Understanding IRR: The key to evaluating fixed income investments

When faced with multiple investment options, we need a tool that allows us to compare them objectively. This is where the IRR formula comes into play, a fundamental metric that many investors underestimate but which is decisive when making informed decisions.

Why is IRR so important?

The Internal Rate of Return is not just another number in the spreadsheet. Imagine you have two bonds in front of you: one promises an 8% coupon and the other 5%. Most naive investors would choose the first without hesitation. But here’s the problem: if you bought the bond at 8% at a price of €105 and only recover €100 at maturity, that premium is eating into your return.

IRR is precisely what reveals: the real profitability you will obtain, considering not only the coupons you will receive but also the gain or loss from the difference between the purchase price and the nominal value.

Breaking down the components of a bond

To understand how the IRR formula works, you first need to understand what happens in the fixed income market:

The cash flow of a standard bond:

• You make an initial investment paying a price (P)
• You receive periodic payments in the form of coupons ©, usually annual, semiannual, or quarterly
• At maturity (n years later), you recover the nominal value plus the last coupon

The important thing here is that the price you pay today in the secondary market can differ from the nominal. This occurs due to changes in interest rates, alterations in the issuer’s credit quality, and other market factors.

Three possible purchase scenarios

At par: You buy the bond at the same price as its nominal value (example: nominal €1,000, buy at €1,000)

Premium: You buy above the nominal (example: buy at €1,086 a bond with a nominal of €1,000). This premium will reduce your final return.

Discount: You buy below the nominal (example: buy at €975 a bond with a nominal of €1,000). Here you gain an additional profit at maturity.

How to calculate IRR

The mathematical formula is more complex than a simple ratio. It requires solving an equation where the current price of the bond equals the present value of all future flows discounted at the IRR rate:

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

Where P is the purchase price, C are the coupons, N is the nominal, and n is the number of years until maturity.

Practical example 1: You have a bond trading at €94.5, pays a 6% annual coupon, and matures in 4 years.

Applying the formula, you get: IRR = 7.62%

Notice how the IRR )7.62%( exceeds the coupon )6%(. Why? You bought below par, which increases your total return.

Practical example 2: The same bond now trades at €107.5 )above par(.

Result: IRR = 3.93%

Here, the IRR drops dramatically compared to the coupon. The premium paid penalizes your return severely, turning a 6% promise into a 3.93% reality.

For those who prefer to avoid mathematical complexities, there are online calculators that greatly facilitate this task.

Distinguishing IRR from other indicators

It’s crucial not to confuse IRR with other rates circulating in the market:

Nominal Interest Rate )TIN(: It’s simply the agreed rate, without including additional expenses. It’s the most basic and pure form of interest.

Annual Percentage Rate )TAE(: It includes all expenses, commissions, and other costs. That’s why a mortgage can have a TIN of 2% but a TAE of 3.26%. The Bank of Spain recommends using TAE to compare real offers.

Technical Interest: Mainly used in insurance, it includes costs like life insurance underlying the product. A savings insurance may offer 1.50% technical interest but only 0.85% nominal.

The key difference: IRR shows you the absolute profitability of the specific bond; the others measure contractual base rates.

What moves IRR

If you understand these factors, you can anticipate how IRR will behave without calculations:

Coupon: Higher coupon = higher IRR )and vice versa(

Purchase price: Low price )below par( = more attractive IRR; high price )above par( = less attractive IRR

Special features: Convertible bonds vary their IRR depending on the underlying stock; inflation-linked bonds fluctuate with economic changes

Final warning

IRR is an excellent compass, but it shouldn’t be your only map. A Greek bond during the Grexit crisis offered an IRR over 19%: tempting? Yes. Safe? Absolutely not. That country was on the verge of default.

The lesson: use the IRR formula as your main tool to compare investment opportunities, but always also check the issuer’s credit health. A spectacular IRR is useless if the bond ends up in bankruptcy.