A corporate bond with an 8.5 percent coupon has 10 years left to maturity. It has had a credit rating of A and a yield to maturity of 10 percent. The firm has recently gotten into some trouble and the rating agency is downgrading the bonds to BBB. The new appropriate discount rate will be 11.5 percent. What will be the change in the bond's price in dollars? Assume interest payments are paid semiannually and par value is $1,000.

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To calculate the change in the bond's price, we first find the price before and after the downgrade. The bond's price is calculated using the formula for the present value of its cash flows, which include the semiannual coupon payments and the par value at maturity. Before the downgrade: Coupon payment = 8.5% of $1,000 / 2 = $42.50 per period. Number of periods = 10 years * 2 = 20 periods. Discount rate per period = 10% / 2 = 5%. Price before downgrade = PV of annuity (coupons) + PV of lump sum (par value) = $42.50 * [1 - (1 + 0.05)^-20] / 0.05 + $1,000 * (1 + 0.05)^-20 = $772.17 + $376.89 = $1,149.06. After the downgrade: New discount rate per period = 11.5% / 2 = 5.75%. Price after downgrade = $42.50 * [1 - (1 + 0.0575)^-20] / 0.0575 + $1,000 * (1 + 0.0575)^-20 = $744.09 + $322.84 = $1,066.93. Change in price = $1,066.93 - $1,149.06 = -$82.13.

A Corporate Bond with an 8