# Bond Equivalent Yield

###### What is bond equivalent yield ?

The bond equivalent yield is the annualized return earned by an investor holding a discount bond or zero coupon bond. In other words, is the annualized equivalent yield for those bonds that do not pay annual interest or pay no interest at all. The main objective of calculating a Bond equivalent yield of a bond issued at discount is to make it comparable to the annual yield of other bonds in the money market.

###### Why do we calculate bond equivalent yield ?

The short-term capital market or money market comprises of several instruments that are issued by companies at different interest rates and maturity periods. For an investor to take a decision on the basis of just the interest rate being offered, may not be correct. The interest rate offered is for a specific period in a year and not annual rate. In order to take an informed investing decision, the bond equivalent yield is calculated which gives the annualized return for a given investment in the money market. This makes comparison of two or more instruments feasible and enables an informed investment decision.

###### How do you calculate Bond equivalent yield ?

The bond equivalent yield is the difference between the Face value and purchase price of a discount bond divided by the purchase price, which is then annualized by multiplying the result by 365  and dividing by the number of days to maturity.

The formula for calculating the Bond equivalent yield is

BEY = [ ( F – P ) / P ] * ( 365 / N )

Where

F = Face value or par value on the bond   ;  P = Purchase price of the bond  ;

N = Number of days to maturity   ;

###### What is the difference between bank discount yield and bond equivalent yield ?

Bank discount yield is the annualized return of a financial instrument that has been issued at a discount. It is calculated for a period of 360 days. The yield of most Treasury bills issued by the US Department of Treasury are quoted at the bank discount rate.

This is in contrast to the annualized return calculated under Bond equivalent yield which uses a 365 day period.

###### What are the drawbacks of Bond equivalent yield ?

1.The Bond equivalent yield formula simply annualizes the yield of the discount bond without effecting the benefit of compounding.

2.It can be used to calculate bond equivalent yield of only those instruments that are issued at a discount and do not pay any interest during its holding period.

Example :

Calculate the bond equivalent yield of a bond with a face value of \$ 100,000 that was purchased at a discounted price of \$ 95,000 and has a maturity period of 270 days. ( Round the solution to two decimal places )

Solution :

The formula for calculation of Bond equivalent yield is

= [ ( Face value – Purchase Price ) / Purchase Price ] * ( 365 / Number of days to Maturity)

As per the Information provided in the question we have

Face Value = \$ 100,000   ;  Purchase Price = \$ 95,000    ;  No. of days to maturity = 270

Applying the above values in the formula we have the bond equivalent yield as

= [ ( 100000 – 95000 ) / 95000 ] * ( 365/270 )

=( 5000 / 95000 ) * 1.351852

= 0.052632 * 1.351852

= 0.071150

= 7.1150 %

= 7.12 %

Thus the bond equivalent yield = 7.12 %

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