Capital Equivalence Calculator

When two cash flows are equivalent

Two sets of cash flows count as financially equivalent when, discounted to a common date at the same rate, they land on the same present value. For each stream the math is PV(flow) = Σ value_k / (1+i)^t_k, and once PV(A) equals PV(B) the trade is fair. At 10% per year, R$ 1,000 today is worth the same as R$ 1,100 a year out, or R$ 1,210 in two years, or a run of R$ 263.80 a year across five years.

Refinancing, debt renegotiation, swapping one payment plan for another — all of it rests on this idea. When a bank wants to trade a single installment for a handful of smaller ones, the honest check is whether the present values still match at an agreed rate. Pick the wrong rate and the swap quietly hands value to whichever side compounding favors.

Where it shows up in Brazil

Debt renegotiation under Law 14.181/2021 (overindebtedness), contract amendments that shift installment dates, lease buyouts, anticipation of receivables (factoring, antecipação de recebíveis em cartões), trades on the Tesouro Direto secondary market, offers to "pull" or "push" payment plans. Courts lean on present-value equivalence too, when they update compensation to the trial date.

FAQ

Which rate should I use for equivalence? Whatever the money is worth to the holder as opportunity cost. A consumer should use the best net fixed-income rate they can actually get; a company uses its WACC. In legal disputes it's the rate written into the contract, or the Selic when the contract is silent.

Can equivalence be inflation-adjusted? Yes. Switch to the real rate (rate − inflation) and keep the cash values in constant currency. That's the way to go for long comparisons stretching across decades.

What about taxes and fees? Run the equivalence on after-tax cash. Compare gross against net and you've mixed two different things, which leaves you overpaying or undercharging.