The coupon rate and market price for the 10-year US Treasury bond are 2.50% and

Question

The coupon rate and market price for the 10-year US Treasury bond are 2.50% and 96.3828 respectively. Note, the price is expressed as a percentage of par (like other bonds). If par is $1000, then this bond is selling for $963.828.

Q1 Assume that this bond will mature in precisely 10 years, pay coupons semi-annually, and has a par value of $1000. Determine the yield to maturity for this bond.

Q2 Compute the duration of this bond and use it to estimate the new value of the bond if rates were to suddenly decline by 0.80%.

Q3 Calculate the bond's value directly (using the present value approach) assuming that rates declined 0.80% from the yield to maturity you estimated in the first question.

Q4 Compare your answers to Questions 2 and 3. Explain the source of any difference. Which is more correct

Explanation / Answer

Answer Q1. Coupon Rate 2.50% Face Value 1000 Annual Interest earnings 25 Market Value 963.828 PV at Year Cashflows 1% 2% 2.922% 3% 0 -963.828 -963.828 -963.828 -963.828 -963.828 1 25 24.752 24.510 24.290 24.272 2 25 24.507 24.029 23.601 23.565 3 25 24.265 23.558 22.931 22.879 4 25 24.025 23.096 22.280 22.212 5 25 23.787 22.643 21.647 21.565 6 25 23.551 22.199 21.032 20.937 7 25 23.318 21.764 20.435 20.327 8 25 23.087 21.337 19.855 19.735 9 25 22.858 20.919 19.292 19.160 10 1025 927.919 840.857 768.496 762.696 Total 286.172 178.242 81.085 0.031 -6.479 Yield to Maturity 2.92% Answer Q2. at 2.5% Period x Present Value Year Cashflows Cash flow at 1.7% 1 25 25 24.582 2 25 50 48.342 3 25 75 71.301 4 25 100 93.479 5 25 125 114.896 6 25 150 135.571 7 25 175 155.522 8 25 200 174.768 9 25 225 193.328 10 1025 10250 8659.929 Total 1250 9671.718857 Macaulay duration is 9280.36/1000=9.67 year. at 1.7% Present Value Year Cashflows at 2.92% 0 -963.828 -963.828 1 17 16.518 2 17 16.049 3 17 15.594 4 17 15.151 5 17 14.721 6 17 14.304 7 17 13.898 8 17 13.504 9 17 13.121 9.67 1011.39 765.677 Total 200.562 -65.29 Cash flows for Last 9.67 year = 17 x (0.67) +1000 = 1011.39 Value of the Bond 898.54 (963.828-65.29) Answer Q3. PV at Year Cashflows 2.92% 0 -963.828 -963.828 1 17 16.518 2 17 16.049 3 17 15.594 4 17 15.151 5 17 14.721 6 17 14.304 7 17 13.898 8 17 13.504 9 17 13.121 10 1017 762.646 Total 206.172 -68.323 Value of the Bond 895.51 (963.828 -68.323) Answer Q4 Bond price under the derived under 2 is greater than it is calculated under Q3. The discounted value in each year are same except after 9th year. Value Calculated under Q3 is Less than Q2. This is because of time period of 0.33 year for which cash inflows in the last year are discounted. Answer derived in Q.3 are more correct.

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