How to calculate IRR: the metric that defines your actual profitability in bonds

What is the Internal Rate of Return (TIR)?

The IRR or Internal Rate of Return is a fundamental tool for any fixed income investor. It is a percentage rate that allows you to objectively compare different investment options, especially when choosing between various bonds or debt securities.

The key point of the IRR is that it shows you the actual profitability you will obtain, not only considering the coupons you will receive but also the impact of the price at which you buy the security in the market. That is, if you acquire a bond below or above its face value, that difference will directly affect your final return.

Why is it important to differentiate between IRR, TIN, TAE, and technical interest?

These terms are often confused, but each means something different:

TIN (Nominal Interest Rate): It is the pure interest rate agreed upon, without considering additional costs. For example, a 2% rate on a mortgage is the TIN.

TAE (Annual Equivalent Rate): It includes all associated expenses (commissions, insurance, etc.). In a mortgage, you might have 2% TIN but 3.26% TAE. The Bank of Spain recommends using the TAE to compare financing offers.

Technical Interest: Used in insurance products, includes costs such as the inherent life insurance.

IRR: Unlike the previous ones, IRR is specific for valuing fixed income securities in the secondary market, considering both coupons and gains or losses from price changes.

How bonds work: the basis for understanding IRR

Imagine a regular bond with a 5-year maturity. When you buy it, you make an initial outlay. Each year (or each semester/quarter, depending on the bond) you receive a coupon representing interest. At maturity, you recover the nominal capital plus the last coupon.

The important thing here is that the bond’s price fluctuates constantly in the secondary market while it is active. It can quote:

• At par: At the same price as the face value. If the face value is €1,000, you buy at €1,000.
• Below par: Below the face value. You buy a €1,000 nominal bond at €975.
• Above par: Above the face value. You buy a €1,000 nominal bond at €1,086.

Here is the crucial point: buying below par benefits you because at maturity you will recover the full face value, gaining a capital profit. Buying above par harms you because you will lose money on the reversal to face value.

The IRR captures this effect precisely. It accounts not only for the coupon profitability but also for the gain or loss from acquiring the security at a different price than its face value.

What is the purpose of calculating IRR?

IRR is your compass for choosing fixed income investments more intelligently. Imagine you have two bonds:

• Bond A: 8% coupon, but IRR of 3.67%
• Bond B: 5% coupon, but IRR of 4.22%

If you only looked at the coupon, you would choose Bond A. But IRR reveals that Bond B is more profitable. Why? Probably because Bond A is trading well above par, offsetting the high coupon with a significant capital loss.

Additionally, IRR helps you evaluate the viability of investment projects in general, allowing you to select those with higher profitability or risk-adjusted returns.

Formula for calculating IRR

The mathematical formula for IRR is as follows:

P = Σ [C / (1 + IRR)^n] + [N / (1 + IRR)^n]

Where:

• P = Current price of the bond
• C = Periodic coupon
• N = Nominal value
• n = Period or years
• IRR = Internal Rate of Return (the value we seek)

Solving this equation requires complex calculations, so there are specialized online calculators that streamline the process by simply inputting the price, coupon, and term.

Practical example 1: Bond bought below par

We have a bond quoting at €94.5 that pays an annual coupon of 6% and matures in 4 years. What is its IRR?

Applying the formula, we get: IRR = 7.62%

Notice how the IRR (7.62%) is higher than the nominal coupon (6%). The reason is that we buy below par, gaining a capital of €5.5 at maturity (€100 nominal minus €94.5 purchase).

Practical example 2: Bond bought above par

The same bond as above, but now it quotes at €107.5. What is its IRR?

The result is: IRR = 3.93%

Here we see the opposite effect. Although the coupon remains at 6%, the IRR drops to 3.93% because we lose €7.5 of capital at maturity (pay €107.5 but only recover €100).

Factors influencing IRR

Understanding what affects IRR allows you to anticipate changes without recalculating each time:

Coupon: A higher coupon generates a higher IRR, and vice versa. This relationship is direct.

Purchase price: If you buy below par, your IRR increases. If you buy above par, your IRR decreases.

Special features: Convertible bonds may see their IRR affected by the underlying action. Bonds linked to inflation will vary according to the evolution of that economic measure.

Final reflection: IRR and credit risk

IRR is invaluable, but it should never be your only criterion. The credit quality of the issuer is equally important.

During the Greek crisis of Grexit, 10-year Greek bonds traded with an IRR above 19%. It seemed like a bargain, but it reflected extreme default risk. Only the intervention of the Eurozone prevented Greece from being unable to pay those bonds.

Therefore, use IRR as your main tool to evaluate profitability, but always verify the credit health of the issuer before investing.