Question

Midland Utilities has a bond issue outstanding that will mature to its $1,000 par value in 16 years. The bond has a coupon interest rate of 13​% and pays interest annually.

a.Find the value of the bond if the required return is​ (1)13​%, (2) 17​%, and​ (3) 10​%.

b.Use your finding in part a and the graph​ here

1,500 1,400- 1,300 1,2004 Bond Value ($) 1,100 1,000 900 800- 700 600 500 10 16 17 11 12 13 14 15 Required return (%)

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. Par Value =1000
Coupon =13%*1000 =130
Number of Years =16
Price of Bond at 13%=PV of Coupons+PV of Par Value =130*((1-(1+13%)^-16)/13%)+1000/(1+13%)^16 =1000
Price of Bond at 17%=PV of Coupons+PV of Par Value =130*((1-(1+17%)^-16)/17%)+1000/(1+17%)^16 =783.79
Price of Bond at 10%=PV of Coupons+PV of Par Value =130*((1-(1+10%)^-16)/10%)+1000/(1+10%)^16 =1234.71

b. If Coupon rate is same as required rate bond is sold at par.
If coupon rate is less than required rate bond is sold at discount (Price of bond is less than par)
If coupon rate is more than required rate bond is sold at discount (Price of bond is more than par)

c. Two reasons that causes the required rate to differ from coupon interest rate
1. Coupon rate is fixed whereas interest rates may vary due to rating of bonding by credit rating agency. Higher the rating lower the interest rate and lower the rating higher the interest rate.
2. Interest rate may vary due to increase in demand of the bonds . Higher the demand of bonds lower is the interest rate and lower the demand higher is the interest rate.