A bond has the following terms: principal amount $1,000 semi-annual interest $50 maturity 10 years ? a. What is the bond's price if comparable debt yields 12%? b. What would be the price if comparable debt yields 12% and the bond matures after five years? c. What are the current yields and yields to maturity in a. and b.? d. What would be the bond's price in a. and b. if interest rates declined to 8%? e. What are the current yields and yield to maturity in d.? f. What two generalizations may be drawn from the above price changes?

Question

What will be an ideal response?

Answer 1

a. P = interest(PV of an annuity at 6% for 20 periods)    + principal (PV of $1 at 6% for 20 years)     = $50(11.470) + $1,000(.312) = $885?    (PV = ?; I = 6; N = 10; PMT = 50, and FV = 1000.    PV = -885.)?b. P = $50(7.360) + $1,000(.558) = $926?    (PV = ?; I = 6; N = 10; PMT = 50, and FV = 1000.    PV = -926.)?c. Current yield       Yield to maturity    in a: $100/$885 = 11.3%    12%    in b: $100/$926 = 10.8%    12%?Notice that the yield to maturity is the yield on the comparable debt. Students may confirm this by calculating the yield to maturity.
d. Price at 4% for 20 periods:    P = $50(13.590) + $1,000(.456) = $1,136?    (PV = ?; I = 4; N = 20; PMT = 50, and FV = 1000.    PV = -1136.)?    Price at 4% for 10 periods:    P = $50(8.111) + $1,000(.676) = $1,082?    (PV = ?; I = 4; N = 10; PMT = 50, and FV = 1000.    PV = -1081.)?e. Current yields      Yield to maturity    a: $100/$1,136 = 8.8%        8%    b: $100/$1,082 = 9.2%       8%?f. (1) The inverse relationship between bond prices and current interest rates: when interest rates fall (12% to 8%), the price of the bond rises.?   (2) The longer the term of the bond (ten versus five years), the greater is the price fluctuation.