Question

In: Finance

Calculate the Macaulay duration of an 8%, $1,000 par bond that matures in three years if...

Calculate the Macaulay duration of an 8%, $1,000 par bond that matures in three years if the bond's YTM is 14% and interest is paid semiannually. You may use Appendix C(https://cnow.apps.ng.cengage.com/ilrn/books/reia11h/appendix_c.jpg) to answer the questions.

  1. Calculate this bond's modified duration. Do not round intermediate calculations. Round your answer to two decimal places.

      years

  2. Assuming the bond's YTM goes from 14% to 13.0%, calculate an estimate of the price change. Do not round intermediate calculations. Round your answer to three decimal places. Use a minus sign to enter negative value, if any.

      %

Solutions

Expert Solution

a

                  K = Nx2
Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2
                   k=1
                  K =3x2
Bond Price =∑ [(8*1000/200)/(1 + 14/200)^k]     +   1000/(1 + 14/200)^3x2
                   k=1
Bond Price = 857

Period Cash Flow Discounting factor PV Cash Flow Duration Calc
0 ($857.00) =(1+YTM/number of coupon payments in the year)^period =cashflow/discounting factor =PV cashflow*period
1                 40.00                                                             1.07                    37.38                  37.38
2                 40.00                                                             1.14                    34.94                  69.88
3                 40.00                                                             1.23                    32.65                  97.96
4                 40.00                                                             1.31                    30.52                122.06
5                 40.00                                                             1.40                    28.52                142.60
6           1,040.00                                                             1.50                  693.00              4,157.98
      Total              4,627.85
Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)
=4627.85/(857*2)
=2.70
Modified duration = Macaulay duration/(1+YTM)
=2.7/(1+0.14)
=2.52

b

Using only modified duration
Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price
=-2.52*-0.01*857
=--21.63
%age change in bond price=Mod.duration prediction/bond price
=21.63/857
=2.52%
New bond price = bond price+Modified duration prediction
=857--21.63
=878.63

Related Solutions

Calculate the Macaulay duration of a 9%, $1,000 par bond that matures in three years if...
Calculate the Macaulay duration of a 9%, $1,000 par bond that matures in three years if the bond's YTM is 14% and interest is paid semiannually. You may use Appendix C to answer the questions. A. Calculate this bond's modified duration. Do not round intermediate calculations. Round your answer to two decimal places. B. Assuming the bond's YTM goes from 14% to 13.0%, calculate an estimate of the price change. Do not round intermediate calculations. Round your answer to three...
a. Calculate the duration of a 6 percent, $1,000 par bond maturing in three years if...
a. Calculate the duration of a 6 percent, $1,000 par bond maturing in three years if the yield to maturity is 10 percent and interest is paid semiannually. b. Calculate the modified duration for a 10-year, 12 percent bond with a yield to maturity of 10 percent and a Macaulay duration of 7.2 years.
Pete plans to buy an 8 percent, $1,000 par bond that matures in three years and...
Pete plans to buy an 8 percent, $1,000 par bond that matures in three years and the interest is paid semiannually, and the bond’s YTM is 10 percent. Calculate the bond’s duration.    (b) Calculate the bond’s modified duration.    (c) Assuming the bond’s YTM declines from 10 percent to 9.5 percent, calculate the bond’s price change. Explain your answer. (d) Explain how changes in YTM affects the bond’s market price risk and reinvestment risk.
Pete plans to buy an 8 percent, $1,000 par bond that matures in three years and...
Pete plans to buy an 8 percent, $1,000 par bond that matures in three years and the interest is paid semiannually, and the bond’s YTM is 10 percent. Calculate the bond’s duration.    (b) Calculate the bond’s modified duration.    (c) Assuming the bond’s YTM declines from 10 percent to 9.5 percent, calculate the bond’s price change. Explain your answer. (d) Explain how changes in YTM affects the bond’s market price risk and reinvestment risk.
Pete plans to buy an 8 percent, $1,000 par bond that matures in three years and...
Pete plans to buy an 8 percent, $1,000 par bond that matures in three years and the interest is paid semiannually, and the bond’s YTM is 10 percent. Calculate the bond’s duration.    (b) Calculate the bond’s modified duration.    (c) Assuming the bond’s YTM declines from 10 percent to 9.5 percent, calculate the bond’s price change. Explain your answer. (d) Explain how changes in YTM affects the bond’s market price risk and reinvestment risk.
Calculate the value of a bond that matures in 15 years and has a $1,000 par...
Calculate the value of a bond that matures in 15 years and has a $1,000 par value. The annual coupon interest rate is 14 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 11 percent.
Calculate the value of a bond that matures in 16 years and has a $1,000 par...
Calculate the value of a bond that matures in 16 years and has a $1,000 par value. The annual coupon interest rate is 12 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 16 percent.
Calculate the value of a bond that matures in 18 years and has a $1,000 par...
Calculate the value of a bond that matures in 18 years and has a $1,000 par value. The annual coupon interest rate is 13 percent and the​ market's required yield to maturity on a comparable-risk bond is 15 percent.
Calculate the value of a bond that matures in 13 years and has a $1,000 par...
Calculate the value of a bond that matures in 13 years and has a $1,000 par value. The annual coupon interest rate is 9 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 11 percent. The value of the bond is
  ​(Bond valuation) A bond that matures in 8 years has a ​$1,000 par value. The annual...
  ​(Bond valuation) A bond that matures in 8 years has a ​$1,000 par value. The annual coupon interest rate is 9 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 18 percent. What would be the value of this bond if it paid interest​ annually? What would be the value of this bond if it paid interest​ semiannually? *Someone previously answered this with annually = $604.56 and semiannually = $596.89 and the annual number is incorrect*
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT