Question

The current date is March 14, 2015 and you have your mind set on an 8.75% U.S. Treasury bond that happens to come due on July19, 2018. What would be the cash price of the bond if the quoted price is 104-13?

Answer 1

The Cash Price of a treasury bond is composed of 2 components: 1) The Quoted Price and 2)The Accrued Interest since the last coupon date.

In this case, we have the Quoted Price as $104.13 and the coupon rate for the bond is 8.75%. U.S. Treasury bonds pay interest semi-annually.

While the actual interest payment dates may be slightly different, since the maturity of this bond is on the 19th of July, 2018, I am assuming that the bond pays interest on the 19th of January and 19th of July (twice in a year i.e. the $8.75 interest would be paid in two tranches of $4.375 each on the these mentioned dates) every year until it matures.

In order to calculate the Accrued Interest since the last coupon date, we just need to calculate the number of days elapsed since the last coupon was paid. In our case, since it is the 14th of March, 2015 today, basis our assumption above, the last coupon must have been paid on the 19th of January, 2015. The number of days between 19th of January, 2015 and 14th of March, 2015 comes at 54 days. For a Face Value of $100 per bond, the coupon payment is $8.75 for each 365 days (until maturity).

We can thus calculate the Accrued Interest = $8.75 x 54/365 = $1.29

Thus, the Cash Price of the Bond = Quoted Price + Accrued Interest since the last coupon date = $104.13 + $1.29 = $105.42

As per our assumption of the last coupon payment date being 19th January, 2015, the Cash Price would come at $105.42.

Note: If the last coupon payment date is advanced or delayed by 1 or more days based on business day applicability, the answer may change by 2 to 3 cents per bond.