Question

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?

Answer 1

Answer:

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%