 # Don’t give in blindly to high yield claims

| Updated on October 13, 2012 Published on October 13, 2012 illus 66.jpg

## Yields should ideally be calculated using the formula for compound interest and not simple interest.

When it came to fixed income investment options, the Indian public was spoilt for choice this year. Banks, non-banking financial companies, lending institutions and many companies wooed investors with high interest rates on their fixed deposits and non-convertible debentures (NCDs).

What is surprising are the significantly high ‘yields’ on deposits often publicised by companies. For instance, a few days back, Jaypee Infratech, in its advertisement, said that the yield on its 36-month cumulative deposit was 15.07 per cent a year. Big numbers attract eyeballs and investor money. But what you see is often not what you get. Here’s why.

### Not based on compound interest

If you invest Rs 20,000 in its cumulative deposit for 36 months, Jaypee Infratech promises Rs 29,044 at maturity. The maturity amount is arrived at by monthly compounding of interest at 12.5 per cent a year. The interest earned over the 3-year period is Rs 9,044. But how did the company arrive at the yield of 15.07 per cent a year?

This it did by using the formula used to calculate simple interest — (Principal*Period*Rate)/100. Re-arranging, Rate = (Interest*100)/(Principal*Period). So, (9,044*100)/(20,000*3) worked out to 15.07 per cent. But this is presenting a picture better than what it actually is.

Yield should ideally be calculated using the formula for compound interest, which is Amount = Principal*[(1 + Rate)^Period]. Re-arranging, the yield (rate) would work out to 13.24 per cent a year. This is 1.83 percentage points lower than what the company advertised. The compound interest based yield can also be calculated using the ‘Rate’ function in Microsoft Excel.

Why should compound interest be used instead of simple interest to calculate yields? That’s because in cumulative deposits, the interest amount earned instead of being paid out periodically is re-invested. Thus, the interest also earns interest. But the simple interest based formula does not take this into account.

Jaypee Infratech is not alone. A perusal of the fixed deposit options of many companies such as Sundaram Finance, M&M Finance, and Dewan Housing shows that they mention yields on fixed deposits based on the simple interest formula. So, this seems to be a widely followed industry practice, in the absence of a standard definition of ‘yield’.

### Not post-tax yields

Also, note that these advertised returns are pre-tax. Interest on fixed deposits and NCDs is, in most cases, taxable. So, the post-tax return will be lower depending upon the tax slab the investor is in. For instance, in the above example, an investor in the 30 per cent tax slab who puts money in Jaypee Infratech’s cumulative deposit would earn post-tax yield (using compound-interest based calculation) of 9.5 per cent. An investor in the 20 per cent slab would have a post-tax return of 10.8 per cent. The higher the tax slab, the lower is the post-tax return.

The practice of dangling the carrot of high ‘yields’ was also prevalent during the close of the last financial year. Banks and financial institutions advertised yields as high as 15 per cent to 17 per cent a year on infrastructure bonds and long-term (5 years or more) bank deposits. This, they did by considering the initial tax-saving which would be available by investing in these instruments.

Say, an investor in the 30 per cent tax slab invested Rs 20,000 for five years in infrastructure bonds which offered an interest rate of 8.5 per cent. Say, she went for the cumulative option. At 30.9 per cent (including cess), the investor’s tax break in the year of investment would be Rs 6,180 and her net investment was considered at Rs 13,820. At the end of five years, she receives Rs 30,073. Considering the initial net investment and a five-year period, the bond-issuer claims a ‘yield’ of 16.8 per cent a year. What’s right in this calculation? The bond issuer has correctly used the compound interest formula to calculate yield. What’s not right? The interest earned (Rs 10,073) in excess of the original investment (Rs 20,000) is taxable, but this has not been considered in the advertised yield.

If the initial tax break has been considered, then the tax liability at the end of the investment period should also be taken into account. The effective interest thus reduces to Rs 6,960 and the yield then reduces to 14.3 per cent. Also, another flaw in the advertised yield is assuming the highest tax slab of 30 per cent which gives the maximum initial tax-break. For a person in the 20 per cent tax slab, the advertised yield will reduce to 13.6 per cent and the actual post-tax yield will be 12 per cent. For an investor in the 10 per cent tax bracket, the advertised yield will be 10.9 per cent and the actual post-tax yield will be 10.1 per cent.

The bottom-line is: Calculate yields on cumulative deposits using the compound interest based formula. Also, consider the post-tax yield when evaluating investment options.

Published on October 13, 2012