Question

A $1,400 face value corporate bond with a 6.9 percent coupon (paid semiannually) has 13 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. What will be the change in the bond’s price in dollars and percentage terms? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 3 decimal places. (e.g., 32.161))

Change in the bond’s price in dollars

Change in the bond’s price in percentage%

Answer 1

The value of the bond if yield is 7.6% is computed as shown below:

The coupon payment is computed as follows:

= 6.9% / 2 x $ 1,400 (Since the payments are semi annually, hence divided by 2)

= $ 34.50

The YTM will be as follows:

= 7.6% / 2 (Since the payments are semi annually, hence divided by 2)

= 3.8% or 0.038

N will be as follows:

= 13 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 26

So, the price of the bond is computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= $ 34.50 x [ [ (1 - 1 / (1 + 0.038)²⁶ ] / 0.038 ] + $ 1,400 / 1.038²⁶

= $ 34.50 x 16.33683108 + $ 530.88055868

= $ 1,094.501259

The value of the bond if yield is 8.9% is computed as shown below:

The coupon payment is computed as follows:

= 6.9% / 2 x $ 1,400 (Since the payments are semi annually, hence divided by 2)

= $ 34.50

The YTM will be as follows:

= 8.9% / 2 (Since the payments are semi annually, hence divided by 2)

= 4.45% or 0.0445

N will be as follows:

= 13 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 26

So, the price of the bond is computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= $ 34.50 x [ [ (1 - 1 / (1 + 0.0445)²⁶ ] / 0.0445 ] + $ 1,400 / 1.0445²⁶

= $ 34.50 x 15.2272096 + $ 451.3448418

= $ 976.683573

So, the change in price in terms of dollar will be as follows:

= $ 976.683573 - $ 1,094.501259

= - $ 117.818

Change in terms of % is computed as follows:

= ($ 976.683573 - $ 1,094.501259) / $ 1,094.501259

= - 10.765%

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