Master the IRR formula: The key to choosing your bonds correctly

Have you ever wondered why two bonds with different coupons can have such different real yields? The answer lies in a concept every investor should master: the IRR formula.

Why do you need to understand the IRR formula?

Imagine you have two bonds in front of you. The first offers an 8% annual coupon, but you’re buying it above its face value. The second pays only 5%, but you purchase it at a discount. Which one is truly more profitable? Without knowing the IRR formula, it’s impossible to tell.

The Internal Rate of Return (IRR) is the tool that allows you to compare investments objectively, beyond what the coupons indicate. It shows you the real return you will get if you hold the bond until maturity, considering both periodic payments and the difference between what you paid and what you’ll receive at the end.

What exactly is IRR?

In practical terms, IRR is a percentage that reflects your actual annualized gain. It’s not just the interest you’ll receive each year; it’s much more comprehensive. It includes:

1. Periodic coupons - The payments you’ll receive annually, semiannually, or quarterly. These can be fixed (always the same), variable, or even floating (linked to inflation).

2. The gain or loss from the purchase - If you buy a bond with a face value of 100 euros at 95 euros, you gain 5 euros at maturity just from that difference. If you buy it at 105 euros, you lose 5 euros.

This is why a bond with a low coupon can have a higher IRR than one with a generous coupon.

How a regular bond really works

Let’s see the basics: you buy a bond at its face value. During its term, you receive regular interest payments. When it matures, you get back your initial money plus the last coupon.

The important thing is that the bond’s market price fluctuates constantly. This is where the IRR formula comes into play. If the price drops, your potential IRR increases (because you’ll recover more money at maturity than you spent). If it rises, your IRR decreases.

The three purchase situations

• At par: You buy a bond with a face value of 100 at exactly 100 euros.
• Below par: You buy it at 95 euros. At maturity, you’ll receive 100, gaining 5.
• Above par: You buy it at 105 euros. At maturity, you’ll only receive 100, losing 5.

The IRR formula explained

The mathematical formula for IRR discounts all future cash flows (coupons and face value) to the current price of the bond. It may sound complex, but essentially it’s an equation that equates what you pay today with everything you’ll receive tomorrow.