Question

Last year, Forest Products issued both 5-year and 10-year bonds at par. The bonds each have a coupon rate of 5.5 percent, paid semiannually, and a face value of $1,000. Assume the yield to maturity on each of these bonds is now 7.4 percent. What is the percentage change in the price of the 5-year bond since it was issued

Answer 1

Answer:

Price at issuance is $1,000 for both bonds.

Price of the 5 year bond after the market rate increased to 7.4% is:

PV of face value = $1,000 / (1 + 3.7%)⁸ = $747.77

PV of coupon payments = $27.50 x 6.81694 (PV annuity factor, 3.7%, 8 periods) = $187.47

Market price = $935.24

this bond's price decreased by 64.76/1,000 = 0.06476 = 6.48%

Price of the 10 year bond after the market rate increased to 7.4% is:

PV of face value = $1,000 / (1 + 3.7%)¹⁸ = $519.97

PV of coupon payments = $27.50 x 12.97365 (PV annuity factor, 3.7%, 18 periods) = $356.78

Market price = $876.75

this bond's price decreased by 123.25/1,000 = 0.12325 = 12.33%