Assume the following information about a Treasury bond: You may assume that the

Question

Assume the following information about a Treasury bond: You may assume that the par value of this bond is 100. Also remember that Treasuries pay coupons SEMI-ANNUALLY. Find the Accrued Interest, the Price, and the Modified Duration of this bond. Using the Modified Duration, what is the approximate percentage change in price for a 25 basis point change in yield? Find the price if the yield is 5.5% (why is the total cost not equal to Par?). Find the price if the yield is 5.0%, did the price change by more or less than was predicted? Why? Suppose you hold this bond for example 6 months and the yield does indeed increase to 5.5%. What is your total return for this bond?

Explanation / Answer

1. Last Interest date = 31st July

No, of days since last payment of interest = 30th june 2005 to 13th Sep 2009 = 75 days

No, of days between payments = 31st Dec 2004 to 30th june 2005 = 181 days

Accrued Interest = Interest Payment x No. of days since last payment / No. of days between payments

= 100*5.5% x 75 / 181

= $2.279 per bond

Bond Value = Present Value of Coupon Payments + Present Value of Par Value

Present Value of Coupon payments discounted at Yield half year (i.e. 2.625%) = (5.5*7.132) + (100*0.813) = $120.526

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