Skip to Main Content
HBS Online
  • Courses
    Open Courses Mega Menu
    • Business Essentials
      • Credential of Readiness (CORe)
      • Business Analytics
      • Economics for Managers
      • Financial Accounting
    • Leadership & Management
      • Leadership Principles
      • Management Essentials
      • Negotiation Mastery
      • Organizational Leadership
      • Strategy Execution
      • Power and Influence for Positive Impact
      • Leadership, Ethics, and Corporate Accountability
      • Leading Change and Organizational Renewal
      • Dynamic Teaming
      • Transforming Customer Experiences
    • Credential of Leadership, Impact, and Management in Business (CLIMB)
    • Credential of Digital Innovation and Strategy
    • Entrepreneurship & Innovation
      • Entrepreneurship Essentials
      • Disruptive Strategy
      • Negotiation Mastery
      • Design Thinking and Innovation
      • Launching Tech Ventures
      • Winning with Digital Platforms
      • Leading Change and Organizational Renewal
      • Entrepreneurial Marketing
      • Transforming Customer Experiences
    • Strategy
      • Strategy Execution
      • Business Strategy
      • Economics for Managers
      • Disruptive Strategy
      • Global Business
      • Sustainable Business Strategy
    • Marketing
      • Digital Marketing Strategy
      • Creating Brand Value
      • Entrepreneurial Marketing
    • Digital Transformation
      • Winning with Digital Platforms
      • AI Essentials for Business
    • Finance & Accounting
      • Financial Accounting
      • Leading with Finance
      • Alternative Investments
      • Sustainable Investing
      • Strategic Financial Analysis
    • Business in Society
      • Sustainable Business Strategy
      • Global Business
      • Sustainable Investing
      • Power and Influence for Positive Impact
      • Leadership, Ethics, and Corporate Accountability
      • Business and Climate Change
    • All Courses
  • For Organizations
    Open For Organizations Mega Menu
    • Corporate Learning
      Help your employees master essential business concepts, improve effectiveness, and expand leadership capabilities.
    • Academic Solutions
      Integrate HBS Online courses into your curriculum to support programs and create unique educational opportunities.
    • Need Help?
      • Frequently Asked Questions
      • Contact Us
    • Insights
      Open Insights Mega Menu
      • Business Insights Blog
        • Career Development
        • Communication
        • Decision-Making
        • Earning Your MBA
        • Entrepreneurship & Innovation
        • Finance
        • Leadership
        • Management
        • Negotiation
        • Strategy
      • All Topics
      • Learner on computer exploring HBS Online business lessons
        Sample Business Lessons and E-Books

        Gain new insights and knowledge from leading faculty and industry experts.

      • HBS Online Parlor Room podcast logo
        Podcast

        The Parlor Room: Where business concepts come to life. Listen now on your favorite podcast platform.

    • More Info
      Open More Info Mega Menu
      • Learning Experience
        Master real-world business skills with our immersive platform and engaged community.
      • Certificates, Credentials, & Credits
        Learn how completing courses can boost your resume and move your career forward.
      • Learning Tracks
        Take your career to the next level with this specialization.
      • Financing & Policies
        • Employer Reimbursement
        • Payment & Financial Aid
        • Policies
      • Connect
        • Student Stories
        • Community
      • Need Help?
        • Frequently Asked Questions
        • Request Information
        • Support Portal
      • Enroll Now
    Login
    My Courses
    Access your courses and engage with your peers
    My Account
    Manage your account, enrollment, and payments.
    HBS Home
    • About HBS
    • Academic Programs
    • Alumni
    • Faculty & Research
    • Baker Library
    • Giving
    • Harvard Business Review
    • Initiatives
    • News
    • Recruit
    • Map / Directions
    HBS Online
    • Courses
    • Business Essentials
    • Leadership & Management
    • Credential of Leadership, Impact, and Management in Business (CLIMB)
    • Credential of Digital Innovation and Strategy
    • Entrepreneurship & Innovation
    • Strategy
    • Marketing
    • Digital Transformation
    • Finance & Accounting
    • Business in Society
    • For Organizations
    • Insights
    • More Info
    • About
    • Support Portal
    • Media Coverage
    • Founding Donors
    • Leadership Team
    • Careers
    • My Courses
    • My Account
    • Enroll Now
    • …→
    • Harvard Business School→
    • HBS Online→
    • Business Insights→

    Business Insights

    Harvard Business School Online's Business Insights Blog provides the career insights you need to achieve your goals and gain confidence in your business skills.

     
    Filter Results Arrow Down Arrow Up

    Topics

    Topics

    • Accounting
    • Analytics
    • Business Essentials
    • Business in Society
    • Career Development
    • Communication
    • Community
    • ConneXt
    • Decision-Making
    • Digital Transformation
    • Earning Your MBA
    • Entrepreneurship & Innovation
    • Finance
    • Leadership
    • Management
    • Marketing
    • Negotiation
    • News & Events
    • Productivity
    • Staff Spotlight
    • Strategy
    • Student Profiles
    • Technology
    • Work-Life Balance

    Courses

    Courses

    • AI Essentials for Business
    • Alternative Investments
    • Business Analytics
    • Business Strategy
    • Business and Climate Change
    • CLIMB
    • CORe
    • Creating Brand Value
    • Credential of Digital Innovation and Strategy
    • Design Thinking and Innovation
    • Digital Marketing Strategy
    • Disruptive Strategy
    • Dynamic Teaming
    • Economics for Managers
    • Entrepreneurial Marketing
    • Entrepreneurship Essentials
    • Financial Accounting
    • Global Business
    • Launching Tech Ventures
    • Leadership Principles
    • Leadership, Ethics, and Corporate Accountability
    • Leading Change and Organizational Renewal
    • Leading with Finance
    • Management Essentials
    • Negotiation Mastery
    • Organizational Leadership
    • Power and Influence for Positive Impact
    • Strategic Financial Analysis
    • Strategy Execution
    • Sustainable Business Strategy
    • Sustainable Investing
    • Transforming Customer Experiences
    • Winning with Digital Platforms
    Subscribe to the Blog
    *
    Please complete this required field.
    Email must be formatted correctly.
    Please complete all required fields.
    RSS feed

    Filters

    Topics

    Topics

    • Accounting
    • Analytics
    • Business Essentials
    • Business in Society
    • Career Development
    • Communication
    • Community
    • ConneXt
    • Decision-Making
    • Digital Transformation
    • Earning Your MBA
    • Entrepreneurship & Innovation
    • Finance
    • Leadership
    • Management
    • Marketing
    • Negotiation
    • News & Events
    • Productivity
    • Staff Spotlight
    • Strategy
    • Student Profiles
    • Technology
    • Work-Life Balance

    Courses

    Courses

    • AI Essentials for Business
    • Alternative Investments
    • Business Analytics
    • Business Strategy
    • Business and Climate Change
    • CLIMB
    • CORe
    • Creating Brand Value
    • Credential of Digital Innovation and Strategy
    • Design Thinking and Innovation
    • Digital Marketing Strategy
    • Disruptive Strategy
    • Dynamic Teaming
    • Economics for Managers
    • Entrepreneurial Marketing
    • Entrepreneurship Essentials
    • Financial Accounting
    • Global Business
    • Launching Tech Ventures
    • Leadership Principles
    • Leadership, Ethics, and Corporate Accountability
    • Leading Change and Organizational Renewal
    • Leading with Finance
    • Management Essentials
    • Negotiation Mastery
    • Organizational Leadership
    • Power and Influence for Positive Impact
    • Strategic Financial Analysis
    • Strategy Execution
    • Sustainable Business Strategy
    • Sustainable Investing
    • Transforming Customer Experiences
    • Winning with Digital Platforms
    Subscribe to the Blog
    *
    Please complete this required field.
    Email must be formatted correctly.
    Please complete all required fields.
    RSS feed

    How to Price a Bond: An Introduction to Bond Valuation

    Pricing a Bond
    • 02 Jun 2017
    Brian Misamore Author Staff
    tag
    • Finance
    • Leading with Finance

    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.

    DOWNLOAD NOW

    What Is a Bond?

    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.

    What Is Bond Valuation?

    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:

    • Maturity date: This refers to the length of time until the bond’s principal is scheduled to be repaid to the bondholder. The maturity date can be short- or long-term. Once the date is reached, the bond’s issuer—whether corporate or governmental—must repay the bondholder the full face value of the bond.
    • Coupon rate/discount rate: This refers to the interest payments that a bondholder receives. Typically, it's represented as a fixed percentage of the bond’s face value. Payments may be made annually or semi-annually, depending on the specifics of the bond.
    • Current price: This refers to a bond’s current value, and is typically what’s discussed when someone mentions “bond valuation.” Depending on several different factors, including market conditions, the current price of a bond may be at, above, or below par value.

    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.

    How to Price a Bond

    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.

    1. Determine the Face Value, Annual Coupon, and Maturity Date

    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.

    2. Calculate Expected Cash Flow

    Next, calculate cash flows using the bond’s face value, annual coupon, and maturity date.

    Cash Flow = Annual Coupon Rate x Face Value

    3. Discount the Expected Cash Flow to the Present

    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.

    4. Value the Various 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.

    Leading with Finance | Gain an intuitive understanding of finance | Learn More

    Bond Valuation: An Example

    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.

    Which HBS Online Finance and Accounting Course is Right for You? | Download Your Free Flowchart

    The Bottom Line

    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.

    About the Author

    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.
     
    All FAQs

    Top FAQs

    How are HBS Online courses delivered?

    +–

    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.

    Are HBS Online programs available in languages other than English?

    +–

    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.

    Do I need to come to campus to participate in HBS Online programs?

    +–

    No, all of our programs are 100 percent online, and available to participants regardless of their location.

    How do I enroll in a course?

    +–

    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.

    Does Harvard Business School Online offer an online MBA?

    +–

    No, Harvard Business School Online offers business certificate programs.

    What are my payment options?

    +–

    We accept payments via credit card, wire transfer, Western Union, and (when available) bank loan. Some candidates may qualify for scholarships or financial aid, which will be credited against the Program Fee once eligibility is determined. Please refer to the Payment & Financial Aid page for further information.

    We also allow you to split your payment across 2 separate credit card transactions or send a payment link email to another person on your behalf. If splitting your payment into 2 transactions, a minimum payment of $350 is required for the first transaction.

    In all cases, net Program Fees must be paid in full (in US Dollars) to complete registration.

    What are the policies for refunds and deferrals?

    +–

    After enrolling in a program, you may request a withdrawal with refund (minus a $100 nonrefundable enrollment fee) up until 24 hours after the start of your program. Please review the Program Policies page for more details on refunds and deferrals. If your employer has contracted with HBS Online for participation in a program, or if you elect to enroll in the undergraduate credit option of the Credential of Readiness (CORe) program, note that policies for these options may differ.

     

    Sign up for News & Announcements


    • • Please complete this required field.
    • • Email must be formatted correctly.
    • • Please complete all required fields.

    Subject Areas

    • Business Essentials
    • Leadership & Management
    • Entrepreneurship & Innovation
    • Strategy
    • Marketing
    • Finance & Accounting
    • Business & Society
    • Digital Transformation

    Quick Links

    • FAQs
    • Contact Us
    • Request Info
    • Enroll Now
    • Support Portal

    About

    • About Us
    • Media Coverage
    • Founding Donors
    • Leadership Team
    • Careers @ HBS Online

    Legal

    • Legal
    • Policies
    Harvard Business School
    Copyright © President & Fellows of Harvard College
    • Site Map
    • Trademark Notice
    • Digital Accessibility