Going through an example in regards to DR and AOR where BEY is required to calculate. Data given is below along with the solution but it looks a bit messy due to format.
Now the question is- why is PV calculation the first step using 100 as FV for DR whereby for AOR the first step would be calculate FV using 100 as PV?
A Discount Rate 360 4.33%
B Add-On Rate 360 4.35%
Solution A:
Use Equation 9 to get the price per 100 of par value, where FV = 100, Days = 180, Year = 360, and DR = 0.0433.
PV =100×⎛1−180×0.0433⎞=97.835 ⎜⎝ 360 ⎟⎠
Use Equation 12 to get the bond equivalent yield, where Year = 365, Days = 180, FV = 100, and PV = 97.835.
AOR = ⎛365⎞ × ⎛100 − 97.835⎞ = 0.04487 ⎜⎝180 ⎟⎠ ⎜⎝ 97.835 ⎟⎠
The bond equivalent yield for Bond A is 4.487%.
Solution B
First, determine the redemption amount per 100 of principal (PV = 100), where Days = 180, Year = 360, and AOR = 0.0435.
FV = 100 + ⎛100 × 180 × 0.0435⎞ = 102.175 ⎜⎝ 360
Use Equation 12 to get the bond equivalent yield, where Year = 365, Days = 180, FV = 102.175, and PV = 100.
AOR = ⎛365⎞ × ⎛102.175 − 100⎞ = 0.04410 ⎜⎝180 ⎟⎠ ⎜⎝ 100 ⎟⎠
The bond equivalent yield for Bond C is 4.410%.
Another way to get the bond equivalent yield for Bond C is to observe that the AOR of 4.35% for a 360-day year can be obtained using Equation 12 for Year = 360, Days = 180, FV = 102.175, and PV = 100.
AOR = ⎛360⎞ × ⎛102.175 − 100⎞ = 0.0435 ⎜⎝180 ⎟⎠ ⎜⎝ 100 ⎟⎠
Therefore, an add-on rate for a 360-day year only needs to be multiplied by the factor of 365/360 to get the 365-day year bond equivalent yield.
365/360× 0.0435 = 0.04410
