Question

An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 8% annual coupon. Bond L matures in 16 years, while Bond S matures in 1 year.

Assume that only one more interest payment is to be made on Bond S at its maturity and that 16 more payments are to be made on Bond L.

What will the value of the Bond L be if the going interest rate is 5%? Round your answer to the nearest cent.

What will the value of the Bond S be if the going interest rate is 5%? Round your answer to the nearest cent.

What will the value of the Bond L be if the going interest rate is 8%? Round your answer to the nearest cent.

What will the value of the Bond S be if the going interest rate is 8%? Round your answer to the nearest cent.

What will the value of the Bond L be if the going interest rate is 11%? Round your answer to the nearest cent.

What will the value of the Bond S be if the going interest rate is 11%? Round your answer to the nearest cent.

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

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

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

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

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

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

Answer 1

Solution to question 1:

Given conditions for bond L:
Face value = $1,000
Coupon rate=8%
Time to maturity or number of periods=16 years

Given conditions for bond S:
Face value = $1,000
Coupon rate=8%
Time to maturity or number of periods=1 year

Part 1: Value of the Bond L at interest rate=5%
Face value = $1,000
Coupon rate=8%
Annual coupon payment= Face value* Coupon rate=$1000*8%=$80
Time to maturity or number of periods=16 years
Discount rate=5%
Value of the Bond L=$1,325.13
Note: Present value of the bond is showing as negative in excel as it is a cash outflow.

Part2: Value of the Bond S at interest rate=5%
Face value = $1,000
Coupon rate=8%
Annual coupon payment= Face value* Coupon rate=$1000*8%=$80
Time to maturity or number of periods=1 year
Discount rate=5%
Value of the Bond S=$1,028.57

Part 3: Value of the Bond L at interest rate=8%
Face value = $1,000
Coupon rate=8%
Annual coupon payment= Face value* Coupon rate=$1000*8%=$80
Time to maturity or number of periods=16 years
Discount rate=8%
Value of the Bond L=$1,000.00

Part 4: Value of the Bond S at interest rate=8%
Face value = $1,000
Coupon rate=8%
Annual coupon payment= Face value* Coupon rate=$1000*8%=$80
Time to maturity or number of periods=1 year
Discount rate=8%
Value of the Bond S=$1,000.00

Part 5: Value of the Bond L at interest rate=11%
Face value = $1,000
Coupon rate=8%
Annual coupon payment= Face value* Coupon rate=$1000*8%=$80
Time to maturity or number of periods=16 years
Discount rate=11%
Value of the Bond L=$778.63

Part 6: Value of the Bond S at interest rate=11%
Face value = $1,000
Coupon rate=8%
Annual coupon payment= Face value* Coupon rate=$1000*8%=$80
Time to maturity or number of periods=1 year
Discount rate=11%
Value of the Bond S=$972.97

Explanation to question 2:

When interest rates change, in a 1 year bond, amount can be reinvested very quickly at the new rate. However, in case of long term bond (here the bond with 16 years of maturity), return is locked in for longer period of time.