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CDB vs LCA/LCI Comparison

Compare tax-exempt (LCA, LCI, CRI, CRA) with taxed (CDB, Debentures) fixed income.

Prefix mode uses direct annual rates (% p.a.). Example: CDB 15% p.a. vs LCA 13% p.a.

No initial amount is needed because crossover timing depends on relative rates and taxes, not absolute capital.

Effective annualized rate chart by holding period. X axis starts at 0 and ends a few months after crossover.

Effective rates by horizon
 
Real CDB (after tax)
LCA/LCI
1 year
82.50%
94.00%
3 years
90.84%
94.00%
5 years
93.82%
94.00%
Comparison result

Net CDB beats after 5 years and 3 months (63 months)

Real CDB applies Brazilian regressive income tax on total nominal gain (including IPCA in IPCA+ mode).

User Guide & Methodology

This calculator compares Taxable assets against Tax-Exempt assets. While the default is CDB vs. LCA, the logic applies to any fixed-income pair with the same indexing (Prefix, CDI, or IPCA+), such as Standard vs. Incentivized Debentures or CDBs vs. CRI/CRA.

Prefix mode uses direct annual rates (% p.a.). CDI mode uses a CDI base rate and % of CDI. IPCA+ mode combines expected inflation with a fixed spread.

1. The Weight of Maturity

The longer the time to maturity, the more competitive a CDB becomes relative to an LCA. This happens for two primary reasons:

  • Regressive Tax Table: Income tax on CDBs decreases over time, dropping from 22.5% to a minimum rate of 15% after 720 days.
  • Compound Interest on Face Value: Since the tax on a CDB is only paid at redemption, compound interest works on the gross value (which is higher) throughout the investment. In the long run, this larger base tends to make the LCA's tax exemption less relevant, allowing the CDB to win the comparison.

2. Prefix, CDI, and IPCA+

In Prefix mode, you enter direct annual rates (% p.a.). In CDI mode, you enter a CDI base rate and % of CDI for CDB and LCA/LCI. In IPCA+ mode, the effective return is (1 + IPCA) × (1 + spread) − 1, and tax is levied on the total gain (IPCA + fixed rate). In high-inflation scenarios, tax-exempt assets like CRIs and Incentivized Debentures gain a disproportionate advantage because you don’t pay tax on the inflation adjustment.

3. Private Credit (Debentures, CRI, CRA)

You can use this simulator to compare standard Debentures with tax-exempt papers. Just remember that, unlike CDBs/LCAs, these assets are not covered by the FGC (Credit Guaranty Fund), requiring a more careful analysis of the issuing company's risk.

Regressive Tax Table (IR)

  • Up to 180 days22.5%
  • 181 to 360 days20.0%
  • 361 to 720 days17.5%
  • Over 720 days15.0%

Common Pitfalls

  • Gross Rate Illusion: An IPCA+ 8% Debenture might yield less than an IPCA+ 6.5% CRA depending on the maturity date.
  • Inflation Effect: In IPCA+ bonds, tax "eats" part of your protected purchasing power, as the government taxes the inflationary adjustment as profit.

The Math of Equivalence

Real Return Calculation

r =
(1 + i)(1 + I)
- 1

Equivalent Tax-Exempt Rate (Horizon n)

y = (1 + ((1 + x)n - 1)·(1 - IR))1/n - 1

Variable Legend

  • r = Net Real Rate
  • i = Gross Nominal Rate
  • I = Inflation (IPCA)
  • y = Exempt Rate (LCA/CRI)
  • x = Taxable Rate (CDB)
  • IR = Tax Rate (Income Tax)
  • n = Horizon (periods)

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