Fixed-income Cash Flow Structures and Contingency Provisions

Fixed-income Cash Flow Structures and Contingency Provisions

Fixed income instruments have different cash flow structures that provide investors and issuers with various options to meet their specific financial goals, manage risks, and tailor their investments to suit their particular circumstances.

Standard, Fixed-Rate Bond (“Bullet Bond”)

A standard fixed-rate bond, commonly known as a “Bullet Bond,” is a frequently used debt instrument. In this, the issuer gets the principal amount at bond issuance and promises to repay it at maturity. During the bond’s term, the issuer makes regular fixed coupon payments to the bondholder. If the final payment includes a lump sum along with the interest from the last period, it’s referred to as a balloon payment.

One of the primary appeals of a bullet bond for both issuers, such as governments and corporations, and investors is its straightforward cash flow structure. For issuers, this bond provides a consistent and predictable financing mechanism. On the flip side, investors prefer bullet bonds due to the assured income stream from fixed coupon payments and the certainty of receiving the principal back on a predetermined date. This reliability is valuable for funding specific future cash flow needs.

Example: Bullet Bond

Consider a $2,000 face value 7-year bond with an annual coupon rate of 4%. With a bullet structure, the bond’s promised payments at the end of each year would be as follows.

$$ \begin{array}{c|c|c|c|c|c|c|c}
\textbf{Year} & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline
\textbf{PMT} & \$80 & \$80 & \$80 & \$80 & \$80 & \$80 & \$2,080 \\ \hline
\textbf{Principal} & \$2,000 & \$2,000 & \$2,000 & \$2,000 & \$2,000 & \$2,000 & \$0 \\
\textbf{remaining} & & & & & & & \end{array} $$

In the example above, every year for 6 years, the bondholder receives an interest payment of $80 (which is 4% of $2,000). At the end of the 7th year, the bondholder receives the final interest payment along with the face value of the bond, totaling $2,080.

Amortizing Principal

This structure is commonly seen in bonds, where the principal amount is gradually paid off over time through a series of periodic payments. The coupon payments, representing the interest, are made regularly throughout the life of the bond. At maturity, the final principal payment is made, completing the amortization process. This structure is frequently used in corporate and government bonds to manage repayment obligations.

Fully Amortized Loan

In the case of loans, such as mortgage loans, the cash flows consist of both interest and principal portions. Borrowers make regular payments that include both the interest accrued and a portion that reduces the principal balance. Over the life of the loan, the principal is gradually paid down until the entire debt is repaid. This structure allows borrowers to build equity while repaying the loan.

The periodic payment is calculated as follows:

$$ PMT=\frac{i\times \text{Principal}}{1-\left(1+i\right)^{-n}} $$


\(PMT\) = Periodic payment amount.

\(i\) = Interest rate.

\(\text{Principal}\) = Principal amount of loan or bond.

\(n\) = Number of payment periods.

Example: Fully Amortizing Bond

Consider a $2,000 face value 7-year bond with an annual coupon rate of 4%. With a fully amortizing structure, the bond’s promised payments at the end of each year would be as follows.

$$ \begin{array}{c|c|c|c|c|c|c|c}
\textbf{Year} & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline
\text{PMT} & 333.22 & 333.22 & 333.22 & 333.22 & 333.22 & 333.22 & 333.22 \\ \hline
\text{Interest} & 80.00 & 69.87 & 59.34 & 48.38 & 36.99 & 25.14 & 12.82 \\ \hline
\text{Principal} & 253.22 & 263.35 & 273.88 & 284.84 & 296.23 & 308.08 & 320.40 \\
\text{payment} & & & & & & & \\ \hline
\text{Principal} & 1,746.78 & 1,483.43 & 1,209.55 & 924.71 & 628.48 & 320.40 & -0.01 \\
\text{Remaining} & & & & & & & \\ \hline
\end{array} $$


$$ \begin{align*} PMT & =\frac{i\times \text{Principal}}{1-\left(1+i\right)^{-n}} \\
PMT & =\frac{4\%\times2,000}{1-\left(1+4\%\right)^{-7}}=333.22 \end{align*} $$

Partially Amortizing Bond

A partially amortizing bond is a unique financial instrument where not all the principal amount borrowed is paid off over the bond’s life. Unlike the standard bullet bond, where the full principal is repaid at maturity, in a partially amortizing bond, periodic payments are made that cover both interest and a portion of the principal. However, there remains a certain portion of the principal, referred to as the “balloon payment,” that is paid off only at the bond’s maturity.

In our previous example, if the final payment includes $800 to repay the remaining principal outstanding, the principal outstanding at the end of every year is indicated in the following table:

$$ \begin{array}{c|c|c|c|c|c|c|c}
\textbf{Year} & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline
\textbf{PMT} & 231.93 & 231.93 & 231.93 & 231.93 & 231.93 & 231.93 & 231.93 \\ \hline
\textbf{Principal} & 1,848.07 & 1,690.06 & 1,525.74 & 1,354.83 & 1,177.10 & 992.25 & 0.01 \\
\textbf{Remaining} \end{array} $$

Subtracting the present value of the balloon payment from the $2,000 price of the bond gives us $1392.07 in principal repayment to amortize over 7 years to leave a remaining principal of $800 at maturity. Using this $1392.07 principal amount, we can compute the periodic payment amount as:

$$ PMT=\frac{4\%\times1392.07 }{1-\left(1+4\%\right)^{-7}}=231.93 $$

Year 1:

\(PMT\) = 231.93

Interest paid: \(4\%\times 2000 = \$80\)

Principal payment = \(231.93 – 80 = 151.93\)

Principal remaining = \(2000 – 151.93 = 1848.07\)

The last payment of $992.25 consists of the regular $231.93 payment combined with the remaining principal of $800.

Sinking Funds

A sinking fund is an arrangement predominantly used by bond issuers, including governments and select corporate entities. In this setup, issuers systematically allocate funds into a special escrow or sinking fund account. This proactive strategy is deployed to ensure they can meet their repayment obligations, thereby reducing the inherent credit risk of default. Through the sinking fund, issuers retire a predetermined amount of the bond’s principal over its lifetime. This retirement can either be executed by redeeming bonds chosen at random or by exercising the option to repurchase bonds prior to maturity at a specified price, as outlined during the bond issuance. While this strategy undeniably minimizes credit risk by ensuring funds are set aside for repayment, it introduces a layer of reinvestment risk for bondholders. This stems from the potential early retirement of bonds, compelling bondholders to possibly reinvest in securities with lower returns.

Waterfall Structures

Waterfall structures are integral to the functioning of asset-backed securities (ABS) and mortgage-backed securities (MBS). Within a waterfall structure, the distribution of cash flows is organized in a hierarchical manner among various tranches or investor classes. While interest or coupon payments are generally disbursed to all tranches without any specific order, the repayment of the principal observes a defined pecking order. The tranche designated as the most senior receives its principal payment first. Upon its complete repayment, the next tranche in line begins receiving its principal, and this sequence persists until the most junior tranche is addressed.

Variable Interest Debt

Variable interest debt instruments, such as certain bonds and loans, adjust their interest payments based on a market reference rate (MRR) coupled with a credit spread. This dynamic structure makes them favorable for various stakeholders. For instance, financial intermediaries, especially banks, show a predilection for these assets because they conveniently align with their variable-rate liabilities. Moreover, floating-rate notes (FRN), another form of this debt, are especially attractive to investors keen on capitalizing on rising interest rates. A simple mathematical representation to determine the FRN coupon is: \(\text{FRN coupon} = \text{MRR} + \text{Credit spread}.\)

Interest Rate and Credit Risks

Although variable-rate instruments aim to minimize interest rate risk by adjusting coupon payments with changing interest rates, they are not without risks. Credit risk is a significant concern; if an issuer’s credit quality is perceived to decline, the instrument’s price may drop, regardless of the MRR’s status.

Mechanisms of Rate Adjustments

Beyond the regular adjustments based on MRR, these instruments come with various innovative features:

  • Step-up Bonds: These bonds have an in-built mechanism where the coupon rates ascend at predetermined intervals.
  • Event-based Adjustments: These are contingent on specific events, like a drop in an issuer’s creditworthiness. Sometimes, these adjustments might even be tethered to certain financial covenants or credit ratings.

Leveraged Loans

Leveraged loans, typically extended to issuers perceived as lower credit quality, have their own set of dynamics. The coupon rate, for example, may surge if the issuer’s credit quality takes a hit. This surge ensures that investors are compensated with a higher yield. A case in point is the Antelas AG scenario, where a loan’s credit spread might be recalibrated based on specific financial ratios.

Payment-in-Kind (PIK) Bond

Certain issuers, wary of future cash flow challenges, might opt for the PIK feature in their loans or bonds. This unique feature allows these issuers to pay interest by augmenting the bond or loan principal instead of traditional cash payments. Notably, this arrangement is more prevalent among firms that are heavily reliant on debt.

Sustainability and ESG-linked Bonds

The financial world is becoming increasingly conscious of environmental, social, and governance (ESG) factors. Responding to this trend, bonds with provisions related to ESG have emerged. A prominent example is the sustainability-linked bond issued by the Public Power Corporation. Here, bonds might undergo step-up margins if they don’t meet certain ESG benchmarks.

Index-Linked Bonds

Index-linked bonds offer another layer of sophistication. Their payments are tethered to specific indices. The most prevalent among these are the inflation-linked bonds, colloquially known as ‘linkers.’ Their primary function is to act as a shield against inflation, offering stakeholders inflation-adjusted cash flows. A widely recognized example is the U.S.’s Treasury Inflation-Protected Securities (TIPS), which modulate their cash flows based on inflation metrics like the Consumer Price Index.

Classifications of Index-linked Bonds

  • Capital-indexed Bonds: These types, exemplified by TIPS, adjust their principal in line with inflation metrics, safeguarding the real value of the debt principal against inflation.
  • Interest-indexed Bonds: These bonds keep the maturity amount constant, adjusting only the coupon against an index. They are essentially variations of FRNs where inflation acts as the MRR. Significantly, they find more favor with private entities than with governments.

Zero-Coupon Bonds

These fixed-income instruments do not make regular interest payments like traditional bonds. Instead, they are sold at a discount to their face value and do not provide periodic income. Investors earn their return by purchasing the bonds at a discount and receiving the full face value at maturity. Zero-coupon bonds are often used in situations where investors are seeking a predictable lump sum payout in the future.

Deferred Coupon Bonds

This structure includes bonds that have a deferred coupon payment, meaning they do not pay interest for a specified initial period. After the deferral period, the bond starts making regular coupon payments that are typically higher than the market rate to compensate for the earlier period without interest. This structure is commonly utilized in projects or financial instruments where cash flows are expected to be limited in the early stages, such as infrastructure projects or issuances from entities with lower credit quality.

Fixed-Income Contingency Provisions

Bonds often come with certain conditional provisions known as contingency provisions. These provisions dictate actions that may be taken contingent upon specific events. They embed within the bond contract the rights but not obligations to undertake certain actions. Depending on their nature, these provisions can either add value to the issuer or the bondholder. Among the numerous types of bonds with such embedded options are callable, putable, and convertible bonds.

Callable Bonds

Callable bonds primarily benefit the issuer by granting the right to redeem or “call” the bond before maturity, a measure to guard against declining interest rates. This allows the issuer to replace an old, higher-interest-rate bond with a potentially lower-interest-rate one, reducing borrowing costs. However, this introduces reinvestment risks for investors, as a falling interest rate may prompt the issuer to call the bond, forcing the investor to reinvest in a lower-yielding environment. To offset this risk, callable bonds typically offer a higher yield.

A call premium is the amount over the par value that the issuer pays if they decide to redeem the bond before maturity. The call protection period, also referred to as the lockout period or cushion, represents the initial period during which the issuer cannot call the bond. This protection incentivizes investors by offering them some security against early redemption.

There’s also a unique callable bond variant called a make-whole call. Instead of a fixed call premium, the issuer makes a payment determined by the present value of future coupons, making early redemption significantly more expensive.

Furthermore, the manner in which a bond can be called can vary:

  1. American-style: These continuously callable bonds can be called at any time post the call protection period.
  2. European-style: The bond can only be called once, specifically on the designated call date.
  3. Bermuda-style: This is a mix of the two, allowing for the bond to be called on certain specified dates following the end of the call protection period.

Putable Bonds

While callable bonds cater to issuers, putable bonds cater to bondholders. These bonds grant bondholders the right to “put” or sell the bond back to the issuer at predetermined prices on specified dates. This is particularly advantageous if interest rates spike, as bondholders can then liquidate the bond and reinvest the proceeds at higher yields. Consequently, putable bonds often fetch a higher price compared to regular bonds. Like their callable counterparts, putable bonds also have the European and Bermuda styles based on the frequency and timing of the put option.

Convertible Bonds

Blurring the lines between debt and equity, convertible bonds offer bondholders a choice: they can either hold onto the bond or convert it into a predetermined number of common shares of the issuing company. This dual feature–bond downside protection and potential equity upside–makes convertibles relatively attractive, thus often garnering a higher price.

An alternative to convertibility is the inclusion of warrants. Unlike the embedded nature of the convertible option, a warrant is an additional, separable option that grants the holder the right to purchase shares at a given price within a set timeframe. Often considered a “sweetener”, warrants can make bonds more appealing, especially for younger firms. They offer the potential for additional returns if the company’s shares are appreciated.

Lastly, there’s a unique bond variant known as Contingent Convertible Bonds or CoCos. Primarily issued by some European banks, these bonds automatically convert from debt to equity upon the occurrence of specific events, as the issuer’s equity drops below a particular level.

Question #1

Calculate the periodic payment and the interest and principal components of the first payment for a fully amortizing bond based on the following:

  1. Loan amount: $15 million.
  2. Annual interest rate: 3.5%.
  3. Loan term: 8 semiannual periods (4 years).



$$ PMT=\frac{i\times {\text{Principal} }}{1-(1+i)^{-n}} $$


  • \(i=\frac {(3.5\%)}{2}=1.75\%\)
  • Principal =$15 million
  • n=8

Solve for the periodic payment as follows:

$$ PMT=\frac{0.0175\times15}{1-(1.0175)^{-8}}=\$2.026 \text{ Million} $$

The initial $2.026 Million periodic payment comprises the following:

  • Initial interest payment: \(\$15 \times 1.75\% = \$0.2625 \text{ million}\)
  • Initial principal repayment: =\(\$2.026 \text{ Million} – \$0.2625 \text{ million} =\$1.7635 \text{ million}\)

Question #2

Which bond structure involves periodic payments that cover both interest and a portion of the principal, but not all of the principal amount is paid off over the bond’s life?

  1. Bullet Bond.
  2. Fully Amortizing Bond.
  3. Partially Amortizing Bond.


The correct Answer is C.

A partially amortizing bond includes periodic payments that cover both interest and some of the principal, leaving a portion of the principal, known as a “balloon payment,” to be paid off at maturity.

A is incorrect: A bullet bond involves only interest payments throughout its life with the full principal returned at maturity.

B is incorrect: A fully amortizing bond involves periodic payments that cover both interest and principal such that the entire principal is paid off by maturity.

Question #3

For which bond structure are funds allocated into a special account to ensure repayment obligations and reduce credit risk?

  1. Amortizing Principal.
  2. Sinking funds.
  3. Waterfall Structures.


The correct answer is B.

Sinking funds are provisions used by bond issuers to systematically allocate money into a special account. This strategy is used to ensure that they can meet their repayment obligations, reducing the credit risk of default.

A is incorrect: Amortizing principal’s structure involves the gradual repayment of principal over the bond’s life.

C is incorrect: Waterfall Structures relate to the hierarchical distribution of cash flows among various tranches or investor classes in asset-backed securities.

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