Before I actually elaborate...watch this first....
This section describes the various types of bonds that a company might issue. (To learn about government-issued bonds, read Basics Of Federal Bond Issues, Savings Bonds For Income And Safety and 20 Investments: Municipal Bonds.)
Corporate Bonds
A company can issue bonds just as it can issue stock. Large corporations have a lot of flexibility as to how much debt they can issue: the limit is whatever the market will bear. Generally, a short-term corporate bond has a maturity of less than five years, intermediate is five to 12 years and long term is more than 12 years.
Corporate bonds are characterized by higher yields because there is a higher risk of a company defaulting than a government. The upside is that they can also be the most rewarding fixed-income investments because of the risk the investor must take on. The company's credit quality is very important: the higher the quality, the lower the interest rate the investor receives.
Variations on corporate bonds include convertible bonds, which the holder can convert into stock, and callable bonds, which allow the company to redeem an issue prior to maturity.
Convertible Bonds
A convertible bond may be redeemed for a predetermined amount of the company's equity at certain times during its life, usually at the discretion of the bondholder. Convertibles are sometimes called "CVs."
Issuing convertible bonds is one way for a company to minimize negative investor interpretation of its corporate actions. For example, if an already public company chooses to issue stock, the market usually interprets this as a sign that the company's share price is somewhat overvalued. To avoid this negative impression, the company may choose to issue convertible bonds, which bondholders will likely convert to equity should the company continue to do well.
From the investor's perspective, a convertible bond has a value-added component built into it: it is essentially a bond with a stock option hidden inside. Thus, it tends to offer a lower rate of return in exchange for the value of the option to trade the bond into stock.
Callable Bonds
Callable bonds, also known as "redeemable bonds," can be redeemed by the issuer prior to maturity. Usually a premium is paid to the bond owner when the bond is called.
The main cause of a call is a decline in interest rates. If interest rates have declined since a company first issued the bonds, it will likely want to refinance this debt at a lower rate. In this case, the company will call its current bonds and reissue new, lower-interest bonds to save money.
Term Bonds
Term bonds are bonds from the same issue that share the same maturity dates. Term bonds that have a call feature can be redeemed at an earlier date than the other issued bonds. A call feature, or call provision, is an agreement that bond issuers make with buyers. This agreement is called an "indenture," which is the schedule and the price of redemptions, plus the maturity dates.
Some corporate and municipal bonds are examples of term bonds that have 10-year call features. This means the issuer of the bond can redeem it at a predetermined price at specific times before the bond matures.
A term bond is the opposite of a serial bond, which has various maturity schedules at regular intervals until the issue is retired.
Amortized Bonds
An amortized bond is a financial certificate that has been reduced in value for records on accounting statements. An amortized bond is treated as an asset, with the discount amount being amortized to interest expense over the life of the bond. If a bond is issued at a discount - that is, offered for sale below its par (face value) - the discount must either be treated as an expense or amortized as an asset.
As we discussed in Section 4, amortization is an accounting method that gradually and systematically reduces the cost value of a limited life, intangible asset. Treating a bond as an amortized asset is an accounting method in the handling of bonds. Amortizing allows bond issuers to treat the bond discount as an asset until the bond's maturity. (To learn more about bond premium amortization, read Premium Bonds: Problems And Opportunities.)
Adjustment Bonds
Issued by a corporation during a restructuring phase, an adjustment bond is given to the bondholders of an outstanding bond issue prior to the restructuring. The debt obligation is consolidated and transferred from the outstanding bond issue to the adjustment bond. This process is effectively a recapitalization of the company's outstanding debt obligations, which is accomplished by adjusting the terms (such as interest rates and lengths to maturity) to increase the likelihood that the company will be able to meet its obligations.
If a company is near bankruptcy and requires protection from creditors (Chapter 11), it is likely unable to make payments on its debt obligations. If this is the case, the company will be liquidated, and the company's value will be spread among its creditors. However, creditors will generally only receive a fraction of their original loans to the company. Creditors and the company will work together to recapitalize debt obligations so that the company is able to meet its obligations and continue operations, thus increasing the value that creditors will receive.
Junk Bonds
A junk bond, also known as a "high-yield bond" or "speculative bond," is a bond rated "BB" or lower because of its high default risk. Junk bonds typically offer interest rates three to four percentage points higher than safer government issues.
Angel Bonds
Angel bonds are investment-grade bonds that pay a lower interest rate because of the issuing company's high credit rating. Angel bonds are the opposite of fallen angels, which are bonds that have been given a "junk" rating and are therefore much more risky.
An investment-grade bond is rated at minimum "BBB" by S&P and Fitch, and "Baa" by Moody's. If the company's ability to pay back the bond's principal is reduced, the bond rating may fall below investment-grade minimums and become a fallen angel.
Corporate Bonds
A company can issue bonds just as it can issue stock. Large corporations have a lot of flexibility as to how much debt they can issue: the limit is whatever the market will bear. Generally, a short-term corporate bond has a maturity of less than five years, intermediate is five to 12 years and long term is more than 12 years.
Corporate bonds are characterized by higher yields because there is a higher risk of a company defaulting than a government. The upside is that they can also be the most rewarding fixed-income investments because of the risk the investor must take on. The company's credit quality is very important: the higher the quality, the lower the interest rate the investor receives.
Variations on corporate bonds include convertible bonds, which the holder can convert into stock, and callable bonds, which allow the company to redeem an issue prior to maturity.
Convertible Bonds
A convertible bond may be redeemed for a predetermined amount of the company's equity at certain times during its life, usually at the discretion of the bondholder. Convertibles are sometimes called "CVs."
Issuing convertible bonds is one way for a company to minimize negative investor interpretation of its corporate actions. For example, if an already public company chooses to issue stock, the market usually interprets this as a sign that the company's share price is somewhat overvalued. To avoid this negative impression, the company may choose to issue convertible bonds, which bondholders will likely convert to equity should the company continue to do well.
From the investor's perspective, a convertible bond has a value-added component built into it: it is essentially a bond with a stock option hidden inside. Thus, it tends to offer a lower rate of return in exchange for the value of the option to trade the bond into stock.
Callable Bonds
Callable bonds, also known as "redeemable bonds," can be redeemed by the issuer prior to maturity. Usually a premium is paid to the bond owner when the bond is called.
The main cause of a call is a decline in interest rates. If interest rates have declined since a company first issued the bonds, it will likely want to refinance this debt at a lower rate. In this case, the company will call its current bonds and reissue new, lower-interest bonds to save money.
Term Bonds
Term bonds are bonds from the same issue that share the same maturity dates. Term bonds that have a call feature can be redeemed at an earlier date than the other issued bonds. A call feature, or call provision, is an agreement that bond issuers make with buyers. This agreement is called an "indenture," which is the schedule and the price of redemptions, plus the maturity dates.
Some corporate and municipal bonds are examples of term bonds that have 10-year call features. This means the issuer of the bond can redeem it at a predetermined price at specific times before the bond matures.
A term bond is the opposite of a serial bond, which has various maturity schedules at regular intervals until the issue is retired.
Amortized Bonds
An amortized bond is a financial certificate that has been reduced in value for records on accounting statements. An amortized bond is treated as an asset, with the discount amount being amortized to interest expense over the life of the bond. If a bond is issued at a discount - that is, offered for sale below its par (face value) - the discount must either be treated as an expense or amortized as an asset.
As we discussed in Section 4, amortization is an accounting method that gradually and systematically reduces the cost value of a limited life, intangible asset. Treating a bond as an amortized asset is an accounting method in the handling of bonds. Amortizing allows bond issuers to treat the bond discount as an asset until the bond's maturity. (To learn more about bond premium amortization, read Premium Bonds: Problems And Opportunities.)
Adjustment Bonds
Issued by a corporation during a restructuring phase, an adjustment bond is given to the bondholders of an outstanding bond issue prior to the restructuring. The debt obligation is consolidated and transferred from the outstanding bond issue to the adjustment bond. This process is effectively a recapitalization of the company's outstanding debt obligations, which is accomplished by adjusting the terms (such as interest rates and lengths to maturity) to increase the likelihood that the company will be able to meet its obligations.
If a company is near bankruptcy and requires protection from creditors (Chapter 11), it is likely unable to make payments on its debt obligations. If this is the case, the company will be liquidated, and the company's value will be spread among its creditors. However, creditors will generally only receive a fraction of their original loans to the company. Creditors and the company will work together to recapitalize debt obligations so that the company is able to meet its obligations and continue operations, thus increasing the value that creditors will receive.
Junk Bonds
A junk bond, also known as a "high-yield bond" or "speculative bond," is a bond rated "BB" or lower because of its high default risk. Junk bonds typically offer interest rates three to four percentage points higher than safer government issues.
Angel Bonds
Angel bonds are investment-grade bonds that pay a lower interest rate because of the issuing company's high credit rating. Angel bonds are the opposite of fallen angels, which are bonds that have been given a "junk" rating and are therefore much more risky.
An investment-grade bond is rated at minimum "BBB" by S&P and Fitch, and "Baa" by Moody's. If the company's ability to pay back the bond's principal is reduced, the bond rating may fall below investment-grade minimums and become a fallen angel.
and lastly.......
This bond I can eloborate more than all the above mentioned bonds. And I know you'll like it. You can do so much research on this type of bond. This is also one of the investment. Hahaha. Therefore, I would like to share the history of bonds since 1962...
Read more: Types Of Bonds http://www.investopedia.com/walkthrough/corporate-finance/3/bonds/types.aspx#ixzz4qdkLAS7B
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Ok...enough of that, now let's proceed to Valuing of Bonds
The fundamental principle of bond valuation is that the bond's value is equal to the present value of its expected (future) cash flows. The valuation process involves the following three steps:
1. Estimate the expected cash flows.
2. Determine the appropriate interest rate or interest rates that should be used to discount the cash flows.
3. Calculate the present value of the expected cash flows found in step one by using the interest rate or interest rates determined in step two.
Determining Appropriate Interest Rates
The minimum interest rate that an investor should accept is the yield for a risk-free bond (a Treasury bond for a U.S. investor). The Treasury security that is most often used is the on-the-run issue because it reflects the latest yields and is the most liquid.
For non-Treasury bonds, such as corporate bonds, the rate or yield that would be required would be the on-the-run government security rate plus a premium that accounts for the additional risks that come with non-Treasury bonds.
As for the maturity, an investor could just use the final maturity date of the issue compared to the Treasury security. However, because each cash flow is unique in its timing, it would be better to use the maturity that matches each of the individual cash flows.
Computing a Bond's Value
First, we need to find the present value (PV) of the bond's future cash flows. The present value is the amount that would have to be invested today to generate that future cash flow. PV is dependent on the timing of the cash flow and the interest rate used to calculate the present value. To figure out the value, the PV of each individual cash flow must be found. Then, just add the figures together to determine the bond's price.
After you calculate the expected cash flows, you will need to add the individual cash flows:
Let's throw some numbers around to further illustrate this concept.
Example: The Value of a Bond
Bond GHJ matures in five years with a coupon rate of 7% and a maturity value of $1,000. For simplicity's sake, let's assume that the bond pays annually and the discount rate is 5%.
The cash flow for each of the years is as follows:
Year One = $70
Year Two = $70
Year Three = $70
Year Four = $70
Year Five = $1,070
Thus, the PV of the cash flows is as follows:
Year One = $70 / (1.05) to the 1st power = $66.67
Year Two = $70 / (1.05) to the 2nd power = $ 63.49
Year Three = $70 / (1.05) to the 3rd power = $ 60.47
Year Four = $70 / (1.05) to the 4th power = $ 57.59
Year Five = $1,070 / (1.05) to the 5th power = $ 838.37
Now to find the value of the bond:
Value = $66.67 + $63.49 + $60.47 + $57.59 + $838.37
Value = $1,086.59
How Does the Value of a Bond Change?
As rates increase or decrease, the discount rate that is used also changes. Let's change the discount rate in the above example to 10% to see how it affects the bond's value.
Example: The Value of a Bond when Discount Rates Change
PV of the cash flows is:
Year One = $70 / (1.10) to the 1st power = $ 63.63
Year Two = $70 / (1.10) to the 2nd power = $ 57.85
Year Three = $70 / (1.10) to the 3rd power = $ 52.63
Year Four = $70 / (1.10) to the 4th power = $ 47.81
Year Five = $1,070 / (1.10) to the 5th power = $ 664.60
Value = 63.63 + 57.85 + 52.63 + 47.81 + 664.60 = $ 886.52
If the discount rate is higher than the coupon rate the PV will be less than par. If the discount rate is lower than the coupon rate, the PV will be higher than par value.
How Does a Bond's Price Change as it Approaches its Maturity Date?
As a bond moves closer to its maturity date, its price will move closer to par. There are three possible scenarios:
1.If a bond is at a premium, the price will decline over time toward its par value.
2. If a bond is at a discount, the price will increase over time toward its par value.
3. If a bond is at par, its price will remain the same.
To show how this works, let's use our original example of the 7% bond, but now let's assume that a year has passed and the discount rate remains the same at 5%.
Example: Price Changes Over Time
Let's compute the new value to see how the price moves closer to par. You should also be able to see how the amount by which the bond price changes is attributed to it being closer to its maturity date.
PV of the cash flows is:
Year One = $70 / (1.05) to the 1st power = $66.67
Year Two = $70 / (1.05) to the 2nd power = $ 63.49
Year Three = $70 / (1.05) to the 3rd power = $ 60.47
Year Four = $1,070 / (1.05) to the 4th power = $880.29
Value = $66.67 + $63.49 + $60.47 + $880.29 = $1,070.92
As the price of the bond decreases, it moves closer to its par value. The amount of change attributed to the year's difference is $15.67.
An individual can also decompose the change that results when a bond approaches its maturity date and the discount rate changes. This is accomplished by first taking the net change in the price that reflects the change in maturity, then adding it to the change in the discount rate. The two figures should equal the overall change in the bond's price.
Computing the Value of a Zero-coupon Bond
A zero-coupon bond may be the easiest of securities to value because there is only one cash flow - the maturity value.
The formula to calculate the value of a zero coupon bond that matures N years from now is as follows:
Example: The Value of a Zero-Coupon Bond
For illustration purposes, let's look at a zero coupon with a maturity of three years and a maturity value of $1,000 discounted at 7%.
I = 0.035 (.07 / 2)
N = 3
Value of a Zero-Coupon Bond
= $1,000 / (1.035) to the 6th power (3*2)
= $1,000 / 1.229255
= $813.50
Arbitrage-free Valuation Approach
Under a traditional approach to valuing a bond, it is typical to view the security as a single package of cash flows, discounting the entire issue with one discount rate. Under the arbitrage-free valuation approach, the issue is instead viewed as various zero-coupon bonds that should be valued individually and added together to determine value. The reason this is the correct way to value a bond is that it does not allow a risk-free profit to be generated by "stripping" the security and selling the parts at a higher price than purchasing the security in the market.
As an example, a five-year bond that pays semi-annual interest would have 11 separate cash flows and would be valued using the appropriate yield on the curve that matches its maturity. So the markets implement this approach by determining the theoretical rate the U.S. Treasury would have to pay on a zero-coupon treasury for each maturity. The investor then determines the value of all the different payments using the theoretical rate and adds them together. This zero-coupon rate is the Treasury spot rate. The value of the bond based on the spot rates is the arbitrage-free value.
Determining Whether a Bond Is Under or Over Valued
What you need to be able to do is value a bond like we have done before using the more traditional method of applying one discount rate to the security. The twist here, however, is that instead of using one rate, you will use whatever rate the spot curve has that coordinates with the proper maturity. You will then add the values up as you did previously to get the value of the bond.
You will then be given a market price to compare to the value that you derived from your work. If the market price is above your figure, then the bond is undervalued and you should buy the issue. If the market price is below your price, then the bond is overvalued and you should sell the issue.
How Bond Coupon Rates and Market Rates Affect Bond Price
If a bond's coupon rate is above the yield required by the market, the bond will trade above its par value or at a premium. This will occur because investors will be willing to pay a higher price to achieve the additional yield. As investors continue to buy the bond, the yield will decrease until it reaches market equilibrium. Remember that as yields decrease, bond prices rise.
1. Estimate the expected cash flows.
2. Determine the appropriate interest rate or interest rates that should be used to discount the cash flows.
3. Calculate the present value of the expected cash flows found in step one by using the interest rate or interest rates determined in step two.
Determining Appropriate Interest Rates
The minimum interest rate that an investor should accept is the yield for a risk-free bond (a Treasury bond for a U.S. investor). The Treasury security that is most often used is the on-the-run issue because it reflects the latest yields and is the most liquid.
For non-Treasury bonds, such as corporate bonds, the rate or yield that would be required would be the on-the-run government security rate plus a premium that accounts for the additional risks that come with non-Treasury bonds.
As for the maturity, an investor could just use the final maturity date of the issue compared to the Treasury security. However, because each cash flow is unique in its timing, it would be better to use the maturity that matches each of the individual cash flows.
Computing a Bond's Value
First, we need to find the present value (PV) of the bond's future cash flows. The present value is the amount that would have to be invested today to generate that future cash flow. PV is dependent on the timing of the cash flow and the interest rate used to calculate the present value. To figure out the value, the PV of each individual cash flow must be found. Then, just add the figures together to determine the bond's price.
| PV at time T = expected cash flows in period T / (1 + I) to the T power |
After you calculate the expected cash flows, you will need to add the individual cash flows:
| Value = present value @ T1 + present value @ T2 + present value @Tn |
Let's throw some numbers around to further illustrate this concept.
Example: The Value of a Bond
Bond GHJ matures in five years with a coupon rate of 7% and a maturity value of $1,000. For simplicity's sake, let's assume that the bond pays annually and the discount rate is 5%.
The cash flow for each of the years is as follows:
Year One = $70
Year Two = $70
Year Three = $70
Year Four = $70
Year Five = $1,070
Thus, the PV of the cash flows is as follows:
Year One = $70 / (1.05) to the 1st power = $66.67
Year Two = $70 / (1.05) to the 2nd power = $ 63.49
Year Three = $70 / (1.05) to the 3rd power = $ 60.47
Year Four = $70 / (1.05) to the 4th power = $ 57.59
Year Five = $1,070 / (1.05) to the 5th power = $ 838.37
Now to find the value of the bond:
Value = $66.67 + $63.49 + $60.47 + $57.59 + $838.37
Value = $1,086.59
How Does the Value of a Bond Change?
As rates increase or decrease, the discount rate that is used also changes. Let's change the discount rate in the above example to 10% to see how it affects the bond's value.
Example: The Value of a Bond when Discount Rates Change
PV of the cash flows is:
Year One = $70 / (1.10) to the 1st power = $ 63.63
Year Two = $70 / (1.10) to the 2nd power = $ 57.85
Year Three = $70 / (1.10) to the 3rd power = $ 52.63
Year Four = $70 / (1.10) to the 4th power = $ 47.81
Year Five = $1,070 / (1.10) to the 5th power = $ 664.60
Value = 63.63 + 57.85 + 52.63 + 47.81 + 664.60 = $ 886.52
- As we can see from the above examples, an important property of PV is that for a given discount rate, the older a cash flow value is, the lower its present value.
- We can also compute the change in value from an increase in the discount rate used in our example. The change = $1,086.59 - $886.52 = $200.07.
- Another property of PV is that the higher the discount rate, the lower the value of a bond; the lower the discount rate, the higher the value of the bond.
If the discount rate is higher than the coupon rate the PV will be less than par. If the discount rate is lower than the coupon rate, the PV will be higher than par value.
As a bond moves closer to its maturity date, its price will move closer to par. There are three possible scenarios:
1.If a bond is at a premium, the price will decline over time toward its par value.
2. If a bond is at a discount, the price will increase over time toward its par value.
3. If a bond is at par, its price will remain the same.
To show how this works, let's use our original example of the 7% bond, but now let's assume that a year has passed and the discount rate remains the same at 5%.
Example: Price Changes Over Time
Let's compute the new value to see how the price moves closer to par. You should also be able to see how the amount by which the bond price changes is attributed to it being closer to its maturity date.
PV of the cash flows is:
Year One = $70 / (1.05) to the 1st power = $66.67
Year Two = $70 / (1.05) to the 2nd power = $ 63.49
Year Three = $70 / (1.05) to the 3rd power = $ 60.47
Year Four = $1,070 / (1.05) to the 4th power = $880.29
Value = $66.67 + $63.49 + $60.47 + $880.29 = $1,070.92
As the price of the bond decreases, it moves closer to its par value. The amount of change attributed to the year's difference is $15.67.
An individual can also decompose the change that results when a bond approaches its maturity date and the discount rate changes. This is accomplished by first taking the net change in the price that reflects the change in maturity, then adding it to the change in the discount rate. The two figures should equal the overall change in the bond's price.
Computing the Value of a Zero-coupon Bond
A zero-coupon bond may be the easiest of securities to value because there is only one cash flow - the maturity value.
The formula to calculate the value of a zero coupon bond that matures N years from now is as follows:
| Maturity value / (1 + I) to the power of the number of years * 2 Where I is the semi-annual discount rate. |
Example: The Value of a Zero-Coupon Bond
For illustration purposes, let's look at a zero coupon with a maturity of three years and a maturity value of $1,000 discounted at 7%.
I = 0.035 (.07 / 2)
N = 3
Value of a Zero-Coupon Bond
= $1,000 / (1.035) to the 6th power (3*2)
= $1,000 / 1.229255
= $813.50
Arbitrage-free Valuation Approach
Under a traditional approach to valuing a bond, it is typical to view the security as a single package of cash flows, discounting the entire issue with one discount rate. Under the arbitrage-free valuation approach, the issue is instead viewed as various zero-coupon bonds that should be valued individually and added together to determine value. The reason this is the correct way to value a bond is that it does not allow a risk-free profit to be generated by "stripping" the security and selling the parts at a higher price than purchasing the security in the market.
As an example, a five-year bond that pays semi-annual interest would have 11 separate cash flows and would be valued using the appropriate yield on the curve that matches its maturity. So the markets implement this approach by determining the theoretical rate the U.S. Treasury would have to pay on a zero-coupon treasury for each maturity. The investor then determines the value of all the different payments using the theoretical rate and adds them together. This zero-coupon rate is the Treasury spot rate. The value of the bond based on the spot rates is the arbitrage-free value.
Determining Whether a Bond Is Under or Over Valued
What you need to be able to do is value a bond like we have done before using the more traditional method of applying one discount rate to the security. The twist here, however, is that instead of using one rate, you will use whatever rate the spot curve has that coordinates with the proper maturity. You will then add the values up as you did previously to get the value of the bond.
You will then be given a market price to compare to the value that you derived from your work. If the market price is above your figure, then the bond is undervalued and you should buy the issue. If the market price is below your price, then the bond is overvalued and you should sell the issue.
How Bond Coupon Rates and Market Rates Affect Bond Price
If a bond's coupon rate is above the yield required by the market, the bond will trade above its par value or at a premium. This will occur because investors will be willing to pay a higher price to achieve the additional yield. As investors continue to buy the bond, the yield will decrease until it reaches market equilibrium. Remember that as yields decrease, bond prices rise.
- If a bond's coupon rate is below the yield required by the market, the bond will trade below its par value or at a discount. This happens because investors will not buy this bond at par when other issues are offering higher coupon rates, so yields will have to increase, which means the bond price will drop to induce investors to purchase these bonds. Remember that as yields increase, bond prices fall.
Read more: Bond Valuation http://www.investopedia.com/walkthrough/corporate-finance/3/bonds/valuation.aspx#ixzz4qdnYNWGq
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