TIR: The formula that changes the way you choose bond investments

Have you ever compared two bonds and didn’t know which one was better for you? The high coupon of the first attracts you, but something tells you that the second might be better. This is where the YTM formula comes into play, the metric that professional investors use to make objective decisions without being fooled by superficial numbers.

The YTM: beyond the coupon

The Internal Rate of Return — known as YTM — is that magical percentage that shows you the actual profitability of your fixed income investment. While the coupon only tells you what percentage you’ll receive annually in payments, the YTM formula reveals the total return considering also what you gain or lose from the difference between the price you paid and what you’ll recover at maturity.

Imagine two bonds: one pays an 8% coupon but you buy it at an inflated price, the other pays 5% but you acquire it at a discount. Without YTM, you’d choose the first. With it, you’d discover that the second is more profitable.

How a bond really works

To understand why the YTM formula is so important, you need to see how a bond behaves in the market. Suppose you invest €1,000 in a five-year bond:

• Now: you pay the current price (which can be 1,000 €, less or more)
• During five years: you receive periodic coupons (usually annual, semiannual, or quarterly)
• At maturity: you recover the original €1,000 plus the final coupon

The bond’s price fluctuates during those five years. If you buy it when it’s at €950 instead of €1,000, you have a guaranteed gain at maturity. If you pay €1,050, you’ll have a guaranteed loss. That’s why the YTM formula exists: to capture all that reality in a single number.

The three purchase scenarios

Below par: You pay less than the nominal. Example: buy something valued at €1,000 for €975. Result: extra gain at maturity.

At par: You pay exactly the nominal value. Example: €1,000 for €1,000. Result: your return is only the coupon.

Above par: You pay more than the nominal. Example: €1,086 for €1,000. Result: guaranteed loss at maturity that reduces your real return.

The YTM formula in action

The YTM formula mathematically breaks down all those cash flows to give you a single percentage. It’s not as simple as dividing two numbers — it requires solving equations — but online calculators make it easy.

Let’s look at a real example:

Case 1 - Discounted bond:
A bond trades at €94.50, pays 6% annually, and matures in 4 years.
YTM result: 7.62%

Notice how the YTM (7.62%) exceeds the coupon (6%) because you bought it cheaply. It’s like earning extra profit just for negotiating well.

Case 2 - Overpriced bond:
The same bond now trades at €107.50.
YTM result: 3.93%

Here, the opposite happens. Although you receive 6% in coupons, you paid too much, so your real return drops to 3.93%. It’s a penalty that only the YTM formula reveals.

YTM vs TIN vs APR: Don’t confuse the rates

• YTM: your real return on fixed income, including gains or losses from price
• TIN (Nominal Interest Rate): the pure interest without other costs
• APR (Annual Percentage Rate): includes commissions and additional expenses

Mortgage example: TIN 2%, APR 3.26%. The difference is commissions, insurance, and various costs. The APR shows the actual cost.

What moves YTM up or down

High coupon → YTM rises
Low coupon → YTM falls

Low purchase price (below par) → YTM rises
High purchase price (supra par) → YTM falls

Special bonds (convertibles, inflation-linked): their YTM varies according to other external factors.

The mistake many make

Here’s the danger: a very high YTM sometimes hides risk. During the Greek crisis in 2012, Greek bonds traded with YTM above 19%. Why? The market was assuming a high default risk. If you had invested just by looking at that seemingly attractive YTM, you would have lost everything when Greece nearly declared insolvency.

Therefore: use the YTM formula to compare similar bonds, but always check the issuer’s credit health.

Conclusion

The YTM formula is your tool to stop fooling yourself. A high coupon is not a guarantee of real profitability. An attractive market price is. When choosing among multiple bonds, let the YTM speak. It will tell you which one is truly more profitable, considering price, coupons, and maturity all together. But remember: YTM is only the first half of the decision. The second is verifying that the issuer of that bond is trustworthy.