Question

(Bond valuation) Doisneau 16​-year bonds have an annual coupon interest of 8 ​percent, make interest payments on a semiannual​ basis, and have a ​$1,000 par value. If the bonds are trading with a​ market's required yield to maturity of 14 ​percent, are these premium or discount​ bonds? Explain your answer. What is the price of the​ bonds? a. If the bonds are trading with a yield to maturity of 14​%, then ​ (Select the best choice​ below.)

A. the bonds should be selling at a premium because the​ bond's coupon rate is greater than the yield to maturity of similar bonds.

B. the bonds should be selling at par because the​ bond's coupon rate is equal to the yield to maturity of similar bonds.

C. there is not enough information to judge the value of the bonds.

D. the bonds should be selling at a discount because the​ bond's coupon rate is less than the yield to maturity of similar bonds.

Answer 1

The answer is:

D. the bonds should be selling at a discount because the​ bond's coupon rate is less than the yield to maturity of similar bonds.

We will verify this calculating the price of teh bonds.

The formula for the price of a bond is

1 - (1 i) +Face Value x (1i)" Price -n Coupon Payment x

1 (1i -n Face Value X r x (1 -n Face Value x

where

n=number of peiods

i= interest rate  per period

r=coupon rate per period

In this case

Face Value=1000

i=14%/2=7%=0.07

r=8%/2=4%=0.04

n=16 x 2= 32

Therefore the price is

1 (1.07) -32 1000 x (1.07)32-620.60 1000 x 0.04 x 0.07

Since the price is less than the face value, then the bond is selling at a discount.