Your firm has a $10,000 par value U.S. Treasury bond with 30 years to maturity,

Question

Your firm has a $10,000 par value U.S. Treasury bond with 30 years to maturity, annual coupon rate of 3.00% with semiannual coupon payments. Assume that the market annual yield to maturity on 30-year “T” bonds, found in the US Treasury Yield curve, is 3.04%. http://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/Historic-Yield-Data-Visualization.aspx A. What should the asked price (price you would pay) be for the bond? Assume: YTM from US Treasury Yield Curve = 3.04% or semiannual rate = 1.52% Hint: VB = B. If the 30 US Treasury Bond rate jumps immediately to 4.5%, what is the new price for the 30-year “T” bond? How much, in percent, would you lose or gain if you had purchased the bond in part A. VB = 150 (32.748953) + 10,000(0.263149) =$4,912.34 + 2,631.49= $7,543.83 Gain/Loss%=(price@ r= 4.5%) - (price@ r= 3.14%)/(price@ r= 3.14%)=

Explanation / Answer

1.
Price=(10000*3%/2)/(3.04%/2)*(1-1/(1+3.04%/2)^(30*2))+10000/(1+3.04%/2)^(30*2)=9921.64289

2.
Price=(10000*3%/2)/(4.5%/2)*(1-1/(1+4.5%/2)^(30*2))+10000/(1+4.5%/2)^(30*2)=7543.828536

3.
%gain=(7543.828536/9921.64289-1)=-23.966%

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