FIN 300 â Chapter 7: Interest Rates and Bond Valuation 7.1 Bonds ...
FIN 300 – Chapter 7: Interest Rates and Bond Valuation 7.1 Bonds and Bond Valuation When a corporation or a government wishes to borrow money from the public on a long-term basis, it usually does so by issuing or selling debt securities that are generically called bonds. Bond Features and Prices Bond is normally an interest-only loan, meaning the borrower pays the interest every period, but none of the principal is repaid until the end of the loan. Coupons – The stated interest payments made on a bond. o If coupon is constant and paid every year, those types of bonds are called level coupon bond. Face Value – The principal amount of a bond hat is repaid at the end of the term. Also called par value. Coupon Rate – The annual coupon divided by the face value of a bond. Maturity Date – Specified date at which the principal amount of a bond is paid. o Once a bond is issued, the number of years to maturity declines as time goes by. Bond Values and Yields Interest rates change in the marketplace as time goes by, but the cash flows from a bond, however, stay the same because the coupon rate and maturity date are specified when it is issued. o Due to this, the value of the bond fluctuates. o When interest rates rise, the PV of the bond‟s remaining cash flows declines, and the bond is worth less. When interest rates fall, the bond is worth more. To determine the value of a bond on a particular date; the number of periods remaining until maturity, the face value, the coupon, and the market interest rate for bonds with similar features is needed. o Yield to Maturity (YTM) – The market interest rate that equates a bond‟s present value of interest payments and principal repayment with its price. A bond that sells for less than face value, or at a discount, is called a discount bond. A bond that sells for more than face value, or at a premium, is called a premium bond. A general expression can be created for the value of a bond. If a bond has (1) a face value of F paid at maturity, (2) a coupon of C paid per period, (3) t periods to maturity, and (4) a yield of r per period, its value is: o Bond Value = C × (1 – 1/(1 + r)t)/r + F/(1+r)t o Bond Value = PV of the coupons + PV of the face amount Bond prices and interest rates (or market yields) are inversely related and move in opposite directions. Most bonds are issued at par, with the coupon rate set equal to the prevailing market yield or interest rate. Interest Rate Risk The risk that relates for bond owners from fluctuating interest rates (market yields) is called interest rate risk. Interest risk a bond has depends on how sensitive its price is to interest rate changes. o Sensitivity directly depends on two things: the time to maturity and the coupon rate. Keep these two things in mind when looking at a bond: 1. All other things equal, the longer the time to maturity, the greater the interest rate risk. 2. All other things equal, the lower the coupon rate, the greater the interest rate risk.
Finding the Yield to Maturity The only way to find the yield to maturity is through trial and error because you cannot solve the equation because of the equation and the one unknown, r. o You can speed up the trial and error method by knowing bond prices. If the bond is selling at discount, then the coupon rate is suppose to be higher, but if it is selling at a premium, then the coupon rate should be lower. 7.2 More on Bond Features Securities issued by corporations may be classified as equity securities and debt securities. The person or firm making the loan is called the creditor or lender. The corporation borrowing the money is called the debtor, or borrower. There are three major differences between debt and equity: o Debt is not an ownership interest in the firm. Generally no voting power. o Corporation‟s payment of interest on debt is considered a cost of doing business and is fully tax deductible. Dividends paid to shareholders are not tax deductible. o Unpaid debt is a liability of the firm. If not paid, creditors can legally claim the assets of the firm; can result in liquidation and reorganization. Is It Debt or Equity? General rule, equity represents an ownership interest, and it is a residual claim. o Equity holders are paid after debt holders. The risks and benefits associated with owning debt and equity are different. o The maximum reward for owning a debt security is ultimately fixed by the amount of the loan, whereas there is no upper limit to the potential reward from owning an equity interest. Long-Term Debt: The Basics Long-term debt securities are promises by the issuing firm to pay the principal when due and to make timely interest payments on the unpaid balance. The maturity of a long-term debt instrument refers to the length of time the debt remains outstanding with some unpaid balance. Debt securities are typically called notes, debentures, or bonds. The two major forms of long-term debt are public-issue and privately placed. o Main difference between public and private is that the latter is directly placed with a lender and not offered to the public. The Indenture Indenture – Written agreement between the corporation and the lender detailing the terms of the debt issue, it is also known as the deed of trust. Usually a trust company is hired to represent the bondholders. The trust company must (1) make sure the terms of the indenture are obeyed, (2) manage the sinking fund, and (3) represent the bondholders in default, that is, if the company defaults on its payments to them. The indenture is a large document that is very important and generally includes the following provisions: (1) basic terms of the bonds, (2) amount of bonds issued, (3) description of property used as security if he bonds are secured, (4) repayment agreements, (5) call provisions, and (6) details of protective covenants. Terms of Bond Registered Form – Registrar of company records ownership of each bond; payment is made directly to the owner of record. o Cheque or a coupon attached to the bond certificate is sent for interest payments.
Bearer Form – Bond issued without record of the owner‟s name; payment is made to whoever holds the bond. o Certificate is basic evidence of ownership, and corporation pays the bearer. o Two drawbacks: (1) difficult to recover if lost or stolen, and (2) company doesn‟t know who owns bonds, so can‟t notify bondholders of important events. o The advantage: easing transactions for investors who trade their bonds frequently. Security Debt securities are classified according to the collateral and mortgages used to protect the bondholder. Collateral is a general term that means securities pledged as security for payment. o Usually of stock or bonds. Mortgage Securities are secured by a mortgage on real property of the borrower. o Real estate, transportation, or other property is valid. o Can also be called mortgage trust indenture or trust deed. o Specific property = chattel mortgage, all real property = blanket mortgage Debenture – Unsecured debt, usually with a maturity of 10 years or more. Note – Unsecured debt, usually with a maturity under 10 years. Seniority Seniority indicates preference in position over other lenders, and debts are sometimes labelled as “senior” or “junior” to indicate seniority. Some debt is subordinated, which means that in the event of a default, holders of subordinated debt must give preference to other specified creditors. Repayment Bonds can be repaid at maturity, at which time the bondholder receives the stated or face value of the bonds, or they may be repaid in part or in entirety before maturity. Sinking Fund – Account managed by the bond trustee for early bond redemption. Reduces the risk that the company will be unable to repay the principal at maturity, it also improves the marketability of the bonds. The Call Provision Call Provision – Agreement giving the corporation the option to repurchase the bond at a specified price before maturity. Call Premium – Amount by which the call price exceeds the par value of the bond. Deferred Call – Call provision prohibiting the company from redeeming the bond before a certain date. Call Protected – Bond during period in which it cannot be redeemed by the issuer. Canada Plus Call – Call provision which compensates bond investors for interest differential, making call unattractive for issuer. Protective Covenants Protective Covenants – Part of the indenture limiting certain transactions that can be taken during the term of the loan, usually protect the lender‟s interest. o Reduce agency costs faced by bondholders and by controlling company activities, they reduce the risk of the bonds. Classified into two types: negative covenants and positive (or affirmative) covenants. o A negative covenant is a “thou shall not” because it limits and prohibits actions that the company may take. o Positive covenant is a “thou shalt” because it specifies actions that the company agrees to take or a condition the company must abide by. 7.3 Bond Ratings Firms frequently pay to have their debt rated.
The debt ratings are an assessment of the creditworthiness of the corporate issuer. o Creditworthiness – how likely the firm is to default and what protection creditors have in the event of a default. Ratings only concern the possibility of default. Highest rating a firm can have is AAA and such debt is judged to be the best quality and to have the lowest degree of risk. AA is good quality. Junk bonds are also called high-yield bonds.
7.4 Some Different Types of Bonds There are many types of bonds that can be issued, which are the products of financial engineering: stripped bonds, floating-rate bonds, and others. Financial Engineering When financial managers or their investment bankers design new securities or financial processes, their efforts are referred to as financial engineering. o Successful engineering reduces risk, and minimizes taxes. o Also seeks to reduce financing costs of issuing and servicing debt as well as cost of complying with rules laid down by regulatory authorities. When applied to debt securities, a hybrid security is created that have features of equity but are debt. o Convertible bond – can change bond to shares. Stripped Bonds Stripped Bonds/Zero-Coupon Bonds – A bond that makes no coupon payments, thus initially priced at a deep discount. Start life as normal coupon bonds but investment dealers engage in bond stripping when they sell the principal and coupon separately. Floating-Rate Bonds The coupon payments are adjustable. Introduced to control the risk of price fluctuation as interest rates change. Majority of floater bonds have the features that the holder has the right to redeem his or her note at par on the coupon payment date after some specified amount of time, this is called put provision. o Also the coupon rate has a floor and a ceiling. Other Types of Bonds Income bonds are where the coupon payments depend on company income. o Coupons paid only if company‟s income is sufficient. o Purchasers of these bonds receive favourable tax treatment on interest received. Real return bonds have coupons and principal indexed to inflation to provide a stated real return. Convertible bonds can be swapped for a fixed number of shares of stock anytime before maturity at the holder‟s option. Asset-backed bonds are backed by a diverse pool of illiquid assets such as accounts receivable collections, credit card debt, or mortgages. Retractable Bonds – Bonds that may be sold back to the issuer at a pre-specified price before maturity. 7.5 Bond Markets Bonds are bought and sold on a daily basis and that too in enormous quantites.
How Bonds are Bought and Sold Most trading in bonds takes place over the counter. o Means no particular place for buying and selling to occur. o Bond market due to this has little or no transparency. Transparency means to easily observe its prices and trading volume. More bonds are issued than stock. Since the lack of transparency in the bond market, getting up-to-date prices on individual bonds is often difficult or impossible, particularly for smaller corporate or municipal issues. A Note on Bond Price Quotes Clean Price – The price of a bond net of accrued interest; this is the price that is typically quoted. Dirty Price – The price of a bond including accrued interest, also known as the full or invoice price. This is the price the buyer actually pays. 7.6 Inflation and Interest Rates Inflation also has an impact on bonds along with interest rates, yields, and returns. Real versus Nominal Rates Real Rates – Interest rates or rates of return that have been adjusted for inflation. Nominal Rates – Interest rates or rates of return that have not been adjusted for inflation. The nominal rate on an investment is the percentage change in the number of dollars you have. The real rate on an investment is the percentage change in how much you can buy with your dollars, in other words, the percentage change in your buying power. The Fisher Effect Fisher Effect – The relationship between nominal returns, real returns, and inflation. Let R stand for the nominal rate, let r stand for the real rate, and let h stand for the inflation rate. Due to the relationship between nominal rates, real rates, and inflation, a formula can be written: o 1 + R = (1 + r) × (1 + h) We can also rearrange things and create different formulas o R=r+h+r×h This tells us that the nominal rate has three components. 1. Real rate on the investment, r. 2. Compensation for the decrease in the value of the money originally invested because of inflation, h. 3. Compensation for the fact that the dollars earned on the investment are also worth less because of inflation. Since the third component is usually small it is dropped and then the nominal rate is approximately equal to the real rate plus the inflation rate: o R≈r+h Financial rates, such as interest rates, discount rates, and rates of return, are almost always quoted in nominal returns, meaning they are not adjusted for inflation. Inflation and Present Values Either discount nominal cash flows at a nominal rate or discount real cash flows at a real rate. o As long as you are consistent, the answer will remain the same. 7.7 Determinants of Bond Yields The yield on any particular bond is a reflection of a variety of factors, some common to all bonds and some specific to the issue under consideration.
The Term Structure of Interest Rates Term Structure of Interest Rates – The relationship between nominal interest rates on default-free, pure discount securities, and time to maturity; that is, the pure time value of money. o Tells us what nominal interest rates are on default-free, pure discount bonds of all maturities. When long-term rates are higher than short-term rates, the term structure is upward sloping. When short-term rates are higher, the term structure is downward sloping. Term structure can also be „humped‟. Interest rates increase at first, but then begin to decline as we look at a longer and longer term rates. The shape of the term structure is based on three basic components: o The real rate of interest Compensation investors demand for forgoing h use of their money. o Rate of inflation Pure time value of money after adjusting for the effects of inflation. o Interest rate risk Longer-term bonds have greater risk than shorter-term bonds. Real interest rate is the basic component underlying every interest rate; regardless of the time of maturity. o Real rate is high; all interest rates will tend to be higher, and vice versa. o Doesn‟t really determine the term structure shape, instead, it mostly influences the overall level of interest rates. Prospect of future inflation very strongly influences the shape of the term structure. o Inflation Premium – The portion of a nominal interest rate that represents compensation for expected future inflation. If rate of inflation will be higher in the future, then long-term nominal interest rates will be higher than short-term causing an upwards-sloping term structure. Interest Rate Risk Premium – The compensation investors demand for bearing interest rate risk. o Longer the term for maturity, the greater the interest rate risk premium increases with maturity. Bond Yields and the Yield Curve: Putting It All Together Canada Yield Curve – A plot of the yields on Government of Canada notes and bonds relative to maturity. o Default-free, taxable, and they are highly liquid. Default Risk Premium – The portion of a nominal interest rate or bond yield that represents compensation for the possibility of default. Liquidity Premium – The portion of a nominal interest rate or bond yield that represents compensation for lack of liquidity. Conclusion Bond yields represent the combined effects of no fewer than six things: o Real rate of interest o Expected future inflation o Interest rate risk o Default risk o Tax status o Lack of liquidity
Finding the Yield to Maturity The only way to find the yield to maturity is through trial and error because you cannot solve the equation because of the equation and the one unknown, r. o You can speed up the trial and error method by knowing bond prices. If the bond is selling at discount, then the coupon rate is suppose to be higher, but if it is selling at a premium, then the coupon rate should be lower. 7.2 More on Bond Features Securities issued by corporations may be classified as equity securities and debt securities. The person or firm making the loan is called the creditor or lender. The corporation borrowing the money is called the debtor, or borrower. There are three major differences between debt and equity: o Debt is not an ownership interest in the firm. Generally no voting power. o Corporation‟s payment of interest on debt is considered a cost of doing business and is fully tax deductible. Dividends paid to shareholders are not tax deductible. o Unpaid debt is a liability of the firm. If not paid, creditors can legally claim the assets of the firm; can result in liquidation and reorganization. Is It Debt or Equity? General rule, equity represents an ownership interest, and it is a residual claim. o Equity holders are paid after debt holders. The risks and benefits associated with owning debt and equity are different. o The maximum reward for owning a debt security is ultimately fixed by the amount of the loan, whereas there is no upper limit to the potential reward from owning an equity interest. Long-Term Debt: The Basics Long-term debt securities are promises by the issuing firm to pay the principal when due and to make timely interest payments on the unpaid balance. The maturity of a long-term debt instrument refers to the length of time the debt remains outstanding with some unpaid balance. Debt securities are typically called notes, debentures, or bonds. The two major forms of long-term debt are public-issue and privately placed. o Main difference between public and private is that the latter is directly placed with a lender and not offered to the public. The Indenture Indenture – Written agreement between the corporation and the lender detailing the terms of the debt issue, it is also known as the deed of trust. Usually a trust company is hired to represent the bondholders. The trust company must (1) make sure the terms of the indenture are obeyed, (2) manage the sinking fund, and (3) represent the bondholders in default, that is, if the company defaults on its payments to them. The indenture is a large document that is very important and generally includes the following provisions: (1) basic terms of the bonds, (2) amount of bonds issued, (3) description of property used as security if he bonds are secured, (4) repayment agreements, (5) call provisions, and (6) details of protective covenants. Terms of Bond Registered Form – Registrar of company records ownership of each bond; payment is made directly to the owner of record. o Cheque or a coupon attached to the bond certificate is sent for interest payments.
Bearer Form – Bond issued without record of the owner‟s name; payment is made to whoever holds the bond. o Certificate is basic evidence of ownership, and corporation pays the bearer. o Two drawbacks: (1) difficult to recover if lost or stolen, and (2) company doesn‟t know who owns bonds, so can‟t notify bondholders of important events. o The advantage: easing transactions for investors who trade their bonds frequently. Security Debt securities are classified according to the collateral and mortgages used to protect the bondholder. Collateral is a general term that means securities pledged as security for payment. o Usually of stock or bonds. Mortgage Securities are secured by a mortgage on real property of the borrower. o Real estate, transportation, or other property is valid. o Can also be called mortgage trust indenture or trust deed. o Specific property = chattel mortgage, all real property = blanket mortgage Debenture – Unsecured debt, usually with a maturity of 10 years or more. Note – Unsecured debt, usually with a maturity under 10 years. Seniority Seniority indicates preference in position over other lenders, and debts are sometimes labelled as “senior” or “junior” to indicate seniority. Some debt is subordinated, which means that in the event of a default, holders of subordinated debt must give preference to other specified creditors. Repayment Bonds can be repaid at maturity, at which time the bondholder receives the stated or face value of the bonds, or they may be repaid in part or in entirety before maturity. Sinking Fund – Account managed by the bond trustee for early bond redemption. Reduces the risk that the company will be unable to repay the principal at maturity, it also improves the marketability of the bonds. The Call Provision Call Provision – Agreement giving the corporation the option to repurchase the bond at a specified price before maturity. Call Premium – Amount by which the call price exceeds the par value of the bond. Deferred Call – Call provision prohibiting the company from redeeming the bond before a certain date. Call Protected – Bond during period in which it cannot be redeemed by the issuer. Canada Plus Call – Call provision which compensates bond investors for interest differential, making call unattractive for issuer. Protective Covenants Protective Covenants – Part of the indenture limiting certain transactions that can be taken during the term of the loan, usually protect the lender‟s interest. o Reduce agency costs faced by bondholders and by controlling company activities, they reduce the risk of the bonds. Classified into two types: negative covenants and positive (or affirmative) covenants. o A negative covenant is a “thou shall not” because it limits and prohibits actions that the company may take. o Positive covenant is a “thou shalt” because it specifies actions that the company agrees to take or a condition the company must abide by. 7.3 Bond Ratings Firms frequently pay to have their debt rated.
The debt ratings are an assessment of the creditworthiness of the corporate issuer. o Creditworthiness – how likely the firm is to default and what protection creditors have in the event of a default. Ratings only concern the possibility of default. Highest rating a firm can have is AAA and such debt is judged to be the best quality and to have the lowest degree of risk. AA is good quality. Junk bonds are also called high-yield bonds.
7.4 Some Different Types of Bonds There are many types of bonds that can be issued, which are the products of financial engineering: stripped bonds, floating-rate bonds, and others. Financial Engineering When financial managers or their investment bankers design new securities or financial processes, their efforts are referred to as financial engineering. o Successful engineering reduces risk, and minimizes taxes. o Also seeks to reduce financing costs of issuing and servicing debt as well as cost of complying with rules laid down by regulatory authorities. When applied to debt securities, a hybrid security is created that have features of equity but are debt. o Convertible bond – can change bond to shares. Stripped Bonds Stripped Bonds/Zero-Coupon Bonds – A bond that makes no coupon payments, thus initially priced at a deep discount. Start life as normal coupon bonds but investment dealers engage in bond stripping when they sell the principal and coupon separately. Floating-Rate Bonds The coupon payments are adjustable. Introduced to control the risk of price fluctuation as interest rates change. Majority of floater bonds have the features that the holder has the right to redeem his or her note at par on the coupon payment date after some specified amount of time, this is called put provision. o Also the coupon rate has a floor and a ceiling. Other Types of Bonds Income bonds are where the coupon payments depend on company income. o Coupons paid only if company‟s income is sufficient. o Purchasers of these bonds receive favourable tax treatment on interest received. Real return bonds have coupons and principal indexed to inflation to provide a stated real return. Convertible bonds can be swapped for a fixed number of shares of stock anytime before maturity at the holder‟s option. Asset-backed bonds are backed by a diverse pool of illiquid assets such as accounts receivable collections, credit card debt, or mortgages. Retractable Bonds – Bonds that may be sold back to the issuer at a pre-specified price before maturity. 7.5 Bond Markets Bonds are bought and sold on a daily basis and that too in enormous quantites.
How Bonds are Bought and Sold Most trading in bonds takes place over the counter. o Means no particular place for buying and selling to occur. o Bond market due to this has little or no transparency. Transparency means to easily observe its prices and trading volume. More bonds are issued than stock. Since the lack of transparency in the bond market, getting up-to-date prices on individual bonds is often difficult or impossible, particularly for smaller corporate or municipal issues. A Note on Bond Price Quotes Clean Price – The price of a bond net of accrued interest; this is the price that is typically quoted. Dirty Price – The price of a bond including accrued interest, also known as the full or invoice price. This is the price the buyer actually pays. 7.6 Inflation and Interest Rates Inflation also has an impact on bonds along with interest rates, yields, and returns. Real versus Nominal Rates Real Rates – Interest rates or rates of return that have been adjusted for inflation. Nominal Rates – Interest rates or rates of return that have not been adjusted for inflation. The nominal rate on an investment is the percentage change in the number of dollars you have. The real rate on an investment is the percentage change in how much you can buy with your dollars, in other words, the percentage change in your buying power. The Fisher Effect Fisher Effect – The relationship between nominal returns, real returns, and inflation. Let R stand for the nominal rate, let r stand for the real rate, and let h stand for the inflation rate. Due to the relationship between nominal rates, real rates, and inflation, a formula can be written: o 1 + R = (1 + r) × (1 + h) We can also rearrange things and create different formulas o R=r+h+r×h This tells us that the nominal rate has three components. 1. Real rate on the investment, r. 2. Compensation for the decrease in the value of the money originally invested because of inflation, h. 3. Compensation for the fact that the dollars earned on the investment are also worth less because of inflation. Since the third component is usually small it is dropped and then the nominal rate is approximately equal to the real rate plus the inflation rate: o R≈r+h Financial rates, such as interest rates, discount rates, and rates of return, are almost always quoted in nominal returns, meaning they are not adjusted for inflation. Inflation and Present Values Either discount nominal cash flows at a nominal rate or discount real cash flows at a real rate. o As long as you are consistent, the answer will remain the same. 7.7 Determinants of Bond Yields The yield on any particular bond is a reflection of a variety of factors, some common to all bonds and some specific to the issue under consideration.
The Term Structure of Interest Rates Term Structure of Interest Rates – The relationship between nominal interest rates on default-free, pure discount securities, and time to maturity; that is, the pure time value of money. o Tells us what nominal interest rates are on default-free, pure discount bonds of all maturities. When long-term rates are higher than short-term rates, the term structure is upward sloping. When short-term rates are higher, the term structure is downward sloping. Term structure can also be „humped‟. Interest rates increase at first, but then begin to decline as we look at a longer and longer term rates. The shape of the term structure is based on three basic components: o The real rate of interest Compensation investors demand for forgoing h use of their money. o Rate of inflation Pure time value of money after adjusting for the effects of inflation. o Interest rate risk Longer-term bonds have greater risk than shorter-term bonds. Real interest rate is the basic component underlying every interest rate; regardless of the time of maturity. o Real rate is high; all interest rates will tend to be higher, and vice versa. o Doesn‟t really determine the term structure shape, instead, it mostly influences the overall level of interest rates. Prospect of future inflation very strongly influences the shape of the term structure. o Inflation Premium – The portion of a nominal interest rate that represents compensation for expected future inflation. If rate of inflation will be higher in the future, then long-term nominal interest rates will be higher than short-term causing an upwards-sloping term structure. Interest Rate Risk Premium – The compensation investors demand for bearing interest rate risk. o Longer the term for maturity, the greater the interest rate risk premium increases with maturity. Bond Yields and the Yield Curve: Putting It All Together Canada Yield Curve – A plot of the yields on Government of Canada notes and bonds relative to maturity. o Default-free, taxable, and they are highly liquid. Default Risk Premium – The portion of a nominal interest rate or bond yield that represents compensation for the possibility of default. Liquidity Premium – The portion of a nominal interest rate or bond yield that represents compensation for lack of liquidity. Conclusion Bond yields represent the combined effects of no fewer than six things: o Real rate of interest o Expected future inflation o Interest rate risk o Default risk o Tax status o Lack of liquidity
