The theoretical fair value of a bond is calculated by discounting the present value of its coupon payments by an appropriate discount rate.

**Table of contents**

- Coupon and Yield
- Bond valuation
- Bond Valuation using Yield to Maturity & Spot Interest Rates
- Bond Price

In either case, the next payment will occur in exactly six months. 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.

The value of any asset is the present value of its cash flows. Therefore, we need to know two things:. We have already identified the cash flows above. Take a look at the time line and see if you can identify the two types of cash flows. 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.

Adding those together gives us the total present value of the bond. We don't have to value the bond in two steps, however. Assuming that your required return for the bond is 9. We can calculate the present value of the cash flows using the TVM keys. Enter the data: 6 into N , 4. Notice that the bond is currently selling at a discount i. This discount must eventually disappear as the bond approaches its maturity date. A bond selling at a premium to its face value will slowly decline as maturity approaches. In the chart below, the blue line shows the price of our example bond as time passes.

The red line shows how a bond that is trading at a premium will change in price over time. Both lines assume that market interest rates stay constant. In either case, at maturity a bond will be worth exactly its face value. Keep this in mind as it will be a key fact in the next section.

In the previous section we saw that it is very easy to find the value of a bond on a coupon payment date. However, calculating the value of a bond in-between coupon payment dates is more complex. As we'll see, the reason is that interest does not compound between payment dates. That means that you cannot get the correct answer by entering fractional periods e. Let's start by using the same bond, but we will now assume that 6 months have passed.

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That is, today is now the end of period 1. What is the value of the bond at this point? To figure this out, note that there are now 5 periods remaining until maturity, but nothing else has changed. Therefore, simply change the value in N to 5.

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Notice that the value of the bond has increased a little bit since period 0. As noted previously, this is because the discount must eventually vanish as the maturity date approaches. Now, is there another way that we might arrive at that period 1 value? Of course. Remember that your required return is 4. Therefore, the value of the bond must increase by that amount each period.

### Coupon and Yield

Wait a minute! That's not the same answer. However, remember that this is the total value of your holdings at the end of period 1. If we subtract that, you can see that we do get the same result:. This is one of the key points that you must understand to value a bond between coupon payment dates.

## Bond valuation

Let me recap what we just did: We wanted to know the value of the bond at the end of period 1. Step 3: Now, the total number of periods till maturity is computed by multiplying the number of years till maturity and the frequency of the coupon payments in a year. The number of periods till maturity is denoted by n. Step 4: Now, the yield to maturity YTM is the discounting factor and it is determined based on the current market return from an investment with similar risk profile.

The YTM is denoted by r. Step 5: Now, the present value of the first, second, third coupon payment and so on so forth along with the present value of the par value to be redeemed after n periods is derived as,. Step 6: Finally, adding together the present value of all the coupon payments and the par value gives the bond price as below,. Below are some of the Examples of Bond Pricing Formula. Let us take an example of a bond with annual coupon payments.

## Bond Valuation using Yield to Maturity & Spot Interest Rates

Since the coupon rate is lower than the YTM , the bond price is less than the face value and as such the bond is said to be traded at discount. Let us take an example of a bond with semi-annual coupon payments. Since the coupon rate is higher than the YTM, the bond price is higher than the face value and as such, the bond is said to be traded at a premium. Let us take the example of a zero coupon bond.

The concept of bond pricing is very important because bonds form an indispensable part of the capital markets, and as such investors and analysts are required to understand how the different factors of a bond behave in order to determine its intrinsic value.

Similar to stock valuation, the pricing of a bond is helpful in understanding whether it is a suitable investment for a portfolio and consequently forms an integral part of bond investing. This has been a guide to Bond Pricing Formula.

## Bond Price

Here we discuss how to perform bond pricing calculations along with practical examples and downloadable excel templates. You may learn more about Fixed Income from the following articles —. Your email address will not be published. Save my name, email, and website in this browser for the next time I comment.

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