Funds Mathematics (FINA183 - SIGAFIN)

The majority of existing funds present daily liquidity, but IOF is levied on redemptions effected up to the 29th consecutive day as of the date of each investment, according to the table.

As of the 30th day, each investment is exempted from IOF.
To calculate the yield, you must know the number of quotas into which the capital invested was transformed, which means, how many quotas comprise the capital. The value of this quota is daily published in the Economy section of the main newspapers, bank website where the investment was effected, at the Brazilian Securities and Exchange Commission - CVM (www.cvm.gov.br), etc. Considering the investment value – suppose R$ 10,000.00 – and divide it by the value of the quota in the investment day. – R$ 1.263745 (the value of the quota are usually published with six decimal places), for example. The result is the number of the quotas the person has. The system considers the quota registered in the contract, so when adding the investment the conversion is made, and then, investment is controlled by quotas.

Number of quotas existing in the fund is equal to:

Example:
R$ 10,000.00/R$1.263745 = 7,912.988775 quotas
Once the number of quotas is known, by multiplying the value of the quota of the day, the amount of the balance is displayed. For example, after twenty-five consecutive days, quotas were appreciated and correspond to R$ 1.283459. This numbers provides the updated value of the investment. This quota is registered in the field SE0, through the option Files/Bank Contracts/Quota Update.
Value of an updated investment
7,912.988775 multiplied by R$ 1.283459 = R$ 10,156.00
Calculation of total gross yield in the period.

1. Quotas balance of 7,912.988775 multiplied by the quota of the last business day of the previous month, or the quota on the date of investment: 7,912.988775 x 1.263745 = 10,000.00
2. Quotas balance of 7,912.988775 multiplied by the quota of the redemption day or appropriation minus the balance in item 1. Then, 7,912.988775 x 1.283459 – 10,000.00 = R$ 156.00 (gross yield).

For yield proportional to redemption:

1. The value of the redemption must be in quotas and then divided by the value of the quota of the day, for example: 1,000.00 / 1.283459 = 779.144484, considering a redemption in the amount of R$ 1,000.00
2. The value in quotas obtained in item 1 is multiplied by the quota of the last business day of the previous month or by the quota on the investment day: 779.144484 x 1,263745 = 984.64
3. The amount obtained in item 2 must be deducted from the redemption amount to get the proportional yield for 1,000.00: Example 1,000.00 – 984.64 = 15.36

For better understanding, in partial redemption, the yield is calculated using cross-multiplication.

Example:

If 156.00 is the yield on updated 10,000.00, what is the yield on 1,000.00?

X = ( 156.00 x 1,000.00 ) / 10,156.00 = 15.36

where X = yield on partial redemption.

Observe that, since the calculation was made after twenty five running days and, hence, is NOT exempt from IOF, if there is redemption or allocation, the amount relating to IOF payable must be calculated. By the tax collection table, if there is a redemption on the 25th day after investment, the amount payable as IOF will be equivalent to 16% of the yield (see in the IOF table that 25 days correspond to 16% of IOF on the yield).
IOF value to be paid
16% = 0.16 x R$ 156.00 = R$ 24.96
IOF collection is only exempt when redemption is effected as of the 30th day of the investment.

Income Tax calculation on gross yield. The administrator of the Investment Fund collects the withheld Income Tax. Collecting always occurs on the last business day of the current month or at redemption, whichever is first. If redemption is not effected, on the last business day of the month, the Administrator automatically debits from the investors' balance in quotas the equivalent to the IR amount due in the current month. There is a 20% rate on gross yields in the event of a Fixed Income Fund.
Then, on the gross yield amount levies a 20% rate to be collected by the Federal Revenue Service. The IOF due is already deducted from the gross yield if the redemption is effected within 30 consecutive days period.
Income Tax amount to be collected
Without attracting IOF (redemption period starting from the 30th day after the investment)
R$ 156.00 multiplied by 20% = 0.20 equivalent to R$ 31.20
If there is no redemption till the end of the month, quotas balance on the last business day of the month is reduced as follows:
$ 31.20 divided by $ 1.283459 (quota of the last business day of the month) = 24.309308 quotas.

 
IOF Incidence
If redemption is effected on the 25th day, there is IOF tax of R$ 24.96, in addition to the IRF :
IRF = (156.00 - 24.96) = $ 131.04 multiplied by 20% = $ 26.21
Calculate final yield and taxes net profitability. Considering a redemption effected on the 25th day after the investment, including IOF and IR.

Profitability Calculation:

a) Net Yield
= Gross Yield – IOF – IR = R$ 156.00 – R$ 24.96 – R$ 26.21

IR = R$ 104.83

b) Net Profitability

= Net Profitability divided by initial amount invested x 100 = R$ 104.83 / R$ 10,000.00

= 1.05%, in a period of 25 consecutive days.

In the following month, the investment is calculated using the quota of the last business day of the previous month and the quota of the allocation date. The value of this quota must be filed in SE0, both for redemption as for monthly allocation. The system updates this file with the amount of the quota entered in the redemption or in the allocation.