Question

A $1,000 face value corporate bond with a 6.75 percent coupon (paid semiannually) has 10 years left to maturity. It has had a credit rating of BB and a yield to maturity of 8.2 percent. The firm recently became more financially stable and the rating agency is upgrading the bonds to BBB. The new appropriate discount rate will be 7.1 percent. What will be the change in the bond’s price in dollars and percentage terms? round your answers to 3 decimal places. (e.g., 32.161))

Answer 1

Assuming interest payments are done semi annually

Computing the current bond price:

Bond price = $33.75 * [(1-1/(1+0.041)^20)/0.041] + 1000/(1+0.041)^20

= $454.64+$447.70

= $902.34

Or N = 20, I = 4.1, PMT = 33.75, FV = 1000 CPT PV = -902.34

Now computing the price after the rate change:

Bond Price = $33.75 * [(1-1/(1+0.0355)^20)/0.0355]+ 1000/(1+0.0355)^20

= $477.51+$497.73

= $975.24

Or N = 2-, I = 3.55, PMT = 33.75, FV = 1000 CPT PV = -975.24

So the dollar change in price is

$975.24 - $902.34 = $72.90

The percentage return is : 72.90 / 902.34 = 8.08%.