Question

Midland Utilities has a bond issue outstanding that will mature to its $ 1 comma 000 par value in 19 years. The bond has a coupon interest rate of 9​% and pays interest annually.

a.  Find the value of the bond if the required return is​ (1) 9​%, ​(2) 13​%, and​ (3) 6​%.

b.  Use your finding in part a and the graph​ here, ^ to discuss the relationship between the coupon interest rate on a bond and the required return and the market value of the bond relative to its par value.

c.  What two possible reasons could cause the required return to differ from the coupon interest​ rate?

Answer 1

a)

Given:

Face Value of bond (FV)= $1000

Years to maturity( N) = 19 Years

Coupon Payment (PMT) = $90               [$1000 x 9%]

Value of bond is required (PV) = ? for

Required Return (I/Y) = 9%/13%/6%

Set the following in financial calculators

FV = 1000, N = 19, PMT = 90, I/Y = 9%

Press CPT + PV , result would be $1000, so price of Bond is same as its face value when coupon rate and required return is same.

Set the following in financial calculators

FV = 1000, N = 19, PMT = 90, I/Y = 13%

Press CPT + PV , result would be $722.48, so price of Bond is Less than its face value when coupon rate is less than its required return.

Set the following in financial calculators

FV = 1000, N = 19, PMT = 90, I/Y = 6%

Press CPT + PV , result would be $1,334.74, so price of Bond is More than its face value when coupon rate is More than its required return.

b)

Coupon Rate	Required Return	Price of bond
9%	9%	1000
9%	13%	722.48
9%	6%	1334.74

As can be seen there is an inverse relationship between required return and value of bond, higher the required return lower the bond value, and when required return is more than coupon rate, bond issues at discount, or when required return is less than coupon rate bond issues at premium.

c)

1. Government set policies for market rate of interest and required return depends on market rate.
2. Credit rating of issuing firm also affects the required return, higher the risk involved, higher the required return.