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Eduzan / MODULE 07 — Fixed Income

FI 1 Fixed-Income Instrument Features

Worked examples are fully visible. Check-yourself items are study aids you can reveal one at a time.

The features that define a bond and the legal contract that governs it. Check-yourself items are study aids.

Fixed-income instruments are debt: an issuer borrows money from investors under a contractual agreement and promises to pay interest and repay the principal. Loans and bonds are the two main forms, and they are the most common way businesses, governments, and not-for-profit organizations raise financing. A loan is a private agreement, usually between a single borrower and a bank. A bond is a more standardized contract designed to trade easily, so it suits larger corporations, governments, and special purpose issuers that want their debt to change hands readily. For big institutions such as pension funds, insurers, mutual funds, and central banks, bonds make up a large share of the portfolio.

The distinguishing feature of a bond is its committed periodic cash flows. An investor buys the bond by paying cash to the issuer, then receives scheduled interest payments over the life of the instrument and the return of principal at the end. That fixed promise separates a bond from equity, where payments are discretionary. A single corporate issuer typically has only one or two classes of equity outstanding, yet it may run many separate debt obligations at once, differing in currency, in seniority, and in how much time each one has left to run.

Which liabilities count as fixed income

Accounting standards define liabilities broadly as present obligations to transfer economic resources because of past events. That definition sweeps in amounts owed to suppliers, customers, employees, governments, retirees, and lessors. The key relationship to remember is one-directional: all fixed-income instruments are liabilities, but not all liabilities are fixed-income instruments. When we study fixed income from a corporate issuer point of view, we focus only on loans and bonds, that is, obligations settled in cash whose counterparty is an investor or a bank. Leases and pension obligations share some traits with debt but sit outside this scope.

Liabilities on a corporate balance sheet: which are fixed income

Liability	Obligation to	Fixed-income instrument
Accounts payable	Suppliers	No
Deferred revenue	Customers	No
Accrued payroll	Employees	No
Taxes payable	Governments	No
Lease liability	Lessors	No (out of scope)
Pension liability	Retirees	No (out of scope)
Loan	Banks	Yes
Bonds	Investors	Yes

Who issues bonds

Any legal entity is capable of issuing a bond, and whoever does so remains liable for all interest and all principal. Issuers split into two broad camps. The government sector covers national governments (the sovereigns), regional and local governments, supranational bodies (the World Bank among them), and quasi-government entities. That last label means an agency a government owns or backs, for instance a postal service or a national railway. Since a sovereign bond draws on the government’s power to tax and to run its finances, within its own region it normally ranks as the lowest credit risk and anchors the benchmark used to price everything else. Government issuers tend to finance themselves with bonds rather than loans, though exceptions exist, such as loans from supranational bodies like the International Monetary Fund.

Private sector issuers include ordinary corporate issuers and special purpose entities. A special purpose entity is created to take ownership of assets such as loans or receivables, which are then financed by asset-backed securities (ABS) sold to investors. Those structures are covered in later lessons.

Check yourself

A company records a pension obligation and a bank loan on its balance sheet. Which one is a fixed-income instrument for the purpose of these modules?

The bank loan. It is settled in cash with a bank as counterparty. A pension obligation is a liability but sits outside the fixed-income scope, alongside leases.

Why are sovereign bonds usually the lowest-credit-risk instruments in their region?

Because a national government stands behind them, wielding its authority to levy taxes and steer public finances; it can raise revenue, or in some cases issue currency, to honor what it owes.

Every bond issue can be described by a compact set of features: the issuer, the time to maturity, the principal amount, the coupon rate and its frequency, the seniority, and any contingency provisions. Taken together, these features fix how much the instrument pays and when, and they are typically set out for investors in a document called a prospectus.

Maturity and tenor

The maturity date is simply when investors collect the issuer’s last payment. Tenor is the remaining time to that date. An instrument whose tenor at issuance is one year or less is a money market security, with Treasury bills from governments and commercial paper from corporations as the usual examples. Instruments issued with a tenor longer than one year are capital market securities. Rarer still is the perpetual bond, which never fixes a maturity at all. Public sector bodies were the earliest to sell them, and current examples include certain local government issues and bonds that banks use to meet regulatory capital rules. A perpetual bond still differs from equity: it carries contractually defined cash flows, gives no voting rights, and ranks ahead of equity in the capital structure.

Principal

Principal, which also goes by par value or face value, is what the issuer promises to hand back when the bond matures. It is also the amount investors advance at issuance. Some instruments repay principal in increments rather than in a single lump sum: a mortgage loan is the classic case, where each monthly payment blends principal repayment with interest so the balance is amortized over time.

Coupon rate and frequency

Interest can reach the investor in three ways: as a fixed coupon on set dates; as a variable coupon that is reset and paid on set dates; or rolled together with the principal into one lump sum when the bond matures.

A fixed-coupon bond hands over the same amount each period, be that period a month, a quarter, half a year, or a full year; for corporate bonds the norm is twice a year. A bond with variable interest is a floating-rate note (FRN). An FRN coupon is built from two parts: a market reference rate (MRR) plus an issuer-specific spread called the credit spread.

The reference rate itself is the prevailing borrowing or lending rate for the strongest issuers, quoted per currency and per maturity; it was historically set by polling lenders (Libor) but now derives from an average of observed market transactions. The MRR resets periodically over the life of the bond, so the coupon and the interest payment move with it. The credit spread, by contrast, is fixed at issuance, usually stays constant, and is quoted in basis points (bps), each one hundredth of a percentage point. The stronger the issuer credit quality, the smaller the spread.

The third pattern is the zero-coupon bond, also called a pure discount bond, which pays no periodic interest. It is issued below par, and the gap between the issue price and the par value repaid at maturity is the entire accumulated interest.

Seniority

Seniority is the priority of a debt issue among all of an issuer obligations, and it is a major driver of risk. Senior debt ranks ahead of other claims in bankruptcy or liquidation. Junior debt, also called subordinated debt, ranks below senior debt and is paid only after senior claims are satisfied.

Contingency provisions

Such a clause, known as a contingency provision, lets a particular action take effect once a defined event occurs. The most common ones for bonds are embedded options, namely call options, put options, and conversion-to-equity options. These behave like option contracts but cannot be traded apart from the bond. Their value can be inferred by comparing a bond that carries the provision against an otherwise identical standard bond from the same issuer.

A worked prospectus and its cash flows

Consider a five-year note issued by Bright Wheels Automotive Corporation (BRWA), whose prospectus terms are summarized below. The note is senior, unsecured, and ranks pari passu (on equal footing) with the issuer other unsecured, unsubordinated debt.

BRWA Corporation bond: summary of terms

Term	Detail
Issuer	Bright Wheels Automotive Corporation
Maturity	Five years from settlement
Principal amount	USD 300 million
Interest	3.2 percent fixed coupon
Interest payment	Semiannual, first payment six months after settlement
Seniority	Unsecured and unsubordinated; ranks pari passu with other such debt

With a 3.2 percent coupon on USD 300 million of par, the annual interest is USD 9.6 million, split into two semiannual payments of USD 4.8 million. Investors advance USD 300 million at issuance and receive USD 4.8 million every six months. On the maturity date they collect the final USD 4.8 million coupon together with the USD 300 million principal, a final flow of USD 304.8 million.

Figure 1: Cash flows of the five-year BRWA bond (USD millions)

Nine level coupons of 4.8 arrive every six months. At year five the investor receives the last coupon plus the 300 principal, a combined 304.8.

Example 1 · Worked

The annual coupon amount on a fixed-rate bond equals the coupon rate times the par value; a payment made more often than yearly simply divides that annual amount into equal parts.

1. Confirm the semiannual coupon on the BRWA bond (3.2 percent on USD 300 million).

Solution.

Each semiannual payment is USD 4,800,000.

2. A separate bond carries a 2.5 percent coupon on GBP 100,000 of par and pays semiannually. What is each coupon payment?

Solution.

Each payment is GBP 1,250.

Example 2 · Worked

A European corporation issues an FRN of EUR 10 million; its coupon, paid every quarter, is the three-month MRR with 125 bps added on top. Suppose the three-month MRR for the period is negative 0.50 percent.

Determine the FRN coupon rate and the interest payable for the quarter.

Solution. The coupon is the reference rate plus the fixed spread. A negative MRR is allowed and simply lowers the coupon.

The coupon is 0.75 percent and the quarterly interest payable is EUR 18,750.

A perpetual bond in practice

Airport Authority Hong Kong runs one of the busiest cargo airports anywhere and a major hub for passengers. In late 2020, after passenger volumes collapsed during the COVID-19 pandemic, it announced a two-part USD 1.5 billion perpetual bond to fund a third runway and general corporate needs. Even with no stated maturity, investor confidence in the recovery was strong enough that orders exceeded the offer amount by more than ten times.

Check yourself

An FRN pays the MRR plus a spread. Which part resets over the life of the bond, and which is fixed at issuance?

The MRR resets periodically with market conditions; the issuer-specific credit spread is set at issuance and usually stays constant. As the MRR moves, so does the coupon.

Where does the return on a zero-coupon bond come from, given that it pays no periodic interest?

It is issued at a discount to par, and the difference between the issue price and the par value repaid at maturity is the whole accumulated interest.

Once a bond has a price and a schedule of expected cash flows, we can compute a return, or yield. Price and yield move inversely: as one rises the other falls. The simplest measure is the current yield (CY), the annual coupon divided by the current price, expressed as a percentage. It is the fixed-income analogue of the dividend yield on a stock.

A richer and far more common measure is the yield-to-maturity (YTM), the internal rate of return implied by the bond’s price together with the cash flows it is expected to pay through to maturity, and it is normally stated on an annual basis. An investor actually earns the purchase-date YTM only if three conditions hold: all promised interest and principal arrive on schedule (no default), the bond is held to maturity, and every interim cash flow is reinvested at the YTM. These are the standard internal-rate-of-return assumptions; if any fails, the realized return will differ from the quoted YTM.

The yield-to-maturity is the rate r that makes the discounted cash flows equal to the price.

The yield curve and the credit spread

Most issuers have many bonds outstanding. Plotting the YTM of an issuer bonds against their times to maturity produces a yield curve. When longer maturities show higher yields, as they often do, investors are demanding extra return to bear the added risk of lending for longer. Comparing an issuer yield curve with the curve for comparable sovereign bonds, which carry little or no credit risk, isolates the extra compensation for credit risk. That difference in yield is the credit spread.

Figure 2: Corporate yield curve versus the sovereign curve

At the five-year point the corporate bond yields 3.2 percent against the sovereign 2.3 percent. The 90 bps gap is the credit spread.

Example 3 · Worked

The five-year BRWA bond (3.2 percent coupon, paid semiannually) trades at a price of USD 101 per USD 100 of face value shortly after issuance.

1. Compute the current yield.

Solution.

The current yield is 3.168 percent.

2. Set up the yield-to-maturity. The 3.2 percent coupon is paid semiannually, so each period pays 1.6 per 100 of face over 10 periods.

Solution. The semiannual rate r solves the pricing equation:

Solving gives r of about 1.49 percent per semiannual period, which annualizes to 1.49 percent times 2, or roughly 2.98 percent. Notice the YTM of 2.98 percent sits below the 3.2 percent coupon, consistent with a price above par.

Example 4 · Worked

The five-year BRWA bond yields 3.2 percent to maturity, while the comparable five-year US Treasury yields 2.3 percent.

What is the credit spread, and what does it represent?

Solution.

The 90 bps spread is the extra yield investors require for taking on the credit risk of BRWA relative to a near-riskless sovereign bond of the same maturity.

Check yourself

If a bond price falls while its coupon is unchanged, what happens to its current yield?

It rises. The current yield is the annual coupon divided by the price, so a lower price in the denominator raises the yield.

A downward-sloping yield curve tells you what about an issuer longer-term versus shorter-term yields?

That yields on the longer-term bonds are lower than yields on the shorter-term bonds of the same issuer.

The features of a bond are set out in a legal contract called the bond indenture. The indenture lays out the form the bond takes, what the issuer is bound to do, and the rights the holders enjoy. Beyond listing the features, it identifies the issuer sources of repayment, records any commitments the issuer makes to bondholders, and it details anything that props up or strengthens the issuer’s capacity to repay in full.

Sources of repayment

Where the money to repay a bond comes from varies by issuer and is central to assessing relative risk. A national government wields the sovereign power to tax activity across its economy, and in some cases to issue currency, which is why their bonds often carry the highest credit quality in a region; developed-market sovereign bonds are frequently treated as free of default risk and used as the benchmark for the whole market. Local or regional governments may pledge their taxing authority, or instead earmark fees from an infrastructure project, such as a bridge, toll road, or transit system, to service an associated bond.

Corporate bond investors usually look first to the operating cash flows of the firm for interest and principal. Higher-quality corporate issuers can borrow on an unsecured basis, meaning those operating cash flows are the sole source of repayment, as in the BRWA example. Issuers with less stable cash flows tend to face more restrictions and may hand investors a legal claim (a lien, or pledge) over particular assets to act as a backup source of repayment; these are secured bonds. In liquidation, secured holders may receive the value of the pledged assets, while unsecured holders receive only what remains afterward. A junior unsecured holder stands last in line, behind every secured and senior unsecured claim. Collateral of this sort can be tangible property, a stream of cash flows like licensing fees, or a guarantee supplied by a third party. An issuer weighs the benefit of such credit enhancement, namely a lower borrowing cost, against the cost of reduced operating flexibility.

Primary sources of repayment by bond type

Bond type	Primary source of repayment	Secondary source
Sovereign bond	Tax revenues	None needed
Unsecured corporate bond	Operating cash flows	None
Secured corporate bond	Operating cash flows	Collateral cash flows or sale
Asset-backed security	Cash flows of the underlying loans or receivables	Set by tranche priority

For an asset-backed security, repayment flows from the cash that the pool of loans or receivables held by the special purpose issuer throws off. An ABS transaction slices these claims into classes called tranches, ordered by priority. Tranche A might have first claim on the periodic cash flows, then Tranche B; Tranche C investors are paid only after A and B have been served.

Example 5 · Worked

An issuer in default is being liquidated. It has three classes of debt outstanding: senior secured notes, senior unsecured notes, and junior subordinated notes.

1. Rank the three classes from highest to lowest priority of claim.

Solution. Senior secured, then senior unsecured, then junior. Secured holders first receive the value of the pledged assets; senior unsecured holders are paid next from remaining value; junior subordinated holders are last.

2. Both senior secured notes contain a pari passu clause. What does that ensure among them?

Solution. A pari passu, or equal footing, clause ensures each such obligation is treated the same as the issuer other debt of the same seniority. Neither senior secured note is subordinated to the other simply because it was issued earlier; priority does not depend on the timing of issuance.

Check yourself

What is the sole source of repayment for a typical unsecured corporate bond, and how does a secured bond differ?

An unsecured corporate bond relies solely on the issuer operating cash flows. A secured bond adds a claim on specific pledged assets as a secondary source of repayment.

In an ABS with Tranche A, B, and C notes, which investors are paid last?

Tranche C investors, who are paid only once Tranche A and then Tranche B have taken their cash flows.

Unlike equity investors, bondholders have no voting rights, so their main protection comes from covenants: legally enforceable rules that borrower and lender agree to when the bond is issued or the loan is made. Affirmative covenants specify what the issuer must do; negative covenants specify what the issuer must not do.

Affirmative covenants

Affirmative covenants are mostly administrative. Common examples include stating the use of proceeds from the issue, providing timely financial reports, and giving holders the right to redeem above par should the issuer be taken over. Two further examples matter for seniority. A pari passu clause, meaning equal footing, ensures the debt is treated the same as the borrower other obligations of similar seniority. A cross-default clause treats the borrower as in default on this bond if it defaults on another obligation. These clauses generally add no cost and do not meaningfully constrain how the issuer runs its business.

Negative covenants

Negative covenants restrict the issuer, and they matter most for weaker credits. They include limitations on liens (restricting the pledging of assets as security for other debt), limitations on sale-and-leaseback transactions, and restrictions on mergers or consolidations that would breach those limits. A negative pledge clause specifically bars pledging assets as collateral for new debt so that existing creditors are not subordinated. Other negative covenants limit investments, the sale of assets, the payment of dividends, share buybacks, and the amount of additional debt the issuer may take on.

The BRWA senior unsecured notes, being high quality, carry a broadly defined use of proceeds and only a few negative covenants: limitations on liens, on sale-and-leaseback deals, and on mergers or consolidations. Each protects senior bondholders from having their claims diluted.

A weaker issuer faces tighter terms. Consider Vivivyu Inc. (VIVU), a digital media company that issued senior secured callable notes.

Vivivyu Inc. callable notes: summary of terms

Term	Detail
Maturity	Seven years from settlement
Principal amount	USD 400 million
Interest	6.5 percent fixed coupon, semiannual
Seniority	Secured and unsubordinated; ranks pari passu with other such debt
Call provision	Redeemable on any business day starting three years after settlement, per the call price schedule

Vivivyu call price schedule (percent of principal, plus accrued interest)

Years after settlement	Call price
Three to four years	103.25
Four to five years	102.50
Five to six years	101.75
Six to seven years	101.00

The Vivivyu bondholders are also protected by financial covenants that restrict dividends, share repurchases, and additional debt unless tighter thresholds are met under what is called an incurrence test. Two sets of ratios apply: an ongoing debt restriction test the issuer must always satisfy, and a stricter incurrence test that must be met before the issuer may take certain restricted actions.

Vivivyu financial covenant thresholds

Test	Net debt to EBITDA	Interest coverage ratio
Debt restriction test (ongoing)	Not greater than 5.00x	Greater than 2.50x
Incurrence test (to act)	Not greater than 4.50x	Greater than 3.00x

Covenants are not costless to the bondholder either. Terms that are too strict may not serve the bondholders best interest if they push an issuer into default that could otherwise have been avoided, for instance by blocking the issuer from raising the very funds it needs to meet its obligations. When a covenant is violated, bondholders have recourse in several forms: a change in financial terms, such as a higher interest rate, accelerated repayment of the debt, or termination of the debt agreement.

Example 6 · Worked

Classify each of the following clauses as an affirmative covenant or a negative covenant.

1. A cross-default clause.

Solution. Affirmative. It specifies a condition the issuer is bound by, namely that defaulting on another obligation counts as a default here; it requires the issuer to honor a stated term rather than prohibiting a business action.

2. A restriction on issuing additional debt.

Solution. Negative. It prohibits the issuer from taking an action, in this case increasing leverage beyond the agreed limits.

3. A minimum interest coverage requirement.

Solution. Negative. By capping leverage relative to operating income or EBITDA, it constrains what the issuer may do.

Example 7 · Worked

Antelas AG, a German technology company earning revenue from licensing royalties and consulting, issues four-year floating-rate notes: EUR 250 million principal, interest of MRR plus 250 bps paid quarterly, secured and unsubordinated, ranking pari passu with the issuer other secured, unsubordinated debt.

1. The phrases “four years” and “MRR plus 250 bps per annum” describe which two bond features?

Solution. Time to maturity and coupon rate. The notes mature four years after settlement, and the coupon is variable, set by the MRR plus a fixed 250 bps spread.

2. One year after issuance, the issuer credit spread rises by 25 bps. How does the FRN coupon respond?

Solution. It does not change. The spread on this FRN is fixed at 250 bps for the life of the bond; only movements in the MRR alter the coupon.

3. If the MRR for the final interest period is 0.25 percent, what is the total payment to bondholders on the maturity date?

Solution. The maturity payment is the final coupon plus the principal.

The total payment is EUR 251,718,750.

Check yourself

In one sentence, what is the difference between an affirmative and a negative covenant?

An affirmative covenant states what the issuer is required to do, while a negative covenant states what the issuer is prohibited from doing.

Name two forms of recourse bondholders may have when a covenant is violated.

Any two of: a change in financial terms such as a higher interest rate, accelerated repayment of the debt, or termination of the debt agreement.

End of lesson.

Back to MODULE 07 — Fixed Income

FI 1 Fixed-Income Instrument Features

Overview

Fixed-Income Instruments and Their Issuers

Which liabilities count as fixed income

Who issues bonds

Key Bond Features

Maturity and tenor

Principal

Coupon rate and frequency

Seniority

Contingency provisions

A worked prospectus and its cash flows

Yield Measures and the Yield Curve

The yield curve and the credit spread

Bond Indentures and Sources of Repayment

Sources of repayment

Bond Covenants

Affirmative covenants

Negative covenants