Question

An investor has two bonds in his portfolio that have a face value of $1,000 and pay an 11% annual coupon. Bond L matures in 15 years, while Bond S matures in 1 year.

A. What will the value of the Bond L be if the going interest rate is 7%, 8%, and 12%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 15 more payments are to be made on Bond L. Round your answers to the nearest cent.

	7%	8%	12%
Bond L	$ __	$ __	$__
Bond S	$ __	$ __	$__

B. Why does the longer-term bond’s price vary more than the price of the shorter-term bond when interest rates change?

I. The change in price due to a change in the required rate of return increases as a bond's maturity decreases.

II. Long-term bonds have greater interest rate risk than do short-term bonds.

III. The change in price due to a change in the required rate of return decreases as a bond's maturity increases.

IV. Long-term bonds have lower interest rate risk than do short-term bonds.

V. Long-term bonds have lower reinvestment rate risk than do short-term bonds.

Answer 1

A.At 7%:

Bond L

Information provided:

Face value=future value= $1,000

Time= 15 years

Coupon rate= 11%

Coupon payment= 0.11*1,000= $110

Yield to maturity= 7%

The value 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

N= 15

PMT= 110

I/Y= 7

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

The value obtained is 1,364.32.

Therefore, the price of the bond is $1,364.32.

At 8%:

Bond L

Information provided:

Face value=future value= $1,000

Time= 15 years

Coupon rate= 11%

Coupon payment= 0.11*1,000= $110

Yield to maturity= 8%

The value 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

N= 15

PMT= 110

I/Y= 8

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

The value obtained is 1,256.78.

Therefore, the price of the bond is $1,256.78.

At 12%:

Bond L

Information provided:

Face value=future value= $1,000

Time= 15 years

Coupon rate= 11%

Coupon payment= 0.11*1,000= $110

Yield to maturity= 12%

The value 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

N= 15

PMT= 110

I/Y= 12

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

The value obtained is 931.89.

Therefore, the price of the bond is $931.89.

A.At 7%:

Bond S

Information provided:

Face value=future value= $1,000

Time= 1 years

Coupon rate= 11%

Coupon payment= 0.11*1,000= $110

Yield to maturity= 7%

The value 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

N= 1

PMT= 110

I/Y= 7

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

The value obtained is 1,037.38.

Therefore, the price of the bond is $1,037.38.

At 8%:

Information provided:

Face value=future value= $1,000

Time= 1 year

Coupon rate= 11%

Coupon payment= 0.11*1,000= $110

Yield to maturity= 8%

The value 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

N= 1

PMT= 110

I/Y= 8

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

The value obtained is 1,027.78.

Therefore, the price of the bond is $1,027.78.

At 12%:

Bond L

Information provided:

Face value=future value= $1,000

Time= 1 year

Coupon rate= 11%

Coupon payment= 0.11*1,000= $110

Yield to maturity= 12%

The value 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

N= 1

PMT= 110

I/Y= 12

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

The value obtained is 991.07.

Therefore, the price of the bond is $991.07.

B.The answer is option II. Long term bonds have greater interest rate risk than short term bonds.