Question

What is the effective annual yield of a $1000 par value bond that pays semi-annual coupons, has an annual coupon rate of 5% with a current trading price of $950 and a time to maturity of 10 years? What will happen to the value of the bond if the YTM falls by 1%? Will it trade at a discount, par or premium? (Round to the nearest percent).

                                                                   

Answer 1

$EAY=(\frac{1+YTM}{2})^2-1$

$PV=\frac{\frac{C}{m}}{(1+\frac{YTM}{2})}+\frac{\frac{C}{m}}{(1+\frac{YTM}{2})^2}+...+\frac{\frac{C}{m}}{(1+\frac{YTM}{2})^n}+\frac{N}{(1+\frac{YTM}{2})^n}$

$950=\frac{\frac{50}{2}}{(1+\frac{YTM}{2})}+\frac{\frac{50}{2}}{(1+\frac{YTM}{2})^2}+...+\frac{\frac{50}{2}}{(1+\frac{YTM}{2})^{10}}+\frac{1000}{(1+\frac{YTM}{2})^{10}}$

YTM=5.66 %

$EAY=(\frac{1+0.0566}{2})^2-1=0.0574$ 5.74%

if it falls by one percent, then

$PV=\frac{\frac{50}{2}}{(1+\frac{0.04}{2})}+\frac{\frac{50}{2}}{(1+\frac{0.04}{2})^2}+...+\frac{\frac{50}{2}}{(1+\frac{0.04}{2})^{10}}+\frac{1000}{(1+\frac{0.04}{2})^{10}}=1045$

Will it trade at a premium