Bond Price Calculator

How to Calculate Bond Price

Calculating the price of a bond is a fundamental skill in finance and investment analysis. The bond price represents the present value of all future cash flows, including coupon payments and the face value at maturity. This guide will walk you through the process of calculating a bond's price and yield.

Bond Price Formula

The formula for calculating the price of a bond is:

$$\text{Bond Price} = \sum_{t=1}^{n} \frac{C}{(1+r)^t} + \frac{F}{(1+r)^n}$$

Where:

• C = Coupon payment
• r = Periodic interest rate (market rate)
• n = Total number of periods
• F = Face value
• t = Time period

Calculation Steps

1. Determine the bond's face value, coupon rate, years to maturity, and market interest rate.
2. Calculate the periodic interest rate by dividing the annual market rate by the number of payments per year.
3. Calculate the number of periods by multiplying the years to maturity by the number of payments per year.
4. Calculate the coupon payment by multiplying the face value by the coupon rate and dividing by the number of payments per year.
5. Calculate the present value of all coupon payments using the formula: $$\text{PV of Coupons} = C \times \frac{1 - (1+r)^{-n}}{r}$$
6. Calculate the present value of the face value using the formula: $$\text{PV of Face Value} = \frac{F}{(1+r)^n}$$
7. Sum the present values of coupon payments and face value to get the bond price.
8. Calculate the bond yield by dividing the annual coupon payment by the bond price and multiplying by 100%.

Example Calculation

Let's calculate the price of a bond with the following characteristics:

• Face Value: $1,000
• Coupon Rate: 5% (annual)
• Years to Maturity: 10
• Market Interest Rate: 6% (annual)
• Payments Per Year: 2 (semi-annual)

1. Calculate the periodic interest rate:

   $$r = \frac{6\%}{2} = 3\% \text{ per period}$$

2. Calculate the number of periods:

   $$n = 10 \text{ years} \times 2 \text{ payments/year} = 20 \text{ periods}$$

3. Calculate the coupon payment:

   $$C = \frac{$1,000 \times 5\%}{2} = $25 \text{ per period}$$

4. Calculate the present value of coupon payments:

   $$\text{PV of Coupons} = $25 \times \frac{1 - (1+0.03)^{-20}}{0.03} = $373.12$$

5. Calculate the present value of face value:

   $$\text{PV of Face Value} = \frac{$1,000}{(1+0.03)^{20}} = $553.68$$

6. Calculate the bond price:

   $$\text{Bond Price} = $373.12 + $553.68 = $926.80$$

7. Calculate the bond yield:

   $$\text{Bond Yield} = \frac{$25 \times 2}{$926.80} \times 100\% = 5.39\%$$

Visual Representation

This pie chart illustrates the components of the bond price in our example. The blue slice represents the present value of all coupon payments ($373.12), while the orange slice shows the present value of the face value ($553.68). Together, these components sum up to the total bond price of $926.80.