Final answer:
To determine the price of the bond, we use the present value formula and the appropriate discount rate. If Andrew Industries maintains the A rating, the price of the bond is approximately $1,056.38. If it is downgraded to BBB, the price is approximately $1,030.54.
Step-by-step explanation:
To determine the price of the bond if Andrew Industries maintains the A rating, we need to calculate the present value of its future cash flows. The cash flows include annual coupon payments of 7.19% of the face value of $1,000 and the final repayment of the face value after 30 years. Since the bond is A-rated, we use the yield of A-rated bonds, which is 6.53%, as the discount rate. Using the formula for the present value of a bond, we can calculate the price as follows:
PV = (Coupon Payment / Discount Rate) * (1 - (1 / (1 + Discount Rate)^n)) + (Face Value / (1 + Discount Rate)^n)
Where PV is the present value, Coupon Payment is the annual coupon payment, Discount Rate is the discount rate, n is the number of years to maturity, and Face Value is the face value of the bond.
For this bond, the calculation would be:
PV = (70.19 / 0.0653) * (1 - (1 / (1 + 0.0653)^30)) + (1000 / (1 + 0.0653)^30)
By solving this equation, we find that the price of the bond, if Andrew Industries maintains the A rating, is approximately $1,056.38.
If Andrew Industries is downgraded to BBB, we need to use the yield of BBB-rated bonds, which is 6.81%, as the discount rate. We can use the same formula to calculate the price:
PV = (Coupon Payment / Discount Rate) * (1 - (1 / (1 + Discount Rate)^n)) + (Face Value / (1 + Discount Rate)^n)
For this bond, the calculation would be:
PV = (70.19 / 0.0681) * (1 - (1 / (1 + 0.0681)^30)) + (1000 / (1 + 0.0681)^30)
By solving this equation, we find that the price of the bond, if Andrew Industries is downgraded, is approximately $1,030.54.