Question
In: Finance
A zero coupon bond has a par value of $1,000 and will mature in eight years....
A zero coupon bond has a par value of $1,000 and will mature in eight years.
a Calculate the current price of this bond if the market yield is: 1) 7.75 percent; ii) 5.25 percent.
b. In each case, calculate the percentage change in the price of the bond if the market yield rises by 1 percent.
Solutions
Expert Solution
a.i.Information provided:
Face value= future value= $1,000
Time= 8 years
Yield to maturity= 7.75%
The current price of the bond is calculated by computing the present value.
Enter the below in a financial calculator to compute the present value:
FV= 1,000
I/Y= 7.75
N= 8
Press the CPT key and PV to compute the present value.
The value obtained is 550.38.
Therefore, the current price of the bond is $550.38.
ii.Information provided:
Face value= future value= $1,000
Time= 8 years
Yield to maturity= 5.25%
The current price of the bond is calculated by computing the present value.
Enter the below in a financial calculator to compute the present value:
FV= 1,000
I/Y= 5.25
N= 8
Press the CPT key and PV to compute the present value.
The value obtained is 664.08.
Therefore, the current price of the bond is $664.08.
b.i.New price of the bond with increase in market yield is calculated first.
Information provided:
Face value= future value= $1,000
Time= 8 years
Yield to maturity= 7.75% + 1%= 8.75%
The current price of the bond is calculated by computing the present value.
Enter the below in a financial calculator to compute the present value:
FV= 1,000
I/Y= 8.75
N= 8
Press the CPT key and PV to compute the present value.
The value obtained is 511.17.
Therefore, the new price of the bond is $511.17.
Percentage change in price of the bond:
= $511.17 - $550.38/ $550.38*100
= -$39.21/ $550.38*100
= -0.0712*100
= -7.12%.
Therefore, the price of the bond decreases by 7.12% with an increase in yield by 1 percent.
iiInformation provided:
Face value= future value= $1,000
Time= 8 years
Yield to maturity= 5.25% + 1%= 6.25%
The current price of the bond is calculated by computing the present value.
Enter the below in a financial calculator to compute the present value:
FV= 1,000
I/Y= 6.25
N= 8
Press the CPT key and PV to compute the present value.
The value obtained is 615.70
Therefore, the new price of the bond is $615.70.
Percentage change in price of the bond:
= $615.70 - $664.08/ $664.08*100
= -$48.38/ $664.08*100
= -0.0729*100
= -7.29%.
Therefore, the price of the bond decreases by 7.29% with an increase in yield by 1 percent.
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