Question

In: Finance

Consider two bonds: bond XY and bond ZW . Bond XY has a face value of...

Consider two bonds: bond XY and bond ZW . Bond XY has a face value of $1,000 and 10 years to maturity and has just been issued at par. It bears the current market interest rate of 7% (i.e. this is the yield to maturity for this bond). Bond ZW was issued 5 years ago when interest rates were much higher. Bond ZW has face value of $1,000 and pays a 13% coupon rate. When issued, this bond had a 15-year, so today its remaining maturity is 10 years. Both bonds make annual coupon payments.

a) (5 points) What is the price of Bond ZW , given that market interest rates are 7%? b) (15 points) Compute the duration for bond bonds (use Excel).

Solutions

Expert Solution

Price of the bond can be calculated by discounting the future cash flows at the current rate of interest:

Note: when the coupon rate > than the discount rate, the price > par and vice versa

Duration of the two bonds are calculated below:

Bond ZW
Year CF PV PV x t
1 130 130*1/1.09^(1)= 119.266055 119.266055045872*1= 119.266055
2 130 130*1/1.09^(2)= 109.4183991 109.418399124653*2= 218.8367982
3 130 130*1/1.09^(3)= 100.3838524 100.383852407938*3= 301.1515572
4 130 130*1/1.09^(4)= 92.09527744 92.0952774384755*4= 368.3811098
5 130 130*1/1.09^(5)= 84.49108022 84.4910802187849*5= 422.4554011
6 130 130*1/1.09^(6)= 77.51475249 77.5147524942981*6= 465.088515
7 130 130*1/1.09^(7)= 71.11445183 71.1144518296312*7= 497.8011628
8 130 130*1/1.09^(8)= 65.24261636 65.2426163574599*8= 521.9409309
9 130 130*1/1.09^(9)= 59.85561134 59.8556113371191*9= 538.700502
10 130 130*1/1.09^(10)= 54.9134049 54.9134048964396*10= 549.134049
10 1000 1000*1/1.09^(10)= 422.4108069 422.410806895689*10= 4224.108069
SUM 1256.706308 SUM 8226.86415
Macaulay's duration 8226.86415/1256.706308 = 6.546369742
Modified duration Macaulay's duration/(1.07)= 6.118102563
Bond XY
Year CF PV PV x t
1 70 70*1/1.09^(1)= 64.22018349 64.2201834862385*1= 64.22018349
2 70 70*1/1.09^(2)= 58.91759953 58.9175995286592*2= 117.8351991
3 70 70*1/1.09^(3)= 54.0528436 54.0528436042745*3= 162.1585308
4 70 70*1/1.09^(4)= 49.58976477 49.5897647745638*4= 198.3590591
5 70 70*1/1.09^(5)= 45.49519704 45.4951970408842*5= 227.4759852
6 70 70*1/1.09^(6)= 41.73871288 41.7387128815451*6= 250.4322773
7 70 70*1/1.09^(7)= 38.29239714 38.2923971390322*7= 268.04678
8 70 70*1/1.09^(8)= 35.13063958 35.1306395770938*8= 281.0451166
9 70 70*1/1.09^(9)= 32.22994457 32.2299445661411*9= 290.0695011
10 70 70*1/1.09^(10)= 29.56875648 29.5687564826982*10= 295.6875648
10 1000 1000*1/1.09^(10)= 422.4108069 422.410806895689*10= 4224.108069
SUM 871.646846 SUM 6379.438266
Macaulay's duration 6379.438266/871.646846=7.318833649
Modified duration Macaulay's duration/(1.07)= 6.840031448

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