You purchase a 20year bond today with a 10000 face value tha

You purchase a 20-year bond today with a $10,000 face value that makes annual coupon payments at a 5% coupon rate.

(a) If the yield to maturity on 20 year bonds at the time of purchase was 4%, how much did you pay for the 20 year bond?

(b) After holding the bond for 1 year, you find that the yield to maturity on 19 year bonds is 5%. What is new price of your bond and what has been the rate of return from holding the bond over the first year?

(c) After holding the bond for a second year, you find that the yield to maturity on 18 year bonds is 3.5%. What is new price of your bond and what has been the rate of return from holding the bond from the first year to the second?

Solution

Bond price = Present value (PV) of all coupon payments + PV of maturity price

Maturity (par) value = $10,000

Coupon per year = $10,000 x 5% = $500

(a) Bond price ($) = 500 x PVIFA (4%, 20 years) + 10,000 x PVIF (4%, 20 years)

= 500 x 13.5903 + 10,000 x 0.4564

= 6,795 + 4,564

= 11,359

(b) Bond price ($) = 500 x PVIFA (5%, 19 years) + 10,000 x PVIF (5%, 19 years)

= 500 x 12.0853 + 10,000 x 0.3957

= 6,043 + 3,957

= 10,000

Rate of return from holding the bond = [$10,000 / $11,359] - 1 = 0.8804 - 1 = - 0.1196, or - 11.96%

(c) Bond price ($) = 500 x PVIFA (3.5%, 18 years) + 10,000 x PVIF (3.5%, 18 years)

= 500 x 13.1897 + 10,000 x 0.5384

= 6,595 + 5,384

= 11,979

Return from holding the bond = [$11,979 / $10,000] - 1 = 1.1979 - 1 = 0.1979, or 19.79%