Question

Use the Excel spreadsheet Bond Price-Yield Calculator to answer these questions. However, you should try to replicate some of the calcuations by hand with your personal calculators to help learn the concepts. Make sure you think through the intuition behind the calculations and make sure you understand why the answers are what the Excel spreadsheet produces.

(1)       A 4.50% coupon bond matures on 8/15/2023. The settlement date for the trade is 5/26/2017. The issue date was 8/15/2013. The first coupon date was 2/15/2014. The face value owned is 100,000. The bond pays coupons semiannually.

(a) Calculate accrued interest assuming the bond is a U.S. Treasury bond.

(b) Calculate accrued interest assuming it is a U.S. domestic corporate bond.

(c) Why are the results different?

(d) Calculate the yield to maturity for the above security, assuming it is a U.S. Treasury bond priced at 99.25. Explain why it is above or below the coupon rate.

           

Answer 1

Coupon amount on the Bond = Face value x Coupon rate = 100,000 x 4.5% = 4500

A) If the bond is a US Treasury Bond then we will take the number of days in a year as 365 for accrued interest calculation:

Number of days for accrued interest - from Issue date - 8/15/2013 to settlement date - 5/26/2017 :

2013: August - 17 , September - 30 , October -31, November -30, December -31 = 139 days

2014 = 365 days , 2015 = 365 days , 2016 = 366 days (leap year) , 2017 : 31 + 28 + 31 + 30 + 25 days = 145 days

Hence, Total number of days for accrued interest = 139 + 365 + 365 + 366 + 145 = 1380 days

Accrued Interest = 4,500 x (1380 / 365) days = 4500 x 3.781 = $ 17,014.50

B) In this case , for US Corporate Bonds, the convention is to take 360 days in a year.

Accrued Interest = 4,500 x (1380 / 360) days = 4500 x 3.833 = $ 17,248.50

C) The results are different because the convention is to use 365 days in a year for accrued interest in case of US Treasury Bond, while it is 360 days in case of a US Corporate Bond.

D) Given, Price = 99.25

Yield to Maturity (using approximation formula) = [Coupon amount + (Maturity Value - Price) / n] / (Maturity Value + Price) / 2

= [ 4500 + (100,000 - 99.25) / 10 years] / (100,000 + 99.25) / 2 = [4,500 + 9,990] / 50,049.63 = 0.2895 or 28.95% p.a.

YTM is higher than the coupon rate because the Current Price of the bond is lower than its Maturity value. Yield to Maturity keeps on changing beacuse it is based on the current price at which the bond is selling, as opposed to coupon rate which is a fixed periodic payment on the face value of the bond.