What is the value of the bond at this point? That is, today is now the end of period 1. Let's start by using the same bond, but we will now assume that 6 months have passed. That means that you cannot get the correct answer by entering fractional periods (e.g., 5.5) into N. As we'll see, the reason is that interest does not compound between payment dates. However, calculating the value of a bond in-between coupon payment dates is more complex. In the previous section we saw that it is very easy to find the value of a bond on a coupon payment date. Keep this in mind as it will be a key fact in the next section. In either case, at maturity a bond will be worth exactly its face value. Both lines assume that market interest rates stay constant. The red line shows how a bond that is trading at a premium will change in price over time. In the chart below, the blue line shows the price of our example bond as time passes. A bond selling at a premium to its face value will slowly decline as maturity approaches. This discount must eventually disappear as the bond approaches its maturity date. ![]() Notice that the bond is currently selling at a discount (i.e., less than its face value). Please see the Initial Setup section of the HP 10B tutorial for how to correct this problem.) (If you get $1,213.29 instead, then you have the calculator set to assume monthly compounding. Now, press PV and you will find that the value of the bond is $961.63. We can calculate the present value of the cash flows using the TVM keys. The TVM keys on the HP 10B or 10BII can handle this calculation as we will see in the next example:Īssuming that your required return for the bond is 9.5% per year, what is the most that you would be willing to pay for this bond? We don't have to value the bond in two steps, however. Adding those together gives us the total present value of the bond. Using the principle of value additivity, we know that we can find the total present value by first calculating the present value of the interest payments and then the present value of the face value. The face value is a $1,000 lump sum cash flow. Notice that the interest payments are a $40, six-period regular annuity. ![]() Take a look at the time line and see if you can identify the two types of cash flows. We have already identified the cash flows above. The required rate of return ( discount rate) that is appropriate given the riskiness of the cash flows.The value of any asset is the present value of its cash flows. This will be important because we are going to use the time value of money keys to find the present value of the cash flows. In either case, the next payment will occur in exactly six months. We will begin our example by assuming that today is either the issue date or a coupon payment date. We will use this bond throughout the tutorial. Therefore, the time line looks like the one below: Finally, the $1,000 will be returned at maturity (i.e., the end of period 6). However, the annual interest is paid in two equal payments each year, so there will be six coupon payments of $40 each. The bond will pay 8% of the $1,000 face value in interest every year. The bond has three years until maturity and it pays interest semiannually, so the time line needs to show six periods. ![]() Let's look at an example:ĭraw a time line for a 3-year bond with a coupon rate of 8% per year paid semiannually. Bond Cash FlowsĪs noted above, a bond typically makes a series of semiannual interest payments and then, at maturity, pays back the face value. You may also be interested in my tutorial on calculating bond yields using the HP 10B or 10BII. If you aren't comfortable doing time value of money problems on the HP 10B or HP 10BII, you should work through those tutorials first. If you aren't familiar with the terminology of bonds, please check the Bond Terminology page. ![]() The purpose of this section is to show how to calculate the value of a bond, both on a coupon payment date and between payment dates. bonds typically pay interest every six months (semi-annually), though other payment frequencies are possible. Most commonly, bonds are promises to pay a fixed rate of interest for a number of years, and then to repay the principal on the maturity date. Are you a student? Did you know that Amazon is offering 6 months of Amazon Prime - free two-day shipping, free movies, and other benefits - to students? Click here to learn moreĪ bond is a debt instrument, usually tradeable, that represents a debt owed by the issuer to the owner of the bond.
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