## What Is Bond Valuation?

A bond is a debt that is incurred by a company or government entity to finance a project or 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 that purchased the bond but does not wish to hold onto 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 is 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 whether 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 bought for $950 was purchased below par.

If a credit rating firm raises the rating of a bond's issuer, investors tend to be willing to pay more for the bond because it is viewed as a safer purchase. A bond's price also tends to go up, toward the par value, as the maturity date approaches, because the principal will be paid on it soon.

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.

U.S. Treasury savings bonds are zero-coupon bonds that are sometimes used to help pay 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 advisors 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

Here are the steps you must take to value a bond. In this example, you will find the present value of a five-year Treasury bond issued in November 2019.

**Determine the amount of each coupon payment and the number of remaining payments:**If the coupon rate on a five-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 a single annual payment). If you were pricing this in September 2021, there would be four payments remaining (T in the formula below) because the bond matures in November 2024. The final payment includes the face value of the bond, so the payments would be as follows: year 1: $16.20; year 2: $16.20; year 3: $16.20; and 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 five-year 2019 T-bond, look at the interest rate being offered on new five-year T-bonds. Use the current interest rate (market rate) as the discount rate (r in the formula below). The rate on new five-year T-bonds on September 24, 2021, was 0.97%. 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 expressed as a decimal. For a bond with four payments left, t=1 for the next year’s payment, and t=2 for the payment two years out, for example.

- Present value of the next payment = $16.20/1.0097 = $16.04

- Present value of payment two years out = $16.20/(1.0097)^{2}= $15.89

- Present value of payment three years out = $16.20/(1.0097)^{3}= $15.74

- Present value of the final payment = $1,016.20/(1.0097)^{4}= $977.71**Calculate the value of the bond by adding together the present values of all future payments:**$16.04 + $15.89^{ }+ $15.74 + $977.71 = $1,025.38

Source for five-year T-bond interest rate: Y Charts

The present value of the 2019 five-year T-bond in this example is $1,025.38, or $25.38 above par. This makes sense, because the current rate dropped to 0.97%, which is 0.65 percentage point, or 65 basis points, less than the 1.62% rate on the 2019 T-bond we priced.

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

where T = the total number of remaining payments (four)

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

r = the discount rate

and ∑ indicates to sum each number calculated by substituting in 1, 2, 3, or 4 for t.

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

## 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.

Fidelity Investments suggests asking three questions to help you 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 that 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, if you are an investor who has a long-term horizon, you may want to choose a long-term bond fund that might offer higher yields in return for riding 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 that could offer higher yields.

**What is your risk tolerance?** The risk-averse investor should stick with money market funds, because they offer higher yields than savings accounts but are usually safer than bonds. Those who are seeking a higher return and 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 the potential for higher yields.

### Key Takeaways

- Accurately determining a bond’s value is recommended for deciding whether 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 at the time of issuance, compared with current interest rates.
- The complexity of proper bond valuation makes bond mutual funds a sound alternative for many investors.