# Policy rates and real borrowing costs

Data Note · Monetary Economics
A decline in a nominal policy benchmark does not establish that a firm's real financing cost has fallen. The borrower may face a different credit spread, a different repricing date or a different expectation of inflation over the repayment horizon. Those elements must be matched before a comparison of financing conditions is meaningful.

The Bundesbank's [description of expected real interest rates](https://www.bundesbank.de/en/statistics/money-and-capital-markets/interest-rates-and-yields/expected-real-interest-rates) pairs nominal yields with inflation expectations for the corresponding term. That horizon discipline is equally relevant to Brazilian borrowing analysis. The calculations below are hypothetical and do not report a Selic setting, a Brazilian lending rate or a survey forecast.

## State which real rate is being calculated

For a one-period loan with nominal interest rate \(i\) and a specified expected price increase \(\pi^e\), a simple purchasing-power calculation gives:

\[
r^e=\frac{1+i}{1+\pi^e}-1.
\]

The familiar subtraction \(i-\pi^e\) is an approximation. With uncertain inflation, this expression using one stated expectation is a simplified ex-ante calculation, not a complete valuation of inflation risk.

Suppose a nominal benchmark is 12 percent and the expected price increase over the same year is 4 percent. The illustrated real benchmark is 1.12/1.04 − 1, or about 7.69 percent. A company borrowing at 18 percent faces an illustrated real loan rate of 13.46 percent under the same price assumption. The nominal credit spread is 6 percentage points, but the corresponding real-rate difference is about 5.77 percentage points.

Now assume the benchmark falls to 11 percent while the borrower's spread increases from 6 to 8 percentage points. Its nominal loan rate rises to 19 percent. With expected inflation still at 4 percent, the illustrated real borrowing rate rises to 14.42 percent. The company faces more expensive financing despite the lower policy benchmark.

## Inflation expectations can change the result

Keep the company's nominal rate at 18 percent, but lower expected inflation from 4 to 3 percent. The same simplified real-rate calculation rises from 13.46 to approximately 14.56 percent. Slower expected price increases raise the purchasing-power burden of a fixed nominal repayment under these assumptions.

This does not mean that lower inflation is generally adverse for businesses. Greater price stability can change uncertainty, risk premia, planning and future policy. The example holds those channels constant to isolate one arithmetic relationship; it is not an assessment of the overall effects of disinflation.

A firm's own sales prices can also move differently from a general consumer-price index. Deflating debt service by expected consumer prices answers a broad purchasing-power question. Comparing debt service with projected operating cash flow requires the firm's actual revenue, cost and contract exposures. The two exercises should not share a label that conceals their different denominators.

## Match the contract to the observation

An overnight policy rate is not a one-year fixed borrowing contract. A floating-rate loan may reset along a future path of benchmarks, while a fixed-rate loan preserves its contractual coupon. A comparison of annualized rates should also account for compounding, fees and repayment structure where those affect the decision.

For analysis of Brazilian financing conditions, the useful record therefore includes the benchmark, borrower spread, maturity, reset rule, effective cost and corresponding inflation expectation. Historical realized inflation can be used for an ex-post calculation, but it should not silently replace the expectation available when borrowing occurred. Separating those objects reveals whether a change reflects policy, credit pricing or the purchasing-power convention used by the analyst.

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American Economic Senate