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.

jeff jeffy answered 1 year ago

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