Question

            An investor purchased the following three bonds. Each bond has a par value of $500. Each bond has a 5% yield on maturity on purchase day. Immediately after the purchase, the interest rate fell, and each had a new yield to maturity of 4%. What is the percentage change in the price of each bond after the fall in interest rates? Please complete the table below:

            Bond                                         Price at 5%                   Price at 4%                Percentage Change

            5 year, 5% annual coupon          ___________              ________            ________

           

            2-year zero                               ___________              _________            ________

            $15 perpetuity                          ___________              _________            ________

Answer 1

Bond                                         Price at 5%                   Price at 4% Percentage Change

5 year, 5% annual coupon = ∑   C + F
(1+r)t (1+r)t


5 year, 5% annual coupon =    25   +   500       25   +    500
(1+.05)5 (1+.05)5   (1+.04)5 (1+.04)5

   = 411.32 431.51 4.90%

  2-year zero = F = 500 500   4.90%
    (1+r)t (1+.05)5   (1+.04)5
= 391.76 410.96   

$15 perpetuity = I/r = 15/(1+.05) 15/(1+.04)    

= 300 375 25%