856 percent Question 35 25 pts A bond has a coupon rate of 8

?856 percent Question 35 2.5 pts A bond has a coupon rate of 8 percent, 7 years to maturity, semiannual interest payments, and a YTM of 7 percent If interest rates suddenly rise by 2 percent, what will be the percentage change in the bond price? O -10.16 percent 9.87 percent D10.67 percent D9.56 percent D 10.02 percent Question 36 2.5 pts

Solution

The Correct answer is -10.02 percent

Price of Bond = Cupon Amount * Present Value of Annuity Factor (r,n) + Redemption Amount * Present Value of Interest Factor (r,n)

Bonds usually have a face value of $1000

Where Cupon Amount = $1000 * 8% * 1/2

= $40

Why we multipled with 1/2 ? - as compounding is semi annual

Redemption Amount = $1000

r = 7% * 1/2

r = 3.5%

(Since compounding is Semi annual)

n = 7 years * 2

n = 14

(Since compounding is Semi annual)

Present Value of Annuity Factor (3.5% ,14) = 10.9205

Present Value of Interest Factor (3.5% ,14) = 0.6178

Therefore

Bond Price = $40 * 10.9205 + $1000 * 0.6178

Bond Price =$436.82 + $617.8

Bond Price = $1054.62

Now interest rate rises by 2%

Therefore r = (7+2) * 1/2

r =4.5%

n = 14

Therefore

Present Value of Annuity Factor (4.5% ,14) = 10.2228

Present Value of Interest Factor (4.5% ,14) = 0.5400

Bond Price = $40 * 10.2228 + $1000 * 0.5400

Bond Price = $408.912 + $540

Bond Price = $948.912

There exists an inverse relationship between price and yield.

Percentage change in bond price =($948.912 - 1054.62) / $1054.62

Percentage change in bond price = -105.708 / $1054.62

Percentage change in bond price = -0.1002 or -10.02 percent.