A $2,400 face value corporate bond with a 6.3 percent coupon (paid semiannually) has 15 years...

A $2,400 face value corporate bond with a 6.3 percent coupon (paid semiannually) has 15 years left to maturity. It has had a credit rating of BBB and a yield to maturity of 6.8 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 8.1 percent. What will be the change in the bond’s price in dollars and percentage terms?

Solutions

Expert Solution

First we will calculate the price of the bond with rating BBB

Face value = $2400, Coupon rate = 6.3% and No of years to maturity = 15, Yield to maturity = 6.8%

Since the bond pays coupons semi annually

Semi annual coupon payment = (Coupon rate x face value) / 2 = (6.3% x 2400) / 2 = 151.20 / 2 = $75.60

No of half years to maturity = 2 x no of years to maturity = 2 x 15 = 30

Semi annual Yield to maturity = Yield to maturity / 2 = 6.8% / 2 = 3.4%

We can find the price of bond with BBB rating using PV function in excel

Formula to be used in excel: =PV(rate,nper,-pmt,-fv)

Using PV function in excel, we get price of bond with BBB rating = $2288.2520

If rating is bond is downgraded to BB, then new yield to maturity = new discount rate = 8.1%

New semi annual yield to maturity = new yield to maturity / 2 = 8.1% / 2 = 4.05%

Now we can find the new price of bond using PV function in excel

Formula to be used in excel: =PV(rate,nper,-pmt,-fv)

Using PV function in excel, we get New price = price of bond with BB rating = $2028.7491

Dollar change in price = price of bond with BB rating - Price of bond with BBB rating = 2028.7491 - 2288.2520 = -259.5029

Dollar change in price = -259.5029

Percentage change = (Dollar change in price / Price of bond with BBB rating) = (-259.5029 / 2288.2520) = -0.1134066 = 11.34066%

Percentage change in price = -11.34066%

jeff jeffy answered 2 hours ago

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