GS FIN 304 CH 7 Bonds and Their Valuation

Municipal Bonds or munis,

Bonds issued by state and local governments Like corporates, munis are exposed to some default risk, but they have one major advantage over all other bonds: As we discussed in Chapter 3, the interest earned on most munis is exempt from federal taxes and from state taxes if the holder is a resident of the issuing state. Consequently, the market interest rate on a muni is considerably lower than on a corporate bond of equivalent risk.

Default risk is influenced by the financial strength of the

issuer and the terms of the bond contract, including whether collateral has been pledged to secure the bond.

Warrants

long-term options to buy a stated number of shares of common stock at a specified price similar to convertibles; but instead of giving the investor an option to exchange the bonds for stock, warrants give the holder an option to buy stock for a stated price, thereby providing a capital gain if the stock's price rises. Because of this factor, bonds issued with warrants, like convertibles, carry lower coupon rates than otherwise similar nonconvertible bonds.

Bond Markets

Corporate bonds are traded primarily in the over-the-counter market. Most bonds are owned by and traded among large financial institutions (e.g., life insurance companies, mutual funds, hedge funds, and pension funds, all of which deal in very large blocks of securities), and it is relatively easy for over-the-counter bond dealers to arrange the transfer of large blocks of bonds among the relatively few holders of the bonds. It would be more difficult to conduct similar operations in the stock market among the literally millions of large and small stockholders, so a higher percentage of stock trades occur on the exchanges.

Original Issue Discount (OID) Bond

any bond originally offered at a price below its par value Other bonds pay some coupon interest, but not enough to induce investors to buy them at par.

Subordinated Debentures The term subordinate means "below" or "inferior to," and in the event of bankruptcy, subordinated debt has a claim on assets only after senior debt has been paid in full.

Bonds having a claim on assets only after the senior debt has been paid in full in the event of liquidation. In the event of liquidation or reorganization, holders of subordinated debentures receive nothing until all senior debt, as named in the debentures' indenture, has been paid.

Whenever the bond's market, or going, rate, rd, is equal to its coupon rate, a fixed-rate bond will

sell at its par value. Normally, the coupon rate is set at the going rate in the market the day a bond is issued, causing it to sell at par initially.

Sinking Fund Provision example Suppose a company issued $100 million of 20-year bonds and it is required to call 5% of the issue, or $5 million of bonds, each year. In most cases, the issuer can handle the sinking fund requirement in either of two ways:

1. It can call in for redemption, at par value, the required $5 million of bonds. The bonds are numbered serially, and those called for redemption would be determined by a lottery administered by the trustee. 2. The company can buy the required number of bonds on the open market. The firm will choose the least-cost method. If interest rates have fallen since the bond was issued, the bond will sell for more than its par value. In this case, the firm will use the call option. However, if interest rates have risen, the bonds will sell at a price below par; so the firm can and will buy $5 million par value of bonds in the open market for less than $5 million.

A 2009 article in The Wall Street Journal highlighted the concerns that bond investors face in today's environment. The article offers what it refers to as "five key pointers":

1. Watch Out for Defaults. Investors should be wary of low-rated corporate bonds on the edge of default. 2. Limit Your Rate Risk. Rates are likely to increase over time as the economy hopefully continues to recover. As we see in this chapter, increasing interest rates reduce the value of bonds, and this effect is particularly important for investors of long-term bonds. 3. Consider a Passive Strategy. This advice is directed specifically to investors in bond mutual funds. 4. Have an Inflation Hedge. Many analysts worry that down the road, higher government spending and a relaxed monetary policy will ultimately lead to higher levels of inflation. 5. Don't Try to Time the Market. As we have seen in recent years, bond prices can move quickly and dramatically, which makes it difficult to effectively bet on where the market is heading next.

Over the long run, rating agencies have done a reasonably good job of measuring the average credit risk of bonds and of changing ratings whenever there is a significant change in credit quality. However, it is important to understand that ratings do

not adjust immediately to changes in credit quality, and in some cases, there can be a considerable lag between a change in credit quality and a change in rating. For example, Enron

The yield to maturity can also be viewed as the bond's

promised rate of return, which is the return that investors will receive if all of the promised payments are made. However, the yield to maturity equals the expected rate of return only when (1) the probability of default is zero. (2) The bond cannot be called. Note also that a bond's calculated yield to maturity changes whenever interest rates in the economy change, which is almost daily. An investor who purchases a bond and holds it until it matures will receive the YTM that existed on the purchase date, but the bond's calculated YTM will change frequently between the purchase date and the maturity date.

To summarize, here is the situation: (rd = market interest rate)

rd = coupon rate, fixed-rate bond sells at par; hence, it is a par bond. rd > coupon rate, fixed-rate bond sells below par; hence, it is a discount bond. rd < coupon rate, fixed-rate bond sells above par; hence, it is a premium bond.

par value

the face value of a bond The par value generally represents the amount of money the firm borrows and promises to repay on the maturity date.

Original Maturity

the number of years to maturity at the time a bond is issued Most bonds have an original maturity (the maturity at the time the bond is issued) ranging from 10 to 40 years, but any maturity is legally permissible.

investment horizon

the period of time an investor plans to hold a particular investment

Yield to Call If current interest rates are well below an outstanding bond's coupon rate, a callable bond is likely to be called, and investors will estimate its most likely rate of return as the yield to call (YTC) rather than the yield to maturity.

the rate of return earned on a bond when it is called before its maturity date If you purchase a bond that is callable and the company calls it, you do not have the option of holding it to maturity. Therefore, the yield to maturity would not be earned.

To be most useful, the bond's yield should give us an estimate of

the rate of return we would earn if we purchased the bond today and held it over its remaining life. • If the bond is not callable, its remaining life is its years to maturity. • If it is callable, its remaining life is the years to maturity • if it is not called or the years to the call if it is called.

Price (Interest Rate) Risk Because interest rates can and do rise, rising rates cause losses to bondholders; people or firms who invest in bonds are exposed to risk from increasing interest rates. Price risk relates to the current market value Steps You would obtain the first value with a financial calculator by entering N = 1, I/YR = 5, PMT = 100, and FV = 1000 and then pressing PV to get $1,047.62. With all the data still in your calculator, enter I/YR = 10 to override the old I/YR 5 and press PV to find the bond's value at a 10% rate; it drops to $1,000. Then enter I/YR 15, and press the PV key to find the last bond value, $956.52.

the risk of a decline in a bond's price due to an increase in interest rates Price risk is higher on bonds that have long maturities than on bonds that will mature in the near future. This follows because the longer the maturity, the longer before the bond will be paid off and the bondholder can replace it with another bond with a higher coupon. You would obtain the first value with a financial calculator by entering N 1, I YR 5, PMT 100, and FV 1000 and then pressing PV to get $1,047.62. With all the data still in your calculator, enter I YR 10 to override the old I YR 5 and press PV to find the bond's value at a 10% rate; it drops to $1,000. Then enter I YR 15, and press the PV key to find the last bond value, $956.52.

coupon payment

the specified number of dollars of interest paid each year set at the time the bond is issued and remains in force during the bond's life. Typically, at the time a bond is issued, its coupon payment is set at a level that will induce investors to buy the bond at or near its par value.

coupon interest rate

the stated annual interest rate on a bond When this annual coupon payment is divided by the par value, the result is the coupon interest rate. For example, Allied's bonds have a $1,000 par value, and they pay $100 in interest each year. The bond's coupon payment is $100, so its coupon interest rate is $100/$1,000 = 10%. In this regard, the $100 is the annual income that an investor receives when he or she invests in the bond.

Not all bonds are alike, and they don't always move in the same direction.

For example, corporate bonds are often callable, and issuers can default on them, whereas Treasury bonds are not exposed to these risks. To compensate investors for these additional risks, corporate bonds typically have higher yields. When the economy is strong, corporate bonds generally produce higher returns than Treasuries because their promised returns are higher, and most make their promised payments because few go into default. However, when the economy weakens, concerns about defaults rise, which lead to declines in corporate bond prices.

Two words of caution about zeros are in order.

First, as we show in Web Appendix 7A, investors in zeros must pay taxes each year on their accrued gain in value, even though the bonds don't pay any cash until they mature. Second, buying a zero coupon bond with a maturity equal to your investment horizon enables you to lock in a nominal cash payoff, but the real value of that payment still depends on what happens to inflation during your investment horizon.

Importance of Bond Ratings Bond ratings are important to both firms and investors.

First, because a bond's rating is an indicator of its default risk, the rating has a direct, measurable influence on the bond's interest rate and the firm's cost of debt. Second, most bonds are purchased by institutional investors rather than individuals, and many institutions are restricted to investment-grade securities. Thus, if a firm's bonds fall below BBB, it will have a difficult time selling new bonds because many potential purchasers will not be allowed to buy them. As a result of their higher risk and more restricted market, lower-grade bonds have higher required rates of return, rd, than high-grade bonds. Figure 7.4 illustrates this point.

Bond Valuation Formula The cash flows for a standard coupon bearing bond, like those of Allied Food, consist of interest payments during the bond's 15-year life plus the amount borrowed (generally the par value) when the bond matures. Because the PV is an outflow to the investor, it is shown with a negative sign. Spreadsheets can also be used to solve for the bond's value. The PV of this bond can be calculated using Excel's PV function: =PV(rate,nper,pmt,[fv],[type]) Note that type is left blank because cash flows occur at year-end.

For a "regular" bond with a fixed coupon, like Allied's, here is the situation: Where: rd = the market rate of interest on the bond, 10%. This is the discount rate used to calculate the present value of the cash flows, which is also the bond's price. Note that rd is not the coupon interest rate. However, rd is equal to the coupon rate at times, especially the day the bond is issued; and when the two rates are equal, as in this case, the bond sells at par. N = the number of years before the bond matures INT = dollars of interest paid each year Coupon rate x Par value = 0.10 x $1,000 = $100. In calculator terminology, INT = PMT = 100. If the bond had been a semiannual payment bond, the payment would have been $50 every 6 months. M = the par, or maturity, value of the bond = $1,000. This amount must be paid at maturity.

Junk Bonds

High-risk, high-yield bonds. Double-B and lower bonds are speculative, or junk bonds; and they have a significant probability of going into default.

Corporate Bonds

bonds issued by corporations Unlike Treasuries, corporates are exposed to default risk—if the issuing company gets into trouble, it may be unable to make the promised interest and principal payments and bondholders may suffer losses.

Convertible Bonds

bonds that are exchangeable at the option of the holder for the issuing firm's common stock Convertibles offer investors the chance for capital gains if the stock price increases, but that feature enables the issuing company to set a lower coupon rate than on nonconvertible debt with similar credit risk.

Zero Coupon Bonds (zeros)

bonds that pay no annual interest but are sold at a discount below par, thus compensating investors in the form of capital appreciation

Fixed-Rate Bonds

bonds whose interest rate is fixed for their entire life

Putable Bonds

bonds with a provision that allows investors to sell them back to the company prior to maturity at a prearranged price If interest rates rise, investors will put the bonds back to the company and reinvest in higher coupon bonds.

In most cases, the provisions in the bond contract are set so that the call premium

declines over time as the bonds approach maturity. Also, although some bonds are immediately callable, in most cases, bonds are often not callable until several years after issue, generally 5 to 10 years. This is known as a deferred call, and such bonds are said to have call protection.

Companies are not likely to call bonds unless

interest rates have declined significantly since the bonds were issued.

The coupon rate remains fixed after the bond is issued, but

interest rates in the market move up and down. Looking at Equation 7.1, we see that an increase in the market interest rate rd causes the price of an outstanding bond to fall, whereas a decrease in the rate causes the bond's price to rise.

Accrued Interest

interest revenue or expense that is recognized before cash has been exchanged

mortgage bond

A bond backed by fixed assets. First mortgage bonds are senior in priority to claims of second mortgage bonds. To illustrate, in 2016, Billingham Corporation needed $10 million to build a regional distribution center. Bonds in the amount of $4 million, secured by a first mortgage on the property, were issued. (The remaining $6 million was financed with equity capital.) If Billingham defaults on the bonds, the bondholders can foreclose on the property and sell it to satisfy their claims. If Billingham had chosen to, it could have issued second mortgage bonds secured by the same $10 million of assets. In the event of liquidation, the holders of the second mortgage bonds would have a claim against the property, but only after the first mortgage bondholders had been paid in full. Thus, second mortgages are sometimes called junior mortgages because they are junior in priority to the claims of senior mortgages, or first mortgage bonds.

Who Issues Bonds? A bond is a long-term contract under which a borrower agrees to make payments of interest and principal on specific dates to the holders of the bond.

A bond is a long-term contract under which a borrower agrees to make payments of interest and principal on specific dates to the holders of the bond. Bonds are issued by corporations and government agencies that are looking for long-term debt capital.

Discount Bond

A bond that sells below its par value; occurs whenever the going rate of interest is above the coupon rate

Bankruptcy and Reorganization When a business becomes insolvent, it doesn't have enough cash to meet its interest and principal payments.

A decision must then be made whether to dissolve the firm through liquidation or to permit it to reorganize and thus continue to operate. The decision to force a firm to liquidate versus permitting it to reorganize depends on whether the value of the reorganized business is likely to be greater than the value of its assets if they were sold off piecemeal.

Debenture

A long-term bond that is not secured by a mortgage on specific property. an unsecured bond, and as such, it provides no specific collateral as security for the obligation. Therefore, debenture holders are general creditors whose claims are protected by property not otherwise pledged.

Maturity Date

A specified date on which the par value of a bond must be repaid.

Accrued Interest and the Pricing of Coupon Bonds Clearly, all else equal, you would be willing to pay more for a bond the day before a coupon is paid, than you would the day after it has been paid. So, if you purchase a bond between coupon payments, you also have to pay what is called accrued interest. In most cases, bonds are quoted net of accrued interest—in what is often referred to as a clean price. The actual invoice price you pay (often referred to as the dirty price) is the clean price plus accrued interest.

Accrued interest represents the amount of interest that has accumulated between coupon payments, and it can be calculated as follows: Let's consider, for example, a corporate bond that was issued on March 21, 2015. The bond has an 8% semiannual coupon and a par value of $1,000—which means six months later, on September 21, 2015, the bond will pay its first $40 coupon, and on March 21, 2016, it will pay its second $40 coupon. If you buy the bond on June 8, 2015 (79 days since the bond's last coupon payment on March 21), you will have to pay the seller $17.56 in accrued interest: You can also use the Accrued Interest function in Excel (ACCRINT) to easily calculate a bond's accrued interest.

Foreign Bonds

Bonds issued by foreign governments or by foreign corporations All foreign corporate bonds are exposed to default risk, as are some foreign government bonds. Indeed, recently, concerns have risen about possible defaults in many countries including Greece, Ireland, Portugal, and Spain. An additional risk exists when the bonds are denominated in a currency other than that of the investor's home currency.

Treasury Bonds

Bonds issued by the federal government, sometimes referred to as government bonds. It is reasonable to assume that the U.S. government will make good on its promised payments, so Treasuries have no default risk. However, these bonds' prices do decline when interest rates rise; so they are not completely riskless.

investment grade bonds

Bonds rated triple-B or higher; many banks and other institutional investors are permitted by law to hold only investment-grade bonds

outstanding bond

Bonds that have been previously issued also called a seasoned issue. The prices of outstanding bonds can vary widely from par. Except for floating-rate bonds, coupon payments are constant; so when economic conditions change, a bond with a $100 coupon that sold at its $1,000 par value when it was issued will sell for more or less than $1,000 thereafter.

Floating-Rate Bonds

Bonds whose interest rate fluctuates with shifts in the general level of interest rates.

Corporate bonds have different levels of default risk depending on the issuing company's characteristics and the terms of the specific bond.

Default risk is often referred to as "credit risk"; and as we saw in Chapter 6, the larger this risk, the higher the interest rate investors demand.

Bond Rating Criteria The framework used by rating agencies examines both qualitative and quantitative factors. Quantitative factors relate to financial risk—examining a firm's financial ratios. Published ratios are, of course, historical—they show the firm's condition in the past, whereas bond investors are more interested in the firm's condition in the future. Qualitative factors considered include an analysis of a firm's business risk, such as its competitiveness within its industry and the quality of its management.

Determinants of bond ratings include the following: 1. Financial Ratios. All of the ratios are potentially important, but those related to financial risk are key. 2. Qualitative Factors: Bond Contract Terms. The indenture spells out all the terms related to the bond. Included in the indenture are the maturity, the coupon interest rate, a statement of whether the bond is secured by a mortgage on specific assets, any sinking fund provisions, and a statement of whether the bond is guaranteed by some other party with a high credit ranking. 3. Miscellaneous Qualitative Factors. Included here are issues like the sensitivity of the firm's earnings to the strength of the economy, the way it is affected by inflation, a statement of whether it is having or likely to have labor problems, the extent of its international operations (including the stability of the countries in which it operates), potential environmental problems, and potential antitrust problems. Today the most important factor is exposure to subprime loans, including the difficulty to determine the extent of this exposure as a result of the complexity of the assets backed by such loans.

Key Characteristics of Bonds Although all bonds have some common characteristics, different types of bonds can have different contractual features.

Differences in contractual provisions (and in the fundamental underlying financial strength of the companies backing the bonds) lead to differences in bonds' risks, prices, and expected returns.

In the years since the crisis, these spreads have narrowed as investors have slowly become once again more willing to hold riskier securities. This point is highlighted in Figure 7.5, which gives the yields on the three types of bonds and the yield spreads for AAA and BBB bonds over Treasuries in January 2009 and January 2015.

Note first from Figure 7.5 that the risk-free rate, or vertical axis intercept, was lower in January 2015 than it was in January 2009. Second, the slope of the line has decreased. In the crisis period of 2009, investors were both pessimistic and risk-averse, so spreads were quite high.

refunding operation

Occurs when a company issues debt at current low rates and uses the proceeds to repurchase one of its existing high-coupon rate debt issues. Often these are callable issues, which means the company can purchase the debt at a call price lower than the market price. thus reducing interest expense. Thus, the call privilege is valuable to the firm but detrimental to long-term investors, who will need to reinvest the funds they receive at the new and lower rates.

Changes in Ratings Changes in a firm's bond rating affect its ability to borrow funds and its cost of that capital.

Rating agencies review outstanding bonds on a periodic basis, occasionally upgrading or downgrading a bond as a result of its issuer's changed circumstances.

Default Risk Potential default is another important risk that bondholders face. If the issuer defaults, investors will receive less than the promised return.

The quoted interest rate includes a default risk premium—the higher the probability of default, the higher the premium and thus the yield to maturity. Default risk on Treasuries is zero, but this risk is substantial for lower-grade corporate and municipal bonds.

Yield to Maturity (YTM) the interest rate generally discussed by investors when they talk about rates of return and the rate reported by The Wall Street Journal and other publications. Suppose you were offered a 14-year, 10% annual coupon, $1,000 par value bond at a price of $1,494.93. What rate of interest would you earn on your investment if you bought the bond, held it to maturity, and received the promised interest payments and maturity value? To find the YTM, all you need to do is solve Equation 7.1 for rd as follows:

The rate of return earned on a bond if it is held to maturity. You can substitute values for rd until you find a value that "works" and force the sum of the PVs in the equation to equal $1,494.93. or use calculator Simply enter • N = 14, • PV = -1494.93, • PMT = 100, and • FV = 1000; • then press the I/YR key. The answer, 5%, will appear. You can also find the YTM with a spreadsheet. In Excel, you use the RATE function: = RATE(14, 100, -1494.93, 1000) Note that we didn't need to specify a value for type (because the cash flows occur at the end of the year) or guess.

In a reorganization, the firm's creditors negotiate with management on the terms of a potential reorganization.

The reorganization plan may call for restructuring the debt, in which case the interest rate may be reduced; the term to maturity, lengthened; or some of the debt may be exchanged for equity. The point of the restructuring is to reduce the financial charges to a level that is supportable by the firm's projected cash flows. Of course, the common stockholders also have to "take a haircut"—they generally see their position diluted as a result of additional shares being given to debt-holders in exchange for accepting a reduced amount of debt principal and interest. A trustee may be appointed by the court to oversee the reorganization, but the existing management generally is allowed to retain control.

Reinvestment Risk Reinvestment risk relates to the income the portfolio produces. As we saw in the preceding section, an increase in interest rates hurts bondholders because it leads to a decline in the current value of a bond portfolio. But can a decrease in interest rates also hurt bondholders? The answer is yes because if interest rates fall, long-term investors will suffer a reduction in income. Reinvestment risk is obviously high on callable bonds. It is also high on short-term bonds because the shorter the bond's maturity, the fewer the years before the relatively high old coupon bonds will be replaced with the new low-coupon issues.

The risk that a decline in interest rates will lead to a decline in income from a bond portfolio For example, consider a retiree who has a bond portfolio and lives off the income it produces. The bonds in the portfolio, on average, have coupon rates of 10%. Now suppose interest rates decline to 5%. Many of the bonds will mature or be called; as this occurs, the bondholder will have to replace 10% bonds with 5% bonds. Thus, the retiree will suffer a reduction of income.

Bond Ratings Since the early 1900s, bonds have been assigned quality ratings that reflect their probability of going into default.

The three major rating agencies are • Moody's Investors Service (Moody's), • Standard & Poor's Corporation (S&P), and • Fitch Investors Service. The triple- and double-A bonds are extremely safe. Single-A and triple-B bonds are also strong enough to be called investment-grade bonds, and they are the lowest-rated bonds that many banks and other institutional investors are permitted by law to hold.

Bonds with Semiannual Coupons Although some bonds pay interest annually, the vast majority actually make payments semiannually.

To evaluate semiannual bonds, we must modify the valuation model (Equation 7.1) as follows: 1. Divide the annual coupon interest payment by 2 to determine the dollars of interest paid each six months. 2. Multiply the years to maturity, N, by 2 to determine the number of semiannual periods. 3. Divide the nominal (quoted) interest rate, rd, by 2 to determine the periodic (semiannual) interest rate. On a time line, there would be twice as many payments, but each would be half as large as with an annual payment bond. Making the indicated changes results in the following equation for finding a semiannual bond's value:

Yield to Call (formula) To calculate the YTC, we modify Equation 7.1, using • years to call as N and • the call price rather than the maturity value as the ending payment. Here's the modified equation:

To illustrate, suppose Allied's bonds had a deferred call provision that permitted the company, if it desired, to call them 10 years after their issue date at a price of $1,100. Suppose further that interest rates had fallen and that 1 year after issuance, the going interest rate had declined, causing their price to rise to $1,494.93.Here is the time line and the setup for finding the bonds' YTC with a financial calculator: The YTC is 4.21%—this is the return you would earn if you bought an Allied bond at a price of $1,494.93 and it was called 9 years from today. (It could not be called until 10 years after issuance because of its deferred call provision. One year has gone by, so there are 9 years left until the first call date.)

Bond Yields If you examine the bond market table of The Wall Street Journal or a price sheet put out by a bond dealer, you will typically see information regarding each bond's maturity date, price, and coupon interest rate. You will also see a reported yield.

Unlike the coupon interest rate, which is fixed, the bond's yield varies from day to day, depending on current market conditions.

Liquidation occurs if the company is deemed to be worth more "dead" than "alive." If the bankruptcy court orders a liquidation, assets are auctioned off and the cash obtained is distributed as specified in Chapter 7 of the Bankruptcy Act.

Web Appendix 7C provides an illustration of how a firm's assets are distributed after liquidation. For now, you should know that (1) the federal bankruptcy statutes govern reorganization and liquidation. (2) Bankruptcies occur frequently. (3) A priority of the specified claims must be followed when the assets of a liquidated firmare distributed. (4) Bondholders' treatment depends on the terms of the bond. (5) Stockholders generally receive little in reorganizations and nothing in liquidations because the assets are usually worth less than the amount of debt outstanding.

Indexed (Purchasing Power) Bond

a bond that has interest payments based on an inflation index so as to protect the holder from inflation The interest rate is based on an inflation index such as the consumer price index (CPI), so the interest paid rises automatically when the inflation rate rises, thus protecting bondholders against inflation. As we mentioned in Chapter 6, the U.S. Treasury is the main issuer of indexed bonds.

new issue

a bond that has just been issued -generally sell at prices very close to par

Income Bond

a bond that pays interest only if it is earned pays interest only if the issuer has earned enough money to pay the interest. Thus, income bonds cannot bankrupt a company; but from an investor's standpoint, they are riskier than "regular" bonds.

Premium Bond

a bond that sells above its par value; occurs whenever the going rate of interest is below the coupon rate

Indenture

a formal agreement between the issuer and the bondholders legal document that spells out in detail the rights of the bondholders and the corporation. The indentures of many major corporations were written 20, 30, 40, or more years ago. These indentures are generally "open ended," meaning that new bonds can be issued from time to time under the same indenture. However, the amount of new bonds that can be issued is usually limited to a specified percentage of the firm's total "bondable property," which generally includes all land, plant, and equipment.

Bond

a long-term debt instrument

Call Provision

a provision in a bond contract that gives the issuer the right to redeem the bonds under specified terms prior to the normal maturity date The call provision generally states that the issuer must pay the bondholders an amount greater than the par value if they are called. The additional sum, which is termed a call premium, is often equal to one year's interest.

Sinking Fund Provision Note that a call for sinking fund purposes is generally different from a refunding call because most sinking fund calls require no call premium. However, only a small percentage of the issue is normally callable in a given year.

a provision in a bond contract that requires the issuer to retire a portion of the bond issue each year facilitates the orderly retirement of the bond issue. Today, though, sinking fund provisions require the issuer to buy back a specified percentage of the issue each year. A failure to meet the sinking fund requirement constitutes a default, which may throw the company into bankruptcy. Therefore, a sinking fund is a mandatory payment.

One way to manage both price and reinvestment risk is to buy a zero coupon Treasury bond with a duration equal to the investor's investment horizon. A very simple way to do this is to buy

a zero coupon bond with a maturity that matches the investment horizon. For example, assume your investment horizon is 10 years. If you buy a 10-year zero, youwill receive a guaranteed payment in 10 years equal to the bond's face value.16Moreover, as there are no coupons to reinvest, there is no reinvestment risk. This explains why investors with specific goals often invest in zero coupon bonds.

Duration To account for the effects related to both a bond's maturity and coupon, many analysts focus on a measure called duration.

the weighted average of the time it takes to receive each of the bond's cash flows It follows that a zero coupon bond whose only cash flow is paid at maturity has a duration equal to its maturity. On the other hand, a coupon bond will have a duration that is less than its maturity. You can use Excel's DURATION function to calculate a bond's duration.

Although sinking funds are designed to protect investors by ensuring that the bonds are retired in an orderly fashion, these funds work

to the detriment of bondholders if the bond's coupon rate is higher than the current market rate. For example, suppose the bond has a 10% coupon, but similar bonds now yield only 7.5%. A sinking fund call at par would require a long-term investor to give up a bond that pays $100 of interest and then to reinvest in a bond that pays only $75 per year. This is an obvious disadvantage to those bondholders whose bonds are called. On balance, however, bonds that have a sinking fund are regarded as being safer than those without such a provision; so at the time they are issued, sinking fund bonds have lower coupon rates than otherwise similar bonds without sinking funds.

Many people view Treasury securities as a lackluster but

ultrasafe investment. From a default standpoint, Treasuries are indeed our safest investments, but their prices can still decline in any given year if interest rates increase.

OTHER FEATURES Several other types of bonds are used sufficiently often to warrant mention.

• Convertible Bonds • Warrants • Putable Bonds • Income Bond • Indexed (Purchasing Power) Bond

Comparing Price Risk and Reinvestment Risk Note that price risk relates to the current market value of the bond portfolio, while reinvestment risk relates to the income the portfolio produces. Which type of risk is "more relevant" to a given investor depends on how long the investor plans to hold the bonds—this is often referred to as his or her investment horizon.

• If you hold long-term bonds, you will face significant price risk because the value of your portfolio will decline if interest rates rise, but you will not face much reinvestment risk because your income will be stable. • On the other hand, if you hold short-term bonds, you will not be exposed to much price risk, but you will be exposed to significant reinvestment risk. Consequently, investors with shorter investment horizons should view long-term bonds as being more risky than short-term bonds. By contrast, the reinvestment risk inherent in short-term bonds is especially relevant to investors with longer investment horizons.

Assessing a Bond's Riskiness In this section, we identify and explain the two key factors that impact a bond's riskiness.

• Price Risk • Reinvestment Risk

Bonds are grouped in several ways. One grouping is based on the issuer:

• the U.S. Treasury, • corporations, • state and local governments, and • foreigners. Each bond differs with respect to risk and consequently its expected return.