Question

Bond J is a 3.5% coupon bond. Bond K is a 9.5% coupon bond. Both bonds have 15 years to maturity, make semiannual payments and have a YTM of 6.5%. (Do not round intermediate calculations. Negative answers should be indicated by a minus sign. Round the final answers to 2 decimal places.)

If interest rates suddenly rise by 2%, what is the percentage price change of these bonds?

What if rates suddenly fall by 2% instead?

How to solve these problems with BA calculator?

Answer 1

J:
FV=1000, N=30, PMT=17.5, I/Y=3.25, PV=?--->715.27

where FV is the face Value=$1000

N= number of terms calculated semi annually = 15*2=30

PMT is the payment made semi annually= 3.5%1000/2=17.5

P.V. is the bond price =715.27

I/Y is the yield to maturity calculated swmi annually =3.25

IF interest rate Rise by 2%

then
FV=1000, N=30, PMT=17.5, I/Y=4.25, PV=?-->580.52
580.52-715.27= -134.75/715.27= -0.1883=-18.83% change
Fall by 2%
FV=1000, N=30, PMT=17.5, I/Y=2.25 PV=?--->891.77
891.77-715.27 = 176.5/715.27= 0.247=24.7% change

K: FV=1000, N=30, PMT=47.5, I/Y=3.25, PV=?--->1284.73

Rise by 2%
FV=1000, N=30, PMT=47.5, I/Y=4.25, PV=?--->1083.90
1083.90-1284.73 =-200.83/1284.73=-15.6% change
Fall by 2%
FV=1000, N=30 PMT =47.5, I/Y= 2.25, PV=?--->1541.13
1541.13 - 1284.73 = 256.4/1284.73 = 19.96% Change

When using BA calculator,

When we put FV value and PV value , we need to put either of them as negative otherwise we will get error.Usually while entering bond price , we should put negative sign. First we need to clear the calculator display. First we need to to enter the Face value and store it in FV value button. Then we need to enter the coupon payment in PMT value button. Then we will enter the market rate (eg:5%) as 5 and store in I/Y value button. Here we need to use the market rate of return. Never use the coupon rate as it is used to calculate only the coupon button. After that we will enter the time number in n button in the calculator. After that simply press the PV button to get the price of the bond . We may get a negative answer , but its ok as we enter the face value as negative.