Reading 48
MODULE 48.1: FIXED-INCOME CASH FLOWS AND TYPES
Describe common cash flow structures of fixed-income instruments and contrast cash flow contingency provisions that benefit issuers and investors.
Bullet Structure
A typical bond pays interest periodically (the coupons) and repays the entire principal (par value) in a single lump sum at maturity. The periodic payments contain interest only.
Example. A $1,000 par, 5-year bond with a 5% annual coupon issued at par follows this schedule:
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| PMT | $50 | $50 | $50 | $50 | $1,050 |
| Principal remaining | $1,000 | $1,000 | $1,000 | $1,000 | $0 |
Amortizing Loans
An amortizing loan has periodic payments that include both interest and partial repayment of principal. A fully amortizing structure repays the principal entirely by the last payment (typical of car and home loans). Same 5-year, 5% bond, but fully amortizing:
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| PMT | $230.97 | $230.97 | $230.97 | $230.97 | $230.98 |
| Principal remaining | $819.03 | $629.01 | $429.49 | $219.99 | $0 |
Calculator: \(N=5;\ I/Y=5;\ PV=1{,}000;\ FV=0;\ \mathrm{CPT}\to PMT=-230.97\).
In Year 1, interest = \(0.05\times\$1{,}000=\$50\); principal repayment = \(\$230.97-\$50=\$180.97\); opening balance for Year 2 = \(\$1{,}000-\$180.97=\$819.03\). Each subsequent year, the interest portion decreases and the principal portion increases.
A partially amortizing bond has a balloon payment at maturity — the final payment includes only the remaining unamortized principal (smaller than a full bullet). With a $200 balloon:
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| PMT | $194.78 | $194.78 | $194.78 | $194.78 | $394.78 |
| Principal remaining | $855.22 | $703.20 | $543.58 | $375.98 | $0 |
Calculator: \(N=5;\ I/Y=5;\ PV=1{,}000;\ FV=-200;\ \mathrm{CPT}\to PMT=-194.78\).
Sinking Fund & Waterfall Structures
Sinking fund provisions require the issuer to retire a portion of the principal through periodic redemptions over the bond's life. For example, a 20-year, $300 million issue might require the trustee to redeem $20 million of randomly selected bonds each year starting in Year 6.
- Advantage to bondholders: credit risk is reduced because less principal remains outstanding at maturity.
- Disadvantage to bondholders: reinvestment risk — when rates fall, redeemed cash must be reinvested at lower yields.
Waterfall structures govern principal distribution among tranches of asset-backed securities (ABS) and mortgage-backed securities (MBS). Junior tranches typically receive no principal until all senior tranches are fully repaid; interest payments continue to all tranches.
Coupon Structures
Floating-Rate Notes (FRNs)
FRNs (also called floaters) pay coupons that reset with prevailing market rates. The variable rate is the market reference rate (MRR), plus a fixed margin called the credit spread, expressed in basis points (bp), where 1 bp = 0.01%. Most FRNs pay quarterly using a 90-day MRR.
Example. An FRN paying MRR + 75 bp; if the annualized MRR for the current quarter is 2.3%, the coupon paid at quarter-end is \((2.3\%+0.75\%)/4 = 0.7625\%\) of par.
Other Coupon Structures
- Step-up coupon bonds — the coupon rate rises on a predetermined schedule, protecting investors against rising interest rates.
- Credit-linked coupon bonds — coupon rises if the issuer's credit rating deteriorates and falls if it improves. Leveraged loans often have similar provisions (e.g., MRR + 2.5%, stepping up to MRR + 3% if debt/EBITDA exceeds 3).
- Payment-in-kind (PIK) bonds — the issuer may pay coupons by issuing additional bonds rather than cash. Typically issued by highly leveraged firms with weak cash flow expectations; they offer higher yields due to lower perceived credit quality.
- Green bonds — coupon may step up if the issuer fails to meet specified environmental targets (e.g., CO₂ reduction).
Index-Linked Bonds
An index-linked bond ties coupons or principal to a published index. Inflation-linked bonds (linkers) are the most common, indexing cash flows to a CPI to preserve real value.
- Interest-indexed bonds: coupon rate is adjusted for inflation; principal stays unchanged (principal is not inflation-protected).
- Capital-indexed bonds: the most common type (e.g., U.S. TIPS). Coupon rate is constant, but principal is adjusted for inflation/deflation. With deflation, TIPS investors receive the greater of inflation-adjusted principal or unindexed par at maturity.
Example (capital-indexed). A $1,000 par bond with 3% annual coupon paid semiannually. After 6 months with 1% inflation, principal becomes $1,010, and the semiannual coupon = \(\$1{,}010\times1.5\% = \$15.15\). The 3% coupon is therefore a real rate; investors are protected against unexpected inflation in both income and final principal.
Zero-Coupon and Deferred Coupon Bonds
Zero-coupon bonds pay only par at maturity — the simplest fixed-income structure. They eliminate reinvestment risk and must trade below par to provide a positive return. Deferred coupon bonds begin coupon payments only after a specified delay; suitable for issuers with low credit ratings or large projects not yet generating revenue. Zero-coupon bonds can be considered the most extreme form of deferred coupon bond.
Fixed-Income Contingency Provisions
Contingency provisions in bond indentures are embedded options — integral to the bond contract, not separate securities. Some are exercised by the issuer (call), others by the bondholder (put, conversion). Bonds without contingency provisions are straight or option-free.
Callable Bonds
A callable bond grants the issuer the right to redeem all or part of the issue prior to maturity at a predetermined call price.
Example call schedule for a 6%, 20-year bond issued at par on June 1, 2022:
- Callable at 102% of par after June 1, 2027 (the first call date).
- Callable at 101% of par after June 1, 2030.
- Callable at 100% of par after June 1, 2032.
The first 5 years (issuance to first call date) are the call protection period. The issuer benefits from the call when market yields decline (because of falling rates or improved credit quality): the bond can be redeemed and refinanced at the new lower rate.
If the market yield on the 6%, 20-year bond falls to 4% by June 1, 2027, the noncallable equivalent would trade at roughly $1,224. With a call price of 102, the issuer can redeem at $1,020 each and reissue at 4%, lowering annual interest from $60 to $40.80 per bond.
Bondholders bear call risk: an uncertain redemption date and a price ceiling near the call price during the call period. Bondholders demand a higher yield (lower price) on a callable bond than on an otherwise identical option-free bond. The price difference equals the value of the call option to the issuer.
Putable Bonds
A putable bond lets the bondholder sell the bond back to the issuer at a prespecified put price (usually par). Holders are likely to exercise when market price falls below the put price (rising rates or weakening credit). The put option benefits the bondholder; thus a putable bond sells at a higher price (lower yield) than an otherwise equivalent straight bond. The price difference equals the value of the put option.
Convertible Bonds
Convertible bonds let the bondholder exchange the bond for a fixed number of issuer common shares, allowing participation in stock price appreciation. The conversion option is valuable, so issuers can sell convertibles at higher prices (lower yields).
- Conversion price — par per share at which conversion occurs.
- Conversion ratio = par value / conversion price. A $1,000 par bond with a $40 conversion price has a ratio of 25 shares.
- Conversion value = current share price × conversion ratio. With shares at $50 and ratio 25, conversion value = $1,250.
Warrants
Warrants attached to straight bonds give holders the right to buy issuer common shares at a fixed price within a stated period. Warrants gain value when the share price exceeds the exercise price before expiration. They can be detached and traded separately on exchanges.
Contingent Convertible Bonds (CoCos)
CoCos automatically convert from debt to common equity if a specified event occurs. Issued mainly by European banks, CoCos are typically structured to convert when the bank's equity capital falls below a regulatory threshold — simultaneously reducing debt liabilities and increasing equity, helping the bank meet minimum capital requirements.
子彈型結構（Bullet）：典型債券每期僅支付利息（票息），到期一次性償還全部本金。
攤銷型貸款（Amortizing）：每期支付包含利息與部分本金。完全攤銷型在最後一期還清全部本金（汽車貸款、房貸常見）；部分攤銷型在到期保留一筆大額尾款（balloon payment），最後一期金額較完全攤銷型大但較子彈型小。
償債基金條款：要求發行人按期分次贖回部分本金。對債券持有人而言：①信用風險降低（到期應付本金減少）；②但面臨再投資風險（利率下跌時提早收到現金，只能以較低收益再投資）。
瀑布結構（Waterfall）：用於 ABS / MBS 各分券（tranche）的本金分配；通常初級分券須在所有高級分券本金償付完畢後才獲得本金；利息則對所有分券持續支付。
票息結構：
- 浮動利率票券（FRN／floater）：票息＝市場參考利率（MRR）＋信用價差（以基點 bp 表示，100 bp=1%）。多為季付，使用 90 天 MRR。範例：MRR + 75 bp，若年化 MRR 為 2.3%，當季支付 (2.3%+0.75%)/4 = 0.7625% 票面值。
- 升息型（step-up）：票息按預定時間表逐步調升。
- 信用連結型：票息隨信用評等變動；槓桿貸款常見類似條款。
- 實物支付債（PIK）：發行人以新債支付利息（本金增加），通常為高槓桿、現金流不足之發行人，殖利率較高。
- 綠色債券：未達環保目標時票息上升。
- 指數連結型／通膨連結型：①利息指數型（principal 不調整，僅票息調整）；②資本指數型（最常見，如美國 TIPS：票息率不變，本金按通膨調整；通縮時 TIPS 取「調整後本金」與「原始面值」之較大者）。
資本指數型範例：$1,000 面值、3% 年利率半年付。半年通膨 1%，本金調為 $1,010，半年票息 = $1,010 × 1.5% = $15.15。3% 可視為實質利率，投資人完整對沖通膨。
零息債券：到期僅支付面值，最簡單結構，無再投資風險，必然以折價發行。遞延票息債券：發行後一段期間才開始支付票息（適合信用較差或大型專案發行人）；零息債券可視為遞延票息的極端型。
或有條款（embedded options）：
- 可贖回債（Callable）：發行人可在 call period 內以 call price 贖回。對發行人有利（可在利率下跌時 refi），對投資人造成 call risk，殖利率須較高。call protection 期間禁贖。
- 可賣回債（Putable）：投資人可按 put price（通常為面值）賣回發行人。利率上升或信用惡化時投資人會行使賣回權。價格較高、殖利率較低。
- 可轉換債（Convertible）：投資人可按固定股數轉為發行人普通股。轉換價＝可換股票之每股對應面值；轉換比率＝面值 / 轉換價（如 $1,000 / $40 = 25 股）；轉換價值＝市價 × 轉換比率（市價 $50 × 25 = $1,250）。
- 認股權證（Warrants）：附隨直債發行，賦予持有人於到期前以固定價格買入發行人股票的權利，可與債券分離單獨交易。
- 或有可轉債（CoCo）：當發行人（多為歐洲銀行）資本適足率跌破門檻時自動由債轉股，同時降債、增資，協助滿足監管要求。
內嵌選擇權對擁有行使權的一方有利：call 對發行人有利，put 與 conversion 對投資人有利。價格差額即內嵌選擇權的價值。
Describe how legal, regulatory, and tax considerations affect the issuance and trading of fixed-income securities.
Domestic, Foreign, Eurobonds, and Global Bonds
Bonds are subject to different legal and regulatory requirements depending on issuer domicile and the market in which they trade.
- Domestic bonds — issuer is domiciled in the same country as the market in which the bond is issued and traded.
- Foreign bonds — issuer is from a different country than the market in which the bond trades. Example: a U.K. firm issuing USD-denominated bonds in the U.S. to fund U.S. operations.
- Eurobonds — issued outside the jurisdiction of any single country and may be denominated in any currency. They face less regulation than domestic bonds and were originally introduced to circumvent U.S. regulations. Despite the name, they are not necessarily denominated in euros nor issued in Europe (e.g., a yen-denominated bond by a Chinese issuer trading outside Japan is a Euroyen bond). Eurobonds are referenced by the currency: Eurodollar (USD), Euroyen (yen), etc. Originally most were bearer bonds (no recorded ownership); today most are registered.
- Global bonds — Eurobonds that trade in at least one domestic bond market and in the Eurobond market.
Foreign, global, and Eurobonds involving more than one country are collectively called international bonds. The single factor that best explains yield differences across markets is the currency of denomination, because the relevant interest rates are those of the currency country.
Sukuk bonds are Sharia-compliant bonds. Islamic law restricts the payment of interest and the use of bond proceeds, so the periodic payments are structured as rent on underlying assets rather than interest.
Taxation of Bond Income
- Interest income is typically taxed as ordinary income at the same rate as wages and salaries.
- U.S. municipal bonds: interest is usually exempt from federal income tax and often from state income tax in the state of issue.
- Capital gains/losses: arise when a bond is sold before maturity above or below its constant-yield price trajectory; often taxed at lower rates than ordinary income, with potentially even lower long-term capital gains rates if held beyond a minimum holding period.
- Original issue discount (OID) bonds — including zero-coupon bonds and other bonds issued at significant discounts. The price appreciation toward par represents interest income; many tax jurisdictions tax a portion of the discount as interest income each year, even though no cash interest is received until maturity.
- Premium bonds — some jurisdictions provide symmetric treatment, allowing part of the premium to offset taxable coupon income each year.
依發行地與發行人國籍分類：
- 本國債（domestic）：發行人與發行/交易市場為同一國家。
- 外國債（foreign）：發行人與市場分屬不同國家（如英國公司在美國發行美元債）。
- 歐洲債（Eurobond）：在任何單一國家司法管轄區之外發行，幣別不限；管制較少，最初為規避美國法規而生。名稱中的 "Euro" 不等於歐元亦不等於歐洲發行（中國公司在日本以外市場發行日圓債為 Euroyen bond）。早期多為無記名（bearer），現以記名（registered）為主。
- 全球債（global bond）：同時於 Eurobond 市場與至少一個本國債市場交易。
外國債、全球債、Eurobond 統稱國際債券，以與單一國家的本國債區分。跨市場殖利率差異最主要由計價幣別決定（取決於該幣別的市場利率）。
Sukuk 債券：符合伊斯蘭教法的債券；禁止傳統利息，將定期支付包裝為標的資產之租金。
債券課稅：
- 利息收入通常按一般所得稅率課稅。
- 美國市政債券利息通常免聯邦稅，發行州內亦多免州稅。
- 到期前出售產生的損益視為資本利得（損），稅率通常低於一般所得；長期持有可能更低。
- 原始發行折價債（OID）：包括零息債及大幅折價發行債券。價格朝面值上升的部分被視為利息收入，許多國家逐年將折價的一部分課徵利息所得稅，即使尚未實際收到現金。
- 溢價債券：部分稅務管轄區允許將溢價分攤抵減各年票息應稅金額。
- A. lower regular periodic payments and a higher final payment amount.
- B. higher regular periodic payments and a lower final payment amount.
- C. lower regular periodic payments and a lower final payment amount.
- A. Floating-rate notes.
- B. Sinking fund.
- C. Term maturity structure.
- A. step-up bond.
- B. zero-coupon bond.
- C. deferred coupon bond.
- A. Its par value.
- B. The call price.
- C. The present value of its par value.
- A. a capital gain.
- B. interest income.
- C. tax-exempt income.
A bullet bond pays only periodic coupon interest, with the entire principal repaid at maturity along with the final coupon. An amortizing bond repays part of principal at each payment date. Fully amortizing = equal payments throughout the bond's life. Partially amortizing = a balloon payment at maturity covers the remaining principal.
A sinking fund provision requires the issuer to retire part of the issue at specified times during the bond's life.
Floating-rate notes pay coupons that adjust with a variable market reference rate. Other coupon variations include step-up, credit-linked, payment-in-kind (PIK), deferred coupon, and index-linked bonds.
Callable bonds let the issuer redeem at a specified call price. Putable bonds let the holder sell back at a specified put price. Convertible bonds let the holder exchange the bond for a fixed number of issuer common shares.
Embedded options benefit the party who holds the right to exercise: call options benefit the issuer; put and conversion options benefit the bondholder.
Legal and regulatory treatment of fixed-income securities depends on where they are issued, where they trade, and the issuer's domicile.
Domestic bonds trade in the issuer's home country and currency. Foreign bonds are from foreign issuers but denominated in the local currency of the trading market. Eurobonds are issued outside any single country's jurisdiction and may use any currency. Global bonds trade in both the Eurobond market and at least one domestic market.
Interest income is generally taxed as ordinary income; gains/losses on sale are taxed at capital gains rates. The price appreciation of OID bonds toward par is treated as interest income. In the U.S., interest from municipal bonds is typically exempt from federal tax, and often state tax in the issuer's state.
【LOS 48.a】子彈型債券每期僅付息，到期一次還本；攤銷型每期還部分本金，完全攤銷型每期金額相等，部分攤銷型於到期保留 balloon 尾款。償債基金條款要求發行人按期分次贖回。
FRN 票息隨 MRR 變動；其他結構包括 step-up、credit-linked、PIK、deferred coupon、index-linked。
可贖回債（call）對發行人有利；可賣回債（put）與可轉換債（conversion）對投資人有利；無內嵌選擇權者稱為直債（straight）。
【LOS 48.b】本國債／外國債／Eurobond／全球債依發行地、交易地與發行人國籍區分。Eurobond 不限幣別、管制較鬆。Sukuk 債為符合伊斯蘭教法的債券。
稅務：利息按一般所得稅課；買賣損益按資本利得稅課；OID 折價債的逐年價格上升視為利息所得，逐年課稅；美國市政債利息通常免聯邦稅且發行州內多免州稅。