Bonds are an essential piece of the global financial market, offering companies and governments a straightforward method of raising capital and investors a relatively low-risk alternative to stocks and other commodities.
To know whether a particular bond is a good investment, a financial institution, analyst, or individual investor must be able to calculate the fair value of the bond in question. Without this understanding, making an intelligent investment decision would be next to impossible.
Below are additional details about bonds, the role they play in the global market, and step-by-step instructions you can use to price a bond.
Free E-Book: A Manager's Guide to Finance & Accounting
Access your free e-book today.
A bond is a type of debt instrument that represents a loan made by a creditor to a bond issuer—typically a government or corporate entity. The issuer borrows the funds for a defined period at a variable or fixed interest rate.
Companies, municipalities, states, and sovereign governments issue bonds in order to raise capital and finance a variety of projects, activities, and initiatives. For companies, bond issuance offers an alternative to stock issuance, which can impact company value.
Investors, on the other hand, purchase bonds because of the predictable and stable income they offer compared to other investment vehicles, like stocks. If a bond is held until it matures, the bondholder will have earned back their entire principal, making bonds a way for investors to preserve capital while earning a profit.
Bond valuation is the process of determining the fair price, or value, of a bond. Typically, this will involve calculating the bond’s cash flow—or the present value of a bond’s future interest payments—as well as its face value (also known as par value), which refers to the bond’s value once it matures.
A bond’s interest payments and face value are fixed. This allows an investor to determine what rate of return a bond needs to provide to be considered a worthwhile investment.
Some other terms that can be helpful in understanding bond valuation include:
In finance, the value of something today is the present value of its discounted cash flows.
But what about bonds? It turns out, much the same is true.
While it may be intimidating if you’re not confident in your financial skills, pricing a bond is fairly simple. The price of a bond can be determined by following a few steps and plugging numbers into equations.
Before performing any calculations to value a bond, you need to identify the numbers that you’ll need to plug in to equations later in the process. Determine the bond’s face value, or par value, which is the bond’s value upon maturity. You also need to know the bond’s annual coupon rate, which is the annual income you can expect to receive from the bond. Lastly, determine what your bond’s maturity date is.
Next, calculate cash flows using the bond’s face value, annual coupon, and maturity date.
Cash Flow = Annual Coupon Rate x Face Value
After calculating cash flow, discount the expected cash flow to the present.
Cash Flow ÷ (1+r) t
In the above formula, “r” represents the interest rate, and “t” represents the number of years for each of the cash flows.
Now, you’re ready to value the individual cash flows and final face value payment in order to value your bond as a whole.
To value your cash flows, use the following formula for each year:
Cash Flow Value = Cash Flow ÷ (1+r) 1 + Cash Flow ÷ (1+r) 2 . + Cash Flow ÷ (1+r) t
Next, value the final face value payment that you’ll receive at the bond’s maturity using the following formula:
Final Face Value Payment = Face Value ÷ (1+r) t
Add together the cash flow value and the final face value placement, and you’ve successfully calculated the value of your bond.
Let's take an imaginary bond: It has a face value of $1,000, an annual coupon of three percent, and a maturity date in 30 years. What does that all mean?
It means that the company or country that owes the bond will pay the bondholder three percent of the face value of $1,000 ($30) every year for 30 years, at which point they will pay the bondholder the full $1,000 face value.
That leads to cash flows. You would have a series of 30 cash flows—one each year of $30—and then one cash flow, 30 years from now, of $1,000.
You would then apply a discounting formula:
Cash Flow ÷ (1+r) t
Represented in the formula are the cash flow and number of years for each of them (called "t" in the above equation). You would then need to calculate the "r," which is the interest rate. Which should you use? You could use the current interest rate for similar 30-year bonds today, but for the sake of this example, plug in five percent.
Now you can value the various cash flows. First, you have the coupon payments:
30 ÷ (1+.05) 1 + 30 ÷ (1+.05) 2 . + 30 ÷ (1+.05) 30
And then you have the final face value payment, in 30 years:
1,000 ÷ (1+.05) 30
Together, these total the price at $692.55. This price will ensure that the bondholder receives an annual return of five percent over the life of the bond.
Now that you have your price, you can play with some of the assumptions to see how things change. What if the prevailing market interest rate were four percent instead of five percent? In that case, the bond price would be $827.08. If it were six percent instead of five percent, the price would be $587.06.
One thing to remember is that the price of a bond is inversely related to the interest rate. When interest rates go up, the price of a bond goes down, and vice versa.
When the price of the bond is beneath the face value, the bond is "trading at a discount." When the price of the bond is above the face value, the bond is "trading at a premium."
This can be important if you don't want to actually own the bond for 30 years. If you want to hold the bond for five years, then you'd receive $30 annually for five years, and then receive that price of the bond at that time, which will depend on the current interest rates. This is why, while some long-term bonds (like government Treasury bonds) can be considered "risk-free" over their full lifetime, they will often vary a great deal in value on a year-to-year basis.
Though the process outlined above may seem confusing and overwhelming, it's a crucial part of determining whether a bond is a sound investment opportunity. As with many other skills, given enough practice and background, pricing a bond will become second nature for individuals in a finance-focused role.
Do you want to develop a toolkit to make smarter financial decisions in your career and life? Explore Leading with Finance, one of our online finance and accounting courses, to learn more about key financial levers, terms, and concepts. Not sure which is the right fit? Download our free course flowchart.
This post was updated on August 5, 2022. It was originally published on June 2, 2017.
Brian is a former member of Harvard Business School Online's Course Delivery Team and was the lead content developer for Leading with Finance and Management Essentials. He is a veteran of the United States submarine force and has a background in the insurance industry. He holds an MBA from McGill University in Montreal.
We offer self-paced programs (with weekly deadlines) on the HBS Online course platform.
Our platform features short, highly produced videos of HBS faculty and guest business experts, interactive graphs and exercises, cold calls to keep you engaged, and opportunities to contribute to a vibrant online community.
We expect to offer our courses in additional languages in the future but, at this time, HBS Online can only be provided in English.
All course content is delivered in written English. Closed captioning in English is available for all videos. There are no live interactions during the course that requires the learner to speak English. Coursework must be completed in English.
No, all of our programs are 100 percent online, and available to participants regardless of their location.
Certificate Programs
HBS Online welcomes committed learners wherever they are—in the world and their careers—irrespective of their professional experience or academic background. To extend the reach of HBS Online, we no longer require an application for our certificate programs. (Applications are still required for our credential programs: CORe and CLIMB.) You can now immediately enroll and start taking the next step in your career.
All programs require the completion of a brief online enrollment form before payment. If you are new to HBS Online, you will be required to set up an account before enrolling in the program of your choice.
Our easy online enrollment form is free, and no special documentation is required. All participants must be at least 18 years of age, proficient in English, and committed to learning and engaging with fellow participants throughout the program.
Updates to your enrollment status will be shown on your account page. HBS Online does not use race, gender, ethnicity, or any protected class as criteria for enrollment for any HBS Online program.
Credential Programs
HBS Online's CORe and CLIMB programs require the completion of a brief application. The applications vary slightly, but all ask for some personal background information. You can apply for and enroll in programs here. If you are new to HBS Online, you will be required to set up an account before starting an application for the program of your choice.
Our easy online application is free, and no special documentation is required. All participants must be at least 18 years of age, proficient in English, and committed to learning and engaging with fellow participants throughout the program.
Updates to your application and enrollment status will be shown on your account page. We confirm enrollment eligibility within one week of your application for CORe and three weeks for CLIMB. HBS Online does not use race, gender, ethnicity, or any protected class as criteria for admissions for any HBS Online program.
