Question

A $1,900 face value corporate bond with a 5.8 percent coupon (paid semiannually) has 15 years left to maturity. It has had a credit rating of BBB and a yield to maturity of 6.3 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 7.4 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))

Answer 1

Face Value of Bond = $1,900

Annual Coupon Rate = 5.80%
Semiannual Coupon Rate = 2.90%
Semiannual Coupon = 2.90% * $1,900
Semiannual Coupon = $55.10

Time to Maturity = 15 years
Semiannual Period = 30

If yield to maturity is 6.30%:

Annual YTM = 6.30%
Semiannual YTM = 3.15%

Price of Bond = $55.10 * PVIFA(3.15%, 30) + $1,900 * PVIF(3.15%, 30)
Price of Bond = $55.10 * (1 - (1/1.0315)^30) / 0.0315 + $1,900 / 1.0315^30
Price of Bond = $1,808.68

If yield to maturity is 7.40%:

Annual YTM = 7.40%
Semiannual YTM = 3.70%

Price of Bond = $55.10 * PVIFA(3.70%, 30) + $1,900 * PVIF(3.70%, 30)
Price of Bond = $55.10 * (1 - (1/1.0370)^30) / 0.0370 + $1,900 / 1.0370^30
Price of Bond = $1,627.32

Change in Price of Bond in dollar = $1,627.32 - $1,808.68
Change in Price of Bond in dollar = -$181.36

Change in Price of Bond in percentage = -$181.36/ $1,808.68
Change in Price of Bond in percentage = -0.1003 or -10.03%