Which is better: LCA at 94% of the CDI or CDB at 110% of the CDI? – 06/16/2023 – From Grain to Grain

Most people are unaware of the negative effect of interest compounding on exempt bank bonds. The rules of thumb used fail in this regard and the investor ends up getting less return than he thought. I explain the care to be taken when comparing exempt titles.

Imagine that you are presented with two investment alternatives for a period of 2 years:
a) LCA or LCI with a return of 94% of the CDI (tax-free);
b) CDB with a return of 110% of the CDI.

Both bonds have the same FGC guarantee of up to R$250,000. Therefore, they have the same risk.

Usually, investors make the following rule of thumb to compare the return on the LCI that is already net of IR with what would be the gross equivalent of IR. Divide the LCI return by 1 – the income tax rate. Within two years of application, the IR rate is 15%.

Thus, using the data in question, divide 0.94/ (1-0.15) = 110.6% of the CDI.

With this 110.6% CDI response, most investors would opt for the LCI or LCA.

However, this answer is wrong. It does not take into account how the bond’s return is compounded over time.

The return on a security that yields a percentage of the CDI is calculated and compounded daily.

By interest compounding, when the CDI is multiplied by something greater than 1, for example, 110% of the CDI which is equivalent to 1.1, the compound result over time becomes even greater than 110% of the CDI.

I will give an illustrative example so that you understand. In this exercise, I will consider an exaggerated 10% daily CDI just to illustrate.

Consider an investment for five days and a 110% return on the CDI. At the end of the fifth day, 100% of the CDI would have yielded 61.05%. The investment at 110% of the CDI would have appreciated by 68.5% (=(1+10%*1.1)^5). Despite being an investment at 110% of the CDI, it yielded the equivalent of 112.2% of the CDI.

If the composition of interest favors the return of investments that yield more than the CDI, what do you think happens to investments that yield less than the CDI, for example, 94% of the CDI?

That’s right, the composition of interest goes against it. Therefore, an LCI or LCA at 94% of the CDI, at the end of 2 years, will have appreciated by less than 94% of the CDI.

In our example with the illustrative CDI, at the end of the 5 days the investment at 94% of the CDI would yield 56.71% (=(1+10%*0.94)^5). However, this final return is equivalent to only 92.89% of the CDI.

Responding to the question at the beginning of the text, if the CDI over the next 2 years remained stable at the current level of 13.65% per year, the investment at 110% of the CDI would appreciate 32.51%. Net of income tax, this return would be 27.63%, which is equivalent to 94.76% of the CDI.

The investment in the LCI at 94% of the CDI would increase in value by 27.2% at the end of two years. However, this return is equivalent to only 93.25% of the CDI.

If you do the calculations in a spreadsheet, you will see that even an investment in LCI or LCA at 95% of the CDI would lose from a CDB to 110% of the CDI in two years.

Therefore, be careful when always preferring exempt titles without doing the right math. Mainly, when you think about the long term, the composition effect ends up being even more cruel for securities that yield a percentage below the CDI.

Michael Viriato is an investment advisor and founding partner of Investor House.

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