In this LessonAn MFI’s assets generate its operating income. As the largest asset, the portfolio earns income through the structure and terms of its loan pricing. The positive cash flow generated from lending is the yield on portfolio. For a financially sustainable MFI, the yield must be high enough to cover all of the operational and financial costs. The interest rate is structured in a loan contract as part of the terms and conditions of the loan. Terms of a loan include the amount, duration, repayment intervals, fees, and commissions as well as the interest rate. |
Interest rates represent the financial costs of the loan to the borrower and the financial income of the loan to the lender. For a borrower, the interest rate is the cost of renting funds; for an investor, it is the return for making this investment. Though loans are often stated in nominal terms (such as 3% monthly), the actual cost to the borrower and the return to the lender can vary. A periodic rate, and its annualized equivalent— either the APR or the EIR—is used to calculate and compare interest rates across financial products.
As you have seen, interest rate calculations depend on cashflows of the borrower and the lender. Depending on the terms of the loan, the cashflows of the borrower and the lender can differ. For example, in a loan contract where the borrower is required to save a certain percentage to access a loan, the effective interest rate cost to the borrower could be higher than the effective interest rate return to the lender. The borrower’s forced savings represent a negative cashflow, and also carry their own opportunity cost to the borrower.
Loan disbursements and repayments form a series of cashflows for both the borrower and the lender. For the lender, these cashflows consist of a large negative outflow, which is the loan disbursement, and several smaller inflows. These inflows are the repayments of principal and interest over a given period, or term. A common finance function, IRR or Internal Rate of Return, allows you to calculate the rate of return on a given series of cashflows. For the borrower, the cashflow consists of a large positive inflow, which is the loan disbursement and several smaller outflows, which constitute the repayments of principal and interest. Loan products often have additional amounts attached to them, such as forced savings or up-front fees. The IRR function allows you to calculate the rate of return for the total loan product, using the net cashflow for each period. For example, if a loan of 1000 was made with 10 payments of 105 over 10 weeks and an up-front fee of 20, the cashflows of the lender would look like this:
The APR calculator (APRcal.xls) included with the CBI uses this function to calculate the periodic rate for a loan product.
This lesson introduced two methods for converting a periodic rate into an annualized, comparable rate—the APR or Annual Percentage Rate and the EIR or Effective Interest Rate. Both reflect an annual rate and both are based on cashflow. However, the approach to calculating them is different with different methods of accounting for interest.
The APR is a simple annualized rate; that is, it represents a simple yield on capital, as the periodic rate ( r ) multiplied by the number of periods ( n ) in a year: r x n. The EIR, on the other hand, calculates a compound yield, one in which interest is considered earned on interest, and is calculated exponentially as the rate ( r ) raised to the number of periods ( n ) in a year: (1+r)n – 1. The EIR calculation will yield a higher rate than APR, and the difference will increase with an increase in the number of periods ( n ).
For regulated MFIs the difference between these two methods of calculation is important. A country’s banking regulations will determine which calculation is used in computing earnings and truth in lending laws.
Financial software, whether on a financial calculator or through a spreadsheet, provides quick yield calculations on an investment. The reality of the cashflows, as entered in the MFI’s accounting system, may however be more complex than quick financial calculations will allow. Consider the case of an up-front ‘group insurance’ fee on the principal of a loan. While a quick financial calculation in a spreadsheet or financial calculator function will record the initial amount as the principal less the fees, the MFI’s accounting system must record the initial balance as the entirety of the principal. The fees will be recorded as income using a separate accounting entry. The average portfolio and earnings recorded will be different in each scenario. Similar discrepancies will arise in other situations with up-front transactions, such as forced savings or loan contracts that require the borrower to pay all interest up-front.
As discussed in lesson 1.3, the MFI’s products and methodology determine what is offered to a customer and how it is delivered. The loan terms are part of this equation. Terms of a loan include several elements that are based on time and price. Time includes repayment intervals (weekly, daily, monthly, etc) as well as the duration of the loan contract (3 months, 6 months, one year, etc.) Any grace period that might exist, which is the time between the disbursement and first repayment, is also a term of the loan. The pricing structure includes interest payments, forced savings and fees (insurance, commissions) that the MFI requires. Taken together, these loan terms determine the yield on an MFI’s portfolio.
The interest rate stated in a loan contract, on a savings account, or with any other financial contract on which interest is earned or paid includes either the nominal or periodic rate. This rate does not account for the impact of inflation on the “real” value of the interest generated or charged. To calculate the real interest rate, use the following formulae:
1) Periodic rate –
inflation rate = real rate; or
2) (1 + periodic rate) / (1 + inflation rate) = (1 + real rate)
Both formulae capture the idea that inflation decreases the real interest rate. The first one represents a simple, though less accurate means to calculate the real interest rate. It is best used in low inflationary environments. As inflation increases or as more precision is needed in the calculation, the second formula is used. The interest rate and the inflation rate must be expressed in the same period, such as on an annual, quarterly, monthly, weekly, or daily basis. If there is a mismatch in periods, the calculation will not yield the correct real interest rate. To determine the impact of inflation on income received from borrowers, this calculation must be understood.
Compare the outcome in real rates using the two formulae with a 15% inflation rate and a 50% interest rate for the period. The first formula yields a 35% real interest rate (0.50-0.15 = 0.35). The second formula shows 30% as the real rate (1.50/1.15 = 1 + real rate; 1.30 – 1 = real = 0.30). As the rates increase, the accuracy of the first formula will decrease.
In order to become financially viable, an MFI must charge a sustainable interest rate, that is, one that covers all the costs of making the loan. The following formula represents the calculation of this required rate (RR):
The numerator accounts for all the costs of making a loan (and of making future loans). Numbers used to calculate this rate should come from the financial statements of a mature MFI operation or from projections of an MFI’s operations when it reaches a mature level. All costs are expressed as a percentage of the average outstanding portfolio. The choice for expressing costs as a percentage of AOP is obvious; all revenues generated for the required interest rate will come from earnings on the MFI’s major asset: its loan portfolio. Moreover, as these costs are taken over a given period, the portfolio must be averaged. Finding the average outstanding portfolio, then, is the first step in calculating the required rate. Refer to the Financial Terms and Formulae section of lesson 2.2 to review how to calculate the average outstanding portfolio.
Administrative expense (AE) represents the recurrent costs of running facilities and paying staff to make loans. These include such things as rent, depreciation, utilities, salaries, training, and benefits. The AE percentage is found by totaling operating costs (minus cost of funds and loan losses) from the income statement for a given year, and dividing by the average outstanding portfolio from that year.
The loan loss (LL) rate covers the cost of capital written off. This calculation is described in the Financial Terms and Formulae section for lesson 2.2. Notice that this percentage is used in both the numerator and the denominator. By subtracting the loan loss rate from the denominator, this formula captures the idea that only performing loans will generate revenue to meet the MFI’s required rate needs.
The cost of funds (CF) rate represents the cost to an MFI of funding and maintaining its loan portfolio. This includes interest paid on savings deposits or debt, as well as the impact of inflation on the institution’s equity. As each of these costs has a different associated rate (interest paid on deposits, interest paid on commercial debt, inflation rate), a weighted average cost of capital must be used to calculate the cost of funds rate. Each funds item must be multiplied by its own cost rate. For example, average savings deposits over the period are multiplied by a deposit rate, average commercial debt is multiplied by the interest rate on borrowing, and average equity (average equity minus fixed assets) is multiplied by the inflation rate. Totaling these costs and dividing by the average outstanding portfolio yields the CF rate, as in the following example:
Capitalization (K) represents the growth rate that the MFI would like to achieve through its net profits and growth in its own equity. Accumulating positive retained earnings will allow the MFI to finance portfolio growth. As with the other cost elements, capitalization is expressed as a percentage of the average outstanding portfolio for the given period.
Investment Income (II) is the sum total of revenues generated from financial assets other than the loan portfolio. As this income reduces the required rate that must be earned from the portfolio. II is subtracted from the formula. Investment Income (taken from the Income statement) for the period is expressed as a percentage of the average outstanding portfolio for that same period.
Yield gap analysis compares the amount of income actually recorded on the books of the MFI with what was supposed to have been earned according to the ‘theoretical yield’ of the loan contracts. Two common measures exist for calculating this gap:
1) actual yield – theoretical yields = yield gap; or
2) 100% - (actual yield / theoretical yield)
The first one, a simple subtraction, resembles the formula for the simple real
interest
rates. It measures the difference between the actual yield and the theoretical
yield. The second calculation measures the percentage variation in actual yield
from the theoretical yield calculated in the initial loan contract. A substantial
yield gap shows that an MFI has earned less total income from loans than what
it should have from the original loan contracts. Gaps can arise from accounting
errors, fraud, or hidden deteriorating portfolio quality.
CGAP. “Microcredit Interest Rates,” Occasional Paper No. 1, August 1996.
Christen, Robert Peck. Banking Services for the Poor: Managing for Financial Success. Somerville, MA: ACCION International, 1997.
Tucker, William R. “Effective Interest Rate,” Paper, Bankakademie Micro Banking Competence Center, 5-6 September 2000. (*)
Hubbard, R. Glenn. (2000): Money, the Financial System and the Economy, Third Edition, Reading, MA, Chapters 4-7.
Some of the following questions will require that you use the APR calculator (file name: APRCal.xls) found on your CD-ROM. You can access this directly without entering the lesson by clicking on the My Computer icon on your desktop, and double-clicking on the CD-ROM drive icon. The file name should appear in the window.
Use the formula that you learned in this lesson to calculate the sustainable interest rate for this institution (see balance sheet and income statement on following page):
