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A $1,700 face value corporate bond with a 5.6 percent coupon (paid semiannually) has 12 years...

A $1,700 face value corporate bond with a 5.6 percent coupon (paid semiannually) has 12 years left to maturity. It has had a credit rating of BBB and a yield to maturity of 7.9 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 9.2 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))

Expert Solution

Price of the Bond at Yield to Maturity of 7.90 percent

Face Value of the bond = $1,700

Semi-annual Coupon Amount = $47.60 [$1,700 x 5.60% x ½]

Semi-annual Yield to Maturity = 3.95% [7.90% x ½]

Maturity Period = 24 Years [12 Years x 2]

Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $47.60[PVIFA 3.95%, 24 Years] + $1,700[PVIF 3.95%, 24 Years]

= [$47.60 x 15.325315] + [$1,700 x 0.394650]

= $729.485 + $670.905

= $1,400.390

Price of the Bond at Yield to Maturity of 9.20 percent

Face Value of the bond = $1,700

Semi-annual Coupon Amount = $47.60 [$1,700 x 5.60% x ½]

Semi-annual Yield to Maturity = 4.60% [9.20% x ½]

Maturity Period = 24 Years [12 Years x 2]

Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $47.60[PVIFA 4.60%, 24 Years] + $1,700[PVIF 4.60%, 24 Years]

= [$47.60 x 14.351898] + [$1,700 x 0.339813]

= $683.150 + $577.682

= $1,260.832

Change in the bond’s price in dollars

= Bond Price at 9.20% Yield to Maturity - Bond Price at 7.90% Yield to Maturity

= $1,260.832 - $1,400.390

= -$139.558 (Negative)

Change in the bond’s price in percentage terms

= [-$139.558 / $1,400.390] x 100

= -9.966% (Negative)

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.

--The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.

jeff jeffy answered 1 year ago

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