fixed income 2: Fixed-Income Cash Flows and Types

What is a bullet bond?

• A standard fixed-coupon bond

• interest is paid periodically and the principal is repaid in full at maturity.

• Common for government and corporate bonds

• offers predictable cash flows for investors.

what is a fully amortizing loan?

• portions of principal are repaid periodically, along with interest.

• level total payments (principal + interest)

• interest decreases and principal repayment increases over time.

• reduces credit risk but increases reinvestment risk.

• e.g. mortgage loans

What is a partially amortizing bond?

• Periodic principal repayments that patrially repay principal

• final lump sum (balloon payment).

formula for periodic payment A

$$A=\frac{r\cdot\text{Principal}}{1-\left(1+r\right)^{-N}}$$

• A = Periodic payment amount

• r = Market interest rate per period (divide if given annualised)

• Principal = Principal amount of loan or bond

• N = Number of payment periods

how to find for partially amortising

1. find present value of baloon payment

• $$PV_{balloon}=\frac{B}{\left(1+r\right)^{N}}$$

  • B = baloon payment

2. Amortised principal = Original principal - $PV_{balloon}$

3. $$A=\frac{\left(P-PV_{balloon}\right)\cdot r}{1-\left(1+r\right)^{-N}}$$

What is a sinking fund provision?

• issuer sets aside funds to retire bonds periodically before maturity

• either at random or predetermined prices

• Reduces credit risk

• increases reinvestment risk.

What is a waterfall structure in ABS/MBS?

• Principal is repaid sequentially to tranches based on priority

• Senior tranches are paid first

• junior tranches bear shortfalls

• Reduces credit risk for senior investors.

What defines a floating-rate note (FRN)?

Coupon = Market Reference Rate (MRR) + credit spread

e..g most bank loans

benefits of FRN to issuers and investors

• Benefit to issuer: Aligns debt cost with market rates.

• Benefit to investor: Less interest rate risk than fixed-rate bonds.

What are step-up bonds

Coupon increases at specified dates or on events

• (e.g., ESG targets, credit deterioration)

• protect investors and compensates for adverse events

• issuer can negotiate lower coupon initially

what are PIK features?

Issuer pays interest by increasing principal instead of cash

• used when cash flow is constrained.

How do index-linked bonds work?

Cash flows tied to an index (usually inflation). Two main types:

1. Capital-indexed (e.g., TIPS): Principal adjusts; interest paid on adjusted principal.

2. Interest-indexed: Principal fixed; interest varies with index. Protects investors against inflation

What is a deferred-coupon bond?

• Pays no interest initially

• higher coupons paid later.

• Used to conserve cash or finance projects before revenue begins.

What is a contingency provision in a bond and three most common examples?

• allows issuer/bondholder to take action if a specific event occurs.

• Callable bonds, putable bonds, and convertible bonds.

What is a callable bond?

• Issuer can redeem part or all of the bond before maturity.

• Provides flexibility to refinance if interest rates fall.

what is a fixed price call

grant an issuer the right to buy back the bond at a predetermined price in the future

What is a call protection period?

• the period during which a callable bond cannot be redeemed by the issuer.

How does the call price schedule work?

• specifies the fixed price at which a bond can be called over time

• Prices usually decline the closer the bond is to maturity.

• Value depends on relationship between the YTM and the coupon of the bond

What is “call risk” for investors?

• The risk that the issuer will redeem the bond early when interest rates fall

• limits price appreciation and reinvestment options.

• Investors expect a higher yield for callable bonds.

What is a make-whole call provision?

• compensates bondholders based on market rates.

• issuer repurchases the bond at a price based on the present value of future payments discounted at a comparable Treasury yield.

• Rarely exercised as little economic value

What is a putable bond?

• Gives bondholders right to sell bond back to issuer at pre-set price.

• Usually par value

• protects against rising interest rates.

• Bondholders can reinvest at higher market rates.

• If YTM < coupon, put feature less valuable; bond behaves like option-free.

• If YTM > coupon, put price acts as price floor.

How does a put provision affect bond price and yield?

• Price of putable bond above similar non-putable bond.

• Yield is lower to compensate issuer for put value.

What is a convertible bond?

• Debt instrument convertible into issuer’s common shares.

• Conversion price determines exchange ratio.

• Common for growth companies with limited cash flow.

• May include call provisions to limit investor gains.

how does share price compared to conversion price affect a convertible bond

• Well below conversion price → behaves like standard bond.

• Well above conversion price → tracks conversion value.

How do you calculate the conversion ratio?

Conversion ratio = Convertible bond par value/Conversion price.

How do you calculate the conversion value?

Conversion value = Conversion ratio × Current share price.

What is a warrant attached to a bond?

• An option allowing purchase of issuer’s stock at fixed price until expiration

• Used as yield enhancement.

• Traded separately from bond.

What is a contingent convertible bond (CoCo)?

• A bond that converts to equity automatically if a specified trigger occurs

• e.g bank’s Tier 1 capital falling below regulatory requirements

• reduces default risk and systemic risk.

For the following bonds, where is the issuer?

1. domestic

2. foreign

3. Eurobonds

• Domestic bonds: issuer incorporated in same country.

• Foreign bonds: issuer incorporated in another country.

• Eurobonds: issued outside any single country

For the following, what is the currency or features?

1. emerging markets

2. corporate issuers

3. developed markers

• Emerging markets: sovereigns issue in foreign currency for wider investor base.

• Corporate issuers match bond currency with foreign operations.

• Developed markets: liquid, specialised, attracting cross-border issuers.

What are sukuk bonds?

• Fixed-income instruments compliant with Islamic law

• paying profit or rental cash flows instead of interest

• backed by assets

• avoiding non-shari’a-compliant sectors.

What is a Eurobond?

• bond issued and traded outside the jurisdiction of any single country

• named after its currency (e.g., Eurodollar, Euroyen).

features of eurobond

• typically unsecured

• Underwritten by intermediaries from multiple jurisdictions.

• Traditionally bearer bonds - ownership not recorded

• now registered bonds - ownership recorded

What is a global bond?

• Issued simultaneously in Eurobond and domestic markets.

• Ensure broad investor access and sufficient demand.

• e.g. World Bank bonds.

Which factor has the strongest effect on a bond’s price: currency of issuance or location of issuance?

currency because market interest rates in that currency drive the bond’s price.

How is tax treated for

1. corporate issuers paying interest

2. investors receiving interest

3. Capital gains/losses

• Interest expense: tax-deductible for corporate issuers.

• Interest income: taxed as ordinary income for investors.

• Capital gains/losses taxed differently from interest income.

  • Long-term gains may have lower tax rate than short-term gains.

government bond taxation in

1. UK

2. US treasuries

3. US municipal bonds

Government bond taxation varies by jurisdiction:

• UK: income taxed, capital gains exempt.

• US Treasuries: federal tax only.

• US municipal bonds: often federal and state tax exempt.

What is Original Issue Discount (OID)?

• difference between a bond’s par value and issuance price for a discount bond

• treated as interest income over time for tax purposes in some jurisdictions (e.g., US).

How is a zero-coupon bond taxed in jurisdictions with and without an OID provision?

• with: taxed on original issue discount (OID) in US annually.

• without: No taxable income is recognised until maturity

  • capital gains tax

How can bonds purchased at a premium be treated for tax purposes?

• some jurisdictions allow prorated deduction of premium paid.