FI 2 Fixed-Income Cash Flows and Types
The cash flows of a fixed-income instrument follow from its features, so reading the structure is the first step in valuing any bond. The most common structure is the standard fixed-coupon bond, usually called a bullet bond. The issuer receives the principal at settlement, pays a fixed periodic coupon, and repays the whole principal in one lump at maturity. Most governments and corporations raise debt this way, and many investors like the predictable income stream and the fixed maturity date for matching known future obligations. As a running example, take the five-year, USD300 million, 3.2 percent semiannual-coupon BRWA bond: each half-year it pays USD4.8 of coupon (300 times 3.2 percent divided by 2), and the final payment of USD304.8 bundles the last coupon with the return of principal.
Not every instrument pays this way. Some spread principal repayment across the life of the loan, some reset their coupon as market rates move, and zero-coupon bonds pay nothing until par arrives at maturity. An instrument that retires part of its principal on each payment date is amortizing debt, and residential and commercial mortgage loans are the classic examples. Because principal is handed back gradually, the borrower spreads the burden more evenly, and the investor collects higher near-term cash flows and carries lower credit risk, since the amount at stake shrinks over time. The trade-off is greater reinvestment risk: those larger early cash flows have to be redeployed at whatever market rate prevails, which may be lower.
Fully amortizing loans
In a fully amortizing loan, principal reduction starts on the first payment date and continues until nothing remains at maturity. The periodic payment is a level amount that blends interest and principal. Early on the interest share is large and the principal share small; as the balance falls, the interest share shrinks and the principal share grows, while the total stays constant. The level payment is found from the annuity relationship below.
Take the BRWA figures but as a fully amortizing loan: five years, a 3.2 percent semiannual coupon, and a USD300 million par value, in millions.
A homeowner takes a 30-year fixed-rate mortgage with these terms: a home price of USD500,000, a loan of USD400,000, a 3.50 percent annual rate, and a 360-month term.
| Month | Total payment | Interest | Principal | Remaining principal |
|---|---|---|---|---|
| 1 | 1,796.18 | 1,166.67 | 629.51 | 399,370.49 |
| 2 | 1,796.18 | 1,164.83 | 631.35 | 398,739.14 |
| 3 | 1,796.18 | 1,162.99 | 633.19 | 398,105.95 |
| 4 | 1,796.18 | 1,161.14 | 635.04 | 397,470.91 |
| 5 | 1,796.18 | 1,159.29 | 636.89 | 396,834.03 |
| 356 | 1,796.18 | 25.97 | 1,770.21 | 7,132.63 |
| 357 | 1,796.18 | 20.80 | 1,775.38 | 5,357.26 |
| 358 | 1,796.18 | 15.63 | 1,780.55 | 3,576.70 |
| 359 | 1,796.18 | 10.43 | 1,785.75 | 1,790.96 |
| 360 | 1,796.18 | 5.22 | 1,790.96 | 0.00 |
Partially amortizing bonds
A partially amortizing bond repays some principal each period but leaves a final lump sum, called a balloon payment, at maturity. It sits between the bullet and fully amortizing cases. Suppose BRWA keeps the same maturity and rate but repays principal down to a USD150 balloon. Think of the structure as two pieces: a fully amortizing loan on the amount that does get repaid, plus the balloon paid at maturity. The present values of the two pieces add up to the USD300 price.
BRWA issues a five-year, 3.2 percent semiannual bond priced at USD300 (in millions) with a USD150 balloon at maturity.
| Year | Bullet bond | Partially amortizing bond | Fully amortizing loan |
|---|---|---|---|
| 0 | −300 | −300 | −300 |
| 0.5 | 4.8 | 18.75 | 32.7 |
| 1 | 4.8 | 18.75 | 32.7 |
| 1.5 | 4.8 | 18.75 | 32.7 |
| 2 | 4.8 | 18.75 | 32.7 |
| 2.5 | 4.8 | 18.75 | 32.7 |
| 3 | 4.8 | 18.75 | 32.7 |
| 3.5 | 4.8 | 18.75 | 32.7 |
| 4 | 4.8 | 18.75 | 32.7 |
| 4.5 | 4.8 | 18.75 | 32.7 |
| 5 | 304.8 | 168.75 | 32.7 |
Borrowers on mortgages usually prefer the constant payment of a fully amortizing loan, because it lines up with steady rental income for a commercial borrower or with a household salary. In the United States, such loans often back mortgage-backed securities, whose cash flows resemble the underlying loan.
Compute the periodic payment and the first payment split for a fully amortizing bond with a USD10,000,000 loan amount, a 2.75 percent annual rate, and a 10-period (five-year) semiannual term.
Two further ways of retiring principal early deserve attention: sinking funds, used mainly by government and some corporate issuers, and waterfalls, widely used in the structuring of asset-backed securities (ABS) as well as mortgage-backed securities (MBS).
Sinking funds
A sinking fund arrangement lets an issuer retire principal on a schedule set at issuance. The name refers to the issuer’s plan to set money aside over time, often in an escrow account, to buy the bonds back before maturity. The mechanism can vary: an issuer may instruct the trustee to redeem a set principal amount chosen at random from among holders, or it may hold the right to repurchase bonds at a fixed price under a contingency feature (covered later). As with any amortization, a sinking fund lowers credit risk while raising reinvestment risk, because principal outstanding shrinks ahead of maturity.
Waterfall structures
A waterfall governs the order in which cash reaches investor classes that hold different priority claims on the same pool. In the most common form, interest is paid to all classes without preference, but principal is repaid strictly in sequence: the most senior class is repaid in full first, then the next class begins to receive principal, and so on down the ranking. Because any shortfall lands on the junior classes first, seniority maps directly onto credit risk. In a three-tranche deal, Tranche A carries the lowest credit risk, then Tranche B, then Tranche C.
| Tranche | Principal repayment order | Relative credit risk |
|---|---|---|
| Tranche A | First to receive principal | Lowest |
| Tranche B | Only after Tranche A is fully repaid | Middle |
| Tranche C | Only after Tranches A and B are fully repaid | Highest |
Some bonds and most loans pay a variable coupon built from a market reference rate (MRR) plus a credit spread. Banks favour floating-rate loan assets, which line up naturally with the variable-rate liabilities they carry, deposits among them, and investors who expect rising rates find floating-rate notes (FRNs) attractive.
Antelas AG’s four-year, EUR250 million FRN pays MRR plus 250 basis points per year, on a quarterly basis. The final four quarters are shown below.
| Quarter | MRR | Coupon rate | Quarterly interest | Principal |
|---|---|---|---|---|
| 13 | −0.50% | 2.00% | 1,250,000 | |
| 14 | 0.15% | 2.65% | 1,656,250 | |
| 15 | 0.25% | 2.75% | 1,718,750 | |
| 16 | 0.50% | 3.00% | 1,875,000 | 250,000,000 |
Predetermined and event-linked adjustments
Coupons can also change on a preset schedule or in response to an event. A step-up bond raises its coupon by specified margins on specified dates. Step-ups protect investors against rising rates and can also nudge an issuer to exercise a contingency provision later. Event-linked coupons instead rise when the issuer’s credit quality deteriorates, reassuring investors that adverse credit moves will be paid for and letting weaker issuers borrow for longer, or at tighter spreads, than a flat coupon would allow. This is common in leveraged loans, that is, loans to lower-credit-quality issuers, where the spread may be tied to financial covenants or credit ratings (as in credit-linked notes).
| Total leverage ratio (TLR) | Credit spread (bps p.a.) |
|---|---|
| TLR at least 3.5x | 325 |
| 3.5x > TLR at least 3.0x | 300 |
| 3.0x > TLR at least 2.5x | 275 |
| TLR at most 2.5x | 250 |
Under this grid Antelas keeps its lowest spread only while leverage stays at or below 2.5 times, and pays more as leverage climbs. The term sheet also sets a debt restriction test: the total leverage ratio, that is net interest-bearing debt over EBITDA, may not exceed 5.00 times, and the interest coverage ratio must stay above 2.50 times each reporting period. An issuer worried about future cash strain may add a payment-in-kind (PIK) feature, which lets it pay interest by increasing the principal outstanding rather than in cash. PIK features appear mostly among heavily debt-reliant firms and usually carry a higher rate to compensate investors for the added principal risk.
Public Power Corporation (PPC), 51 percent owned by the Greek government and the country’s largest electricity utility, issued five-year sustainability-linked bonds in early 2021: EUR775 million at 3.875 percent per year, with a step-up margin of 50 basis points if a step-up event occurred, defined as failing to cut CO2 emissions by 40 percent by December 2022 against a 2019 base year. These were the first such bonds from a European high-yield issuer, and the emissions-linked feature drew demand that pushed the deal past its planned EUR500 million size.
Index-linked bonds tie interest, principal, or both to a specified index. Although any variable could serve, inflation-linked bonds tied to a broad consumer price index (sometimes called linkers) are by far the most common. The fixed cash flows of an ordinary bond are nominal, so their purchasing power erodes with inflation. The return net of inflation is the real interest rate, roughly the nominal rate minus the inflation rate. Investors use inflation-linked bonds to defend purchasing power by collecting inflation-adjusted cash flows. Most are issued by sovereigns, including US Treasury Inflation-Protected Securities (TIPS), with growing demand for emerging market linkers where inflation worries run high.
An investor buys TIPS with a USD115,000,000 principal, a 1.00 percent per year semiannual coupon, and 9.5 years to maturity, whose inflation protection tracks movements in the Consumer Price Index for All Urban Consumers (CPI).
Because TIPS adjust the principal itself with the index, they are a capital-indexed bond, protecting the real value of the principal. Australia, Canada, and the United Kingdom issue similar instruments. Deflation pulls the adjusted principal down over time, yet at maturity holders normally collect whichever is larger, the inflation-adjusted principal or par. An interest-indexed bond works differently: it repays a fixed nominal principal at maturity and index-links only the coupon, so it behaves like an FRN whose reference rate is the inflation rate. Interest-indexed bonds come more often from private financial intermediaries than from governments.
Zero-coupon bonds pay no periodic interest and return principal only at maturity. They are often called discount bonds because, with positive interest rates, they trade below par. The investor’s entire return is the gap between the purchase price and the principal, which stands in for a single cumulative interest payment at maturity. Governments commonly issue them at tenors under 12 months, and after sovereign rates fell to or below zero following the 2008 global financial crisis, longer-dated zeros became more common. Financial intermediaries also manufacture zeros by stripping individual interest or principal payments out of sovereign bullet bonds and selling them separately.
Zeros are well suited to funding a fixed future obligation. A standard coupon bond may fall short if rates decline, because lower reinvestment income drags the realized return below the original yield to maturity (the yield-to-maturity calculation assumes coupons are reinvested at that same yield, an assumption that fails when rates move). A zero has no coupons to reinvest, so it sidesteps that risk entirely.
Deferred-coupon bonds skip interest entirely for an initial stretch of years and then pay a raised coupon from that point to maturity. Issuers typically reach for them to preserve cash right after issuance, which can signal weaker credit quality or a project, such as construction, that produces no income until it is finished. A zero-coupon bond can be viewed as the extreme case of a deferred-coupon bond. Like zeros, deferred-coupon bonds normally price at a discount to par, because the later higher coupon does not usually make up for the interest given up early.
| Structure | Key features | Typical example |
|---|---|---|
| Standard fixed-rate (bullet) | Fixed coupon, interest-only coupons, principal at maturity | Most long-term corporate and government bonds |
| Amortizing principal | Often level payments of interest plus principal, principal repaid over the life | Mortgage loans |
| Variable interest | Cash flows change with a reference rate, index, or inflation rate | Floating-rate notes, most bank loans |
| Zero-coupon | Fixed 0 percent coupon, principal at maturity, sold at a discount | Short-term government bonds |
A contingency provision is a clause that permits an action when a stated event or circumstance arises. The most common ones give the issuer or the bondholders a right, but not an obligation, to act as set out in the indenture. Because these clauses behave like options yet cannot be traded apart from the bond, they are called embedded options. Their value can be gauged by comparing a bond that carries the provision with an otherwise identical bond from the same issuer that does not. The three main types are callable, putable, and convertible bonds.
Callable bonds
A callable bond lets the issuer buy back part or all of the issue, that is, call it, ahead of maturity. Issuers value this flexibility to refinance if market rates fall. Under a fixed-price call, the issuer may repurchase the bond at a preset price. Take the 6.5 percent, seven-year, USD400 million Vivivyu Inc. (VIVU) notes. For the opening three years, the call protection period, calling is not permitted; after that the issuer may call on any business day at the scheduled call price plus accrued interest.
| Period 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% |
So VIVU may call at USD103.25 per USD100 of par during year four, with the fixed price stepping down over the remaining years. Holders face reinvestment risk from year three onward and limited upside once the price reaches the call price. How much the call feature is worth hinges on the yield to maturity relative to the coupon. When the yield to maturity sits above the coupon, the issuer has little reason to call, since the yield to maturity (a proxy for refinancing cost) exceeds the existing coupon, and the callable bond then tracks a comparable non-callable bond. But when the yield to maturity drops below the coupon, the callable bond’s price is effectively capped at the call price, while a non-callable bond keeps rising. Investors therefore demand a higher yield on callable bonds to offset the uncertain maturity and capped upside, a premium known as call risk.
A different kind of call, the make-whole call, compensates investors rather than penalizing them. It is common among highly rated issues and gives the issuer more flexibility than buying bonds in the open market, but it usually requires paying holders a rich price pegged to the yield to maturity on a sovereign bond of comparable maturity. Since that figure usually lands well above where the bond currently trades, make-whole calls seldom get exercised and have little economic effect on either side.
Putable bonds
A put provision hands bondholders the right, on set dates, to return the bond to the issuer at a fixed price, typically par. It protects holders: if rates rise and prices fall after issuance, they can put the bond and redeploy the proceeds at the higher prevailing rates, forcing the issuer to refinance sooner than planned at higher yields. Since the put has value to holders, a putable bond prices above an otherwise similar non-putable bond, and its yield is correspondingly lower, which is how the issuer is compensated for granting the option. When the putable bond’s yield to maturity is below its coupon (so the price is above the put price), the put is worth little and the bond trades like its option-free equivalent. When the yield to maturity rises above the coupon, the put price acts as a floor under the price.
A convertible bond carries a contingency provision linked to the issuer’s common equity. It gives the holder the right to exchange the bond for a number of the issuer’s shares at an effective price per share called the conversion price. The feature gains value as the share price climbs. Unlike a call or a put, which retire debt early, conversion replaces debt with equity when exercised.
Consider the 1.25 percent, five-year, EUR300 million convertible notes of ZTG BioTech S.p.a., an Italian company. The 1.25 percent coupon sits well below the yield to maturity investors would require on a standard ZTG bond of the same maturity, because holders will often accept a very low, or even zero, yield in exchange for conversion rights. The conversion price is EUR42.00 per share against a current price of EUR28.00, a 50 percent premium [= (42.00 − 28.00) divided by 28.00]. Two relationships drive the analysis.
The ZTG bond trades in EUR1,000 face-value units, with a EUR42.00 conversion price.
Growth companies lean heavily on convertible debt: they may not generate enough cash to cover interest and principal, yet they accept issuing equity down the road at a loftier conversion price. Convertibles often bundle in a call provision too, letting the issuer cap investor gains from a rising share price by redeeming early. Some issuers instead attach warrants: a warrant is an attached, not embedded, option that entitles its holder to purchase the issuer’s shares at a set exercise price up to the expiration date. Warrants serve as a yield enhancement and change hands on their own on exchanges such as the Deutsche Boerse and the Hong Kong Stock Exchange.
A number of European banks have brought contingent convertible bonds (CoCos) to market, carrying contingent write-down provisions. Where a standard convertible converts on the upside at the investor’s discretion, a CoCo converts on the downside and does so automatically when a specified event occurs, for example when the issuing bank’s core Tier 1 capital ratio, which measures the equity capital on hand to absorb losses, breaches a minimum regulatory requirement. If losses cut the bank’s capital below that minimum, the CoCo turns debt into equity, rebuilding capital and lowering the odds of default. CoCos were designed to contain systemic risk, the risk of a broad financial system failure, and they pay a higher yield than otherwise similar bonds. The trigger is the capital breach itself, not a particular equity or debt price level.
Fixed-income securities face different legal and regulatory rules that vary with the place of issuance and trading and with the identity of the holder. A bond’s classification follows from two jurisdictions, that of the issuer and that of the issuance, landing it in the domestic, foreign, or Eurobond category, and that label carries legal, tax, and regulatory consequences.
A domestic bond is issued by an entity incorporated in the same country where it is issued; a foreign bond is issued by an entity incorporated elsewhere. Issuers borrow outside their home market for several reasons. Corporations often match the currency of their bond cash flows to that of their foreign operations by issuing foreign bonds. Emerging market sovereigns frequently issue in major foreign currencies to widen and diversify their investor base. As an illustration of reaching a new investor pool, the United Kingdom, in 2014, was the first sovereign outside the Muslim world to issue sukuk, a GBP200 million five-year deal listed on the London Stock Exchange; sukuk follow Islamic law, which bars interest, so they deliver a rental cash flow (a profit rate) generated by underlying assets rather than interest.
In frontier markets, domestic issuance is usually limited to sovereign bonds and the bonds of local banks, with corporate financing done mainly through bank loans; those sovereigns tap international markets for foreign-currency debt, as Romania does alongside its limited leu-denominated market. More developed emerging markets add state-linked enterprises and dominant-industry producers, though many such bonds are in restricted local currencies, so the sovereign and a few issuers also sell in US dollars or euros. Developed markets in major currencies show deep intermediation and specialization, drawing issuers and investors from many jurisdictions. To place the labels: BRWA’s US dollar bonds issued in the United States by a US corporation are domestic; if BRWA or a foreign subsidiary issued euro bonds in Germany or yuan bonds in China, those would be foreign.
Eurobonds and global bonds
The Eurobond market grew up in the 1960s largely to sidestep the legal, regulatory, and tax constraints placed on issuers and investors, especially in the United States. Eurobonds are issued and traded across borders and are usually named for their currency, such as Eurodollar or Euroyen bonds. Falling outside any single country’s jurisdiction, they are typically unsecured and can be denominated in any currency at all, the issuer’s home currency included. A cross-border syndicate typically underwrites them, and most of the paper is placed with buyers across Europe, the Middle East, and Asia. US dollar Eurobonds may not be sold to US investors at the point of issue, since they lack registration with the US Securities and Exchange Commission (SEC), the exception being large qualified institutions. Historically many Eurobonds were bearer bonds, where the trustee kept no record of ownership and only the clearing system knew the holders; today Eurobonds, domestic bonds, and foreign bonds are all registered, with ownership recorded by name or serial number.
A global bond is floated at once in the Eurobond market together with one or more domestic markets, which broadens demand and reaches investors everywhere; the World Bank is a regular global-bond issuer. Foreign bonds, Eurobonds, and global bonds together are often called international bonds, as distinct from domestic bonds.
| Type | Definition |
|---|---|
| Domestic bond | Issued by an entity incorporated in the country of issuance |
| Foreign bond | Sold in a country and in its currency by an entity incorporated in another country |
| Eurobond | Sold outside the jurisdiction of any one country, usually in a non-local currency |
| Global bond | Brought to market in the Eurobond market and one or more domestic markets at the same time |
Cross-border issuance is not just for sovereigns. Consider two examples. Romania’s first 30-year euro bond, issued in 2019, was EUR1.95 billion at a 4.625 percent fixed annual coupon, priced at 99.488 with an issuance spread of 411.4 basis points over a German sovereign benchmark; it was a Eurobond also placed with US investors under the Rule 144A private-placement provision, which limits sales to certain qualified investors. PT Indonesia Infrastructure Finance (IIF), a quasi-government entity, issued USD150 million of US dollar Eurobonds at a 1.50 percent fixed semiannual coupon, priced at 98.808 with a spread of 129 basis points over the five-year US Treasury note. One point stands out: the currency of denomination affects a bond’s price more than where it is issued or traded, because prices respond most to the market interest rates of the denominating currency. IIF could sell five-year US dollar debt at a 1.50 percent coupon even though its domestic Indonesian rupiah bonds of similar tenor yielded 6.97 percent.
Tax treatment matters to both sides of a bond. For corporate issuers weighing debt against equity, how far interest expense can be deducted for tax is a meaningful input to that financing choice. On the investor side, interest received from a bond is normally charged at the ordinary income tax rate, the very rate levied on wages or salary.
Treatment can vary by jurisdiction and by the type of government bond. A UK citizen owes income tax on interest, whether accrued or paid, yet escapes capital gains tax when a bond is sold above its purchase price. In the United States, a Treasury holder pays federal income tax on interest but owes no state or local tax; meanwhile, holders of state and local government bonds (municipal bonds) frequently escape federal income tax as well as the income tax of the state that issued them, which nudges residents to buy local. Where a bond is issued and traded can matter too: some domestic bonds pay interest net of income tax, while others, including some Eurobonds, pay gross (no withholding), giving certain investors more flexibility over how and where they are taxed.
Capital gains and original issue discount
Beyond interest, selling a bond before maturity at a price different from its purchase price produces a capital gain or loss, usually taxed differently from ordinary income and often split by holding period. A gain realized more than a year after purchase may face a lower long-term capital gains rate, while a gain within a year may be taxed as short-term at the ordinary income rate. Exceptions exist, and not every country has a separate capital gains tax or a holding-period distinction.
For bonds issued at a discount, such as zero-coupon bonds, the treatment of the original issue discount (OID) adds another country-specific wrinkle. The OID is the difference between par value and the original issue price. Each year the United States folds a prorated slice of the discount into interest income; Japan does not.
A US-based investor and an investor in a jurisdiction without an OID tax provision each buy the same zero-coupon US Treasury: USD25,000,000 principal, five years to maturity, issued at USD92.83 per USD100 of par.
Some jurisdictions offer a parallel provision for bonds bought at a premium, allowing an investor to write off, pro rata, the sum paid over par from taxable income each year until maturity. This deduction can be a choice rather than a requirement: an investor may amortize the premium annually, or claim nothing yearly and book a capital loss at the point the bond is redeemed at par on the maturity date.