Questions: Problem 7-23 Bond Ratings and Prices (LG7-7) 6.25 points A corporate bond with a coupon rate of 6.9 percent has 15 years left to maturity. It has had a credit rating of BBB and a yield to maturity of 7.6 percent. The firm has recently gotten into some trouble and the rating agency is downgrading the bonds to BB. The new appropriate discount rate will be 8.9 percent. (Assume interest payments are semiannual.) What will be the change in the bond's price in dollars? What will be the change in the percentage? Note: Negative answer should be indicated by a minus sign. Do not round intermediate calculations. Round your final answer to 2 decimal places. Change in bond price Change in bond percent %

Problem 7-23 Bond Ratings and Prices (LG7-7)
6.25 points

A corporate bond with a coupon rate of 6.9 percent has 15 years left to maturity. It has had a credit rating of BBB and a yield to maturity of 7.6 percent. The firm has recently gotten into some trouble and the rating agency is downgrading the bonds to BB. The new appropriate discount rate will be 8.9 percent. (Assume interest payments are semiannual.)

What will be the change in the bond's price in dollars?
What will be the change in the percentage?
Note: Negative answer should be indicated by a minus sign. Do not round intermediate calculations. Round your final answer to 2 decimal places.

Change in bond price
Change in bond percent %

Transcript text: Problem 7-23 Bond Ratings and Prices (LG7-7) 6.25 points A corporate bond with a coupon rate of 6.9 percent has 15 years left to maturity. It has had a credit rating of BBB and a yield to maturity of 7.6 percent. The firm has recently gotten into some trouble and the rating agency is downgrading the bonds to BB. The new appropriate discount rate will be 8.9 percent. (Assume interest payments are semiannual.) What will be the change in the bond's price in dollars? What will be the change in the percentage? Note: Negative answer should be indicated by a minus sign. Do not round intermediate calculations. Round your final answer to 2 decimal places. \begin{tabular}{|l|l|l|} \hline Change in bond price & & \\ \hline Change in bond percent & & $\%$ \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Calculate the initial bond price

The bond has a coupon rate of 6.9%, a yield to maturity (YTM) of 7.6%, and 15 years to maturity. Interest payments are semiannual. This means there are 2 * 15 = 30 periods. The coupon payment per period is (6.9%/2) * 1000 = $34.50. The YTM per period is 7.6%/2 = 3.8%.

Using the bond pricing formula:

Initial Price = 34.50 * [1 - (1 + 0.038)^-30] / 0.038 + 1000 / (1 + 0.038)^30 Initial Price ≈ $930.80

Step 2: Calculate the new bond price

The new YTM is 8.9%. The YTM per period is 8.9%/2 = 4.45%. The coupon payment remains the same at $34.50.

Using the bond pricing formula:

New Price = 34.50 * [1 - (1 + 0.0445)^-30] / 0.0445 + 1000 / (1 + 0.0445)^30 New Price ≈ $811.36

Step 3: Calculate the change in bond price and percentage

Change in price = New Price - Initial Price Change in price = $811.36 - $930.80 Change in price = -$119.44

Change in percentage = (Change in price / Initial price) * 100 Change in percentage = (-$119.44 / $930.80) * 100 Change in percentage ≈ -12.83%