Bond Payables

Bonds, or fixed-income instruments, are the debt the company or the government owes to investors with an unavoidable cost of borrowing added to the principal to derive a final value that the company will repay fully by its maturity.

Specifically, the ‘face value,’ or ‘par value,’ is the price of the bond paid back at the maturity date by the issuer.

The formula to calculate the total value (present value) received from zero coupon bonds/discount bonds is

Face Value / (1 + discount rate)^{number of years to maturity}

Bonds were originally discount bonds and were calculated relatively easily before the idea of coupon bonds was introduced. The way pure discount bonds work is that the principal injected is sold at a discount, and at maturity, the holder receives the face value of the bond.

Coupon bonds are calculated through a cumulative addition of all interest payments made to investors, discounted at all times with a discount rate that changes along with the risk premiums adopted per year (varying circumstances).

Total present bond value = [Coupon/ (1 + discount rate)] + [Coupon/ (1 + discount rate)²] + .. + [Coupon/ (1 + discount rate)^{n number of years}] + [Face Value/ (1 + discount rate)^{n number of years}]

There are also floating-rate bonds or floaters. These are bonds that have an interest rate variable to market conditions.

These bonds, which either corporations or governmental entities can issue, will have interest rates vary based on market conditions of banks borrowing secured overnight financing rates(SOFR) (replaced LIBOR).

If the SOFR increases, then the interest rate or cost of borrowing also increases. Vice-versa, if SOFR decreases, the interest rate falls.

The value of floating rate bonds sees their interest rates vary depending on the SOFR rate. This could be as often as a daily adjustment or as spread apart as yearly adjustments.

Keep in mind that for corporations to issue floaters(corporate floating rate notes or FRNs) is different from commercial paper. The commercial paper involves fixed interest rates, which differs from the concept of the floating-rate bond.

However, FRNs usually have price floors and caps. This limits the amount that a variable SOFR would factor into FRNs and assures investors and the corporation of a certain amount range by which the interest rates of bonds can vary.

Types of Bonds (Hybrid + Bonds)

Bonds are usually payable through one of the three methods outlined above.

To recap, they are:

1. Coupon bonds
2. Discount bonds (zero-coupon bonds)
3. Floating rate bonds

Now, we will go through various types of bonds that investors deal with that are payable through one of the three methods above.

Coupon bonds are debt securities that pay periodic interest payments, known as coupons, to the bondholders. These bonds have coupon rates and fixed interest rates repaid periodically, confirmed by the signed indenture agreement.

Discount bonds, also known as zero-coupon bonds, are sold at a price significantly lower than face value. Unlike coupon bonds, discount bonds do not make periodic interest payments to bondholders.

Floating or variable rate bonds are debt securities with interest rates that are not fixed but fluctuate over time. The interest rates of these bonds are typically tied to a benchmark or reference rate, such as the SOFR or a government bond yield index.

The various bonds we will be going through are:

• Serial bonds
• Amortizing bonds
• Bullet bonds
• Sinking fund bonds
• Vanilla convertible bonds
• Mandatory convertible bonds
• Reverse convertibles
• Contingent convertibles
• Putable bonds

Serial bonds

The bonds that bond with multiple maturity dates are packaged into a single issue.

Since there are a bunch of bonds in the serial bonds, there are different maturity dates for all the bonds involved, and when the maturity dates are reached, the face value of the specific bond will be repaid.

Serial bonds are helpful for investors in that debtors are less likely to default because the dollar amount of bond amount payable outstanding reduces with every maturity date. The debtor chooses to continue paying as it already paid off much of its existing debt.

Along with the percentage of face value repaid with every maturity date reached, interest payments of a certain amount (dictated by the conditions of the bond determined before the debt is issued) will be paid out. 

However, the serial bonds for specific projects by the corporations have infrequent cash flow amounts, and the company has difficulties very early on in repayment of the percentage of face value by the maturity date. The company could find itself seeing a great shortfall in cash.

As a result, companies should only choose to issue serial bonds if they can guarantee that the project undertaken has a good amount of frequent repayments of income to issue back to investors; if not, early defaults spell very badly for a serial bond.

Amortizing bond

Related to a similar front to serial bonds, the amortizing bond is a singular bond that repays a certain amount of the interest and the principal on each coupon payment date.

The key difference herein is that serial bonds are a group of discount bonds. In contrast, amortizing bonds are coupon bonds that involve payments of a certain percentage of the face value of the bond periodically.

Counterparty risk, like the serial bonds outlined above, is low as a certain dollar of the final bond amount payable is reduced with every interest payment.

Amortizing bonds are also callable (redeemable) by the debtor; hence if these bonds should be called, the investor would usually have to reinvest his money returned in other avenues at a lower interest rate.

As a result, amortizing bonds (which are callable) usually price a higher annual return to compensate for the risk of bonds being called early.

Bullet/straight bonds

Directly opposed to amortizing bonds, bullet/straight bonds are coupon bonds that only pay the full principal at maturity. All other interest payments are only coupons based on the bond's interest rate.

In this case, the term “bullet” refers explicitly to a 1-time lump sum repayment to the debtor from the issuer. This repayment is due to the debt owed by issuers to the debtors.

As most of the dollar amount of the bond amount payable is due only at the bond's maturity date, counterparty risk is substantially higher than amortizing bonds. This means the corporation/institution is more likely to default on its debt.

These bonds are usually non-callable. Since companies/corporations/institutions cannot call the bond, should interest rate environments change, the debtor is vulnerable to changes. Bullet bonds fix the interest rate of debtors.

Sinking fund bonds

An opposing idea from serial bonds, sinking fund bonds involves the company doing the purposeful act of setting money aside in a fund to start bond buybacks.

With these self-effected bond buybacks, the final dollar cumulative amount of all bonds payable reduces. As a result, the company would have had less counterparty risk (default) as it is more likely to repay its entire sum due to investors fully.

From the investor's perspective, sinking fund bonds could have the company repurchase its bonds at either the par price or the market price of the bonds, whichever is lower.

Investors could see their investments return at lower prices than expected at the initial date of the indenture agreement.

This presents a drawback as they might have to sell back their notes at unfavorable prices that they did not anticipate when they initially invested and might have to reinvest their funds in bonds with lower interest rates.

Sinking funds are limited because the company can only repurchase a certain amount of bonds at the sinking fund price (par or market price, whichever is lower).

The callable bonds in a company that issued sinking funds bonds are randomly chosen based on the serial number.

Vanilla Convertible bonds

These are bonds that can be converted from debt to common equity. The determination of this decision is dependent on the debtor or the investor.

The price at which the investor can convert into equity depends on the indenture agreement signed before the money is exchanged initially.

The bond's conversion ratio is defined as the number of shares received at the time of conversion for each convertible bond. This and the conversion price are determined at the inking of the indenture agreement.

Investors would usually cover the bond into common equity when the stock price is high, so their initial principal could fully convert to equity trading at high valuations using the conversion price to result in a high return of investments.

These convertible bonds will dilute shareholders' equity as well, so this is a consideration for investors buying the company's common equity, along with investors of vanilla convertible bonds.

Mandatory Convertible bonds

Similar to vanilla convertible bonds, except that the bonds will automatically convert into common equity upon a certain date determined by the debenture agreement.

In this case, the conversion is mandatory, unlike the option presented to investors with vanilla convertible bonds. However, mandatory convertible bonds usually have two conversion prices.

The first price outlines the price the investor will have to pay to receive the equivalent of its par value in terms of shares.

This means that the exact dollar amount of bonds will be converted using the outstanding share price (controlled by the market) to convert into the exact number of common shares in monetary value.

The second conversion price has a set price limit above the original par value, which the investor is forced to convert. 

This means that any stock received through this will be “in the money”, and will be able to get more than the dollar amount of shares in the dollar amount of interest plus face value of the bond.

Reverse convertibles

Similar to mandatory convertibles in that they force the security owner to convert their bonds into company shares but at a designated trigger/barrier price instead of a stipulated date.

Assuming a barrier price that is 30% lower than the asset’s (e.g., reference stock, derivatives) spot reference price, if the value(price) of the reference asset were to drop below the trigger/barrier price, then the par value of the bond is used to buy the stock at the strike price.

As the underlying security's current price (e.g., common stock) is lower than the strike price determined in the indenture agreement, the owner of the reverse convertible will buy the stock at a loss, absorbing the downside.

Because the bond is a reverse convertible, the bond has a barrier (knock-in) option. This means the bond will have both a barrier price (trigger price as explained above) and a strike price (the price by which the bond owner will buy the stock).

Further, the bond also has a put option. Usually, “puts” means that the holder/owner of the security has the right to sell the bond. 

Therefore, the owner/holder of the bond will be obligated to buy the reference asset (auto-call) if the reference asset value (e.g., market price) falls below the percentage stated in the indenture agreement.

Taking the two terms together, reverse convertibles have a “knock-in put” option and an exotic option of being auto-callable.

Further, reverse convertibles will pay coupons if the bond still exists. Coupons will no longer be paid out if the bond is converted into the reference asset (e.g., common stock) upon the activated auto call feature.

Contingent convertibles

Also termed as CoCo bonds, are a form of mandatory convertible bonds.

Still, either the auto-call feature will be triggered, or the principal will be written down upon the issuer’s capital adequacy ratio not meeting regulatory requirements.

With the loss absorption feature upon the capital adequacy ratio not properly met, the hope is to reinstate the issuer’s capital adequacy ratio upon converting these CoCos.

CoCos arose from the 2008 financial crisis, where banks were regulated to have higher solvency capital per the Basel III accords.

CoCos are controversial as although they are meant to be ranked higher than common equity within the bank’s capital structure, 2023 saw G-SIB Credit Suisse default on its CoCo while still paying common shareholders from its sale to UBS.

Event risk is a substantial risk associated with CoCos, therefore. A trigger event that might cause contingent capital to convert to equity or be written down might result in great losses to investors for the principal originally put into CoCos.

However, CoCos are still meant and ranked higher in the capital structure against common equity. Multiple banks have assured that CoCos will be prioritized against common equity should the bank be limited in funds.

Putable bonds

Bonds by which the investor can force a sale back to the bond issuer prematurely (at specified dates). Repurchase prices are determined by indenture agreements inked before money transacts.

The bond's selling price will usually be at par, and the bond is an embedded put option. Investors, therefore, have the right but do not have the obligation, to hold and sell the security back to the issuer.

People invest in putable bonds to stave off the effects of interest rate hikes in the market. As analyzed in the next section, there is an inverse relationship between interest rate and bond pricing/value.

Owners of putable bonds may exercise their option to sell these considerably low-interest-returning putable bonds to invest in bonds with higher yields based on market conditions of high-interest rates for other bonds.

This would ensure they would not suffer the opportunity cost of holding lower interest rates bonds(fixed) and high-interest rates.

Pricing of bond payable

As briefly alluded to, an inverse relationship exists between interest rates and bond value/price. This is attributed to how when interest rates increase, there exist bonds that pay out higher coupon repayments than other bonds priced in the market.

As investors are not currently invested in other such bonds that allow for higher interest payments, an opportunity cost exists in holding the lower interest-paying bonds. Therefore, the future values of any coupons or the bond's interest rate are less valuable in high-interest rate environments.

Importantly, bonds usually issue higher interest rates than market interest rates to be more attractive to investors. The market interest rate is usually the risk-free rate, and any higher increase in the interest rate through bond issuances is called a premium.

Premiums are associated with risk. With increased risk investing in the bond (and a higher chance of counterparty risk), the higher the premium related to the bond.

To calculate the price at which individuals will be willing to purchase the bonds at either a discount or premium, we analyze the interest rate the bond is ready to offer and use present value factors to calculate the bond's present value with interest.

This will be compared to the principal paid for the bond (the present value of the total dollar value repaid to investors must be more than the principal).

General Bond Pricing with Different Interest Rates

Let's look at an example evaluating this; for instance, bonds are usually issued in terms of $1,000 or $100 denominations.

Assume a bond with $1,000 as the sale price of the bond. A hypothetical 10% market interest rate and 10% of interest payments are issued as coupons biyearly. This is sold at par since market value interest is identical to interest payments through coupons.

We know that the bond will repay the face value of the bond ($1,000) by the end of 10 years (maturity). However, we must evaluate the coupon payments.

Coupon payments = 1,000 x 10% x 0.5 = 50 is repaid biyearly through coupons.

Next, we assess the present value factor. This is done through the following equation:

Present Value Factor = 1/ (1 + r)ⁿ

With n being the number of periods and r being the interest rate of the bond per period

Hence, calculating the present value factor for all numbers:

We first calculate the case where the market interest rate is the same as the bond’s interest rate, or the case at par. From here, we can calculate the present value factor for interest at the price of the bond and can calculate any other cases presented.

For instance, with a market interest rate of 10%(this condition must be the same) and a principal of 1,000 (this condition must be the same), the bond interest rate is 8%, paid out biyearly. What is the maximum amount the investor will pay for the bond?

Using the present values derived above, we can conclude (present values are the same as long as the conditions above are met):

Investors will only be willing to pay $875.28 (maximum) for the bond as per the indenture agreement terms listed above. This bond is sold at a discount because market interest rates (risk-free rates) are higher than bond interest rates for bonds selling at a premium.

With a market interest rate of 10% and a principal of 1,000 (both of these conditions are the same), the bond interest rate is 12%, paid biyearly. To calculate the maximum amount the investor is willing to pay for the bond:

Investors will be willing to value the bond at a maximum of $1,124.48 with the prevailing market conditions and the terms listed in the indenture agreement as listed above.

These examples show how market conditions of interest rates affect the present value of bonds. If the interest rate hikes, the present value factor of bonds will decrease (due to the market interest rate (risk-free rate) being higher).

Investors see the opportunity cost in keeping their cash tied up in these lower-yielding bonds. 

Conclusion

In conclusion, understanding the different types of bonds and their characteristics is essential for investors and issuers alike.

Bonds payable, whether they are coupon bonds, discount bonds, or floating rate bonds, provide a means for companies and governments to borrow money from investors.

Serial bonds offer multiple maturity dates and reduce the risk of default while amortizing bonds repay interest and principal periodically.

Bullet/straight bonds pay the full principal at maturity, while sinking fund bonds involve setting aside money to repurchase bonds and reduce counterparty risk.

Convertible bonds, including vanilla convertible bonds, mandatory convertible bonds, and reverse convertibles, allow investors to convert their debt into equity.

Contingent convertibles (CoCos) have additional features based on capital adequacy ratios but come with event risk.

Putable bonds allow investors to sell the bonds back to the issuer at specified dates, providing flexibility in changing market conditions.

Bond pricing is influenced by interest rates, with an inverse relationship between rates and bond value. Bonds usually offer higher interest rates than market rates to attract investors, and the difference is called a premium.

Calculating bond prices involves evaluating coupon payments and present value factors and comparing them to the principal.

Overall, bonds are complex financial instruments with various features and considerations. Investors should carefully assess their risk appetite, time horizon, and market conditions.

Meanwhile, issuers need to consider their cash flow, repayment capabilities, and the suitability of different bond types.

By understanding the key takeaways from this article, individuals can make informed decisions regarding bonds and their investments.

Researched and Authored by Jo Vial | LinkedIn

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