Chapter 6: Bond Valuation and Interest Rates
Chapter 6: Bond Valuation and Interest Rates
Bonds: long-term debt instruments that promise fixed payments and have maturities of longer than 7 years o Major source of financing for companies Notes: bonds with maturities b/w one and seven years Bills or paper: short-term bonds w/ a maturity of less than one year
6.1 The Basic Structure of Bonds
Key feature of bond is that the issuer agrees to pay the bondholder (investor) a regular series of cash payments and to repay the full principal amount by maturity date Although many payment structures are possible, the traditional “coupon-paying” bond provides for identical payments at regular intervals (usually semi-annually or annually) with the full principal to be repaid at the stated maturity rate Bullet payment/ balloon payment: a principal payment made in one lump sum at maturity Bonds are not referred to as fixed income securities b/c the interest payments and the principal repayment are specified or fixed at the time the bond is issued Difference b/w loan/mortgage payments and bond payments: loans and mortgage payments include principal repayment and interest payments whereas bond payments are regular interest payments throughout its life and a balloon payment of principal at maturity
Basic Bond Terminology
Bond indenture: a legal document that specifies the payment requirements and all other salient matters relating to a particular bond issue (e.g. collateral for the bond), held and administered by a trust company Bond indentures include basic features attached to cash payments: o Par value=face value= maturity value: represents the amount that is paid at maturity for traditional bonds Bond prices are typically quoted based on a par value of 100. In other words, if the price of a bond is quoted at 99.583, a $1000 par value bond would be selling for $995.83 o Terms to maturity of a bond: time remaining until the maturity date o Interest payments=coupons: determined by multiplying the coupon rate (which is stated on an annual basis) by the par value of the bond
Security and Protective Provisions
Mortgage bonds: debt instruments that are secured by real assets
Debentures: debt instruments that are similar to bonds but are generally unsecured or are secured by a general floating charge over the company’s unencumbered assets (i.e. assets that have not been pledged as security for other debt obligations)—e.g. govt bonds Collateral trust bonds: secured by a pledge of other financial assets (e.g. common shares, bonds or treasury bills) Equipment trust certificates: secured by equipment Protective covenants: clauses in a trust indenture that restrict the actions of the issuer; covenants can be positive or negative
Additional Bond Features
Good for bondholder
Callable bonds: bonds that give the issuer the option to “call” or repurchase outstanding bonds at predetermined prices at specified times (risk for bondholder) Retractable bonds: allow the bondholder to sell the bonds back to the issuer at predetermined prices at specified times earlier than the maturity date (maturity of bond is shortened) Extendible bonds: allow the bondholder to extend the maturity date of the bond Sinking fund provisions: the requirement that an issuer set aside funds each year to be used to pay off the debt at maturity (two ways to do this): 1. Firm repurchases a certain amount of debt each yr so that the amount of debt goes down 2. The firm pays money into the sinking fund to buy other bonds, usually govt bonds, so that money is available at maturity to pay off the debt, although the amount due at maturity is unchanged Purchase fund provisions: similar to sinking fund provisions but they require the repurchase of a certain amount of debt only if it can be repurchased at or below a given price Convertible bonds: bonds that can be converted into common shares at predetermined conversion prices
6.2 Bond Valuation
The price of a bond equals the present value of the future payments on the bond which is the present value of the interest payments and the par value repaid at maturity
B= bond price, I=interest/coupon payments, kb= the bond discount rate or market rate, n= the term to maturity, F= the face (par) value of the bond Interest payments are multiplied by the standard present value annuity factor while the par value is multiplied by the present value interest factor Discount/premium: the difference b/w the bond’s par value and the price it trades at, when it trades below (above) the par value o Couple rate< market rate When investing in bonds, if interest rates increase, the market prices of bonds decline and vice versa The longer the time to maturity, the more sensitive the bond price is to changes in market rates o Therefore, it is a disadvantage for the investor Interest rate risk: sensitivity of bond prices to changes in interest rates Duration: an important measure of interest rate risk that incorporates several factors 1. The prices of bonds w/ higher durations are more sensitive to interest rate changes than are those w/ lower durations 2. All else being equal, durations will be higher when (1) market yields are lower, (2) bonds have longer maturities and (3) bonds have lower coupons Yield: describes the amount in cash that returns to the owners of a security
Cash Prices versus Quoted Prices:
Prices reported in the media are referred to as “quoted” prices These differ from the actual prices investors pay for bonds whenever bonds are sold at a date other than the date of a coupon payment Therefore, bond purchaser must pay the bond seller the quoted price plus the accrued interest on the bond (AKA “cash price” of the bond)
6.3 Bond Yields
Yield to maturity (YTM): the discount rate used to evaluate bonds o The yield that an investor would realize if he or she bought the bond at the current price, held it to maturity, received all the promised payments on their scheduled dates and reinvested all he cash flows received at the YTM o Use the same formula as above except calculate for kb instead of B:
o
A special form of internal rate of return (IRR)
Yield to Call (YTC):
The yield that is associated w/ a bond’s first call date is known as yield to call Similar to above formula except replace time to maturity (n) w/ the time to first call (c), replace face value (F) with the call price (CP)
If call price is above its current market price, it is unlikely that the bond would be called back by the issuer (selling based on its YTM rather than its YTC)
Current Yield (CY):
Current Yield= Flat Yield= Cash Yield: the ratio of the annual coupon interest divided by the current market price
Price-Yield Relationships Bond Price Par Discount Premium
Relationship Coupon Rate=CY=YTM Coupon Rate < CY < YTM Coupon Rate > CY > YTM
6.4 Interest Rate Determinants Base Interest Rates: Similar to law of supply and demand
Changes in interest rates are referred in terms of “basis points,” each of which represents 1/100th of 1 percent (AKA a decrease in 10 basic pts implies interest rates declined 0.1%) When demand for loans increase, price also increases and thus, interest rates also increase When supply for loans increase, interest rates decrease Nominal interest rates: the rates charged for lending today’s dollars in return for getting dollars back in the future, w/o taking into account the purchasing power of those future dollars
Risk-free rate (RF): the rate of return on risk-free investments which is often used as the base interest rate o RF= Real rate + Expected inflation o Interest rates will be low when expected inflation is low and high when expected inflation is high Default Free: having no risk of non-payment
Global Influences on Interest Rates:
Although interest rates vary from one country to the next, global interest rates interact w/ one another o Foreign exchange restrictions have been removed which allows capital to flow between countries o Canada’s interest rates are heavily influenced by prevailing rates in other countries, esp. U.S. Investors may not invest in bonds of countries offering higher interest rates and companies may not issue bonds in countries w/ lower interest rates because the additional gains could easily be cancelled out (and can incur large losses) as a result of adverse movements in the foreign exchange rates prevailing when funds are converted back into domestic currency Investing or issuing debt abroad creates foreign exchange risks, which offsets the potential advantages that may arise from inter-country interest rate differentials Interest rate parity (IRP) theory: a theory that demonstrates how differences in interest rates b/w countries are offset by expected changes in exchange rates o Theory states that forward exchange rates, which can be locked in today in order to eliminate foreign exchange risk, will be established at levels that ensure investors will end up w/ the same amount whether they invest at home or in another country (w/ no foreign exchange risk) o If Canada had high inflation and high interest rates and US investor bough Cdn bonds in an attempt to benefit from Cda’s higher rates, they would lose these gains when he/she converted the Canadian dollar payments back into US dollars
The Term Structure of Interest Rates:
One important factor affecting debt yields is related to the terms of maturity Term Structure of Interest Rates: the relationship b/w the interest rates and the term to maturity on underlying debt instruments Yield curve: the graphic representation of the term structure of interest rates, based on debt instruments from the same issuer Several theories attempt to account for the various shapes and movements of the yield curve. 3 of the most popular theories are: 1. Liquidity preference theory: a theory that suggests that investors prefer short-term debt instruments (i.e. more liquid instruments) because they exhibit less interest rate
risk while debt issuers prefer to lock in borrowing rates for longer periods to avoid the risk of having to refinance at higher rates. Therefore, issuers must provide investors w/ higher yields to induce them to invest in longer-term bonds. It’s upward sloping b/c long-term rates > than short term rates 2. Expectations theory: a theory that argues that the yield curve reflects investor expectations about future interest rates. Therefore, an upward-sloping yield curve reflects expectations of interest rate increases in the future and a downward-sloping curve reflects expectations of interest rate decreases in the future 3. Market segmentations theory: a theory that suggests that distinct markets (or market segments) exist for interest rate securities of various maturities and that rates are determined w/i these independent market segments by the forces of supply and demand w/i that market
Risk Premiums:
Investors expect extra compensation for assuming additional risks and therefore, they require higher returns. Kb= RF +/- Maturity yield differential +Spread
Spread: a difference in yield that compensates the investor for the assumption of additional risks, which may include some or all of (1) default or credit risk, (2) liquidity, (3) issue-specific features Default risk: the risk associated w/ the bond issuer and its ability to pay o Bondholders require higher yields to compensate them for the possibility that the borrower may default on the promised debt payments Debt ratings: ratings assigned by professional debt-rating services after detailed analyses of bond issuers to determine their ability to sustain the required interest and principal payments o Investment-grade bonds: those w/ bond ratings of BBB and higher o Junk (high-yield or low grade) bonds: bonds with ratings below BBB Some bonds are more liquid than others which means that they are easier to buy and sell and that the required price concessions are lower Liquidity premium: an additional yield offered on bonds that are less liquid Issue-specific premiums: premiums that arise when bonds have features that cause them to be more or less attractive to investors relative to straight (option-free) bonds
6.5 Other Types of Bonds/ Debt Instruments Treasury Bills (T-Bills):
T-Bills: short-term govt debt obligations that mature in one yr or less
Partly b/c of this short term to maturity, they do not make regular interest payments but are sold at a discount from their par value which is paid on the maturity date
Interest earned is the difference b/w purchase price & the face value
P= present value, F= future payment (AKA par value that is to be repaid at maturity), kBEY= bond equivalent yield, n= term to maturity (expressed as # of days)
In the US, the T-Bills formula is a little different:
Zero Coupon Bonds:
Zero coupon bonds (or zero): a bond that is issued at a discount, pays no coupons and repays the par value at the maturity date The return earned represents the difference b/w the purchase price and the redemption price Redemption Price: The price at which a bond may be repurchased by the issuer before maturity
The market prices of zero coupon bonds are even more sensitive to interest rate changes b/c they make no coupon payments at all
Floating Rate and Real Return Bonds:
Floating rate bonds (floaters): bonds that have adjustable coupons that are usually tied to some variable short-term rate o Differ from traditional fixed-income bonds b/c the coupon rates increase as interest rates increase and vice versa
o
Floaters provide protection against rising interest rates and tend to trade near their par value Real Return Bonds: bonds issued by the Government of Canada that provide investors w/ protection against inflation by providing a real yield
Canada Savings Bonds (CSBs):
Canada Savings Bonds: bonds issued by the Government of Canada that have no secondary market and can’t be traded so their prices do not change over time Rates of return on CSBs vary through time 1. Regular interests which pays out annual interest amounts 2. Compound interest which reinvest the interest so interest is also earned on accumulated interest (producing the power of compounding)
Appendix 6A: Interest Rate Parity
F= the current forward exchange rate expressed in the number of units of domestic currency required to purchase one unit of the foreign currency S= the current spot exchange rate Kdomestic= the domestic interest rate Kforeign= the foreign interest rate
Bonds: long-term debt instruments that promise fixed payments and have maturities of longer than 7 years o Major source of financing for companies Notes: bonds with maturities b/w one and seven years Bills or paper: short-term bonds w/ a maturity of less than one year
6.1 The Basic Structure of Bonds
Key feature of bond is that the issuer agrees to pay the bondholder (investor) a regular series of cash payments and to repay the full principal amount by maturity date Although many payment structures are possible, the traditional “coupon-paying” bond provides for identical payments at regular intervals (usually semi-annually or annually) with the full principal to be repaid at the stated maturity rate Bullet payment/ balloon payment: a principal payment made in one lump sum at maturity Bonds are not referred to as fixed income securities b/c the interest payments and the principal repayment are specified or fixed at the time the bond is issued Difference b/w loan/mortgage payments and bond payments: loans and mortgage payments include principal repayment and interest payments whereas bond payments are regular interest payments throughout its life and a balloon payment of principal at maturity
Basic Bond Terminology
Bond indenture: a legal document that specifies the payment requirements and all other salient matters relating to a particular bond issue (e.g. collateral for the bond), held and administered by a trust company Bond indentures include basic features attached to cash payments: o Par value=face value= maturity value: represents the amount that is paid at maturity for traditional bonds Bond prices are typically quoted based on a par value of 100. In other words, if the price of a bond is quoted at 99.583, a $1000 par value bond would be selling for $995.83 o Terms to maturity of a bond: time remaining until the maturity date o Interest payments=coupons: determined by multiplying the coupon rate (which is stated on an annual basis) by the par value of the bond
Security and Protective Provisions
Mortgage bonds: debt instruments that are secured by real assets
Debentures: debt instruments that are similar to bonds but are generally unsecured or are secured by a general floating charge over the company’s unencumbered assets (i.e. assets that have not been pledged as security for other debt obligations)—e.g. govt bonds Collateral trust bonds: secured by a pledge of other financial assets (e.g. common shares, bonds or treasury bills) Equipment trust certificates: secured by equipment Protective covenants: clauses in a trust indenture that restrict the actions of the issuer; covenants can be positive or negative
Additional Bond Features
Good for bondholder
Callable bonds: bonds that give the issuer the option to “call” or repurchase outstanding bonds at predetermined prices at specified times (risk for bondholder) Retractable bonds: allow the bondholder to sell the bonds back to the issuer at predetermined prices at specified times earlier than the maturity date (maturity of bond is shortened) Extendible bonds: allow the bondholder to extend the maturity date of the bond Sinking fund provisions: the requirement that an issuer set aside funds each year to be used to pay off the debt at maturity (two ways to do this): 1. Firm repurchases a certain amount of debt each yr so that the amount of debt goes down 2. The firm pays money into the sinking fund to buy other bonds, usually govt bonds, so that money is available at maturity to pay off the debt, although the amount due at maturity is unchanged Purchase fund provisions: similar to sinking fund provisions but they require the repurchase of a certain amount of debt only if it can be repurchased at or below a given price Convertible bonds: bonds that can be converted into common shares at predetermined conversion prices
6.2 Bond Valuation
The price of a bond equals the present value of the future payments on the bond which is the present value of the interest payments and the par value repaid at maturity
B= bond price, I=interest/coupon payments, kb= the bond discount rate or market rate, n= the term to maturity, F= the face (par) value of the bond Interest payments are multiplied by the standard present value annuity factor while the par value is multiplied by the present value interest factor Discount/premium: the difference b/w the bond’s par value and the price it trades at, when it trades below (above) the par value o Couple rate< market rate When investing in bonds, if interest rates increase, the market prices of bonds decline and vice versa The longer the time to maturity, the more sensitive the bond price is to changes in market rates o Therefore, it is a disadvantage for the investor Interest rate risk: sensitivity of bond prices to changes in interest rates Duration: an important measure of interest rate risk that incorporates several factors 1. The prices of bonds w/ higher durations are more sensitive to interest rate changes than are those w/ lower durations 2. All else being equal, durations will be higher when (1) market yields are lower, (2) bonds have longer maturities and (3) bonds have lower coupons Yield: describes the amount in cash that returns to the owners of a security
Cash Prices versus Quoted Prices:
Prices reported in the media are referred to as “quoted” prices These differ from the actual prices investors pay for bonds whenever bonds are sold at a date other than the date of a coupon payment Therefore, bond purchaser must pay the bond seller the quoted price plus the accrued interest on the bond (AKA “cash price” of the bond)
6.3 Bond Yields
Yield to maturity (YTM): the discount rate used to evaluate bonds o The yield that an investor would realize if he or she bought the bond at the current price, held it to maturity, received all the promised payments on their scheduled dates and reinvested all he cash flows received at the YTM o Use the same formula as above except calculate for kb instead of B:
o
A special form of internal rate of return (IRR)
Yield to Call (YTC):
The yield that is associated w/ a bond’s first call date is known as yield to call Similar to above formula except replace time to maturity (n) w/ the time to first call (c), replace face value (F) with the call price (CP)
If call price is above its current market price, it is unlikely that the bond would be called back by the issuer (selling based on its YTM rather than its YTC)
Current Yield (CY):
Current Yield= Flat Yield= Cash Yield: the ratio of the annual coupon interest divided by the current market price
Price-Yield Relationships Bond Price Par Discount Premium
Relationship Coupon Rate=CY=YTM Coupon Rate < CY < YTM Coupon Rate > CY > YTM
6.4 Interest Rate Determinants Base Interest Rates: Similar to law of supply and demand
Changes in interest rates are referred in terms of “basis points,” each of which represents 1/100th of 1 percent (AKA a decrease in 10 basic pts implies interest rates declined 0.1%) When demand for loans increase, price also increases and thus, interest rates also increase When supply for loans increase, interest rates decrease Nominal interest rates: the rates charged for lending today’s dollars in return for getting dollars back in the future, w/o taking into account the purchasing power of those future dollars
Risk-free rate (RF): the rate of return on risk-free investments which is often used as the base interest rate o RF= Real rate + Expected inflation o Interest rates will be low when expected inflation is low and high when expected inflation is high Default Free: having no risk of non-payment
Global Influences on Interest Rates:
Although interest rates vary from one country to the next, global interest rates interact w/ one another o Foreign exchange restrictions have been removed which allows capital to flow between countries o Canada’s interest rates are heavily influenced by prevailing rates in other countries, esp. U.S. Investors may not invest in bonds of countries offering higher interest rates and companies may not issue bonds in countries w/ lower interest rates because the additional gains could easily be cancelled out (and can incur large losses) as a result of adverse movements in the foreign exchange rates prevailing when funds are converted back into domestic currency Investing or issuing debt abroad creates foreign exchange risks, which offsets the potential advantages that may arise from inter-country interest rate differentials Interest rate parity (IRP) theory: a theory that demonstrates how differences in interest rates b/w countries are offset by expected changes in exchange rates o Theory states that forward exchange rates, which can be locked in today in order to eliminate foreign exchange risk, will be established at levels that ensure investors will end up w/ the same amount whether they invest at home or in another country (w/ no foreign exchange risk) o If Canada had high inflation and high interest rates and US investor bough Cdn bonds in an attempt to benefit from Cda’s higher rates, they would lose these gains when he/she converted the Canadian dollar payments back into US dollars
The Term Structure of Interest Rates:
One important factor affecting debt yields is related to the terms of maturity Term Structure of Interest Rates: the relationship b/w the interest rates and the term to maturity on underlying debt instruments Yield curve: the graphic representation of the term structure of interest rates, based on debt instruments from the same issuer Several theories attempt to account for the various shapes and movements of the yield curve. 3 of the most popular theories are: 1. Liquidity preference theory: a theory that suggests that investors prefer short-term debt instruments (i.e. more liquid instruments) because they exhibit less interest rate
risk while debt issuers prefer to lock in borrowing rates for longer periods to avoid the risk of having to refinance at higher rates. Therefore, issuers must provide investors w/ higher yields to induce them to invest in longer-term bonds. It’s upward sloping b/c long-term rates > than short term rates 2. Expectations theory: a theory that argues that the yield curve reflects investor expectations about future interest rates. Therefore, an upward-sloping yield curve reflects expectations of interest rate increases in the future and a downward-sloping curve reflects expectations of interest rate decreases in the future 3. Market segmentations theory: a theory that suggests that distinct markets (or market segments) exist for interest rate securities of various maturities and that rates are determined w/i these independent market segments by the forces of supply and demand w/i that market
Risk Premiums:
Investors expect extra compensation for assuming additional risks and therefore, they require higher returns. Kb= RF +/- Maturity yield differential +Spread
Spread: a difference in yield that compensates the investor for the assumption of additional risks, which may include some or all of (1) default or credit risk, (2) liquidity, (3) issue-specific features Default risk: the risk associated w/ the bond issuer and its ability to pay o Bondholders require higher yields to compensate them for the possibility that the borrower may default on the promised debt payments Debt ratings: ratings assigned by professional debt-rating services after detailed analyses of bond issuers to determine their ability to sustain the required interest and principal payments o Investment-grade bonds: those w/ bond ratings of BBB and higher o Junk (high-yield or low grade) bonds: bonds with ratings below BBB Some bonds are more liquid than others which means that they are easier to buy and sell and that the required price concessions are lower Liquidity premium: an additional yield offered on bonds that are less liquid Issue-specific premiums: premiums that arise when bonds have features that cause them to be more or less attractive to investors relative to straight (option-free) bonds
6.5 Other Types of Bonds/ Debt Instruments Treasury Bills (T-Bills):
T-Bills: short-term govt debt obligations that mature in one yr or less
Partly b/c of this short term to maturity, they do not make regular interest payments but are sold at a discount from their par value which is paid on the maturity date
Interest earned is the difference b/w purchase price & the face value
P= present value, F= future payment (AKA par value that is to be repaid at maturity), kBEY= bond equivalent yield, n= term to maturity (expressed as # of days)
In the US, the T-Bills formula is a little different:
Zero Coupon Bonds:
Zero coupon bonds (or zero): a bond that is issued at a discount, pays no coupons and repays the par value at the maturity date The return earned represents the difference b/w the purchase price and the redemption price Redemption Price: The price at which a bond may be repurchased by the issuer before maturity
The market prices of zero coupon bonds are even more sensitive to interest rate changes b/c they make no coupon payments at all
Floating Rate and Real Return Bonds:
Floating rate bonds (floaters): bonds that have adjustable coupons that are usually tied to some variable short-term rate o Differ from traditional fixed-income bonds b/c the coupon rates increase as interest rates increase and vice versa
o
Floaters provide protection against rising interest rates and tend to trade near their par value Real Return Bonds: bonds issued by the Government of Canada that provide investors w/ protection against inflation by providing a real yield
Canada Savings Bonds (CSBs):
Canada Savings Bonds: bonds issued by the Government of Canada that have no secondary market and can’t be traded so their prices do not change over time Rates of return on CSBs vary through time 1. Regular interests which pays out annual interest amounts 2. Compound interest which reinvest the interest so interest is also earned on accumulated interest (producing the power of compounding)
Appendix 6A: Interest Rate Parity
F= the current forward exchange rate expressed in the number of units of domestic currency required to purchase one unit of the foreign currency S= the current spot exchange rate Kdomestic= the domestic interest rate Kforeign= the foreign interest rate
