Please read the materials and watch the videos in the following links:
Please Read the Material and Watch The Videos in These 2 Links
Investopedia Dictionary: Bond (1:46).
Investopedia Dictionary: Bond Yield (1:56).
Transcript for Bond Video
Transcript for Bond Yield Video
Investopedia presents: Bond Yields
Two popular bond yield measures are the current yield and the yield to maturity. Current yield is the interest it pays annually divided by the bond’s current price. This calculation tells investors what they will earn from buying a bond and holding it for one year. Jane is thinking about buying a bond for $100 with a $10 annual coupon she divided $10 by $100 to find it’s current yield is 10%. Since bond prices constantly change due to market and economic conditions jane might not actually earn 10% her actual return will depend on how long she holds the bond and its price when she sells it. Jane might sell the bond in two years for $75. So, while she earned $20 for the 2 years she held it since she sold it for $25 less that she bought it for she actually lost $5. The current yield helps her approximate what she might earn which helps her decide whether or not to invest. Since she wants to buy a bond Jane also needs to consider yield to maturity: YTM which is how much she’ll earn if she holds the bond until it matures, that is, if she doesn’t sell before the maturity date of the bond. YTM is expressed as an annual rate and it accounts for what all of a bonds future coupon payments are worth today at their present value. Jane needs to know the bonds market price, par value, coupon interest rate and time to maturity to calculate YTM. She plugs these values into a computer program that assumes coupon payments are reinvested at the same rate as the bonds current yield of 10%. YTM is a complex calculation but it gives Jane a better idea of her future returns and lets her compare bonds with different maturities and coupons.
Please watch the following video, Investing Basics: Bonds (3:56).
Investing Basics: Bonds
Click for the transcript of "Investing Basics: Bonds " video.
PRESENTER: Bonds are a common investment. However, to many investors, they remain a mystery. So let's explore what a bond is, and how it might benefit your investment portfolio.
A bond is simply a loan given to a company or government by an investor. By issuing a bond, a company or government borrows money from investors, who in return are paid interest on the money they've loaned. Companies and governments issue bonds frequently to fund new projects or ongoing expenses. Some investors use bonds in hopes of preserving the money they have, while also generating additional income. Bonds are often viewed as a less risky alternative to stocks, and are sometimes used to diversify a portfolio.
Consider this example. The city of Fairview wants to build a new baseball stadium, so it decides to issue bonds to raise money. Each bond is a loan for $1,000, which Fairview promises to pay back in 10 years. To make this loan more attractive to investors, Fairview agrees to pay an annual interest rate of 5%, which in the bond world is also known as a coupon rate. An investor buys the bond at face value for $1,000.
Now let's fast forward. Each year, the city of Fairview pays the investor $50. These regular interest rates continue for the length of the bond, which is 10 years. Once the bond reaches maturity, the investor redeems his bond, and Fairview returns his $1,000 principal investment. This bond was a good deal for both the city and our investor. Fairview got the money it needed to build the stadium, the investor received regular interest payments and the return of the original investment.
Because a bond offers regularly scheduled payments and the return of invested principal, bonds are often viewed as a more predictable and stable form of investing. Compare regular payments of a bond to the experience of owning a stock. With stocks [although returns are typically greater] profits and losses are driven by market forces, and are considerably less predictable. Of course, like any investment, bonds are not without risk.
One risk that bond investors face is the possibility that the issuer defaults on paying back the principal. This is what is known as default risk. Typically, bonds with higher default risk also come with higher coupon rates. The amount of risk depends on the financial stability of the issuer. For example, most governments are generally considered stable issuers, and issue bonds with a relatively low coupon rate. Corporate bonds typically represent a greater risk of default, as companies can and do go bankrupt. That's why corporate bonds often offer a higher coupon rate.
Several credit rating agencies [such as Moody's and Standard and Poor's] assign rankings to different bonds. This allows bond investors to gauge the financial strength of the bond issuer. These ratings agencies often use different criteria for measuring risk, so it's a good idea to compare ratings when considering a particular bond. And keep in mind rating agencies aren't always accurate. So be sure to research a bond and its risks thoroughly before investing.
Another risk to consider is interest rate risk. This is the risk that interest rates will go up, and any bonds you own will be worth less if sold before their maturity date. After all, when interest rates rise, more investors allocate their money into the new, higher interest rate bonds. If you wanted to unload a low interest rate bond to take advantage of these new rates, you would have to sell your bond at a discount to make it a worthwhile purchase for another investor.
Capital preservation and income generation are just two ways bonds might be part of a diversified portfolio. Many investors use a mix of stocks and bonds to pursue their investment goals. And because bonds move differently from stocks, they can help increase or protect portfolio returns. Keep in mind that this discussion showed you one simplified way that investors might use bonds and only a few of the risks to consider. Like all investments, bonds are complex and have a variety of uses and risks. Before you invest in bonds, It’s important that you invest in your own financial education.
[Take control of your financial future today with premier education brought to you by Investools from TD Ameritrade Holding Corp.]
A bond is a financial tool that can help the government and corporations raise money for their investments. A bond is a document that simply means “I owe you” or “IOU.” The Government and corporations issue the bond for a specified period of time (can be weeks to years). Buyers pay the bond at face value (the price that is written on the bond) and purchase the bond once it is issued. In the end of the specified period (known as maturity date), buyers receive the face value. In return, bond issuers agree to pay a fixed annual amount as interest, called bond’s coupon. Some bonds allow the interest rate to be adjusted with inflation rate. And some bonds can be converted to common stock or other securities after a period of time. A good thing about a bond is that buyers don’t necessarily need to wait until the maturity date; they can sell their bonds before the maturity dates in the market. The price of a bond (a bond that is not new) depends on the financial market and interest rates in the market and can be higher or lower than its face value. If the interest rate in the market drops, then the bond can be sold at a higher price than the face value, and vice versa.
The organization that issues the bond usually backs (supports) it with some selected asset as collateral in case of bankruptcy. And if the issuer organization doesn’t provide real tangible assets for supporting the bond, the bond is called a “junk bond.” In general, bonds with a higher level of risk pay higher interest rates.
Brokers and investors usually measure economic performance in terms of compound interest rate of return, which is referred as “yield to maturity” (YTM), as well as the “current yield." Most bonds, debentures, and notes pay interest on a semiannual basis, but related interest rates are described nominally. This means that the evaluation of a bond must be made on a semiannual basis and then expressed as a nominal value.
The U.S. Government offers different types of securities including:
Please read the materials provided in the above links.
If you would like to know more about the history of bonds and the bond market, you can find some interesting documentaries on YouTube.com.
Example 32
Calculate the rate of return for a new bond with a face value of $1000 dollars and a maturity date of 10 years that pays 30 dollars every six months.
C = $1000 
I=$30 
I=$30 

I=$30 
L = $1000 

0 
1 
2 
... 
20 
C: Cost
I: Interest Income (semiannual)
L: Maturity Value
Present value of cost = present value of income
$$1000=30*\left(P/{A}_{i,20}\right)+1000*\left(P/{F}_{i,20}\right)$$ According to Table 112:
$$\begin{array}{l}1000=30*\left(P/{A}_{i,20}\right)+1000*\left(P/{F}_{i,20}\right)\\ 1000=30*\left[{\left(1+i\right)}^{20}1\right]/\left[i{\left(1+i\right)}^{20}\right]+1000/\left[{\left(1+i\right)}^{20}\right]\end{array}$$
With the trial and error method, we can calculate that i = 3% per semiannual period. So, the nominal rate of return equals 2*3 = 6% per year compounded semiannually. In bond broker terminology, the term “yield to maturity” is used to describe this nominal rate of return and may be listed by acronym “YTM.”
The following figure shows how you can calculate rate of return using IRR function in Microsoft Excel. Please notice the figures and signs, especially the first and last years.
Figure 32: Using the IRR function in Microsoft Excel to calculate rate of return
Credit: Farid Sayari
Old Bond Rate of Return Analysis
As explained before, buyers can sell their bonds in the market before their maturity dates.
Example 33
Assume person A buys the new bond that is explained in Example 32. After two years (in the end of the year), person A decides to sell the old bond to person B for 800 dollars. Calculate the rate of return of investment for person B.
Person B investment can be shown as:
C = $800 
I=$30 
I=$30 

I=$30 
L = $1000 

0 
1 
2 
... 
16 
We can write the equations for this investment as:
Present value of cost = present value of income
$$\begin{array}{l}800=30*\left(P/{A}_{i,16}\right)+1000*\left(P/{F}_{i,16}\right)\\ 800=30*\left[{\left(1+i\right)}^{16}1\right]/\left[i{\left(1+i\right)}^{16}\right]+1000/\left[{\left(1+i\right)}^{16}\right]\end{array}$$
The trial and error technique or IRR function in Microsoft Excel gives that i = 4.82% per semiannual period and a nominal rate of return 2*4.82 = 9.64%per year compounded semiannually.
Note: the only thing different from previous the calculation is the time and investment cost.
Please watch the following video, Calculating return on a bond investment (7:53).
Calculating return on a bond investment
Click for the transcript of "Calculating return on a bond investment" video.
PRESENTER: In this video, I'm going to talk about bonds and how to calculate the return on a bond investment.
Bonds are financial tools that can help governments and corporations raise money for their investments. So a bond is a piece of document that simply says, I owe you. So there are three things that you need to know about the bond. The first one is the face value. When buyers buy bond, they pay the face value. The face value is the amount that is written on the bond at the time that it's issued. The second thing that you need to know about the bond is the maturity date, which actually means the expiration date. It is the date that buyers receive the face value of the bond. The third one is the interest that the issuer of the bond pays to the buyers of the bond, and it is called bond coupon and it will be paid as fixed amount. It can be annually or semiannually, every six months.
Some bonds allow the interest rate to be adjusted with the inflation rate. Some bonds can be converted to some common stock or other securities. The good thing about bond is the buyer of the bond doesn't need to wait until the maturity date and receive his or her money. Buyers of the bond can sell the bond at any time before the maturity date.
The price of a bond is dependent on the financial market and interest rate in the market can be higher or lower than the face value. If the interest rate in the market drops, then bond can be sold at the higher price than the face value. For example, if you buy a bond and in the market, the interest rate drops, you can sell your bond at the higher price than the face value because the bond has coupon, which means that you're going to receive fixed amounts of payments per year or per six months, and these are fixed. If the interest rate in the market drops, your bond has higher value in the market.
Usually, the issuer of the bond has to support or back the bond with some selected asset as collateral in case of bankruptcy. Bonds with higher level of risk pay higher interest rate. The interest rate has to be reported nominally, but the interest can be paid on the semiannual basis.
Let's work on this example. Let's assume you are going to buy a bond that has a face value of $1,000 with a maturity date of 10 years that pays you $30 every six months, and you want to calculate the return on this investment.
First, we draw the time line. We are going to have 20 time intervals because there are 10 years and each six months, we are going to receive $30. We are going to have $1,000 investment at the present time, and we are going to receive $30 every six months, which are going to be 20 payments of $30. And in the end, we are going to receive the $1,000 of the face value of the bond. And we are going to calculate the return on this project.
We write the equation. Present value of the cost should be equal to present value of income. Present value of the cost is the $1,000 that we pay for this investment at the present time, and we are going to receive 20 payments of $30. And in the end of the 10th year, which is going to be the 20th period, we are going to receive the face value of $1,000.
And then we have to solve this equation using the trial and error method or IRR function in Excel, which I'm going to explain in the next video. And we calculate the i as 3% per semiannual. And then we need to calculate the nominal rate of return, which equals 2 multiply 3%, which will be 6% per year, compounded semiannually. So this investment of buying a bond at the present time at the price of $1,000 with a maturity date of 10 years and a coupon of $30 being paid every six months, is going to have the return of 6% per year compounded semiannually. The 6% nominal rate of return that we calculated is also called yield to maturity or YTM.
Now, let's work on an other example old bond rate of return analysis. Let's assume person A buys a new bond that is explained in the previous example, and then this person wants to sell the bond after two years to the person B at $800. Let's calculate the rate of return in this investment for person B.
So again, the first thing that we have to do is we have to draw the time line. And here, because person A is selling the bond after two years to person B, we are going to have 16 periods of six months. Person B is buying the bond at the cost of $800, and person B is going to receive $30 every six months for 16 periods of six months. In the end of the eighth year or 16 six months, person B is going to receive the face value of $1,000. Please note that person B is buying the bond at $800 but is going to receive the face value of the bond at the end of the maturity date.
And we write the rate of return equation. Present value of cost equal to present value of income. Cost is going to be $800, and person B is going to receive 16 payments of $30 every six months and $1,000 in the end of the 16th period. And we calculate the rate of return for this investment using the trial and error technique or IRR function in Excel, which is going to be 4.82%. And again, this is per semiannual period. We need to report that as the nominal rates per year. So we have to multiply by 2. So we are going to get 9.64% per year compounded semiannually. This is the return on this investment.
Credit: Farid Tayari
Example 34
Assume interest rates in the financial market dropped, which causes the price of an old bond to increase. So, person A in Example 32 can sell the old bond after two years (in the end of the year) to person B for 1200 dollars. Calculate the rate of return of investment for person B.
Similar to Example 33, person B's investment can be shown as:
C = $1200 
I=$30 
I=$30 

I=$30 
L = $1000 

0 
1 
2 
... 
16 
Present value of cost = present value of income
$$\begin{array}{l}1200=30*\left(P/{A}_{i,16}\right)+1000*\left(P/{F}_{i,16}\right)\\ 1200=30*\left[{\left(1+i\right)}^{16}1\right]/\left[i{\left(1+i\right)}^{16}\right]+1000/\left[{\left(1+i\right)}^{16}\right]\end{array}$$
And rate of return per semiannual period will be i = 1.58% and the nominal rate of return is: 2*1.58 = 3.16%per year compounded semiannually.
Example 35
Now assume this situation: Since the interest rate dropped in the financial market, the issuer organization can call the old bonds after 4 years (from now  total maturity period of 6 years). This means that at that time, the issuer organization takes the bond and pays the face value. Please calculate the rate of return for person B’s investment if he buys the old bond at $1200.
Person B's investment can be shown as:
C = $1200 
I=$30 
I=$30 

I=$30 
L = $1000 

0 
1 
2 
... 
8 
Note that the old bond will be called in 4 years from now after person B buys it.
Present value of cost = present value of income
$$\begin{array}{l}1200=30*\left(P/{A}_{i,8}\right)+1000*\left(P/{F}_{i,8}\right)\\ 1200=30*\left[{\left(1+i\right)}^{8}1\right]/\left[i{\left(1+i\right)}^{8}\right]+1000/\left[{\left(1+i\right)}^{8}\right]\end{array}$$
The rate of return for person B’s investment will be i = 0.45% per semiannual period and the nominal rate of return: 0.9% per year compounded semiannually.