Bond Formula

What is Bond Formula?

Bond Formula refers to the formula that is used in order to calculate fair value of the bond under consideration and as per the formula value of the bond is calculated by adding the present value of all the coupon payments of the bond after discounting by the appropriate discount rate and the present value of bonds face value which is calculated by diving the Bond’s face value by the sum of 1 plus discount rate or yield to maturity raise to the power number of periods.

Bond Formula = ∑ (Cn/ (1+r)n) + ∑ (Pn / (1+r)N)

Bond Formula

Where,

  • Cn is the coupon on the bond
  • Pn is the Principal of the bond
  • n is the number of periods
  • N is the maturity period
  • r is the discount rate or yield to maturity

Step by Step Calculation of a Bond

The calculation of the bond can be understood in the following steps:

  • Step 1 – Calculate the coupon cash flows depending upon the frequency, which could be monthly, yearly, quarterly, or semi-annually.
  • Step 2 – Discount the coupon by relevant yield to maturity rate
  • Step 3 – Take the total of all the discounted coupons
  • Step 4 – Now, calculate the discounted value of the face value of the bond that will be paid at maturity.
  • Step 5 – Add value arrived in step 3 and step 4, which shall be the value of the bond.

Examples

You can download this Bond Formula Excel Template here – Bond Formula Excel Template

Example #1

Assume that $1,000 face value bond that pays a 6% annual coupon and will mature in 8 years. The current yield to maturity in the market is trending at 6.5%. Based on the given information, you are required to do the calculation of the bond value.

Solution

  • The cash flows on the bond are Annual coupons, which is 1,000 x 6% until period eight, and in period 8, there shall be the return of principal 1,000.

Use the below-given data for calculation of bond value

  • Face Value: 1000
  • Annual Coupon Rate: 6%
  • N (Maturity Period): 8
  • Current Yield: 6.50%

Calculation of the cash flow for Year 1

Bond Formula Example 1.1

  • =1000*6%
  • =60.00

Similarly, we can calculate cash flows for the remaining years.

Bond Formula Example 1.2

Calculation of Bond Value is as follows,

Bond Formula Example 1.3

=60/(1+6.50%)^1+60/(1+6.50%)^2+60/(1+6.50%)^3+60/(1+6.50%)^4+60/(1+6.50%)^5+60/(1+6.50%)^6+60/(1+6.50%)^7+60/(1+6.50%)^8

Bond Value will be –

Bond Formula Example 1.4

  • Bond Value = 969.56

Example #2

FANNIE MAE is one of the popular brands in the US market. One of the bonds pays quarterly interest for 3.5%, and the face value of the bond is $1,000. The bond shall mature in 5 years. The current yield to maturity prevailing in the market is 5.32%. Based on the above information, you are required to do the calculation of bond pricing in percentage points.

Solution

  • The cash flows on the bond are Quarterly coupons, which are 1,000 x 3.5%/4  until period 20 (5 years x 4), and in period 20, there shall be the return of principal 1,000.
  • Now we shall discount them at YTM, which is 5.32%/4, which shall be 1.33%.

Use the below-given data for calculation of bond value

  • Face Value: 1000
  • Quarterly Coupon Rate: 3.5%
  • N (Maturity Period): 5
  • Current Yield: 5.32%

Calculation of Cash Flow for Year 1

Bond Formula Example 2.1

  • =0.88%*1000
  • =8.75

Similarly, we can calculate cash flows for the remaining years

Bond Formula Example 2.2

Discount Rate For Year 1

Bond Formula Example 2.3

  • =1/(1+1.33%)^1
  • =0.986875

Similarly, we can calculate the discount rate for the remaining years

Example 2.4

Calculation of Discounted Cash Flows for Year 1

Bond Formula Example 2.5

  • =8.75*0.986875
  • =8.64

Similarly, we can calculate discounted cash flows for the remaining years

Calculation of Discounted Cash Flows

Example 2.6

Bond Value will be –

Example 2.7

  • Bond Value = 920.56

Therefore, the value of the bond will be 920.56/1000, which is 92.056%.

Example #3

One of the bonds that shall mature in 3 years is trading at $1,019.78 and is paying a 6.78% semiannual coupon. The current yield in the market is 5.85%. Mr. X wants to invest in this bond and wants to know if it is undervalued?

Solution

  • The cash flows on the bond are Quarterly coupons, which are 1,000 x 6.78%/2  until period 6 (3 years x 2), and in period 6, there shall be the return of principal 1,000.
  • Now we shall discount them at YTM, which is 5.85%/2, which shall be 2.93%

Use the below-given data for calculation of bond value

  • Face Value: 1000
  • Semi-Annual Coupon Rate: 3.39%
  • N (Maturity Period): 8
  • Current Yield: 2.93%

Calculation of the cash flow for Year 1

Example 3.1

Similarly, we can calculate cash flows for the remaining years.

Example 3.2

Calculation of Bond Value is as follows,

Example 3.3

=33.90/(1+2.93%)^1+33.90/(1+2.93%)^2+33.90/(1+2.93%)^3+33.90/(1+2.93%)^4+33.90/(1+2.93%)^5+33.90/(1+2.93%)^6

Bond Value will be –

Bond Formula 3.4

  • Bond Value = 1025.25

Relevance and Uses

The bond pricing or valuation shall help the investor to decide whether the investment should be made or not. This bond formula finds out the present value of all the cash flows during the bond’s life. This would also help in judging whether it is a suitable investment or not. One can also find out the rate of return on the bond when they get the pricing of the bond through this bond equation.

Recommended Articles

This has been a guide to the Bond Formula. Here we discuss the formula for calculation of bond value along with practical examples and a downloadable excel template. You can learn more about fixed income from the following articles –