# What Is Bond Valuation?

## What You Need to Know About Bond Valuation

Bond valuation is a means of determining a bond’s fair value based on its worth at maturity and the annual interest rate or coupon payment. There is a lot packed into that definition, so breaking it down can provide clarity.

We review what a bond is, and show you how to determine its value with a step-by-step example. We also discuss bond mutual funds as an alternative way to invest in these securities.

## What Is Bond Valuation?

A bond is debt that is incurred by a company or government entity to finance a project or to fund operations. Investors (also known as bondholders) effectively lend money to the borrower (the issuer of the bond) by buying these debt instruments. The borrower pays an annual interest rate (also referred to as the coupon rate), which can be fixed or variable, depending on the structure of the bond. Every bond has a maturity date (for example, 10 years after issue) at which point the principal amount is paid out to the bondholder, along with the final coupon payment.

A bond can be purchased from the original issuer—a corporation or a municipality, for example—or from another party who purchased the bond but does not wish to hold on to it until it matures. When a bond is purchased from the original issuer, it is typically purchased at its face value. When a bond is purchased on the open market, it’s purchased at its current value, which is affected by current interest rates.

The current value of a bond is determined at any point by totaling expected future coupon payments and adding that to the present value of the amount of principal that will be paid at maturity.

Accurately determining a bond’s value is necessary to decide if it is a good investment. But it’s not a simple process.

## How Bond Valuation Works

A bond’s face value, or “par value,” is the amount an issuer pays to the bondholder once a bond matures. The market price of a bond, which equals the “present value” of its expected future cash flows, or payments to the bondholder, fluctuates depending on a number of factors, including when the bond matures, the creditworthiness of the bond issuer, and the coupon rate at the time of issuance compared with current rates. Depending on these factors, an investor may end up purchasing a bond at par, below par, or above par.

For example, a bond with a $1,000 face value purchased for $950 would be purchased below par.

Recall that a bond’s coupon rate is the annual rate of interest that is payable on a bond. (The term refers to actual paper coupons that used to be issued to bondholders, who would clip and redeem them for their interest payment.)

A zero-coupon bond, as the name suggests, is a bond that does not pay an annual or semiannual interest payment. Instead, the bond is purchased at a discount to its face value and the investor receives a single payment at maturity that includes the principal and accumulated interest earned.

A common example of a zero-coupon bond is a U.S. Treasury Savings Bond, which is often used as a savings vehicle for college. A parent or grandparent may purchase a savings bond with a 10-year maturity and a face value of $20,000 for $16,000, for example. If the bond is held for the full 10 years, the bondholder receives $20,000 once it matures. (Of course, some financial advisers may recommend investing more aggressively over a 10-year time horizon—perhaps in a low-cost, stock index mutual fund that might offer better returns.)

## How to Calculate the Value of a Bond

Calculating the value of a bond can be approximated using the following steps. In this example, we’ll find the present value of a 5-year Treasury bond issued November 2019:

**Determine the amount of each coupon payment and the number of remaining payments**: If the coupon rate on a 5-year $1,000 Treasury bond (T-bond) issued in November 2019 is 1.62%, it would pay $16.20 annually until it matures (based on an annual payment). If you’re pricing this in November 2020, there would be four payments remaining (T in the formula below) because the bond matures in 2024. The final payment includes the face value of the bond. So, Year 1: $16.20; Year 2: $16.20; Year 3: $16.20; Year 4: $1,016.20.**Determine an appropriate discount rate**: The future payments listed above need to be discounted (reduced) to equal their present value “today.” To do this, first look up current rates for new-issue bonds that are similar to the bond you’re pricing. If you want to find the current value of a 5-year 2019 T-bond, look at the interest rate being offered on new 5-year T-bonds. Use the current interest rate (market rate) as the discount rate (r in the formula below). The rate on Nov. 27, 2020, T-bonds was 0.37%. We’ll use this as the discount rate.**Determine the present value of each remaining payment**: The present value is determined by dividing each payment by (1 + r)^{t }where t represents each numbered payment remaining, and r is the discount rate you determined in Step 2. For a bond with four payments left, t=1 for the next year’s payment, t=2 for the payment two years out, and so on.

Present value of the next payment = $16.2/1.0037 = $16.14

Present value of payment two years out = $16.2/(1.0037)^{2}= $16.08

Present value of payment three years out = $16.2/(1.0037)^{3}= $16.02

Present value of the final payment = $1016.2/(1.0037)^{4}= $1001.30**Calculate the value of the bond by adding together the present values of all future payments**: $16.2/1.0037 + $16.2/(1.0037)^{2 }+ $16.2/(1.0037)^{3}+ $1016.2/(1.0037)^{4}= $1,049.54

The present value of the 2019 5-year T-bond in this example is $1,049.54, or about $49.54 above par. This makes sense because the current rate dropped to a paltry 0.37%, which is 1.3 percentage points, or 130 basis points, less than the 1.67% rate on the 2019 T-bond we priced.

The procedure outlined above is illustrated mathematically in the formula below:

T = the total number of remaining payments (four in this illustration)

t = the number for each individual payment (1 for first year, 2 for second year, etc.)

r = the discount rate

∑ indicates to sum each number calculated by substituting in (1, 2, 3, 4) for t

The calculation used above is based on annual interest payments. To calculate for semiannual payments, the formula needs to be adjusted.

## Investing in Bond Mutual Funds

Clearly, bond valuation is a complex process. That’s why many individual investors and even some professionals opt instead to invest in bond mutual funds. Choosing the right bond mutual fund begins with identifying your investment goals and making sure they align with the objectives of any fund you are considering.

The brokerage firm Fidelity suggests asking three questions to help identify a bond fund that is a good fit:

**How long will the money be invested?** A short time horizon (one year or less) may be an indication you should keep the funds in a money market fund. With a slightly longer investment time frame, a short-term bond fund could provide higher yields and total return than a money market fund. In turn, an investor who has a long-term horizon can choose a long-term bond fund offering higher yields if they have the discipline to ride out the market’s ups and downs.

**Are you investing for current income or long-term growth?** Income investors should take a more conservative approach, such as an investment-grade, short-term bond fund. For long-term growth, an investor may seek out a multi-sector bond fund with a high yield.

**What is your risk tolerance?** The risk-averse should stick with money market funds because they offer higher yields than savings accounts but are usually safer than bonds. Those seeking a higher return who have the stomach for moderate risk could look for a high-quality, short- or intermediate-term bond fund. Those with longer time horizons and a higher risk tolerance can seek the best long-term growth through a multi-sector bond fund with high yield.

### Key Takeaways

- Accurately determining a bond’s value is recommended for deciding if it is a solid investment.
- The current value of a bond is determined by totaling expected future coupon payments and adding the amount of principal that will be paid at maturity.
- The market price of a bond fluctuates depending on a number of factors, including when the bond matures, the creditworthiness of the bond issuer, and the coupon rate compared with general interest rates at the time of issuance.
- The complexity of proper bond valuation makes bond mutual funds a sound alternative for many investors.