Due Diligence. The ‘simple’ sleight in deposit yields

With interest rates falling steadily over the past year or so, deposits by banks and other institutions now fetch you 7-8 per cent per annum, on an average, across tenures. In this low interest rate scenario, what if some deposits offered you higher yields, say, 9-12 per cent a year? Before you take the bait, wait and calculate.

When it comes to advertised yields, what you see is often not what you get. That’s because many companies that accept deposits do not follow the conventional definition of yield. With no clear-cut rules on how yield should be calculated, many seem to be stretching the number to attract investors. Here’s how it is being done.

Yield, as per finance terminology, should ideally be calculated using the formula for compound interest. But several deposit-takers calculate yield applying the simple interest equation. Consider this. DHFL offers an interest rate of 8 per cent on its cumulative deposits for tenure of 120 months; interest is compounded half yearly and the company says that ₹1 lakh will grow to ₹2,19,112 in 120 months, that is, 10 years.

The indicative yield is claimed as 11.91 per cent for the 10-year deposit. The company seems to have calculated the yield thus. The formula simple interest = (principal*period*rate)/100 is re-arranged; so, rate (yield) = (interest*100)/(principal*period). The total interest earned is ₹1,19,112 over 10 years on principal of ₹1 lakh. Hence, yield = (1,19,112*100)/(1,00,000*10); this comes to 11.91 per cent.

But this is not the right way to calculate yield. It should be arrived at using the formula for compound interest: Amount = Principal*[(1 + rate)^period]. In a cumulative deposit, the interest earned is reinvested and, in turn, earns interest in the subsequent period. These periodic additions to the capital need to be considered while calculating yield. The compound interest formula does that, the simple interest one does not. So, in the above example, 2,19,112 = 1,00,000*[(1 + yield)^10]. Re-arranging this, the yield comes to 8.16 per cent, much lower than the 11.91 per cent advertised. The compound interest based yield can also be calculated using the ‘rate’ function in Microsoft Excel.

There are several other instances of companies using the simple interest formula to calculate yield. Shriram Transport Finance Company has advertised yield of 9.72 per cent for its 5-year cumulative deposit; if the compound interest equation is applied, it comes to 8.24 per cent. Sundaram BNP Paribas Home Finance has advertised yield of 7.94 per cent for its 5-year term cumulative deposit; the number is 6.92 per cent using the compound interest formula. Mahindra Finance advertises yield of 8.78 per cent for its 5-year deposit; it is 7.55 per cent with the compound interest equation.

Another problem of using the simple interest formula to calculate yield is that longer the tenure, higher is the yield. For instance, in the deposits offered by DHFL, the yield advertised is 9.21 per cent for the 48 months (4 year) tenure and 11.91 per cent for the 120 months (10 year) tenure. This, despite the rate of interest (8 per cent) and compounding frequency (half yearly) being the same for both tenures. Had the compound interest formula been used, the yield would have been the same – 8.16 per cent - for both the tenures, as should be the case.

It also follows that when the compound interest equation is used, there should be no difference in the interest rate and yield when the frequency of compounding is annual. There can be a difference in interest rate and yield only if the frequency of compounding is higher, say half-yearly or quarterly. But when the simple interest equation is used, the yield is higher than the interest rate even when the compounding is annual. For instance, the 10-year cumulative deposit of PNB Housing Finance offers 7.4 per cent compounded annually and the advertised yield is 10.42 per cent. Had the compound interest formula been used, the yield would be 7.4 per cent, the same as the rate of interest, as should be the case.

Yield, as a financial concept, is typically associated only with cumulative debt investments that benefit from compounding. In such investments, interest, rather than being paid at regular intervals, accumulates and is paid out along with the principal at the end of the tenure. But there are cases where yield is calculated even when the interest is paid out regularly and does not cumulate.

For instance, the ongoing debenture issue of SREI Equipment Finance offers 9.25 per cent in the monthly interest payout option in the five year three month tenure, and the prospectus says that the effective yield is 9.65 per cent. How is this? The company assumes that you will reinvest the monthly interest payouts at the same rate (9.25 per cent a year) and get the benefit of compounding.

But there are problems with this assumption. When you choose an interest payout option, you are likely to use the money, not reinvest it. Even assuming reinvestment, you may not able to do so at the same rate. Reinvestment at a lower rate will mean a yield lesser than that advertised.

So the next time you get enamoured by high advertised yields, step back and calculate to see if the number is actually right.

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