Como calcular taxa equivalente?

7/8/2022

Direct treasury: NTN-B or NTN-F which one is better? And if we compare it with exempt debentures. Who gets the best?

In the world of investments, there are many alternatives available to investors.

When we analyze some available alternatives, it is common for some investments to be free of income tax and others to be taxed . Therefore, it is necessary to carry out an adjustment so that we can compare the available alternatives correctly, as I will show below.

What are the income tax free investments in Brazil?

On Brazilian soil, there are many income tax-free alternatives that we have. Here are some of them in fixed income: The traditional Savings Account, Real Estate Receivables Certificate (CRI) , Agricultural Receivables Certificate (CRA ); Agricultural Letters of Credit (LCA) ; Real Estate Credit Letters (LCI) and Incentivized Corporate Credit (Debentures). The latter still requires attention, as not all Debentures are incentivized , so be aware.

Which investments pay income tax?

In Brazil, the vast majority of investments are taxed, the main ones being: all Government Bonds : NTN-B; NTN-F, LFT and LTN . Bank papers such as Bank Deposit Certificates (CDB) ; Interbank Deposit Certificate (CDI) , Financial Bills (LF ), among others.

A small addendum regarding liquidity: government securities have excellent liquidity (up to D+0) , while bank securities and some debentures do not have a guaranteed repurchase , that is, there is often no option to redeem the security before the deadline, and if there is, it is necessary to count on some loss.

How is income tax charged?

Fixed income investments that are taxed fit the regressive income tax table (IR) , the longer you invest, the lower the rate .

Table1: Regressive income tax table.

Many investors do not know, but there is also the Tax on Financial Operations (IOF) which is levied on income from applications redeemed within a period of less than thirty days.

Table2: IOF Table Source:Link

Let it be clear, both the income tax and the tax on financial operations are levied ONLY on the GAIN of capital .

How to transform a gross rate into a net rate?

Now that we know how income tax collection works, let's look at a simple example.

What is the net rate (tax-free) of a fixed-rate government bond with a yield of 12.85% carried to maturity ?

Image 1: Fixed Treasury Direct on July 8, 2022 at 10:30am.

Just check the title's maturity date: 01/01/2025. With this we know that the IOF charge is discarded. Relating to the regressive IR table (Table 1), we see that the investment period is longer than 2 years, consequently the IR rate applied will be 15%.

Using simple mathematics, let's deduct the IR on the annual income, so we have: 12.85% pa. x (1-0.15) = 10.92%aa.

Therefore, upon redemption (01/01/2025) we will obtain a tax-free rate of 10.92% pa .

How to find the yield of an IPCA+ Bond?

Inflation bonds are composed of two rates, a fixed part and a part obviously linked to inflation. I used the title IPCA + 2032 in another article and therefore I will use it as a calculation example here. If there is interest I leave the link to the article.

Image 2: Direct Treasure Card.

As we can see, Treasury IPCA + 2032 ( NTN-B 2032) comprises a fixed yield of 5.79% pa. and a variable that is inflation itself. As we do not know for sure what inflation we will find from today until the security matures on 08/15/2032, we must estimate it. For this, the investor can project his own inflation or he can consult the ANBIMA website to understand what the market is projecting.

Image 2: ANBIMA yield curve July 8th 1:48 pm

The vertices of the table above are the business days until the maturity of each security. Therefore, our bond expiring on 08/15/2032 has a 10-year vertex. As each year has 252 business days, we will use the vertex of 2520. With this, we arrive at an inflation projected by the market of 6.8673% per annum.

The last step to find the gross rate is to add the projected inflation of 6.873% to the fixed part of 5.79%. You know how fees add up, don't you? To add the rates, you multiply one by the other. As a result, we have an expected gross yield for the period of 13.06% pa.

The sum of rates is as follows: (1+0.0579) x (1+ 0.06873) -1 = 13.06% pa.

Now that we have the NTN-B gross rate, we must transform it into a net rate. We know that IOF is not levied on this transaction. We also know that according to the regressive income tax table (see table 1) we are in the range of investments over 2 years that have an income tax rate of 15%.

Transforming it into a net rate, we have: 13.06% x (1-15%) = 11.10% exempt from income tax

As a result, our NTN-B maturing in 2032 has an estimated net yield of 11.10%, which results in IPCA + 3.96% pa exempt from income tax.

Rates are subtracted as follows: Net rate Inflation = (1+ 0.111) / (1+ 0.06873) -1 = 3.96%.

Non-exempt investments x Exempt investments

With this information in hand, we can correctly compare taxed investments with exempt investments . Let's, for example, check the attractiveness of incentive debentures (tax free) in relation to our NTN-B (taxed).

Table of Debentures for sale at Banco do Brasil on July 8, 2022.

We will focus on the bottom part of the table, more precisely on Votorantim Cimentos debentures. Note that it has a renumbering exempt from IPCA IR + 4.01 with maturity on 02/15/2033. In other words, the market prices Votorantim's shares as risky as our government bond paying IPCA + 3.96%. Which is obviously a contradiction, as there is little risk premium . (I leave here a link to the article that comments on Risk Premium)

Only when you calculate the tax-free equivalent rate are you able to answer the question: Would you invest in Votorantim debentures?

decision making

In this case we see that the comparison between two types of investment was only possible because we calculated the equivalent rate that allowed us to correctly relativize one investment in relation to the other. Without this artifice it would be difficult to understand the real dimension of the situation. Therefore, when we have to compare an investment that is taxed against one that is exempt , we must always calculate the equivalent rate .

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