Question

Midland Utilities has outstanding a bond issue that will mature to its $1,000 par value in 11 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 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

Answer:

at 13% --> $1,000

at 17%  -->$806.54

at 10%  --> $1,194.85

When the rates do not match people will only accept the bond if their desired market return can be acheive. Because, the coupon payment are fixed the only way to do so is by changing the price ofthe bond.

So bond with coupon rate above market are trade at a price higher than face value while, below market traded at lower price.

Explanation:

The market value of a bond is the present value of the future coupon payment and maturity given the current market rate

When the market rate matches the coupon rate then the bond is at par and sales at face value.

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 130.000

time 11

rate 0.17

$130 \times \frac{1-(1+0.17)^{-11} }{0.17} = PV$

PV $628.7337

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   11.00

rate  0.17

$\frac{1000}{(1 + 0.17)^{11} } = PV$  

PV   177.81

PV c $628.7337

PV m  $177.8097

Total $806.5435

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 130.000

time 11

rate 0.1

$130 \times \frac{1-(1+0.1)^{-11} }{0.1} = PV$

PV $844.3579

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   11.00

rate  0.1

$\frac{1000}{(1 + 0.1)^{11} } = PV$  

PV   350.49

PV c $844.3579

PV m  $350.4939

Total $1,194.8518