Question

(Bond valuation) You own a bond that pays $120 in annual interest, with a $1,000 par value. It matures in 10 years. Your required rate of return is 11 percent.

a. Calculate the value of the bond.

b. How does the value change if your required rate of return (1) increases to 15 percent or (2) decreases to 6 percent?

c. Explain the implications of your answers in part (b) as they relate to interest rate risk, premium bonds, and discount bonds.

d. Assume that the bond matures in 3 years instead of 10 years. Recompute your answers in part (b).

e. Explain the implications of your answers in part (d) as they relate to interest rate risk, premium bonds, and discount bonds.

a. If your required rate of return is 11 percent, what is the value of the bond? $________(Round to the nearest cent.)

Answer 1

1.
If your required rate of return is 11 percent, what is the value of the bond?

=120/11%*(1-1/1.11^10)+1000/1.11^10=1058.89232011141

2.
If your required rate of return is 15 percent, what is the value of the bond?

=120/15%*(1-1/1.15^10)+1000/1.15^10=849.436941224373

3.
If your required rate of return is 6 percent, what is the value of the bond?

=120/6%*(1-1/1.06^10)+1000/1.06^10=1441.60522308488

4.
Because of the inverse relationship between the required return and bond price, bond prices will decrease if the required rate of return increases. As long as all other variables remain constant, this will be case. To put in context of the industry, bonds will sell with greater discounts than the face value if the required return increase and at the premium if those required returns decrease.

5.
If your required rate of return is 15 percent and the bond matures in 3 years, what is the value of the bond?
=120/15%*(1-1/1.15^3)+1000/1.15^3
=931.50

6.
If your required rate of return is 6 percent and the bond matures in 3 years, what is the value of the bond?
=120/6%*(1-1/1.06^3)+1000/1.06^3
=1160.38

7.
You have what is called an interest rate risk when the value of the bond changes due to interest changes. The longer the maturity date, more exposure bonds will get to that interest rate risk. When the maturity date decreased, the bond became more stable and had less fluctuation. Coupled with that, when the required return increased, there was a greater discount off the face value, and vice versa.