Question

The yield to maturity for 25-year bonds is as follows for four different bond rating categories. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods.

Aaa	9.60%
Aa1	9.80%
Aa2	10.00%
Aa3	11.20%

The bonds of Falter Corporation were rated as Aaa and issued at par a few weeks ago. The bonds have just received a new rating of Aa2. Determine the new price of the bonds, assuming a 25-year maturity and semiannual interest payments. (Do not round intermediate calculations and round your answer to 2 decimal places.)
  

Answer 1

Since the bonds were issued at par and the coupon rate shall be equal to the yield to maturity at the time of issue. At the time of issue of bonds, the bonds were rated as Aaa and hence, its yield to maturity was 9.60%.

Coupon rate = yield to maturity at the time of issue = 9.60%

Market value of bond = Present value of coupon payments + Present value of face value of bond

Maturity of bond = 25 years

Number of semi-annual coupon payments = n = 25 * 2 = 50

Semi-annual coupon payments = $1,000 * 9.60% * ½ = $48

Current yield to maturity = 10%

Semi-annual yield to maturity = r = 10%/2 = 5% = 0.05

Present value of annuity = Annuity amount*{1-(1+r)^-n}/r

Present value of semi-annual coupon payments = $48 * (1-1.05^-50)/0.05 = $876.28

Present value of face value of bond = $1000/1.05⁵⁰ = $87.20

New price of bond = $876.28 + $87.20 = $963.48