Consider a 6 percent coupon bond with twelve years to maturity and a current pri
ID: 2777472 • Letter: C
Question
Consider a 6 percent coupon bond with twelve years to maturity and a current price of $1,062.40. Suppose the yield on the bond suddenly increases by 2 percent.
Use duration to estimate the new price of the bond. (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.)
Calculate the new bond price. (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.)
Consider a 6 percent coupon bond with twelve years to maturity and a current price of $1,062.40. Suppose the yield on the bond suddenly increases by 2 percent.
Explanation / Answer
Consider a 6 percent coupon bond with twelve years to maturity and a current price of $1,062.40. Suppose the yield on the bond suddenly increases by 2 percent.
Use duration to estimate the new price of the bond. (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.)
Current price of Bond = $ 1062.40
YTM = (Annual Coupon + ( par value - market price)/n)/ ( ( par value + market price)/2)
YTM = ((60 + (1000-1062.40)/12)/((1000+1062.40)/2)
YTM = 5.31% approx
Current Yield = 60/1062.40
Current Yield = 5.65%
Macullay Duration = Current yield/YTM * PVA(YTM,nper) *(1+YTM) + (1-Current yield/ytm)*nper
Macullay Duration = 5.65%/5.31% *PVA(5.31%,12)*(1+5.31%) + (1-5.65%/5.31%)*12
Macullay Duration = 5.65%/5.31% *8.71030*(1+5.31%) + (1-5.65%/5.31%)*12
Macullay Duration =8.99 Years
Modified Duration = Duration /(1+ytm)
Modified Duration =8.99/(1+5.31%)
Modified Duration =8.54%
New price of the bond = Current Price - Current Price*(2*8.54%)
New price of the bond = 1062.40 - 1062.40*(2*8.54%)
New price of the bond = $ 880.94
Calculate the new bond price. (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.)
New price of the bond = Coupon*PVA(rate,nper) + Face Value*pv(rate,nper)
New price of the bond = 60*PVA(7.31%,12) + 1000*PV(7.31%,12)
New price of the bond = 60*7.81310 + 1000*0.42886
New price of the bond = $ 897.65
Consider a 6 percent coupon bond with twelve years to maturity and a current price of $1,062.40. Suppose the yield on the bond suddenly increases by 2 percent.
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