Real yield on bonds: how to understand and apply the IRR in your investments

Why Do You Need to Know the IRR to Invest in Fixed Income?

When you have capital available to invest in debt securities, the biggest challenge is not just choosing any bond, but selecting the right one. Imagine comparing two bonds: one offers an 8% coupon while another pays 5%. Which would you choose? Most investors would pick the first without hesitation, but this decision could be a costly mistake.

This is where the Internal Rate of Return (IRR) comes in—the metric that truly indicates how much money you will earn in real terms. The IRR is not simply the nominal interest received in coupons, but the absolute return considering the price paid, periodic cash flows, and maturity date.

What exactly is the IRR?

The IRR is a percentage that allows you to objectively compare different investment opportunities. When applying this concept to fixed income, what you get is the real gain you will experience from the time you buy the bond until it matures.

The profitability of a bond comes from two different sources:

First, periodic income (coupons). These can be annual, semiannual, or quarterly payments. Some bonds offer fixed coupons, while others have variable or floating coupons linked to indicators like inflation. There is also a special category called zero-coupon bonds that do not generate intermediate payments.

Second, the gain or loss from price change. During the bond’s lifespan, its market price fluctuates. If you buy it below its nominal value, you will realize an additional gain at maturity. If you pay above the nominal, you will suffer a guaranteed loss.

How ordinary bonds work

To understand the importance of correctly calculating the IRR, you need to know the basic mechanics of a bond. When you invest in an ordinary (the most common type), the following happens:

You acquire the bond at its nominal value. Periodically, you receive interest payments. At maturity, the issuer returns the nominal plus the last coupon.

The market value of the bond constantly changes during its life due to factors such as: changes in market interest rates, variations in the issuer’s credit quality, and economic events.

A crucial aspect to understand: the most profitable strategy is usually to buy a bond in the secondary market when its price is below 100€ (or its corresponding nominal). Why? Because at maturity, you will always receive exactly the nominal. If you paid less, the difference is pure profit. If you paid more, that difference is a guaranteed loss.

The three categories of purchase prices

Par bond: You buy it exactly at its nominal value. If the nominal is 1,000€, you pay 1,000€.

Premium bond: You acquire it paying more than its nominal. For example, a nominal of 1,000€ but you buy it at 1,086€.

Discount bond: You buy it paying less than its nominal. For example, a nominal of 1,000€ purchased at 975€.

The IRR precisely captures this price difference, showing not only the coupon yield but also the positive or negative effect of having bought at one price or another.

Fundamental differences between IRR, TIN, APR, and technical interest

It is essential to distinguish these metrics because they are easily confused:

The IRR in fixed income shows the total return discounted for all cash flows (coupons) based on the current market price.

The Nominal Interest Rate (TIN) is simply the initially agreed interest rate, without including additional expenses. It is the purest way to measure interest.

The Annual Percentage Rate (APR) includes all hidden costs. A classic example is mortgages: you might have a TIN of 2% but an APR of 3.26% because commissions, insurance, and other expenses are added. The Bank of Spain recommends using APR to compare financing offers.

The technical interest is frequently used in insured products. Like the APR, it includes additional costs such as life insurance premiums, resulting in a lower rate than the nominal interest.

The mathematical formula to calculate IRR

To determine the IRR of a bond, you need three data points: the current market price (P), the periodic coupon ©, and the number of periods until maturity (n).

The formula states that the current price equals the sum of all future cash flows discounted at a rate that is exactly the IRR you seek. Although expressing it algebraically is complex, the concept is straightforward: solve the equation to find that discount rate.

For investors unfamiliar with advanced mathematical calculations, there are specialized online calculators where you input the data and get the result instantly.

Practical example: comparing two bonds

First case: A bond trades at 94.5€ in the market, pays an annual coupon of 6%, and matures in 4 years.

Applying the IRR formula, the result is 7.62%.

Note that the IRR (7.62%) is higher than the nominal coupon (6%). This occurs because you bought the bond below par, which generates additional gains when you sell it or it matures at 100€.

Second case: The same bond but now trading at 107.5€.

In this scenario, the IRR drops to 3.93%.

Here, you see the inverse effect: although you still receive the 6% coupons, paying 107.5€ for something worth 100€ at maturity destroys profitability. Your real gain is significantly reduced.

Practical applications of IRR in investment decisions

IRR serves as a compass to identify which bonds truly deserve your money. In project analysis, IRR evaluates viability. In fixed income, it detects attractive opportunities compared to less profitable alternatives.

Returning to our previous example: suppose you compare a Bond A with an 8% coupon but a 3.67% IRR against a Bond B with a 5% coupon but a 4.22% IRR. If you only go by the coupon, you would choose A. But the IRR shows that B is the superior investment. This contradiction arises precisely when the purchase price is inflated (sobre la par), penalizing the final return.

Factors that influence the IRR outcome

Understanding which variables affect IRR allows you to roughly anticipate how each bond will move, without complex calculations.

The coupon: Higher coupons = higher IRR. Lower coupons = lower IRR. Direct relationship.

The purchase price: Buying below par boosts your IRR. Buying above par decreases it. This effect is linear and predictable.

Special features: Certain bonds have additional sensitivities. Convertibles can see their IRR altered by movements in the underlying stock. Inflation-linked bonds fluctuate as that index changes. Floating rate notes adapt to changes in reference rates.

Final warning: IRR is not synonymous with safety

Although IRR is an invaluable tool, it should never be your sole criterion. The credit quality of the issuer is equally critical.

During the Greek crisis of Grexit, 10-year Greek bonds traded with an IRR above 19%. Does that seem profitable? Without a doubt. But that abnormal figure reflected the real risk of Greece declaring insolvency. Only the intervention of the Eurozone prevented bondholders from suffering a total default.

The lesson is clear: Use IRR to identify the best opportunities, but never forget to research the issuer’s financial solidity. A spectacular return is only viable if the issuer can effectively meet its obligations.