How to master the IRR formula to make better investment decisions

When faced with fixed income investment decisions, especially in bonds and debt securities, we need a tool that goes beyond simple coupon comparisons. That’s where the IRR or Internal Rate of Return comes into play, an indicator that many investors underestimate but can make the difference between a profitable investment and one that only appears to be.

Beyond the coupon: understanding the real return

When we buy a bond, we tend to focus exclusively on the percentage of the coupon it offers. However, this is only half the story. The actual return we will obtain depends on multiple factors that the IRR formula elegantly incorporates.

Imagine two bonds: one pays an 8% annual coupon, while another offers only 5%. At first glance, the first seems clearly superior. But if the first is quoted at €105 (above par) and the second at €95 (below par), you’ll see how their real IRRs are much closer than their coupons suggest. This is precisely where the importance of understanding how to correctly calculate and apply the Internal Rate of Return lies.

Breaking down the IRR concept

The IRR is, in essence, a percentage interest rate that allows for an objective comparison between different investment options. Its strength lies in considering not only the periodic coupons we receive but also the gain or loss experienced due to the difference between the purchase price and the nominal value at maturity.

In the case of fixed income securities, when we talk about the IRR formula, we are calculating the absolute return considering:

1. Periodic coupons: payments that can be annual, semiannual, or quarterly, which may be fixed, variable, or floating. Some special bonds (like zero-coupon bonds) do away with these payments.

2. Reversion to nominal: when we hold the bond until maturity, the issuer returns exactly the nominal value, regardless of the market purchase price.

How an ordinary bond works in practice

To truly understand why the IRR formula is indispensable, it’s necessary to see how a bond evolves over its lifespan. Let’s take a five-year ordinary bond with a nominal value of €100 and a 6% coupon:

• Year 0: we buy the bond at its current price (which can be €100, €95, or €105)
• Years 1-4: we receive €6 annually as coupon
• Year 5: we receive the last €6 coupon plus the €100 nominal repayment

The crucial point is that the market price of the bond fluctuates constantly due to changes in interest rates, credit quality of the issuer, and other factors. If we buy at €100, we get exactly our money back, but if we buy at €95, we will have gained an extra €5, while if we pay €105, we will have lost €5 (unless the coupon compensates for this difference).

Differentiating IRR from other interest rates

It is essential not to confuse IRR with other commonly used indicators:

TIN (Nominal Interest Rate): simply the agreed percentage without considering additional costs. It’s the purest form of interest.

APR (Annual Percentage Rate): includes additional explicit costs. For example, in a mortgage, you might have a TIN of 2% but an APR of 3.26% because it includes fees and insurance.

Technical Interest: used in insurance and savings products, also includes additional costs like life insurance.

Unlike these, the IRR applied to fixed income is specifically the return we will obtain considering the current purchase price and all cash flows until maturity.

The IRR formula explained step by step

The mathematical formula to calculate IRR in bonds may seem complex, but its logic is simple: it seeks the discount rate that equates the current price of the bond with the present value of all its future cash flows.

For a bond with price (P), periodic coupons ©, nominal value (N), and maturity period (n), the formula states:

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

Let’s look at two practical examples:

Case 1: Bond quoting at €94.5, annual coupon 6%, maturity 4 years:

Applying the IRR formula, the result is approximately 7.62%. This IRR is higher than the coupon because the low price allows us to recover additional capital gain.

Case 2: The same bond but quoting at €107.5:

In this scenario, the IRR is just 3.93%, significantly penalized by paying above par. The premium of €7.5 is amortized over the 4 years of holding, diluting the return.

For investors who do not wish to perform these calculations manually, numerous online calculators are available that facilitate obtaining the IRR by simply entering the price, coupon, and years to maturity.

Factors that influence the IRR outcome

Understanding which variables affect IRR allows us to anticipate its movements without complex calculations:

Higher coupon → Higher IRR. An increase in periodic payments directly raises the total return.

Lower coupon → Lower IRR. The relationship is direct and immediate.

Low (below par) price → Higher IRR. Buying cheaply means more capital gain at maturity.

High (sobre la par) price → Lower IRR. Buying expensively penalizes final profitability.

Special features: some bonds (convertible, inflation-linked, FRN) can see their IRR affected by specific evolutions of the underlying asset or economic indicators.

Choosing investments with criteria

The true utility of the IRR formula lies in its ability to reveal real opportunities. Consider a comparative example: bond A offers an 8% coupon but a 3.67% IRR; bond B offers a 5% coupon but a 4.22% IRR. Someone guided only by coupons would choose the first, but IRR analysis shows that the second is more profitable.

This divergence typically occurs when bonds with high coupons trade above par, losing competitiveness. IRR corrects this optical illusion.

Final warning: IRR is not everything

While IRR is crucial, it should not be the sole decision criterion. The credit quality of the issuer is equally important. During the Grexit crisis, Greek 10-year bonds traded with an IRR above 19%, which did not reflect an opportunity but an extreme risk of default. Only the intervention of the Eurozone prevented Greece from declaring default.

Therefore, we maintain that it is prudent to use IRR as a compass but never ignore the underlying credit circumstances. The apparent return should always be corroborated with an issuer solvency analysis.

When correctly applied, the IRR formula will help you identify true fixed income investment opportunities, separating what appears to be profitable from what truly is.