Question

1)

a. Consider a $1,000 par value bond with a 6% coupon rate paid semiannually, and has 9 years to maturity. What is the price of the bond if it is priced to yield 7%?

b.  Cutler Co. issued 11-year bonds a year ago at a coupon rate of 7.8 percent. The bonds make semiannual payments. If the YTM on these bonds is 8.6 percent, what is the current bond price?

c. A $1000 bond with a coupon rate of 6.2% paid semiannually has eight years to maturity and a yield to maturity of 8.3%. If interest rates rise and the yield to maturity increases to 8.6%, what will happen to the price of the bond?

Answer 1

A.Information provided:

Future value= $1,000

Coupon rate= 6%/2= 3%

Coupon payment= 0.03*1,000= $30

Time= 9 years*2= 18 semi-annual periods

Yield to maturity= 7%/2= 3.5%

The price of the bond is calculated by computing the present value with the help of a financial calculator.

Enter the below in a financial calculator:

FV= 1,000

PMT= 30

N= 18

I/Y= 3.5

Press the CPT key and PV to calculate the present value.

The value obtained is $934.05.

Therefore, the price of the bond is $934.05.

B.Information provided:

Future value= $1,000

Time= 11 years*2= 22 semi-annual periods

Coupon rate- 7.8%/2= 3.9%

Coupon payment= 0.039*1,000= $39

Yield to maturity= 8.6%/2= 4.3%

The price of the bond is calculated by computing the present value with the help of a financial calculator.

Enter the below in a financial calculator:

FV= 1,000

N= 22

PMT= 39

I/Y= 4.3

Press the CPT key and PV to calculate the present value.

The value obtained is $943.82.

Therefore, the price of the bond is $943.82.

C.Information provided:

Future value= $1,000

Coupon rate- 6.2%/2= 3.1%

Coupon payment= 0.031*1,000= $31

Time= 8 years*2= 16 semi-annual periods

Yield to maturity= 8.3%/2= 4.15%

The price of the bond is calculated by computing the present value with the help of a financial calculator.

Enter the below in a financial calculator:

FV=1,000

PMT= 31

N= 16

I/Y= 4.15

Press the CPT key and PV to calculate the present value.

The value obtained is $878.9937

Therefore, the price of the bond is $879.

Price of the bond if the yield to maturity increases to 8.6% is calculated below with the help of a financial calculator.

Enter the below in a financial calculator:

FV= 1,000

FV=1,000

PMT= 31

N= 16

I/Y= 4.30

Press the CPT key and PV to calculate the present value.

The value obtained is $863.22.

Therefore, the price of the bond is $863.22.

The price of the bond has decreased with an increase in interest rates.