Tesouro Prefixado Unit Price (PU)

Tesouro Prefixado: pricing zero-coupon Brazilian bonds (PU)

The PU (Preço Unitário) is the present value of a Brazilian government bond with a fixed nominal rate. For a zero-coupon prefixed bond (LTN), the formula is PU = VN / (1 + i)^(du/252), where VN is the face value at maturity (R$ 1,000.00 for LTN), i is the annual contracted rate, and du is the number of business days to maturity. Brazil uses 252 business days per year as the day-count convention — very different from the US 360/365 conventions.

There are two prefixed flavors on Tesouro Direto: LTN (Letra do Tesouro Nacional, zero-coupon — you buy at a discount and receive R$ 1,000 at maturity) and NTN-F (Nota do Tesouro Nacional – F, with semiannual 10% a.a. coupons plus principal at maturity). Both are marked-to-market daily: when market rates rise, PU falls, and vice-versa. If you hold to maturity you lock in the rate you bought at; if you sell early, you face interest-rate risk and may book a loss (or gain).

Applications

Use this PU calculation to verify Tesouro Direto quotes, plan target purchase prices, simulate portfolio mark-to-market in different rate scenarios, or estimate the discount you would receive on early redemption. Treasury desks, brokerages, and personal-finance spreadsheets all rely on this same formula. Liquidity is daily through B3, with the Treasury committing to buy back any holding.

FAQ

Why 252 instead of 365? Brazilian markets quote rates on a business-day basis, aligned with CDI and SELIC conventions. Holidays and weekends are excluded, so a year has roughly 252 trading days. Using 365 would understate the discount and give a wrong PU.

What happens if I sell before maturity? The Treasury buys back at the current market PU, which depends on prevailing rates. If rates rose since purchase, your PU fell — you may sell at a loss. If rates dropped, PU rose and you profit. Holding to maturity always delivers the agreed yield (gross of IR).

How is the income tax applied? Income tax on Tesouro Direto is regressive: 22.5% (up to 180 days), 20% (181–360), 17.5% (361–720), 15% (over 720 days), charged only on the gain at sale or maturity.