Question

Consider the following​ bonds:

Bond	Coupon Rate ​(annual payments)	Maturity ​(years)
A	0.0​%	15
B	0.0​%	10
C	4.2​%	15
D	7.6​%	10

What is the percentage change in the price of each bond if its yield to maturity falls from

6.1 % to 5.1%​?

like,

a.The price of bond A at 6.1 % YTM per $100 face value is $?

b.The price of bond A at 5.1% YTM per $100 face value is ​$?

c. The percentage change in the price of bond A is $?

same with Bond B, C, D, What is the percentage change in the price of each bond if its yield to maturity falls from

6.1% to 5.1%​?

thank you.

Answer 1

The price of bond A at 6.1 % YTM:

FV = 100
Nper = 15
PMT = 0
Rate = 6.1%

Price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(6.1%,15,0,-100)
= $41.14

The price of bond A at 5.1 % YTM:

FV = 100
Nper = 15
PMT = 0
Rate = 5.1%

Price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(5.1%,15,0,-100)
= $47.42

Percentage change in the price of bond A = ($47.42 - $41.14) / $41.14
= 6.28 / 41.14
= 15.26%

Percentage change in the price of bond A = 15.26%

The price of bond B at 6.1 % YTM:

FV = 100
Nper = 10
PMT = 0
Rate = 6.1%

Price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(6.1%,10,0,-100)
= $55.32

The price of bond B at 5.1 % YTM:

FV = 100
Nper = 10
PMT = 0
Rate = 5.1%

Price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(5.1%,10,0,-100)
= $60.81

Percentage change in the price of bond B =
($60.81 - $55.32) / $55.32
= $5.49 / $55.32
= 9.93%

Percentage change in the price of bond B = 9.93%

The price of bond C at 6.1 % YTM:

FV = 100
Nper = 15
PMT = 100 * 4.2% = 4.2
Rate = 6.1%

Price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(6.1%,15,-4.2,-100)
= $81.67

The price of bond C at 5.1 % YTM:

FV = 100
Nper = 15
PMT = 4.2
Rate = 5.1%

Price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(5.1%,15,-4.2,-100)
= $90.72

Percentage change in the price of bond C = ($90.72 - $81.67) / $81.67 = 11.09%

Percentage change in the price of bond C = 11.09%

The price of bond D at 6.1 % YTM:

FV = 100
Nper = 10
PMT = 100 * 7.6% = 7.6
Rate = 6.1%

Price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(6.1%,10,-7.6,-100)
= $110.99

The price of bond D at 5.1 % YTM:

FV = 100
Nper = 10
PMT = 7.6
Rate = 5.1%

Price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(5.1%,10,-7.6,-100)
= $119.21

Percentage change in the price of bond D =($119.21 - $110.99) / $110.99 = 7.41%

Percentage change in the price of bond D = 7.41%