Question

One year ago, Alpha Supply issued 15-year bonds at par. The bonds have a coupon rate of 6.5 percent, paid semiannually, and a face value of $1,000. Today, the market yield on these bonds is 7.2 percent. What is the percentage change in the bond price over the past year?

Answer 1

Answer:

Percentage change in the bond price=0.524%

Explanation:

The current bond price can be expressed as;

Current bond price=(Semi-annual coupon×((1-(1/(1+r)^i)/r)+ (face value/(1+r)^i)

where;

i-maturity period=1 year ,since it has 2 periods in a year,i=2

r-nominal yield to maturity rate=7.2/2=3.6%

Semi-annual coupon rate=6.5/2=3.25%

face value=$1,000

Semi- annual coupon=(3.25/100)×1,000=$32.5

replacing;

Current bond price=Semi-annual coupon×((1-(1/(1+r)^i)/r  + face value/(1+r)^i

(32.5×((1-(1/(1+0.036)^2)/0.036)+1,000/(1+0.036)^2

(32.5×(1-0.93)/0.036)+931.71

(32.5×1.94)+931.71=63.05+931.71=

Current bond price=$994.76

Percentage change=((Face value-Current bond price)/(Face value))×100

Percentage change=((1,000-994.76)/1000)×100

(5.24/1000)×100=0.524%

Percentage change in the bond price=0.524%