Bond Price Calculator

Bonds are a cornerstone of the financial world, offering investors a steady return and a sense of security. Whether you're an investor looking to assess the value of your bonds or a financial professional exploring price trends, understanding bond pricing is essential. Our Bond Price Calculator simplifies this process, helping you calculate the Clean Price, Dirty Price, and Accrued Interest of a bond.

• What Is Bond Price?
• Bond Price Formulas
• How to Use the Bond Price Calculator

What Is Bond Price?

The bond price is the present value of all future cash flows (coupon payments and principal repayment) that an investor expects to receive from a bond. Bond prices fluctuate based on various factors, including market interest rates, time to maturity, and the bond’s coupon rate.

Key Terms

• Face Value: The amount paid to the bondholder at maturity (also known as par value).
• Coupon Rate: The interest rate the bond pays annually, expressed as a percentage of its face value.
• Market Interest Rate: The current rate of return demanded by investors in the market for similar bonds.
• Payment Frequency: How often the bond pays interest (e.g., annually, semi-annually, quarterly).

Bond Price Formulas

The price of a bond can be broken into two components:

• Present Value of Coupons:

  PV_{\text{coupons}} = \sum_{t = 1}^{n} \dfrac{C}{(1+r)^t}

  Where:

  • C: Coupon payment per period \left ( \text{Face Value} \times \dfrac{\text{Coupon Rate}}{\text{Payment Frequency}} \right )
  • r: Periodic market interest rate \left ( \dfrac{\text{Market Rate}}{\text{Payment Frequency}} \right )
  • n: Total number of payments ( \text{Years to Maturity} \times \text{Payment Frequency} )
• Present Value of Face Value:

  PV_{\text{face value}} = \dfrac{\text{Face Value}}{(1+r)^n}

Total Bond Price

\text{Bond Price} = PV_{\text{face value}} + PV_{\text{coupons}}

Dirty Price and Clean Price

Dirty Price: Includes accrued interest since the last coupon payment.

\text{Dirty Price} = \text{Clean Price} + \text{Accrued Interest}

Accrued Interest::

\text{Accrued Interest} = \dfrac{\text{Coupon Payment} \times \text{Accrued Days}}{\text{Days in Coupon Period}}

How to Use the Bond Price Calculator

Inputs:

• Face Value: Enter the bond’s par value (typically $1,000).
• Coupon Rate: Enter the bond’s annual interest rate as a percentage (e.g., 5%).
• Market Rate: Provide the current market interest rate as a percentage.
• Years to Maturity: Enter the number of years remaining until the bond matures.
• Payment Frequency: Select how often the bond pays interest (Annually, Semi-Annually, Quarterly, Monthly, or Daily).
• Settlement Date: Choose the date when you purchase the bond.
• Next Coupon Date: Select the bond's upcoming coupon payment date.

Outputs:

• Clean Price: The bond price excluding accrued interest.
• Dirty Price: The total bond price, including accrued interest.
• Accrued Interest: The interest accumulated since the last coupon payment.
• Interest Accrued Days: The number of days the bond has accrued interest.

Example Calculation

Imagine you want to purchase a bond with these characteristics:

• Face Value: $1,000
• Coupon Rate: 5%
• Market Rate: 3%
• Years to Maturity: 10
• Payment Frequency: Semi-Annually (2 payments per year)
• Settlement Date: March 1, 2024
• Next Coupon Date: June 1, 2024

Step 1: Calculate Coupon Payment

C = \dfrac{\text{Face Value} \times \text{Coupon Rate}}{\text{Payment Frequency}} = \dfrac{1000 \times 0.05}{2} = 25

Step 2: Calculate Periodic Market Rate

r = \dfrac{\text{Market Rate} }{\text{Payment Frequency}} = \dfrac{0.03}{2} = 0.015

Step 3: Calculate Total Payments

n = \text{Years to Maturity} \times \text{Payment Frequency} = 10 \times 2 = 20

Step 4: Present Value of Coupons

PV_{\text{coupons}} = \sum_{t = 1}^{20} \dfrac{25}{(1+0.015)^t} = 359.43

Step 5: Present Value of Face Value

PV_{\text{face value}} = \dfrac{1000}{(1+0.015)^20} = 742.98

Step 6: Bond Price

\text{Bond Price} = PV_{\text{face value}} + PV_{\text{coupons}} = 359.43+742.98 = 1102.41

Step 7: Accrued Interest (if applicable)

If 90 days have passed since the last coupon date, accrued interest is:

\text{Accrued Interest} = \dfrac{25 \times 90}{180} = 12.5

Step 8: Dirty Price

\text{Dirty Price} = \text{Clean Price} + \text{Accrued Interest} = 1102.41+12.50=1114.91