Understanding the Dynamic of the Bond Price Equation
A bond is deemed to be a fixed-income security. Therefore, whenever any issuer issues a bond, it is considered to be a method of getting funds from investors via issuing debt.
Whenever anyone purchases a bond from any bond issuer, they create a loan with them. Therefore, the bond price is the sum investors pay to purchase or acquire the bond. This sum acts as the perfect representative metric, facilitating individuals to calculate the bond price and value it precisely.
How can I calculate Bond Price?
A bond’s price is generally calculated as the current value of cash flow generated by the bond, i.e., which is termed the “coupon,” and the principal payment amount, or the “balloon payment.” A bond’s price keeps changing over time, and calculating its value using the bind price formula is one of the most effective methods.
Using the Bond Price Calculator
To calculate a bond price or its yield, one must input some variables. Here is a detailed look at them:
1. Inputs to the Bond Value Tool
- Bond Face Value/Par Value
The face value or the par value is the total sum that the holder will receive when the bond’s maturity date arrives.
2. Annual Coupon Rate
Any bond’s posted rate of interest is referred to as the annual coupon rate. Another way to look at the bond face value is that it is the sum paid by the bond annually divided by the par value.
- Market Rate
The yield amount an individual could otherwise receive by making another investment is known as the market rate or discount rate. The market rate or discount rate differs from the actual coupon rate of any bond.
- Years to Maturity
Years to maturity refers to the total number of years left before a bond pays the issuer its face value.
- Days Since Last Payout
It refers to the number of days since the bond issued a coupon payment.
- Coupon Payout Frequency
Coupon payout frequency refers to the number of times any bond makes a coupon payment annually. A bond can either make payments at its maturity or every year until the maturity date arrives.
3. Bond Price Tool Outputs
Once you have put in all the variables in the bond price calculator, you will receive the following outputs:
- Dirty Price
The actual predicted market price of a bond whose features match the bond’s inputs is known as the dirty price. There are numerous differences between the clean price and the dirty price. One of the most major ones is that the dirty price’s yield to maturity can be considered to compound without any interruption.
However, the payments of the bond arrive periodically. Therefore, if any organization is not purchasing or selling a bond on the payment’s date, it means that some interest rate is being applied to the bond, thereby increasing its value.
- Clean Price
The clean price of a bond refers to the amount which does not include the resulting interest is not taken into consideration. Hence, the bond price calculation relies on the difference in the value of the market price and the bond’s coupon rate.
- Accrued Interest
Any bond’s accrued interest refers to the accumulated interest amount since its last coupon payment. Even though the interest has been accumulated and earned, the investor does not receive the payments until the coupons’ set intervals arrive.
Calculating Accumulated Interest
One of the easiest methods to calculate accumulated interest is using the day count convention. A day count convention refers to the system used to calculate both the accrued interest and the present value of the bond when the upcoming coupon payment is an entire coupon period away.
A day count convention generally uses the following values when it comes to ‘time between payments:
- 1 year equals 360 days.
- 2x a year equals 180 days
- 1 quarter equals 90 days
- 1 month equals 30 days
- None refers to the maturity date (in case of zero coupon bonds)
The formula used for calculating the accumulated rate of interest is – F x* (r/(PY)) * (E/TP), where F is the bond’s face value, r is coupon rate, PY is the number of payments received in one year, E the days passed since the arrival of the last payment, and TP is the time passed in between payments.
Formulas for Calculating Dirty Price and Bond Price
There are multiple bond price formula following which individuals can calculate the clean and dirty price of bonds. When it comes to the formula for calculating the clean price of bonds, it is a complex job to do it manually. However, you can do it by using a spreadsheet program and applying the present value formula. Here is a detailed look:
Calculating Clean Price
Once you have created a new spreadsheet, add the following formula parameters – face value of the bond, coupon rate, discount rate or the market interest rate, years to maturity, and payments per year. Then, implement the PV formula, which functions like this:
- Rate – obtained by dividing using the number of payouts in a year.
- Number of Periods – obtained by multiplying the number of payouts per year.
- Payment – obtained by dividing the annual payment by payouts per year.
- Future Value – Equal to the face value.
Here is the PV or the present value formula:
Here, C refers to the amount of cash flow to discount, n refers to the number of periods, and i refers to the rate of interest.
Calculating Dirty Price:
All you need to do to calculate the dirty price of bonds is determine the clean price’s value and add to it the accrued interest amount.
YTM, or yield to maturity, is the cumulative rate of return that is earned by any bond after the interest payment is made and the original principal is repaid. It is deemed as a bond’s rate or return or RR if held to the maturity date.
The face value of a bond refers to its dollar value at the time of issue. It is also called par value or nominal value.
The bond price depends on numerous characteristics, such as the coupon or lack thereof, the principal amount, yield to maturity, periods to maturity, etc.