Question

You own two bonds. Both bonds pay annual interest, have 6 percent annual coupons, $1,000 face values, and currently have 6 percent yields to maturity. Bond A has 12 years to maturity and Bond B has 4 years to maturity. If the market rate of interest rises unexpectedly to 7 percent, Bond _____ will be the most volatile with a price decrease of _____ percent.

Answer 1

Answer:

Bond A is most volatile and 7.94%

Explanation:

The computation is shown below;

Particulars                             Bond  A                 Bond B

Interest ($1,000 × 6%)            $60                       $60

Period                                      12                          4

PVAF at 7 for 12 years          7.942886

PVAF  at 7% for 4 years                                       3.387211

PVF at 7% for 12 years           0.444012

PVF at 7% for 4 years                                          0.762895

The present value of interest    $476.56

($60 × 7.942686)

The present value of interest                                 $203.2327

                                                                 ($60 × 3.387211)

Present value of fair value               $444.012

($1,000 × 0.444012)

Present value of fair value                                        $762.8952

                                                                   ($1,000 × 0.762895)

Present value                          $920.57                 $966.1279

The decrease in percentage is

= ($1,000 - $920.57) ÷ $1,000

= 7.94%

Bond A is most volatile