FIN Ch 7

What are the two key factors that impact a bond's riskiness?

The two key factors that impact a bond's riskiness are: 1. Price risk (interest rate risk) 2. Reinvestment risk

Hartwell Corporation's bonds have a 20-year maturity, an 8% semiannual coupon, and a face value of $1,000. The going nominal annual interest rate (rd) is 7%. What is the bond's price?

$1,106.78 N = 40 = 20(2) Coupon Rate = 0.04 = 0.08/2 M = $1,000 rd = 0.035 = 0.07/2 INT = $40 = $1,000(0.035) So N = 40 I/YR = 0.035 PMT = $40 FV = $1,000 =PV(0.035,40,40,1000) = $1,106.78 P. 236

Callaghan Motors's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8%; and the yield to maturity is 9%. What is the bond's current market price?

$935.82 N = 10 M = $1,000 rd = 0.09 Coupon Interest Rate = 0.08 Coupon PMT or INT = Par Value × Coupon Interest Rate = $1,000 × 0.08 = $80 Excel: = PV(rate,nper,pmt,[fv],[type]} PV = Vb I/YR = rd PMT = INT FV = M Excel: = PV(0.09,10,80,1000) = $935.82 = VB

You have just purchased an outstanding noncallable, 15-year bond with a par value of $1,000. Assume that this bond pays interest of 7.5%, with semiannual compounding. If the going (nominal) annual rate is 6%, what price did you pay for this bond? How does the price compare to the price of the annual coupon bond?

*Annual Coupon Bond:* N = 15 M = $1,000 Annual coupon rate = 0.075 INT = $75 = $1,000(0.075) rd = 0.06 Vb = PV(0.06,15,75,1000) = $1,145.68 *Semiannual Coupon Bond* N = 30 = 15(2) M = $1,000 Annual coupon rate = 0.0375 = 0.075/2 INT = $37.5 = $1,000(0.0375) rd = 0.03 = 0.06/2 Vb =PV(0.03,30,37.5,1000) = $1,147 p. 236

____ is 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.

*Call Provision* is 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.

____ are bonds that are exchangeable into shares of common stock at a fixed price at the option of the bondholder. These bonds 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.

*Convertible bonds* are bonds that are exchangeable into shares of common stock at a fixed price at the option of the bondholder. 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.

____ are bonds issued by corporation

*Corporate Bonds* are bonds issued by corporation

____ is the stated annual interest rate on a bond.

*Coupon interest rate* is the stated annual interest rate on a bond.

____ is the specified number of dollars of interest paid each year. It is set at the time the bond is issued and remains in force during the bond's life.

*Coupon payment* is the specified number of dollars of interest paid each year. It is set at the time the bond is issued and remains in force during the bond's life.

Coupon payments are constant for all bond types EXCEPT:

*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. p. 231

___ are bonds whose interest rate is fixed for their entire life.

*Fixed-Rate Bonds* are bonds whose interest rate is fixed for their entire life.

____ are bonds whose interest rate fluctuates with shifts in the general level of interest rate

*Floating-Rate Bonds* are bonds whose interest rate fluctuates with shifts in the general level of interest rate These floating-rate bonds work as follows: The coupon rate is set for an initial period, often 6 months, after which it is adjusted every 6 months based on some open market rate.

____ are bonds issued by foreign governments or by foreign corporation

*Foreign Bonds* are bonds issued by foreign governments or by foreign corporation

____ are a bond that pays interest only if it is earned.

*Income Bond* are a bond that pays interest only if it is earned. Therefore, income bonds cannot bankrupt a company

____ is a bond that has interest payments based on an inflation index so as to protect the holder from inflation.

*Index (Purchasing Power) Bond* is a bond that has interest payments based on an inflation index so as to protect the holder from inflation.

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

*Investment Horizon* is the period of time an investor plans to hold a particular investment.

____ is a specified date on which the par value of a bond must be repaid

*Maturity Date* is a specified date on which the par value of a bond must be repaid

____ are bonds issued by state and local governments.

*Municipal Bonds* are bonds issued by state and local governments.

____ are any bond originally offered at a price below its par value.

*Original Issue Discount (OID) Bonds* are any bond originally offered at a price below its par value.

____ is the number of years to maturity at the time a bond is issue

*Original Maturity* is the number of years to maturity at the time a bond is issue

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

*Par Value* is the face value of a bond. It generally represents the amount of money the firm borrows and promises to repay on the maturity date.

____ is the risk of a decline in a bond's price due to an increase in interest rate

*Price (Interest Rate) Risk* is the risk of a decline in a bond's price due to an increase in interest rate

_____ are bonds with a provision that allows investors to sell them back to the company prior to maturity at a prearranged price

*Putable Bonds* are bonds with a provision that allows investors to sell them back to the company prior to maturity at a prearranged price. With putable bonds, if interest rates rise, investors will put the bonds back to the company and reinvest in higher coupon bonds.

____ is the risk of an income decline due to a drop in interest rates

*Reinvestment Risk* is the risk of an income decline due to a drop in interest rates

____ is the risk that a decline in interest rates will lead to a decline in income from a bond portfolio

*Reinvestment Risk* is the risk that a decline in interest rates will lead to a decline in income from a bond portfolio

Nungesser Corporation's outstanding bonds have a $1,000 par value, a 9% semiannual coupon, 8 years to maturity, and an 8.5% YTM. What is the bond's price?

*The bond's price (Vb) is $1,028.60* M = $1,000 Coupon interest = 0.09 N = 8 YTM (rd) =0.085 Determine the semiannual coupon rate: 0.09/2 = 0.045 Determine INT with semiannual coupon rate = $1,000(0.045) = $45 Determine N with a semiannual coupon: 8(2) = 16 Determine YTM (rd) with semiannual coupon rate: 0.085/2 = 0.045 So, M = $1,000 = FV INT = $45 = PMT N = 16 YTM = 0.045 = I/YR =PV(0.045,16,45,1000) = $1,028.60 p. 253

_____ are bonds issued by the federal government, sometimes referred to as government bonds.

*Treasury Bonds* are bonds issued by the federal government, sometimes referred to as government bonds.

____ are long-term options to buy a stated number of shares of common stock at a specified price.

*Warrants* are long-term options to buy a stated number of shares of common stock at a specified price.

____ is the rate of return earned on a bond when it is called before its maturity date.

*Yield to Call (YTC)* is the rate of return earned on a bond when it is called before its maturity date.

____ is the rate of return earned on a bond if it is held to maturity

*Yield to Maturity (YTM)* is the rate of return earned on a bond if it is held to maturity

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

*Zero Coupon Bonds* are bonds that pay no annual interest but are sold at a discount below par, thus compensating investors in the form of capital appreciation rather than interest income

Which type of bonds have higher reinvestment risk?

1. Callable bonds 2. 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.

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. What are they and when would you choose each strategy?

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.

What are the 4 main issuers of bonds?

1. Treasury bonds 2. Corporate bonds 3. Municipal bonds 4. Foreign bonds

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

A *Discount Bond* is a bond that sells below its par value; occurs whenever the going rate of interest is above the coupon rate.

____ is a provision in a bond contract that requires the issuer to retire a portion of the bond issue each yea

A *Sinking Fund Provision* is a provision in a bond contract that requires the issuer to retire, or buy back, a portion of the bond 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

A ____ is a long-term contract under which a borrower agrees to make payments of interest and principal on specific dates to the holders of it

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

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

A bond that has just been issued is known as a ____. Once it has been issued, it is an ____, also called a ____.

A bond that has just been issued is known as a *new issue*. Once it has been issued, it is an *outstanding bond*, also called a *seasoned issue*.

When is a bond's total return equal to YTM and the market interest rate?

A bond's total return equals YTM and the market interest rate (rd): 1. in the absence of default risk 2. assuming market equilibrium p. 232

When do sinking funds work to the detriment of bondholders?

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 *when 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.

How does an increase in interest rates hurt bondholders? An decrease in interest rates hurts bondholders

An increase in interest rates hurts bondholders because it leads to a decline in the current value of a bond portfolio. If interest rates fall, long-term investors will suffer a reduction in income. 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.

An increase in the market interest rate (rd) causes the price of an outstanding bond to _____, whereas a decrease in the rate causes the bond's price to ____.

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*.

Bonds issued with ____ are similar to convertibles; but instead of giving the investor an option to exchange the bonds for stock, ____ 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 ____, like convertibles, carry lower coupon rates than otherwise similar non-convertible bonds.

Bonds issued with *warrants* are 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 non- convertible bonds.

Describe the cash flows for the following: a. Standard coupon bearing bond b. Floating-rate bond c. Zero-coupon bond

Cash flows for: a. *Standard coupon bearing bonds* consist of interest payment during the bond's life plus the amount borrowed (generally the par value) when the bond matures b. For *Floating-rate bonds*, the interest payment vary over time c. For *Zero coupon bonds*, there are no interest payments so the only cash flow is the face amount when the bond matures

Describe a refunding operation and why companies would use this process.

Companies are not likely to call bonds unless interest rates have declined significantly since the bonds were issued. Suppose a company sold bonds when interest rates were relatively high. Provided the issue is callable, the company could sell a new issue of low-yielding securities if and when interest rates drop, use the proceeds of the new issue to retire the high-rate issue, and thus reduce its interest expense. This process is called a refunding operation. 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. Accordingly, the interest rate on a new issue of callable bonds will exceed that on the company's new noncallable bonds.

Companies raise capital in what two main forms?

Companies raise capital in two main forms: *debts and equity*

*T/F* A bond's yield varies from day to day, depending on current market conditions

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

*T/F* .Bonds do not differ with respect to risk and consequently its expected return.

FALSE Each bond differs with respect to risk and consequently its expected return.

*T/F* When the risk of default on two bonds is exactly the same, both bonds are exposed to the same level of risk regardless differences in maturity dates.

FALSE Even if the risk of default on two bonds is exactly the same, the one with the longer maturity is typically exposed to more risk from a rise in interest rates.

*T/F* If you short- 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 long-term bonds, you will not be exposed to much price risk, but you will be exposed to significant reinvestment risk.

FALSE 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.

5-4 A firm's bonds have a maturity of 10 years with a $1,000 face value, have an 8% semiannual coupon, are callable in 5 years at $1,050, and currently sell at a price of $1,100. What are their nominal yield to maturity and their nominal yield to call? What return should investors expect to earn on these bonds?

If the investor holds the bond until maturity, they should expect to earn the nominal yield to maturity, which is 6.62%. If the bond is called, then the investor should expect to earn the nominal yield to call, which is 6.86%. *Yield to Maturity (YTM)* N = 10(2) = 20 Coupon Rate = 0.08/2 = 0.04 INT = $1,000(0.04) = $40 So N = 20 FV = $1,000 PMT = $40 PV = -$1,000 Semi-Annual YTM =RATE(20,40,-1100,1000) = 3.11% Nominal YTM = 3.11(2) = 6.62% *Yield to Call (YTC)* N = 5(2) = 10 PMT = $1,100(0.04) = $42 PV = -$1,100 FV = $1,050 Semi-Annual YTC =RATE(10,42,-1100,1050) = 3.43% Nominal YTC = 3.43(2) = 6.86%

Investors with shorter investment horizons should view long-term bonds as being ____ *(less/more)* risky than short-term bonds.

Investors with shorter investment horizons should view long-term bonds as being *more risky* than short-term bonds. Example: The investor plans to go to graduate school a year from now and needs money for tuition and expenses. Reinvestment risk is of minimal concern to this investor because there is little time to reinvest. The investor could eliminate price risk by buying a 1-year Treasury security because he would be assured of receiving the face value of the bond 1 year from now (the investment horizon). However, if this investor were to buy a long-term Treasury security, he would bear a considerable amount of price risk because, as we have seen, long-term bond prices decline when interest rates rise.

Explain what a call provision, call premium, deferred call, and call protection are.

Many corporate and municipal bonds contain a call provision that gives the issuer the right to call the bonds for redemption. 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. For example, the call premium on a 10-year bond with a 10% annual coupon and a par value of $1,000 might be $100, which means that the issuer would have to pay investors $1,100 (the par value plus the call premium) if it wanted to call the 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.

You have just purchased an outstanding 15-year bond with a par value of $1,000 for $1,145 68. Its annual coupon payment is $75. We calculated the YTM of this bond (6%) in the Quick Question box on page 228. Now, assume that this bond is callable in 7 years at a price of $1,075. What is the bond's YTC? If the yield curve remains flat at its current level during this time period, would you expect to earn the YTM or YTC?

N = 15 M = $1,000 Vb = $1,145 INT = $75 Nc = 7 Call price = $1,075 Excel: =RATE(7,75,-1145.68,1075) = 0.0581 Here we find the bond's YTC is equal to 5.81%. This bond sells at a premium so interest rates have declined since the bond was originally issued. If the yield curve remained flat at this current level during the next 7 years, you would expect the firm to call the bond and issue bonds at the lower 6% interest rate, assuming the cost of doing so was lower than the $75 - $60 = $15 savings per bond p. 230

*See Table 7.1 on p. 233* Assuming the market interest rate (rd) remains constant at 10% over time, describe the relationship between a bond's price, it's current yield, it's capital gains, and its total yield in the following situations: 1. When a bond's coupon rate = the market interest rate (rd) over time: (10% = 10%) 2. When a bond's coupon rate < the market interest rate (rd) over time: (7% < 10%) 3. When a bond's coupon rate > the market interest rate (rd) over time: (12% > 10%)

NOTE: Total Yield = Current Yield + Capital Gains. Therefore, Capital Gains and Current Yield have an inverse relationship: when one goes up, the other goes down. Total Yield = the market interest rate (rd) *1. When a bond's coupon rate = the market interest rate (rd): (10% = 10%)* a. The coupon bond trades at par and it's price remains at par value b. The bond's Current Yield will remain at 10% c. The bond's Capital Gains will be zero each year *2. When a bond's coupon rate < the market interest rate over time: (7% < 10%)* a. The coupon bond trades at a discount, which means that the bond's price is < par value. However, the company must pay par value at maturity, meaning that the bond's price must rise over time b. The bond's expected Current Yield will decrease over time c. The bond's expected Capital Gains Yield will increase over time *3. When a bond's coupon rate > the market interest rate (rd) over time: (12% > 10%)* a. The coupon bond trades at a premium. However, its price must be equal to its par value at maturity; so the price must decline over time. b. The bond's expected Current Yield will increase over time c. The bond's expected Capital Gains Yield will decrease over time Although the prices of the 7% and 13% coupon bonds move in opposite directions over time, each bond provides investors with the same total return, 10%, which is also the total return on the 10% coupon par value bond. The discount bond has a low coupon rate (and therefore a low current yield), but it provides a capital gain each year. In contrast, the premium bond has a high current yield, but it has an expected capital loss each year

Newly issued bonds generally sell at prices ____, but the prices of outstanding bonds ____

Newly issued bonds generally sell at prices very close to par, but the prices of outstanding bonds can vary widely from par.

A bond's calculated yield to maturity changes:

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

Note that a call for sinking fund purposes is generally different from a refunding call because:

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.* p. 222 for definitions

*T/F* 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.

TRUE

What does the fixed-rate bond sell at when: a. rd = coupon rate b. rd < coupon rate c. rd < coupon rate

Note: 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. *a. rd = coupon rate* 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; this is a *par bond* *b. rd < coupon rate* Whenever the going rate (rd) of interest rises above the coupon rate, a fixed-rate bond's price will fall below its par value; this type of bond is called a *discount bond*. *c. rd < coupon rate* Whenever the going interest rate falls below the coupon rate, a fixed-rate bond's price will rise above its par value; this type of bond is called a *premium bond*.

*T/F* At the time they are issued, sinking fund bonds have lower coupon rates than otherwise similar bonds without sinking funds

On balance, bonds that have a sinking fund are regarded as ing 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

People or firms who invest in bonds are exposed to risk from increasing ____.

People or firms who invest in bonds are exposed to risk from increasing *interest rates.*

Price risk is higher on bonds that have ____ than on bonds that ____.

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.

Price risk relates to: While reinvestment risk relates to: a. the current market value of the bond portfolio b. the income the portfolio produces

Price risk relates to *the current market value of the bond portfolio*, while reinvestment risk relates to *the income the portfolio produces*.

Reinvestment risk relates to: While price risk relates to: a. the current market value of the bond portfolio b. the income the portfolio produces

Price risk relates to *the current market value of the bond portfolio*, while reinvestment risk relates to *the income the portfolio produces*.

With putable bonds, if interest rates rise, investors will:

Putable bonds have a provision that allows investors to sell their bonds back to the company prior to maturity at a prearranged price. Therefore, with putable bonds, if interest rates rise, investors will put the bonds back to the company and reinvest in higher coupon bonds.

*T/F* 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.

TRUE

*T/F* Rising interest rates cause losses to bondholders.

TRUE

*T/F* The market interest rate on a municipal bond is considerably lower than on a corporate bonds of equivalent risk

TRUE 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

*T/F* 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.

TRUE 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.

*T/F* Government bonds have no default risk

TRUE 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.*

When Allied issues 15 year bonds that have a 10% annual coupon at par, what does this tell us about the market interest rate (rd) on the bond's issue date?

The just-issued 15-year bonds have a 10% annual coupon. They were issued at par, which means that the market interest rate on their issue date was also 10%.

The rate at which the interest on a bond is paid to the holder is known as ____

The rate at which the interest on a bond is paid to the holder is known as *coupon rate*

What is the value of any financial assets based on?

The value of any financial assets *is the present value of cash flows the asset is expected to produce*

The yield to maturity equals the expected rate of return only when:

The yield to maturity equals the expected rate of return only when: (1) the probability of default is zero and (2) the bond cannot be called. If there is some default risk or the bond may be called, there is some chance that the promised payments to maturity will not be received, in which case the calculated yield to maturity will exceed the expected ret

How do floating-rate bonds work?

These floating-rate bonds work as follows: The coupon rate is set for an initial period, often 6 months, after which it is adjusted every 6 months based on some open market rate.

Typically, at the time a bond is issued, its coupon payment is set at a level that will:

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.*

When the annual coupon payment of a bond is divided by the par value, the result is the ____.

When the annual coupon payment of a bond is divided by the par value, the result is the *coupon interest payment*

Whenever the bond's market, or going, rate (rd) is equal to its coupon rate, a ____ bond will sell at its par value.

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.

Whenever the going rate of interest rises above the coupon rate, a fixed-rate bond's price will fall below its par value; this type of bond is called a _____.

Whenever the going rate of interest rises above the coupon rate, a fixed-rate bond's price will fall below its par value; this type of bond is called a *discount bond.*

Whereas callable bonds give the ____ the right to retire the debt prior to maturity, putable bonds allow ____ to require the company to pay in advance.

Whereas callable bonds give the *issuer* the right to retire the debt prior to maturity, putable bonds allow *investors* to require the company to pay in advance.

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 ____

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*

Halley Enterprises's bonds currently sell for $975. They have a 7-year maturity, an annual coupon of $90, and a par value of $1,000. What is their yield to maturity?

YTM (rd) = 9.51% Vb = $975 N = 7 INT = $90 M = $1,000 =RATE(7,90,975,1000) = 0.0951

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 and maturity payments?

YTM = 5% N = 14 Icoupon = 0.1 M = $1,000 = FV Vb = $1,494.93 = PV INT (PMT) = $1,000(0.1) = $100 Solve for rd by using excel function: =RATE(14,100,-1494.93,1000) = 0.05

A bond that matures in 12 years has a par value of $1,000 and an annual coupon rate of 10%; the market interest rate is 8%. What is its price? Is this a par bond, a discount bond, or a premium bond?

a. $1,150.72 b. It is a premium bond because the coupon interest rate (0.10) is greater than the market interest rate (0.08) N = 12 M = $1,000 = FV INT = ? = PMT Coupon interest rate = 0.10 rd = 0.08 = I/YR First solve for coupon interest payment (INT) INT = $1,000(0.1) = $100 Excel: =PV(0.08,12,100,1000) = $1,150.72 P. 227

Last year a firm issued 20-year, 8% annual coupon bonds at a par value of $1,000. a. Suppose that one year later the going market interest rate drops to 6%. What is the new price of the bonds, assuming they now have 19 years to maturity? b. Suppose that one year after issue, the going market interest rate is 10% (rather than 6%). What would the price have been?

a. $1,233.16 b. $832.70 N = 19 M = $1,000 Coupon Rate = 0.08 INT = $80 = 1,000(0.08) rd = 0.06 a. =PV(0.06,19,80,1000) = $1,233.16 rd = 0.1 b. =PV(0.1,19,80,1000) = $832.70 p. 234

A bond that matures in 8 years has a par value of $1,000 and an annual coupon payment of $70; its market interest rate is 9%. What is its price? Is this a par bond, a discount bond, or a premium bond?

a. $889.30 b. It is a discount bond because (1,000/70) = 0.07 = coupon interest rate, which is lower than the market interest rate (rd) of 0.09 N = 8 M = $1,000 = FV INT = $70 = PMT rd = 0.09 = I/YR Excel: =PV(0.09,8,70,1000) = $889.30 p. 227

Describe the risk involved with the following bonds: a. Treasury bonds b. Corporate bonds c. Municipal bonds d. Foreign bonds

a. *Treasury 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. b. *Corporate bonds:* . 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. Corporate bonds have different levels of default risk depending on the issuing company's characteristics and the terms of the specific bon c. *Municipal bonds:* 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 d. *Foreign bonds:* 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. Consider, for example, a U.S. investor who purchases a corporate bond denominated in Japanese yen. At some point, the investor will want to close out his investment and convert the yen back to U.S. dollars. If the Japanese yen unexpectedly falls relative to the dollar, the investor will have fewer dollars than he originally expected to receive. Consequently, the investor could still lose money even if the bond does not default

The Henderson Company's bonds currently sell for $1,275. They pay a $120 annual coupon, have a 20-year maturity, and a par value of $1,000, but they can be called in 5 years at $1,120. What are their YTM and their YTC, and if the yield curve remained flat, which rate would investors expect to earn?

a. 8.99% b. 7.31% c. YTC Vb = $1,275 N = 20 INT = $120 M = $1,000 YTM =RATE(20,120,-1275,1000) = 0.899 or 8.99% Ncall = 5 PC = $1,120 YTC =RATE(5,120,-1275,1120) = 0.0731 or 7.31% p. 231

A friend of yours just invested in an outstanding bond with a 5% annual coupon and a remaining maturity of 10 years. The bond has a par value of $1,000 and the market interest rate is currently 7%. How much did your friend pay for the bond? Is it a par, premium, or discount bond?

a. The bond's value is equal to $859.53. b. Because the bond's coupon rate (5%) is less than the current market interest rate (7%), the bond is a discount bond—reflecting that interest rates have increased since this bond was originally issued. Coupon interest rate = 0.05 N = 10 Par Value (M) = $1,000 Market interest rate (rd) = 0.07 Coupon payment or INT = $1,000(0.05) = $50 Use excel's PV function to solve for Vb, where: I/YR = rd = 0.07 PMT = INT = $50 FV = M = $1,000 =PV(0.07,10,50,1000) = *$859.53* p. 227

You have just purchased an outstanding 15-year bond with a par value of $1,000 for $1,145.68. Its annual coupon payment is $75. What is the bond's yield to maturity? Is this a par bond, a discount bond, or a premium bond?

a. YTM = 6% N = 15 M = $1,000 = FV Vb = $1,145.68 = PV INT = $75 = PMT =RATE(15,75,-1145.68,1000) = 0.06 b. The bond is a premium bond To determine this, first determine the bonds coupon rate ($75/$1,000 = 7.5%). Since 7.5% is greater than the bond's YTM (6%), the bond is a premium bond - indicating that interest rates have declined since the bond was originally issued p. 229

What are ways in which a bond can be grouped?

a. by issuer

Define floating-rate bonds, zero coupon bonds, callable bonds, putable bonds, income bonds, convertible bonds, and inflation-indexed bonds (TIPS)

p. 223

In general, how is the rate on a floating-rate bond determined?

p. 223

What are the two ways sinking funds can be handled? Which alternative will be used if interest rates have risen? If interest rates have fallen

p. 223

Which is riskier to an investor, other things held constant—a callable bond or a putable bond? Explain.

p. 223

Why do the prices of fixed-rate bonds fall if expectations for inflation rise?

p. 234

Describe how the annual payment bond valuation formula is changed to evaluate semiannual coupon bonds, and write the revised formula.

p. 236