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 12 years, while Bond S matures in 1 year.

1. What will the value of the Bond L be if the going interest rate is 7%, 9%, and 12%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 12 more payments are to be made on Bond L. Round your answers to the nearest cent.

   	7%	9%	12%
   Bond L	$	$	$
   Bond S	$	$	$

2. Why does the longer-term bond’s price vary more than the price of the shorter-term bond when interest rates change?
   1. Long-term bonds have lower interest rate risk than do short-term bonds.
   2. Long-term bonds have lower reinvestment rate risk than do short-term bonds.
   3. The change in price due to a change in the required rate of return increases as a bond's maturity decreases.
   4. Long-term bonds have greater interest rate risk than do short-term bonds.
   5. The change in price due to a change in the required rate of return decreases as a bond's maturity increases.

choose 1 of the above

Answer 1

A. The FV of bond is : $1000

PMT = 11% * $1000

= $110

N = 12 Years

I/Y = 7%

So, the present value of bond is : $1,317.7075

= $1318 ( ROUNDED OFF TO THE NEAREST CENTS)

When the interest rate is 9%,the present value of bond is :

= ($1143.2145)

= ($1143) ( ROUNDED OFF TO THE NEAREST CENTS)

When the interest rate is 12%,the present value of bond is :

= ($938.0563)

= ($938) ( ROUNDED OFF TO THE NEAREST CENTS)

The maturity of bond S is 1 year,so N = 1 year

When the interest rate is 7%, the present value is :

= ($1037.3832)

= ($1037) ( ROUNDED OFF TO THE NEAREST CENTS)

When the interest rate is 9%, the present value is :

= ($1018.3486)

= ($1018) ( ROUNDED OFF TO THE NEAREST CENTS)

When the interest rate is 12%, the present value of bond is :

= ($991.0714)

= ($991) ( ROUNDED OFF TO THE NEAREST CENTS)

B. The longer term bonds have a higher interest rate risk hence the price of the long term bond varies more than the short term bonds.

So, the correct option is option IV.

The other options are incorrect, the long term bonds have a higher interest rate risk, it has a higher reinvestment risk,as the bonds maturity increases, the changes in the price of the bond due to the changes in the required return is higher.