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%.

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 =

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%)/(p

Explanation / Answer

Semi annually Recieved of Interest rate = 3% / 2 = 1.5%

Present value of Bond or B0 = Interest * PVAF (r , N period) + Maturity Value * PVF (r, N period)

Present value of Bond or B0 = $10,000 * 1.5% * PVAF ( 1.52% , 30 * 2 ) + $10,000 * PVF ( 1.52% , 60)

Present Value of Bond = $150 * PVAF ( 1.52% , 60 ) + $10,000 * PVF ( 1.52% , 60)

Present Value of Bond = $150* 18.312 + $10000 * 0.0478

Present Value of Bond = $2746.85 + $478

Present Value of Bond = $3224.85

The highest price I would like to pay today is $3,224.85

If Rate Jumps to 4.5%, then

Present value of Bond or B0 = Interest * PVAF (r , N period) + Maturity Value * PVF (r, N period)

Present value of Bond or B0 = $10,000 * 1.5% * PVAF ( 2.25% , 30 * 2 ) + $10,000 * PVF ( 2.25% , 60)

Present Value of Bond = $150 * PVAF ( 2.25% , 60 ) + $10,000 * PVF ( 2.25% , 60)

Present Value of Bond = $150* 32.749 + $10000 * 0.2631

Present Value of Bond = $4,912.34 + $2,631

Present Value of Bond = $7,543.34 (approx)

Gain or loss (In %) = ( 4.5% - 3.04% ) / 3.04%

Gain or loss (in %) = -48.03%

Thanks

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