Chapter 11

Applying Investment Banking to Fixed Income


check Getting a primer on bonds

check Looking at different types of bonds

check Considering the position of bondholders

check Seeing how bond prices are calculated

check Considering how companies choose to issue debt versus equity

Typically, investment bankers talk about buying up a company’s stock to acquire a company. With their investment banking gurus at their side, convincing them that the shares are undervalued, financial tycoons often target a company’s stock to buy up.

But behind the scenes, companies often have outstanding debt. The holders of this debt, called bondholders, need to be dealt with, too, when a company is bought, restructured, or otherwise put through the financial engineering machine.

Bondholders usually sit quietly in the background, silently accepting their interest payments from the company. But during times of major upheaval at companies, they tend to raise their voices.

The concerns of bondholders are voiced loud and clear when a company that’s the target for acquisition has issued bonds as well as stock. The bondholders are a constituency that a company must deal with. And when a company hits hard times and can no longer keep up with interest payments, the bondholders often find themselves in the pole position, because their claims to the company outrank the stockholders’ claims.

Bondholders may be behind the scenes, but savvy investment bankers know they’re a group of investors not to be trifled with. And that’s where this chapter comes in. Here, we fill you in on what bonds are and the different varieties they come in. Then we explain where bondholders fall in the hierarchy of who gets paid when. We tell you how bond prices are calculated. And we close the chapter with a brief discussion of when companies opt for issuing bonds instead of stocks.

Introducing Bonds

A bond is a financial security recognizing that an investor is loaning money to a corporation. In essence, it’s an IOU. In return for the bondholder’s money, the corporation is obligated to make periodic interest payments to the bondholder and to repay the loan when the term of the loan ends. The basic terms of the bond include the bond’s maturity (the original length of the loan), the coupon rate of interest (the rate of interest on the bond), and the denomination of the bond (the amount of the loan).

All the basic terms of the bond are detailed in the bond indenture, which is a legal document that lays out all the rights of the bondholder and the obligations of the issuer. The terms of a bond issue represent a compromise between the interests of the firm and the interests of the bond investor — each of them gives up something in order to get something in return.

Remember The firm wants to pay the lowest interest rate possible and have the most business flexibility. On the other hand, the investor wants the highest interest rate possible and to limit the firm from certain actions (such as taking on further burdensome debt, thus weakening the existing bondholders’ positions and lowering the probability that they’ll receive the promised interest and principal payments).

The bond indenture often contains a description of restrictive covenants (terms of the bond indenture that limit the behavior of issuers). Typically, covenants place limitations on the ability of the firm to take on additional debt unless certain tests are satisfied. For example, debt may be limited by covenant to 50 percent of total capitalization (the sum of debt and equity). Unfortunately, bond indentures are written in legalese and are typically incomprehensible to the average investor.

Just as currency comes in different amounts, or denominations, so do bonds. The denomination of a bond is the amount that’s being borrowed. The denominations of corporate bonds are generally $1,000 or $5,000, and the typical bond pays interest semiannually (every six months).

Technical stuff Technically, a bond issue from a large corporation may be for hundreds of millions of dollars, but it’s divided into smaller chunks so that individual investors can afford to purchase the bonds and so that investors can diversify across companies and lower the risk of their holdings.

Remember Unlike stocks, the holder of a bond has no ownership interest in the corporation. A bondholder can only receive what is promised — nothing more. That’s why bonds are often referred to as fixed-income securities. If everything goes as planned, a bondholder knows exactly what she’ll receive and the return she’ll earn if she holds the bond to maturity. If you bought a bond of a wildly successful company — like Microsoft, Apple, or Amazon — and you held it to maturity, the best you could hope for is to receive the promised interest payments and the full return of the principal amount. Contrast that experience with a stockholder of one of these corporations, who would’ve seen her initial investment grow exponentially in value.

So why are bonds bought and sold? Well, corporations issue bonds so that they can obtain the money to build or renovate facilities, purchase new equipment, or, in the case of leveraged buyouts, even purchase other companies — in essence, to grow the business. Issuing bonds is a way of raising money (or capital) — an alternative to selling stock in the company. (For more on stocks, see Chapter 10.)

As for why people buy bonds, an old saying in the financial markets applies: “You can either eat well or sleep well.” Investing in bonds may allow investors to sleep well because, typically, bond returns are much more stable than stock returns. However, over the long term, investing in stocks provides investors with higher returns, allowing them to eat better than bondholders.

Remember “No pain, no gain” applies in the investment banking world as much as in the gym. Investors take on pain (or risk) in exchange for gain (or return). Typically, the more risk (or volatility) that investors accept, the more they may expect in return.

Returns are easy to measure. It’s simply the appreciation in the value of the investment plus any interest or dividends paid. Risk is trickier to measure. Academics typically look at standard deviation, a statistical measure that quantifies how much an asset swings in price. Table 11-1 shows you how much higher stock returns have been than bond returns. The Return column shows how much the investors earned; the Standard Deviation of Return column shows how much the asset class, on average, changed in price during a given year.

TABLE 11-1 Statistics for Various Asset Classes Based on Annual Returns (1926–2018)

Asset Class


Standard Deviation of Return

Large stocks



Small stocks



Long-term corporate bonds



Long-term government bonds



Intermediate-term government bonds



Treasury bills



Source: Duff & Phelps 2019 SBBI Yearbook: Stocks, Bonds, Bills, and Inflation, U.S. Capital Markets Performance by Asset Class 1926–2018 (Duff & Phelps)

Identifying the Various Types of Bonds

The kind of bond we describe in the preceding section is a plain-vanilla bond — the simplest type of corporate bond. Nothing against vanilla — it’s fine for ice cream — but as you may suspect, the bond market is not limited to plain-vanilla bonds. Investment bankers are an innovative and enterprising lot, and they’ve developed many bond variations. We describe the most prominent bond varieties in this section.

Convertible bonds

A convertible bond is just like a plain-vanilla bond, except the bondholder has the right to exchange the bond for a fixed number of shares of stock in the firm. The bondholder gets to decide whether to convert the bond into stock. As you may suspect, in exchange for receiving this valuable option — and it can be quite valuable — the bondholder agrees to receive lower interest payments than he would have in the absence of the option.

If the firm is successful and the stock price rises, the option to convert to common stock becomes more valuable, and the market price of the convertible bond will rise dramatically. Firms issuing corporate bonds hope that they’re eventually converted because that means the corporation was successful and the stock price rose.

Callable bonds

A callable bond gives the issuer — the corporation — the right to pay the bondholder back earlier than the full term of the bond. In essence, the debt is cancelled and the bondholder receives back her principal — and generally a bit more than the principal amount, because most callable bonds have a call premium (the difference between the amount the investor receives if the bond is called and the principal amount of the bond). In this case, the corporation (not the investor) has the option, so callable bonds are issued with higher interest rates than non-callable bonds. Corporations call bonds when doing so is to their advantage — specifically, when interest rates in the market haven fallen since the issue of the bonds and they can re-issue debt at a lower interest rate.

Puttable bonds

A puttable bond gives the investor the right to demand early repayment of the principal, effectively canceling the loan. Because the investor has the right, the interest rates on puttable bonds are lower than those on plain-vanilla bonds from the same issuer. Investors only demand early repayment when interest rates in the market rise and they can find better deals (higher interest rates) on current bond issues.

Floating-rate bonds

The terms fixed income and bond are often used interchangeably. However, there is an entire class of bonds whose holders don’t really receive a fixed income at all, because the interest payments change with reference to other interest rates or even to the price of a commodity. An example of a floating-rate bond (also known as an adjustable-rate bond) is one that changes in relationship to a benchmark such as the six-month Treasury rate. The bond contract states whether the rate can reset several times a year or annually. If rates rise in the market, the holder of a floating-rate bond will receive higher interest payments, and the corporation’s borrowing costs will increase.

Zero-coupon bonds

Some corporations issue zero-coupon bonds, which have no periodic interest payments. All the cash return from these bonds comes at maturity. They’re issued at a pure discount. The big disadvantage of zero-coupon bonds is that the holder must pay annual taxes on the imputed interest on the bonds.

Knowing Their Place: The Position of Bondholders

The capital structure of a firm describes who has supplied the funds to the firm and where those suppliers stand in seniority in terms of being paid back. A company’s capital structure is a breakdown of where the money used by the company has come from, be it stockholders or bondholders.

If a firm gets into financial difficulty and the assets must be liquidated, bondholders are in line to be paid before any money accrues to stockholders. This is an enormous advantage. How well bondholders are protected is related not only to the value of the assets but also to how much of the capital was supplied by bondholders versus stockholders. The larger the proportion of equity in the capital structure, the larger the equity cushion (safety net) for bondholders. A company that has 20 percent debt and 80 percent equity has a much greater equity cushion than one that has 80 percent debt and 20 percent equity.

Remember Not all bonds are created equal. Any investor must know exactly where in that proverbial line she stands. How close you are to the front of the line determines the probability that you’ll be repaid.

Some bonds are secured (backed by certain assets of the borrower). In the case of default, the secured bondholder can force the sale of the pledged assets in order to satisfy her claims. These bonds are also referred to as mortgage bonds.

Only after the secured bondholders have been paid are the debenture holders (the bondholders who hold debt that is not backed or secured by specific assets of the company) eligible to be paid. Debenture holders are often referred to as unsecured creditors. There are even differences in seniority between debenture holders — not all debenture holders have the same place in line for receiving payment if the company runs into trouble because there are senior and junior debenture holders. Last in the bond line are the junior debenture holders. They’re paid only if all the other more senior bondholders’ possessive claims are satisfied. As with most lines for scarce resources — whether Lady Gaga tickets or the latest iPhone — the further back you stand in the line, the greater the probability that you’ll walk away empty-handed.

Understanding Bond Pricing

Overall, valuing bonds is a much easier task than valuing stocks because the expected cash flows are contractually specified (at least for plain-vanilla bonds). In this section, we walk you through how bonds are priced.

Introducing the concept of present value

Valuing bonds relies on the basic principle of present value (a dollar to be received today is worth more than a dollar to be received tomorrow or at some point in the future). The rationale is that a dollar received today can be invested to earn interest and will be worth more at a later date.

Tip It may seem like a great deal of math is required to value bonds — and it is — but the mathematical proficiency needed is around a junior-high level, so don’t be intimidated by it!

Remember The present value of an amount to be received one year (or one period) in the future is


where r is the appropriate interest rate or discount rate (more about that in a bit).

So the present value of a dollar to be received a year from today if the appropriate interest rate is 6 percent is:


In other words, a rational investor shouldn’t care whether she receives $0.9434 today or $1.00 a year from now. The difference between the two amounts — $0.0566 — represents the interest she could earn on the $0.9434 at the rate of 6 percent. This simple idea is the basis for all discounted cash-flow models in finance and investments.

Extending this idea beyond a year, the present value of a dollar to be received in two years is


The subscript 2 after Future Value indicates that the amount is to be received two periods (or two years) from today, and the superscript 2 after (1 + r) indicates that interest on that amount could be earned for two periods (or two years) if it was received today instead of in two years.

So the present value of a dollar to be received in two years if the appropriate interest rate is 6 percent is


In other words, a rational investor shouldn’t care whether he receives $0.8900 today or $1.00 two years from now. The difference between the two amounts — $0.1100 — represents the interest he could earn on the $0.8900 at the rate of 6 percent compounded for two years. Compounding refers to the ability to reinvest the interest earned in year 1 and earn interest in year 2 on both the original amount and the year 1 interest.

Extrapolating this idea, the present value of an amount to be received at any point n in the future is simply


So the present value of a dollar to be received in ten years if the appropriate interest rate is 6 percent is


Again, a rational investor shouldn’t care whether she receives $0.5584 today or $1.00 in ten years. The difference between the two amounts — $0.4416 — represents the interest she could earn on the $0.5584 at the rate of 6 percent compounded annually.

By the way, this is an illustration of compound interest, a concept that none other than Albert Einstein reportedly called the eighth wonder of the world.

Relating yield to maturity and price

What we describe in the preceding section is literally all the math you need to know to value a plain-vanilla bond, because the cash flows are all specified. For example, suppose we have a five-year annual-pay bond with a principal value of $1,000. Assume that the bond pays interest of $40 annually and that the appropriate discount rate for the bond is 6 percent. The value of the bond is


The discount rate used to value a bond is what is known as the yield to maturity on that bond. In other words, the discount rate that equates the value of the future cash flows to the price is the yield to maturity on the bond. In the preceding example, if an investor bought the bond today for $915.75 and held it to maturity, he would earn exactly 6 percent on that investment.

Tip This bond is said to be selling at a discount from par or principal value of $1,000, because the stated interest rate on the bond (known as the coupon rate) of 4 percent is less than the yield to maturity of 6 percent. Alternatively, if the coupon rate on the bond is greater than the yield to maturity, the mathematics show that the bond would be selling for more than the principal or par value and would be selling for a premium. For example, if the same bond had a yield to maturity of 3 percent, it would be selling for $1,046.39 — a premium of $46.39 to par value. Finally, if the bond were selling at a yield to maturity of 4 percent, it would be selling for exactly $1,000 and would be said to be selling at par.

There is an inverse relationship between market interest rates and bond prices: As interest rates in the market rise, the prices of bonds fall. Alternatively, as interest rates in the market fall, the prices of bonds rise. Corporate bonds are issued at or near par value, so when you see a bond selling at a discount, you can infer that since the time that the bond was issued, market interest rates have fallen. Conversely, if a bond is selling at a premium to par value, that bond was issued in a higher interest rate environment.

Playing the spread: How different factors affect bond prices

Credit risk on a bond is related to the risk that an issuer may default on interest payments or repayment of the principal. Of course, if a bond defaults, that doesn’t mean that the investor will lose her entire investment in the bond. Investors in bonds that default typically recover some significant portion of their investment. Suffice it to say, bonds with higher default risk sell at higher yields to maturity.

Credit spreads are defined as the risk premium over similar-maturity Treasury securities. Credit spreads are a mathematical way to measure how much more yield investors get on one bond than another. Credit spreads are critical for investors to make sure they’re being compensated enough for the extra risk they’re taking on a bond with more potential problems. For instance, if ten-year Treasury bonds are yielding 3 percent, and a particular corporate issuer is yielding 5 percent, then the credit spread is 2 percent, or 200 basis points. (A basis point is defined as one-hundredth of a percentage point.)

Tip Credit spreads tend to widen during economic downturns as investors become concerned that corporate profits and cash flows will decline and negatively impact the ability of firms to service their debt. So, during recessions, credit spreads tend to widen on virtually all corporate issues and the prices of bonds decline overall. Conversely, during economic recoveries and booms, credit spreads tend to narrow as investors become more optimistic about firm cash flows.

The combination of these different factors determines the specific yield to maturity for a bond issue. Both economic-wide (macro) and firm-specific (micro) factors affect the yield to maturity on bond issues and, thus, the value of bonds.

Considering bond sensitivity to changes in interest rates

All bonds are sensitive to changes in the general level of market interest rates, but the sensitivity varies from bond to bond. The interest rate sensitivity of a bond varies inversely with the coupon rate and directly with its term to maturity. Analysts have developed a measure of interest rate sensitivity called duration that takes into account both the coupon rate and term to maturity factors.

The coupon rate effect

Bonds with higher coupon rates are less sensitive to changes in interest rates than bonds with lower coupon rates. For example, we can contrast the interest rate sensitivity of a five-year zero-coupon bond with an initial yield to maturity of 5 percent, with that of a five-year 5 percent coupon bond with an initial yield to maturity of 5 percent (assuming that the bond pays interest annually).

The five-year zero-coupon bond selling to yield 5 percent to maturity will be priced at


The price of the five-year, 5 percent coupon bond selling to yield 5 percent will be $1,000 because the yield to maturity and the coupon rate are identical.

Now, assume that yields in the marketplace rise by 100 basis points due to general economic uncertainty and that the bonds both sell at a yield to maturity of 6 percent. The new price of the zero-coupon bond will be


With this increase in interest rates of 100 basis points, the price of the zero-coupon bond fell by 4.63 percent.

If the yield to maturity rises to 6 percent, the price of the 5 percent coupon bond is


With this increase in interest rates of 100 basis points, the price of the 5 percent coupon bond fell by 4.21 percent. Thus, the lower coupon bond is more sensitive to changes in interest rates than the higher coupon bond. If interest rates rise, you would rather be holding higher coupon bonds than lower coupon bonds.

The term to maturity effect

Bonds with longer terms to maturity are more sensitive to changes in interest rates than bonds with shorter terms to maturity. To illustrate this point, contrast the price change of similar zero-coupon bonds, one with 5 years to maturity and one with 30 years to maturity, when yields go from 5 percent to 6 percent.

As shown in the preceding section, the market price of a five-year zero-coupon bond falls from $783.53 to $747.26, a decrease in price of 4.63 percent when the yield to maturity on the bond rises from 5 percent to 6 percent.

Contrast that with the change in price on a 30-year zero-coupon bond when the yield to maturity on the bond rises from 5 percent to 6 percent. At a yield of 5 percent, the price of the bond is


At a yield of 6 percent, the price of the bond is


When yields rise from 5 percent to 6 percent, the price of the 30-year zero-coupon bond falls by 24.75 percent. Suffice it to say, you’d rather be holding shorter-term bonds than longer-term bonds if interest rates rise.


The two preceding sections show that price volatility of a bond varies inversely with its coupon rate and directly with its term to maturity. Duration is a combined measure of interest rate sensitivity that takes into account both of these properties.

Duration is one tool investment bankers use to determine how risky a bond investment is. It’s defined as the time-weighted term to maturity of a bond in which the cash flows are weighted according to when they’re received in a present value sense.

When you compute the duration for a bond, the unit of measurement is in years. You calculate duration simply by finding the present value of each cash flow as a percentage of the price of the bond and multiplying that value by the year in which the cash flow is received. The sum of those values is the time-weighted term to maturity of the bond and represents the duration of the bond.

Table 11-2 calculates the duration for a ten-year, 5 percent coupon bond with a 7 percent yield to maturity (assuming annual interest payments). This bond has a duration of 7.94 years. It will show interest rate sensitivity that is identical to a zero-coupon bond with 7.94 years to maturity.

TABLE 11-2 The Duration of a 5 Percent Coupon, Ten-Year Bond with a Yield to Maturity of 7 Percent


Cash Flow

Present Value of Cash Flow at 7%

Present Value as a Percent of Price

Year x Present Value as a Percent of Price






















































Tip Duration has many useful properties. One is that you can compute the duration of a fixed-income portfolio simply by computing a weighted average (weighted by value) of the bonds in the portfolio. In that way, an investor can determine the interest rate sensitivity of his fixed-income portfolio and can estimate how much the portfolio will change in value given a change in market interest rates.

Portfolio managers often adjust the duration of their portfolios by buying and selling bonds in anticipation of interest rate changes. For example, if you thought interest rates were going to decline (and bond values would rise), you would want to lengthen the duration of your portfolio. Conversely, if you thought interest rates were going to rise, you would want to shorten the duration of your portfolio.

Tracking the Bond Market

The evening news typically tells viewers how the Dow Jones Industrials or S&P 500 stock indexes performed that day, but results in the bond market generally aren’t reported by the popular media. There isn’t the equivalent of a widely followed bond market index to the two popular equity indexes. So bond investors typically consider the U.S. Treasury yield curve the appropriate bond market benchmark and monitor changes to the yield curve to gauge the bond market and interest rates.

The U.S. Treasury yield curve is simply a graph showing the relationship between yield on a U.S. Treasury security in relation to the maturity of the instrument. U.S. Treasury securities are used because they’re always issued by the same entity — the U.S. Treasury — and they have no default risk. So they give an idea of what investors demand for the pure time value of money.

Most often, the yield curve is upward sloping (like the one in Figure 11-1). In other words, longer-maturity (longer-duration) Treasury bonds have a higher yield to maturity than shorter-maturity Treasury bonds. This makes intuitive sense: A longer time period generally has greater risks, just because there’s more time for unexpected things to happen.

Graph depicting a typical U.S. Treasury yield curve with an upward sloping, indicating that longer-maturity Treasury bonds have a higher yield to maturity than shorter-maturity bonds.

FIGURE 11-1: A typical U.S. Treasury yield curve.

Remember Most lenders prefer to lend short term, and most borrowers prefer to borrow long term. To induce lenders to lend long term, lenders must be offered a time premium.

Sometimes, however, the yield curve can become flat or even inverted. A flat yield curve is one in which all yields are very close to one another. An inverted yield curve happens when shorter-term yields are actually higher than longer-term yields. Many people believe that a flat or inverted yield curve is a precursor to an economic recession or slowdown. Lenders are willing to accept a lower long-term yield to lock in the current returns, while borrowers are willing to pay higher rates in the short term because they believe they’ll be able to get more favorable long-term rates in the future.

Tip The inversion of the spread between the 90-day Treasury bill and the 10-year Treasury note has preceded every recession since 1967. And on average, the economy has gone into recession 14 months following the inversion. But just like one can drown in a river with an average depth of one foot, on closer examination, it often takes years before the recession starts. It is a bit like saying autumn forecasts winter.

Investors typically look at the very short end of the yield curve (the 90-day Treasury bill rate), the middle of the yield curve (the 10-year Treasury bond rate), and the long end (the 30-year Treasury bond rate) to get a handle on the bond market. When people in the investment management industry ask how the bond market did, the answer typically involves detailing what happened to both the 90-day Treasury bill and the 30-year Treasury bond.

Debt or Equity: How a Company Chooses

Both debt and equity are issued by companies who need funds to expand their operations. The factors that management considers are numerous, but the goal is always to raise capital in a cost-efficient manner. Just as an investor wants to buy undervalued assets and sell overvalued assets, companies choose between debt and equity based on the relative cost of the capital source.

If a firm’s management believes that interest rates are low and likely to rise in the future, they often choose to issue long-term debt at a fixed rate. If interest rates do indeed rise, the market value of the debt will decline. Because that debt is a liability of the firm and the liability declines in value, the firm wins. A prime example of this was in mid-2019 when Warren Buffett’s Berkshire Hathaway sold corporate debt in Europe denominated in Euros as well as in pounds. Note that he chose to issue debt in jurisdictions with interest rates lower than those prevailing in the U.S. at the time. The Oracle of Omaha was on record as saying that he believed that interest rates were historically low and would likely increase in the future. Issuing debt was a way of selling what he believed was an overvalued asset. (We wonder who feels confident buying these bonds — betting against Mr. Buffett has been a losing proposition for several decades, although it doesn’t stop people from trying.)

If a firm’s management believes that interest rates are high and are likely to decline in the future, they’ll choose to issue shorter-term debt, callable debt, or perhaps debt with a floating interest rate. That way, they aren’t locked into paying a high interest rate for an extended period of time, and they have the flexibility to refinance when rates fall.

Companies generally don’t like to issue equity if they believe that their stock is undervalued. This form of financing is expensive and dilutes the ownership of the current stockholders.

If the equity is undervalued but debt financing appears to be expensive, companies may choose to issue convertible bonds. That way, if the value of the equity rises, the bondholders will convert and extinguish the debt. In addition, the conversion price is generally set at a substantial premium above the market price of the equity at the time the bond is issued. If things work out the way the firm would like, the value of the stock will rise, bondholders will convert, and the firm will have effectively issued stock at a price that is above what it could have received in a straight equity offering.

Companies can also increase their leverage without issuing debt. They can buy back (or repurchase) company stock in the open market, thereby increasing their debt-to-equity ratio. A firm will buy back stock when it has excess cash and the management believes that the market undervalues that stock. Stock buybacks tend to bolster the stock price of the firm, because the percentage of the company that any individual stockholder owns effectively increases after a buyback. Buybacks are often preferred to cash dividends, because only the shareholders who want to sell the stock back will incur a tax liability.

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