Question

In: Finance

You purchase $100 million par of an 8.5% coupon Treasury bond that matures in November 15,...

You purchase $100 million par of an 8.5% coupon Treasury bond that matures in November 15, 2028. Quoted price is 100-12. The settlement date is September 10, 2018. Calculate the cash amount you have to pay. Coupons are paid semiannually.

Solutions

Expert Solution

Given,

Par value of investment= $100 Million, Coupon=8.5% and Quoted price= 100-12

Since it is a Treasury bond (Government), the quote is multiples of 32. Hence 12 has to be converted into % by dividing by 32 and the same is to be added to the handle, ie., 100.

Therefore, quoted price= 100+(12/32)= 100+0.375= 100.375%

Broken period interest:

The bond’s coupon payments are semiannual. Maturity is on November 15, 2028. That means coupon payments are due on November 15 and June 15 every year. Since the settlement is on September 10, 2018, last interest payment was on June 15, 2018. The issuer (Government) will pay the full semiannual interest on the next coupon date to the holder on that day, as records. Since it is being purchased by a new person, coupon payment for half year to will go to him while the seller is entitled to get the portion of interest for the period for which he was holding the same. This is called broken period interest and has to be added to the quoted price in order to arrive at the settlement amount.

Bond market uses the 360 days protocol for interest calculations. Hence the broken period interest in this case is as follows:

Number of days after last coupon payment: 83 (June 15, July 31, August 31 and September 9)

Coupon rate= 8.5%= 0.085

Broken period interest for $100 FV= (100*0.085*83)/360 = 1.959722

Total payment on settlement:

This is the total of price at quoted rate and the broken period.

Par value of bonds= $100 Million

Settlement rate= 100.375 + 1.959722 = 102.334722

Settlement amount= (Par value/100)*Settlement rate = ($100 Million/100)*102.334722 = $ 102,334,722

Hence the amount to be paid on purchase is $ 102,334,772


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