A 12-year, 5 percent coupon bond pays interest annually. The bond has a face value of $1,000. What is the percentage change in the price of this bond if the market yield rises to 6 percent from the current level of 5.5 percent?

Percentage change in price = 1.54%

Explanation:

The price of a bond is the present value (PV) of its interest payments and redemption value.

Note that interest payment = Coupon (%) * Face value

The coupon rate is 12% in this question

The redemption value is the amount payable upon maturity of the bond. Here, it is the face value.

So we discount these cash flows - interest payments and face value

Price of the bond at a yield of 6%

Interest rate payment = 6% * 1000 = 60

PV of interest payments = (1 - (1+r) ^ (-n)) / r

r = yield, n = number of years

PV of interest:

60 * (1 - (1+0.06) ^ (-12)) / 0.06

= 60 * 8.3838

=$530.30

PV of redemption value = 1000 * (1+0.06) ^ (-12)

= 496.96

Price of Bond = 530.30 + 496.96 = $1027.26

Price of bond when yield is 5.5%

= 60 * (1 - (1+0.055) ^ (-12)) / 0.055

= 60 * 8.6185

=$517.11

PV of redemption value = 1000 * (1+0.055) ^ (-12)

= 525.98

Price of Bond = 517.11 + 525,98 = $1043.09

Percentage change in price =

= ((1043.09-1027.26) / 1027.26) * 100

= 1.54%