TIR: The essential metric for evaluating profitability in bonds

Why Internal Rate of Return (IRR) is Your Ally in Fixed Income Investments

When choosing between different bond investment options, many investors make the mistake of focusing solely on the coupon percentage. However, there is a much more powerful tool that allows us to objectively compare the true profitability: the IRR or Internal Rate of Return.

The reason is simple but crucial: a bond with an 8% coupon may be less profitable than one paying 5%, depending on the purchase price. This is where the IRR formula comes into play, providing us with the actual return considering both the coupons and the gain or loss from buying at different prices relative to the face value.

What exactly is the Internal Rate of Return?

IRR is an interest rate expressed as a percentage that summarizes the total profitability of an investment. In the context of debt securities, it represents the actual return we will get if we hold the bond until maturity.

This return comes from two different sources:

Periodic coupon flows: These are the payments made by the issuer during the life of the bond, usually annually, semiannually, or quarterly. Some bonds, called zero-coupon bonds, do not generate these payments.

Price difference at redemption relative to the nominal value: When we acquire a bond in the secondary market, its price may be below (par), equal (to par), or above (s above par) of its face value. This difference is realized at maturity, significantly impacting our total return.

How ordinary bonds work

To understand the importance of correctly calculating IRR, it is essential to understand how these instruments behave. An ordinary bond has simple characteristics: a defined maturity, an established face value, and fixed periodic interest payments.

At the time of purchase, we acquire the security at a certain price. During its life, we receive coupons regularly. Finally, at maturity, the issuer returns the face value plus the last coupon.

The crucial point here is that the purchase price can differ from the face value. If we buy a bond at 105€ that is worth 100€ at maturity, we have a guaranteed loss of 5€. This loss directly reduces our actual return, which is reflected in an IRR lower than the nominal coupon.

Conversely, if we acquire the same bond at 95€ and at maturity we receive 100€, we gain an additional 5€ that adds to the coupons, raising the IRR above the nominal coupon.

IRR vs. TIN, TAE, and Technical Interest: Critical Differences

It is essential not to confuse these metrics, as each measures different aspects:

IRR (Internal Rate of Return): Reflects the actual profitability of a bond considering the current purchase price, the coupons to be received, and the redemption price at maturity.

TIN (Nominal Interest Rate): Simply the agreed-upon interest rate on the agreed amount, without including additional expenses or commissions.

TAE (Annual Equivalent Rate): Incorporates additional costs beyond the nominal interest. For example, in a mortgage, we might have a TIN of 2% but a TAE of 3.26% because it includes commissions, insurance, and other concepts. It is the tool recommended by regulatory bodies to compare financing offers.

Technical Interest: Mainly used in insurance products, includes specific costs such as the underlying life insurance associated with the product.

The practical importance of IRR in investment decisions

When selecting bonds for our portfolio, IRR allows us to identify opportunities that might go unnoticed if we only look at the coupon.

Imagine two bonds: Bond A offers an 8% coupon but has an IRR of 3.67%, while Bond B has a 5% coupon with an IRR of 4.22%. If we only look at the coupon, we would choose A. But IRR clearly shows that B is more profitable.

Why does this happen? Usually because Bond A is traded significantly above par, which penalizes our return at maturity when we only recover the face value.

IRR calculation: Formula and practical examples

The IRR formula is mathematically expressed as:

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

Where P is the current price of the bond, C represents the periodic coupon, N is the face value, and n is the number of periods until maturity.

Although the formula seems complex, fortunately, there are specialized online calculators that save us from performing these calculations manually.

Practical case 1: Bond purchased below par

Consider a bond trading at 94.5€, paying a 6% annual coupon and maturing in 4 years. Applying the formula, we get an IRR of 7.62%.

We see that the IRR exceeds the nominal coupon thanks to the advantageous purchase price. The difference between paying 94.5€ and receiving 100€ at maturity amplifies our return.

Practical case 2: Bond purchased above par

The same bond, but now trading at 107.5€. When calculating, the IRR results in 3.93%.

In this scenario, paying a premium significantly reduces our profitability. Although the annual coupons remain at 6%, recovering only 100€ from the 107.5€ invested erodes the return to almost half.

Factors that modify the IRR result

Understanding which variables influence IRR allows us to make quick estimates without complex calculations:

Coupon: There is a direct relationship between the coupon level and IRR. Higher coupons generate higher IRRs, and vice versa.

Purchase price: This is probably the most determinant factor. Buying below par increases IRR, while buying above par decreases it.

Special features of the bond: Certain bonds respond differently to external factors. Convertible bonds are affected by the evolution of the underlying asset, while FRNs or inflation-linked bonds vary with these economic indicators.

Final considerations: IRR and credit risk

Although IRR is an invaluable metric, it should never be the sole criterion for selection. The credit quality of the issuer is equally important.

An instructive example is the Greek crisis during the Grexit, when Greek 10-year bonds yielded over 19%. This extremely high figure did not reflect an investment opportunity but the massive risk of default. Only the intervention of the Eurozone prevented Greece from declaring its debt default.

Therefore, the correct practice is to use IRR as a fundamental tool to compare returns but always contextualized within the credit and macroeconomic reality of the bond issuer.