Question #138128

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).

Expert's answer

"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

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