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A corporate bond with a 6.5 percent coupon has 15 years left to maturity. It has had a credit rating of BBB and a yield to maturity of 7.2 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 8.5 percent. What will be the change in the bond's price in dollars and percentage terms

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Tundexi

Answer:

Price change in dollars = $104.22

% decrease in price of dollars = 11.13%

Explanation:

We assume the corporate bond have a face value of $1,000

Face Value = $1000

Coupon = 6.5%*1000/2 =32.50

Number of Periods = 15*2 =30

Semi annual rate of BBB bond = 7.2%/2 =3.6%

Price of BBB Bond = PV of Coupons + PV of Par Value =

Price of BBB Bond = 32.50*(((1-(1+3.6%)^-30)/3.6%)+1000/(1+3.6%)^30

Price of BBB Bond = $936.43

Semiannual Discount Rate for BB bond = 8.5%/2 = 4.25%

Price of BB Bond = PV of Coupons + PV of Par Value

Price of BB Bond = 32.50*(((1-(1+4.25%)^-30)/4.25%)+1000/(1+4.25%)^30

Price of BB Bond= $832.21

Price change in dollars = $936.43 - $832.21

Price change in dollars = $104.22

% decrease in price of dollars = $104.22 / $936.43

% decrease in price of dollars = 0.111295025

% decrease in price of dollars = 11.13%

Price change in dollars is 104.22

And, in percentage it is 11.13%.

  • The calculation is as follows:

1. Face Value =1000

Coupon =6.5% ×1000 ÷ 2 =32.50

Number of Periods =15 × 2 =30

Semi annual rate of BBB bond =7.2% ÷ 2 =3.6%

Price of BBB Bond =PV of Coupons + PV of Par Value

=32.50 × (((1-(1+3.6%)^-30) ÷ 3.6%) + 1000/(1+3.6%)^30

=936.43

Now

Semiannual Discount Rate for BB bond =8.5% ÷2 =4.25%

Price of BB Bond =PV of Coupons + PV of Par Value

=32.50 × (((1-(1+4.25%)^-30) ÷ 4.25%)+1000 ÷ (1+4.25%)^30

=832.21

So,

Price change in dollars is

= 936.43 - 832.21

= 104.22

Now  

Percentage decrease in price of dollars is

= 104.22 ÷ 936.43

= 11.13%

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