Question

Bond valuation) New Generation Public Utilities issues a bond with a $1000 par value that pays $80 in annual interest. It matures in 20 years. Your required rate of return is 7%.

a.       Calculate the value of the bond.

b.       How does the value change if your required rate of return 1) increases to 10% or 2) decreased to 6%?

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 10 years instead of 20 years. Recompute your answers in part b.

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

Answer 1

answer a)

Value of the bond is the Present value of all cash flow which bond provide throughout its life at the required rate of return.

Information given in the question

Coupon rate = (80/1000)*100 = 8%
Face value = 1000$
Required rate of return (r) = 7%

So value is

= coupon amount + coupon amount . . . . . . . . . . . . . . coupon amount + c.amt + principal amt.
(1 + r)¹ (1+r)² (1 + r)^n-1 (1+r)ⁿ

where n is no. of years and r is the required rate of return

= 80 + 80 + . . . . . . . . . . . + 80 +   1080  
(1.07) (1.07)²   (1.07)¹⁹   (1.07)²⁰

= 1105.94

answer b)

1) if the required rate of return increases to 10 %
  
Just change the input in the above formula and solve again

= 829.73 will be the value

2) If decreases to 6% then the value will be

= 1229.40

answer c)

in answer b part 1) the required rate of return increases to 10% which means bondholder is demanding at least a 10% return on its money but the bond is providing 8% only, therefore the price of the bond in the market will obviously be lower than the par value of the bond.

Similarly in part b 2) the required rate of return is lower than what is provided by the bond, therefore, it is value is more than the value of the bond.

answer d)

for this answer just change the value in the above formula
ie take n = 10
then the value will be
= 1070.24