In: Finance
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.
Calculate this bond's modified duration. Do not round intermediate calculations. Round your answer to two decimal places.
years
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.
%
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 |