TIR in investment: how to interpret and calculate the actual return of your bonds

▶ Why is IRR essential for bond selection?

If you’ve ever compared two fixed-income investment options and wondered which one is truly more profitable, the answer lies in the Internal Rate of Return. Imagine two bonds: one offers an 8% coupon but its purchase price is inflated, while the other pays only 5% but is sold below its face value. Which one should you choose? Without an objective metric, the decision could cost you money. This is where IRR analysis comes into play, allowing you to compare investments clearly and accurately, considering not only periodic payments but also gains or losses due to price differences.

In the context of bonds and debt securities, this tool is especially valuable because it reflects the absolute profitability you will obtain from the day you buy until maturity.

▶ What exactly is IRR?

The Internal Rate of Return is a percentage that expresses the actual annual gain provided by an investment. Unlike the fixed coupon that simply tells you the nominal interest you’ll receive, IRR incorporates multiple variables: income from coupons (paid annually, semiannually, or quarterly), the difference between the purchase price and the amount you’ll recover at maturity, and the time your money remains invested.

When you acquire a regular bond, two things happen simultaneously. On one hand, you receive periodic interest payments. On the other, the bond’s price fluctuates in the secondary market depending on economic and credit conditions. If you bought below face value, you’ll recover that positive difference; if you paid more, you’ll incur a loss at maturity. IRR captures both effects, giving you a comprehensive view.

▶ Key differences: IRR, TIN, APR, and technical interest

These rates may seem interchangeable, but they serve different functions. The Nominal Interest Rate (TIN) is the pure percentage you agree upon without considering additional costs. The Annual Percentage Rate (APR) is more realistic: it includes commissions, insurance, and other expenses, making it useful for comparing mortgages or loans. Technical interest, common in savings insurance, also incorporates underlying costs such as life coverage.

IRR, on the other hand, is specific to bond investment analysis. It focuses on calculating future returns based on cash flows and current price, without including brokerage fees (although it could be adapted to include them if necessary).

▶ How bonds work: the basis for understanding IRR

A regular bond has a simple structure: you buy at a certain price, receive periodic interest, and at maturity, recover the original amount plus the last coupon payment. However, the interesting part occurs in the secondary market.

Suppose a five-year bond: its price fluctuates depending on how interest rates and the issuer’s creditworthiness evolve. This is where many investors make mistakes. Apparently, buying high would be better because you’d receive more money, but it’s the opposite. When a bond matures, the issuer always returns the face value, regardless of what you paid. If you bought a bond with a face value of 100 € for 107 €, you’ll have a guaranteed loss of 7 €. Conversely, if you bought it for 94 €, you’ll have a gain of 6 € at maturity, plus the coupons.

This can be summarized in three scenarios:

• Par bond: purchase price = face value (no gain or loss from price)
• Premium bond: price > face value (guaranteed loss at maturity)
• Discount bond: price < face value (gain beyond coupons)

IRR precisely reflects this behavior.

▶ IRR formula and calculation

The mathematical equation used is:

0 = -P + C/(1+IRR)¹ + C/(1+IRR)² + … + (C+N)/(1+IRR)ⁿ

Where:

• P = current purchase price
• C = periodic coupon
• N = bond face value
• n = number of periods until maturity

Although the formula seems complex, the good news is that financial calculators solve this automatically. The important thing is to understand which variables feed into the calculation.

▶ Practical calculation examples

Case 1: Bonds trading below par

A bond trades at 94.5 €, pays an annual coupon of 6%, and matures in 4 years. Applying the formula, the resulting IRR is 7.62%. Notice how the return exceeds the nominal coupon: this happens because you bought below the amount you’ll recover.

Case 2: Bonds trading above par

The same bond, but now its market price is 107.5 €. Using the same data, the IRR drops to 3.93%. Despite receiving the 6% coupon, the overpayment significantly reduces your actual return.

These examples illustrate why two bonds with similar coupons can have very different IRRs: the entry price is decisive.

▶ Factors that modify IRR

Understanding what affects IRR allows you to anticipate movements without manual calculations:

Coupon: Higher coupon, higher IRR; lower coupon, lower IRR.

Purchase price: Buying below par increases IRR. Buying above par decreases IRR.

Special bonds: Convertible bonds may see their IRR affected by the underlying stock price. Inflation-linked bonds (FRN) vary as those economic measures change.

▶ Conclusion: real vs. apparent profitability

IRR is your compass for navigating the fixed-income market. While the coupon only shows the nominal interest, IRR reveals the total gain or loss you’ll obtain. Always choose the investment with the higher IRR, but with an important caveat: never ignore the issuer’s credit quality.

An extreme case was during Greece’s Grexit, when 10-year bonds offered an IRR above 19%. That figure was not an opportunity but a warning sign: the market reflected default risk. Without the Eurozone bailout, holders would have experienced total losses. Therefore, use IRR as your main tool but always complement your analysis with credit risk assessments of the issuer.