Bond Equivalent Yield Formula

Bond Equivalent Yield Formula (Table of Contents)

• Bond Equivalent Yield Formula
• Bond Equivalent Yield Formula Calculator
• Bond Equivalent Yield Formula in Excel(With Excel Template)

Bond Equivalent Yield Formula

As we know, that there is only two primary source of raising funds in a company, which are Debt and Equity. Equity is the money raised by issuing shares of the company, which gives ownership rights to the holder of the shares, but it is comparatively an expensive source of funds as Equity owners expect higher return on investment as a result of the risk borne by them of being the last ones to be considered for giving returns once all others including debt holders are paid off, which also sometimes results in no returns if the company fails. However to the contrary Debt is a cheaper source of funds for the company as debt holders get a fixed interest on the money they lend and are safer then Equity as they are paid off first in case the company fails. But, a very high debt increases fixed commitment of the company which if not paid on time may lead to bankruptcy which is not the case with Equity.

Hence, every company requires a proper mix of Debt and Equity to run the company efficiently. Now, there are various means of raising debt like Bank borrowings, Non-Convertible Debentures, Bonds, Zero Coupon Bonds, and Convertible Debentures etc. Although, In India Bonds and Debentures are similar and often used interchangeably, but in some markets, like the U.S., they have different characteristics.

Not all Bonds/Debentures are made equal. Different Bonds are issued by a company with different tenures, interest rates, and payment schedules in order to meet their requirements. Some bonds are paid interest on a quarterly basis, some half-yearly and some annual. Even, for bonds like Zero Coupon Bonds, Interest is paid directly at the maturity of the bond.

There are also some bonds which are sold on discount and do not pay annual payments. To assess these bonds, they are required to be brought to the same level as other fixed income securities with annual payment by using Bond Equivalent Yield Formula. This formula annualizes the return of bonds, which helps in easy comparison and to choose the best out of all in order to invest.

Where,

• F = Face Value
• P = Purchase Price of the bond
• d = Duration of Bond/Days to Maturity

So, a Bond Equivalent Yield Formula is calculated by dividing the difference between Face Value and Purchase price of the bond by the purchase price of a bond and then multiply it by 365 and divide by No. of days to maturity. The first part of the formula is for calculating return on investment and the second part is used to annualize the return.

Examples

Let’s take an example to find out the Bond Equivalent Yield for a company: –

Example #1

Mr. Amar is evaluating two bonds for investors. Bond A is of Rs. 95 (Face Value Rs. 100) for 3 months and Bond B is Rs. 90 (Face Value Rs. 100) for 6 months. Which one should Mr. Amar choose?

This is a common scenario of being confused in choosing different bonds with different price and tenure. Hence, to resolve this issue, we use the Bond Equivalent Yield to calculate the annualized yield of both bonds and then compare.

Let’s calculate Bond Equivalent Yield for both bonds to reach the conclusion:

Bond Equivalent Yield = [{(Face Value – Purchase Price)/ Purchase Price}*{365 (or 12)/Days(or Months) to Maturity of Bond}]

• Bond A = [{(100- 95)/95}*{12/3}]
• Bond A = [{(5)/95}*{4}]
• Bond A = [{0.052632}*{4}]
• Bond A = 0.210526 or 21.1%

Now, we will find out the Bond B

• Bond B = [{(100-90)/90}*{12/6}]
• Bond B = [{(10)/90}*{2}]
• Bond B = [{0.111111}*{2}]
• Bond B = 0.222222 or 22.2%

Based on the above comparison, as we could witness, Bond B is giving higher annualized yield, hence Mr. Amar should choose to invest in Bond B.

Explanation

As stated in the above example, Mr. Amar is confused to choose between Bond A and Bond B to invest his money. Face Value of both bonds is same i.e. Rs. 100. However, Bond A is available at an Rs.5 discount while Bond B is available at Rs. 10 discount. In terms of tenure, Tenure of Bond A is 3 months while that of Bond B is 6 months i.e. post the respective time, bonds will mature and the investor will receive back Face Value of the Bond, in this case, Rs. 100. You could also refer the excel sheet to understand how Bond Equivalent Yield is calculated in Excel.

Example #2

Piramal Capital is willing to invest Rs. 1000 Cr in fixed income government securities. They are evaluating two securities for investment; first government security is a 180 days bond with a Face Value of Rs. 100 and currently selling at Rs. 98 and second government security is a 240 days government security with Face Value of Rs. 100 and currently selling at Rs. 95.

Now, in order to conclude upon which security to be chosen for investment, Piramal Capital used Bond Equivalent Yield Formula and calculated yield of both the securities as mentioned below:

Bond Equivalent Yield = [{(Face Value – currently selling)/ currently selling}*{365 /Days}]

Bond Equivalent of Yield of First Govt. Security

• Bond Equivalent Yield of First Govt. Security = [{(100-98)/98}*{365/180}]
• Bond Equivalent Yield of First Govt. Security = [{(2)/98}*{2.027778}]
• Bond Equivalent Yield of First Govt. Security = [{0.020408}*{2.027778}]
• Bond Equivalent Yield of First Govt. Security = 0.041 or 4.1%

Now, we have to find out Bond Equivalent of Yield of Second Govt. Security by using the above formula

• Bond Equivalent of Yield of Second Govt. Security = [{(100-95)/95}*{365/240}]
• Bond Equivalent of Yield of Second Govt. Security = [{(5)/95}*{1.520833}]
• Bond Equivalent of Yield of Second Govt. Security = [{0.052632}*{1.520833}]
• Bond Equivalent of Yield of Second Govt. Security = 0.08 or 8%

Based on the comparison using the Bond Equivalent Yield, it was clear to invest in Second Govt. Bond having higher annual yield compared to First Govt. Security.

Example #3

An investor has Rs. 1 crore which he wants to invest in fixed income securities. He has filtered various investment options and has shortlisted two securities, one is NCD of Tata Capital with an annualized yield of 13% and other is a ZCB of Indian Railways which is selling at a discount of 5% at Rs. 95 per unit with Face Value Rs. 100. Tenure of ZCB is 120 days.

In order to reach the conclusion, Investor uses the Bond Equivalent Yield to calculate the annualized yield of the ZCB and compare it with the annualized yield of NCD of Tata Capital.

Bond Equivalent Yield = [{(Face Value – Purchase Price)/ Purchase Price}*{365 (or 12)/Days}]

• Bond Equivalent Yield of ZCB = [{(100-95)/95}*{(365/120)}]
• Bond Equivalent Yield of ZCB = [{(5)/95*{(3.041667)}]
• Bond Equivalent Yield of ZCB = [(0.052632)*(3.041667)]
• Bond Equivalent Yield of ZCB = 0.16 or 16%

An annualized yield of ZCB is higher than the NCD, the investor chooses to invest Rs. 1 crore in ZCB of Indian Railways.

Significance and Use of Bond Equivalent Yield Formula

Bond Equivalent Yield is of significant relevance and use for investors who are looking to invest in fixed income securities. However, this formula is primarily used for fixed income securities which are being sold at a discount and does not offer any annual payments.

An investor can use this formula to compute annual yield of such bonds and compare it with annual yields of other available options to choose the best among all.

Bond Equivalent Yield Formula Calculator

You can use the following Bond Equivalent Yield Formula Calculator

Bond Equivalent Yield Formula in Excel (With excel template)

Here we will do the Above example of the Bond Equivalent Yield Formula in Excel. It is very easy and simple. You need to provide the three inputs i.e Face Value, Purchase Price of the bond and Duration of Bond/Days to Maturity

Here first, we have found out the Bond Equivalent Yield for Bond A

Then, we find out the Bond Equivalent Yield for Bond B

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

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