break-even R would have to be 0.74R = 1.45 or R = 1.9595.
At this interest rate, type 2 will accept the loan because 0.5(420-195.95) > 55, but type 1 wouldn't because 0.9(230-195.95) < 52. Hence this setup would not be an equilibrium one. In equilibrium, the bank would charge R = 2.9 and only type 2 entrepreneurs would accept the loan.
4. If banks cannot distinguish between project types, then the market might collapse and socially desirable projects might not be undertaken.

Problem 4-8

1. Suppose the bank believes that investors will exert effort. Then it will charge an interest rate of R=1.5, since all projects are riskless. Remember, the gross cost of the loan is 1.5, so if the bank wants to cover costs, it has to charge at least R=1.5. At this interest rate, exerting effort yields (300-150-80-40) or \$30, while shirking yields 0.75(300-150)-80 = 32.5; so the borrower will shirk. So this is not an equilibrium.
If the bank believes that investors will not exert effort, then it will charge an interest rate of 1.5/0.75 or 2.0. At this rate, though, taking the loan yields 0.75(300-200)-80 or -\$5, so there will be no takers. Hence the bank will simply not lend any money in this economy.
2. Note first of all, that the cost of effort and the opportunity cost are not out-of-pocket costs; hence these costs can be incurred even when cashflows are zero. Now we analyze the different possibilities.

Suppose there is monitoring (which induces return-maximizing effort) and joint liability lending, as well as limited liability for entrepreneurs. In this case, the bank will charge R=1.5, once again. Now, however, for each investor, the payoff from expending effort is (300-150-80-40) = \$30 less monitoring costs of \$20 for a net of \$10. (Since both parties will expend effort, there is no need for bailing out one's partner.)
However, if the parties decide to shirk (but monitor), then the payoff for each will be (300-150)-80-20 or \$50 with probability (0.75)2. It will be 0.5{(300-2(150))}-80-20 or -100 with probability 2(0.75)(0.25) (i.e. if whether his project succeeds or his partner's, all of the payoffs from the project have to be turned over to the bank. It will be 0-80-20 = -\$100 if both parties are unlucky, which happens with probability (0.25)2. The expected payoff, then, is 50((0.75)2)-100(1-(0.75)2) = -\$15.625. Hence both parties will end up finding it optimal not to shirk. Consequently, this is a viable equilibrium solution.

This situation is also desirable from a social point of view because each entrepreneur generates a net profit of \$10,whereas if only individual loans can be made, no loans will be made at all and there will be no gain to society.
This assumes that the bank wants to break even. However, if the bank wants to charge the highest possible interest rate, consistent with forcing the borrowers to not shirk, we have the condition (300-R-80-40-20) > (300-R-80-20) (0.75)2 + (0.5{0}-80-20)(2)(0.75)(0.25) + (-80-20)(0.25)2. In other words, R < 208.57. So the max R will be 208.57.

If we now ignore the ability of the borrowers to shirk when there's monitoring and just assume that there will be no shirking (as the problem may be interpreted to state), the parties can be made to pay as much as they make. That is, if there is no competition for the bank, it can extract all the surplus. In this case, what will the interest rate be? Each borrower will make 300-R-80-40-20, taking into account both out-of-pocket and opportunity costs. However, since the opportunity cost and effort cost are not out-of-pocket, they will not reduce the available wealth that can be taken by the lender. Hence the interest rate cannot be more than R = 300-20 = 280.

At the same time, we must recognize that the borrower has an option of not borrowing at all, if the interest rate is so high. Hence the highest interest rate consistent with borrowing is indeeded R = 300-80-40-20 = 160.
3. In this case, since the groups are self-selected, it makes sense to assume that both parties will think similarly, and hence we can assume that borrowers monitor each other simultaneously. The other possibility -- that borrowers will not monitor each other -- can be ruled out because as we have seen, in this case, there will be no loans made.

Problem 5-6

1. The interest rate charged to the high-type borrowers will be R =1.1. The bank needs to recover \$20 on a \$200 loan, and according to the information in the problem, there are no other borrowing costs for the bank.

For the others, we have to see what the repayment rates will be. Since the borrowers know their types, there will be assortative matching. All type 2s will pair with other type 2s, while all type 3s will pair with type 3s. All the type 2 pairs will repay all the time. The type 3 groups will pay 1-(0.25)2 or 93.75% proportion of the time, assuming that the interest rate is low enough for the one lucky borrower to pay for the unlucky borrower. If so, then the expected return to the bank will (0.9375)R per borrower from the type 3 groups and R per borrower from the type 2 groups. Hence the total return will be 0.5(1.9375R) on average. This has to be enough to recoup \$130; solving 130 = 0.5(1.9375R), we get \$134.19. That is, R = 1.3419, which in fact is sufficient for the type 3 groups to repay 93.75% of the time, as assumed.
2. In this part, we're assuming (for some reason), that there are mixed pairs. (Note, however, that the proportion of type 2 and type 3 among the low type borrowers is 50%, which is the population ratio.) The high type borrowers will pay 100% of the time because they will always have enough money. The group with two type 3 borrowers will also pay in full. However, the mixed groups will not be able to pay fully, since the type 2 borrower only gets a return of \$200, which is not sufficient to make the required payment of 200(1.3419) or \$268.38. If the bank had taken this sort of irrational behavior by borrowers, then it probably would have charged a higher interest rate. The moral of the story might be that individuals don't always act according to theoretical assumptions, and rates that are set by the bank have to take this into account.

Problem 5-7

1. If the borrower repays at time 1, he pays R to the bank, but he gets y; he also gets a further loan of 1, which has to be invested immediately (so it's a partial offset), plus dy, which is the discounted value from the second period payoff. If he doesn't repay, then he gets y, which he keeps. So he would repay if y-R+dy > y, i.e. if dy>R. Of course, the bank needs to cover its costs. How much does the bank pay out? At time 0, it pays out 1, which would be worth K at time 1 (including bank costs) and then it needs to payout another 1 on the new loan. Hence the lower limit is 1+K, i.e. the range is 1+K<R<dy.
2. If I=100, y=200, K=150, d=0.9, then we have the requirement 0.9(2) > R or R<1.8 for borrowing to take place. Since the cost of funds is effectively 1.5 plus 1 from the second loan, there would not be any borrowing and lending.

If y = \$360, then the restriction would be 3.6(0.9) > R and R can be even larger -- as large as 3.24; so in this case, there can be borrowing because the bank can recoup the cost of both loans.

### Portfolios of the Poor

Use the instructions provided in the Syllabus to prepare your report (2-3 pages) and your powerpoint presentation (10-15 minutes). In your report/presentation, make sure to cover the following:

• Summarize the chapter
• What is the primary thesis of the chapter?
• What are the proofs provided for the thesis?
• What are the implications for microfinance providers?  Explain and document.

### MFI Report

Pick one of the microfinance institutions below and investigate them; you can also choose any other microfinance institution -- there are lots of them! Just make sure to check with me, if it's not on the list. Make sure that you can find enough information; if you can't find enough, choose another institution. You can use any materials in the library or on the Internet. However, make sure to cite all your references and quotes (no plagiarism tolerated). Some additional materials may be found on my website and on the class Blackboard site (under Course Documents):

2. ASA*
3. SKS*
4. Fundacion Mundo Mujer*
5. Consumer Credit Union 'Economic Partnership'*
6. Procredito
8. SEWA*
9. BASIX*
10. Wokai
11. Equity Bank, Kenya*
12. Temenos*
13. Microfinanza*
14. M-CRIL
15. Bank Rakyat Indonesia*
16. Share Microfin*
17. Credife*

* This MFI has already been chosen by a student, and is not available to be chosen, any more.

Your paper should be about five to seven pages (double-spaced; not including appendices). The reader of your paper should understand what the institution is about and its important features. Make sure to include in your write-up:

• A history of the organization
• How the organization evolved
• What microfinance services it provides
• How the format of these services deal with moral hazard and information asymmetry issues
• What lessons can be learned by microfinance professionals about achieving service goals effectively

Keep in mind: write-ups and presentations must have structure!

Divide your report into sections. In the first section, make sure you give a road-map of what you're going to present in the paper. In the last section, present a brief summary of your paper and what the reader should take away from reading the report. Use one or middle sections, as necessary. If you have distinct components of the paper, use a section for each component. If you're only using one intermediate section, you should still use sub-sections for the different parts of that section. Start a new paragraph for a new idea, but you should not have paragraphs that are too short or too large. The first sentence in the paragraph should provide a connection to the previous paragraph.

If you have numerical facts, see if you can present them as graphs. You can provide the numerical data, but it is better to put them in an appendix, unless it is important for the readers to refer to the numbers as they read the text.

For your presentations, tell your audience in the beginning what you plan to describe; then go ahead and do what you say you will do. If you're presenting facts, present them in a logical sequence. If you’re making an argument, present slides in the sequence in which the argument makes sense. When writing reports, you will have more flexibility in making your points, but in presentations, you need to decide what your main points are and put them in your powerpoints.

I will grade your reports and write-ups according to a set of rubrics that can be found on Blackboard under Course Documents, as well as on the content of the paper. Make sure that you have a Bibliography, as well, and make sure that this contains not only throw-way online material, but also serious reports and articles.

If you use websites, make sure they are solid websites, like CGAP or the IFMR Blog (http://www.ifmr.co.in/blog/).  To find information on your topic, you can use the Internet, of course, but also look at databases that we have at Pace University, such as ABI Inform, JSTOR etc. Also, look at some of the books on microfinance, they might reference your topic.

You should visit the writing center (E207 Birnbaum Library) for assistance with writing your first draft; on a separate page, attached to your report, note when you visited the writing center and how it did or did not help you. Make sure that you submit this by the first draft deadline (see Calendar) -- no extra time will be given. I will review your draft and provide comments and return the draft to you about a week later (see Calendar for exact date). The final draft must be turned in on the due date (see Calendar for date).

There are also deadlines for choosing the MFI and various other steps that you have to follow.  In particular, you have to give me your MFI choice by the deadline.  Also, remember that you have to visit the writing center (E207 Birnbaum Library) for assistance with writing your first draft.  You have to have the first meeting by the specified deadline.  When you send me your first draft, it should include the name of the person at the Writing Center that you met with, and the date and time that you met with him/her.  If you met with him/her more than once, give me all the times.  Also include information on how the Writing Center person helped you.

1. Please be careful with your English.  Many of you have wrong sentence structure.  Others have sloppy spelling; this makes it look like you have not put much effort into your writing.
2. Discuss how the MFI or other MFI-related organization is financed.
3. Even though I gave you a suggested structure for your report and suggestions as to what to include in the report, you don’t have to follow them precisely; in some cases, you may want to use more appropriate headings, particularly if you report is not about an MFI.  In that case, moral hazard might be irrelevant.  One of you wanted to talk about the way the MFI conducted  its operations, so his/her section heading was something like “Operations Profile.”  It was very interesting.
4. Provide a bibliography!
5. Be more critical and analytical in your report; use sources that are varied.  Do not only rely on the organizations website or other documents that it has published.  These are unlikely to be objective.
6. If you quote from a document, then you have to use quotation marks, of course.  But you also have to know when to quote.  Most of the time, you can paraphrase the information and note the source in a footnote.  Here’s a source for when to quote and when to paraphrase -- http://owl.english.purdue.edu/owl/resource/563/01/.
7. I have asked you to write your report in 5-7 pages, which is not a lot.  So use it to provide as much information, as possible.  Some of you repeated the same information in many ways; it looked like you were simply trying to fill up the 5 pages!
8. If you mention some objective information, then provide the source in a footnote.
9. Many of you don’t seem to have looked very far for your sources.  The internet is not the only source of materials.  As I told you, our textbook, as well as Due Diligence and Portfolios of the Poor often have a lot of material on your MFIs.  Also, look at the library databases for other sources, articles, etc.
10. Some of you have ignored the need for the subject and verb to agree in number.  Also, tense is important in English!
11. Many of you have no numerical information.  You can find at least some information from mixmarket.org.  Use tables to present this information, and graphs where necessary.
12. You can get financial information from the mixmarket.org site.  Use it.  You can even use this information to compare with other MFIs in that country or in that region.  Often you can get the organization’s annual report, which will have financial information.
13. A few of you resorted to plagiarism.  This is very disappointing.  I hope you never do this again; it is a very serious offence.
14. Some of you gave me information on your visit to the Writing Center, as well as first drafts of your paper.  I mistakenly gave some of them back to you; please return them to me.  I need them.
15. Take the report back to the Writing Center and work on it with the writing consultant.  Of course, where the problem is the content, the Writing Center won’t help.  But in almost every single case, you have English issues!

#### Banco Compartamos IPO -- Group Assignment

Read the assigned materials on the Banco Compartamos IPO, which can be found on Blackboard, under Course Documents. You are also encouraged to look elsewhere for other materials about this IPO, reactions to it, and the aftermath. Write a brief two page report, with reference to the following questions:

• Why did Banco Compartamos decide to do an IPO rather than raise money in some other way? What advantages and disadvantages do you see in the IPO? If you had been advising Compartamos, what would you have told its CFO?
• How would you assess Compartamos from a social perspective? How well has it achieved its social goals?
• What are the lessons from the Compartamos IPO for other MFIs looking to raise funds?
• Has the Compartamos IPO been good for the microfinance industry, both from the viewpoint of the suppliers of microfinance and its clients?

Refer also to the following readings:

#### Kiva Zip (The instructor may substitute another assignment for this assignment; details to be provided in class)

Go to https://zip.kiva.org/. Find an borrower that's doing something that you're interested in. Explain why this person's idea is worthwhile, and why s/he can't use conventional techniques to obtain financing. Explain how kiva zip is different from kiva. How does kiva zip solve moral hazard and information asymmetry problems?

#### Listening and Viewing Assignments:

 Topics (PP refers to Portfolios of the Poor by Collins, Morduch, Rutherford and Ruthven) Listening and Viewing Assignments. (For reading Assignments, click here.) Rethinking Banking: An Introduction to Microfinance Why Intervene in Credit Markets? Rationales for Intervention, Introduction to Agency Problems and Adverse Selection Group Lending The Grameen Approach; how it solves the agency and adverse selection problems. Beyond Group Lending Issues with group lending and potential solutions with more dynamic approaches Beyond Microcredit Microfinance is more than microcredit; banking the unbanked Women and Microfinance Measuring Impacts Funding Microfinance The Compartamos IPO, Crowd financing (the Kiva model), equity (Accion), mivs Commercialization and Regulation The Grameen versus the SKS model Microfinance and Social Justice Managing Microfinance Evaluating Microfinance organizations Guest Lecturer: Mr. von Stauffenberg Social Investing Social entrepreneurship, impact investing, social stock markets Frontiers of Microfinance Microfinance in the US Jobs in Microfinance