How to master the IRR formula: your compass in fixed income investments

Have you ever compared two bonds and didn’t know which one to choose? This is where a fundamental tool that many investors are unaware of comes into play: the Internal Rate of Return or IRR. Although it may seem complicated, this metric is exactly what you need to make smarter investment decisions.

▶ Understanding what IRR is and why it matters

The IRR formula measures in percentage terms the actual return you will get from an investment in bonds or debt securities. Imagine you have two options: investing in bond A or bond B. The IRR provides an objective and precise comparison to choose which has greater profit potential.

What’s interesting is that the IRR captures two sources of profitability simultaneously:

1. Periodic coupons: the payments you receive annually, semiannually, or quarterly during the life of the bond. These can be fixed, variable, or floating (indexed to inflation). Some special bonds, called zero-coupon bonds, do not generate these intermediate payments.

2. Gain (or loss) from price: when you buy a bond, its price fluctuates in the market. If you buy it for less than what will be paid back at maturity, you gain the difference. If you buy it for more, that difference is a guaranteed loss.

▶ How a regular bond really works

Let’s take a concrete example: you buy a bond at its face value (100 €). During five years, you receive regular coupons, and at the end, the issuer returns the 100 € plus the last coupon. Sounds simple, right? The crucial detail is that between year zero and year five, the bond’s price fluctuates constantly due to changes in interest rates and the credit quality of the issuer.

Here arises an important paradox: although it seems that a higher price is better, that’s not actually the case. If you buy on the secondary market at 100 € instead of 107 €, you achieve a higher yield because you pay less for something that will be returned at its nominal value.

This is reflected in three possible scenarios:

• At par: you buy something valued at 1,000 € for exactly 1,000 €
• Above par: you pay 1,086 € for something worth 1,000 € (generates a loss)
• Below par: you invest 975 € in something valued at 1,000 € (generates a gain)

The IRR is precisely the rate that encompasses both the income from coupons and the gain or loss you will get from buying at one price or another.

▶ IRR versus other interest measures: don’t confuse them

The market is full of different rates that can confuse you. Let’s look at the main ones:

You already know the IRR: it is the total return considering cash flows and current purchase price.

The Nominal Interest Rate (TIN) is simply the percentage agreed upon between you and the lender or issuer of the bond. It is the “pure interest” without including additional costs.

The Annual Percentage Rate (TAE) includes extra expenses that the TIN does not consider. For example, in a mortgage, you might see a TIN of 2% but a TAE of 3.26% because the TAE adds commissions, insurance, and other charges. The Bank of Spain promotes it precisely because it allows honest comparison of offers.

The Technical Interest often appears in insured products. It includes costs such as life insurance included in the product, which is why it may show 1.50% while the nominal interest is 0.85%.

▶ What is the use of calculating IRR

In investment analysis, IRR determines whether a project is viable and which one deserves your capital. Specifically in fixed income, it reveals which bond opportunities are truly attractive compared to other available options.

Here’s a practical example: suppose two bonds. Bond A pays an 8% coupon but its IRR is 3.67%. Bond B pays a 5% coupon but its IRR is 4.22%. If you only looked at the coupon, you would choose the first, but the IRR clearly shows that the second is more profitable.

Why does this happen? Typically because bond A is trading above par (you paid a high price), and that premium will penalize you when it matures and you only receive the nominal.

▶ Calculating IRR: formula and practical examples

The IRR formula requires three main variables: the current price (P), the coupon you will receive ©, and the number of periods until maturity (n). Since mathematically solving for IRR is complex, many investors use online calculators by inputting these data.

Let’s look at two real cases:

Case 1 - Buying below par: A bond trades at 94.5 €, pays 6% annually, and matures in 4 years. Applying the IRR formula, we get 7.62%. Notice how the IRR exceeds the 6% coupon thanks to buying below face value.

Case 2 - Buying above par: The same bond but now trading at 107.5 €. The IRR turns out to be 3.93%. Here you see how the premium reduces the actual return, diluting the initial 6% coupon.

▶ Factors that move your IRR

Knowing this allows you to anticipate where a bond will move without complex calculations:

• Higher coupon = higher IRR. Conversely, lower coupon = lower IRR.
• Low purchase price (below par) = improved IRR. High price (sobre la par) = penalized IRR.
• Special features: convertible bonds change IRR depending on the underlying stock; inflation-linked bonds fluctuate with that variable, etc.

▶ Conclusion: IRR yes, but with eyes open

The importance of using the IRR formula is undeniable: it shows you the real profitability of a fixed income security, allowing you to choose the one offering the greatest gain. But here’s the critical point: never ignore the credit quality of the issuer.

During the Greece (Grexit) crisis, 10-year Greek bonds reached IRRs above 19%, which was obviously abnormal. Only the intervention of the Eurozone prevented a default that would have meant total loss. So while you use IRR as a compass, also keep an eye on the political and credit circumstances of the country or company behind the bond.