Question

  ​(Bond valuation) Pybus, Inc. is considering issuing bonds that will mature in 23 years with an annual coupon rate of 8 percent. Their par value will be ​$1,000​, and the interest will be paid semiannually. Pybus is hoping to get a AA rating on its bonds​ and, if it​ does, the yield to maturity on similar AA bonds is 10 percent. ​ However, Pybus is not sure whether the new bonds will receive a AA rating. If they receive an A​ rating, the yield to maturity on similar A bonds is 11 percent. What will be the price of these bonds if they receive either an A or a AA​ rating?

Answer 1

The price of these bonds if they receive A rating

The Issue Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $40 [$1,000 x 8% x ½]

Semi-annual Yield to Maturity = 5.50% [11% x ½]

Maturity Period = 46 Years [23 Years x 2]

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

= $40[PVIFA 5.50%, 46 Years] + $1,000[PVIF 5.50%, 46 Years]

= [$40 x 16.63292] + [$1,000 x 0.08519]

= $665.32 + $85.19

= $750.51

The price of these bonds if they receive AA rating

The Issue Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $40 [$1,000 x 8% x ½]

Semi-annual Yield to Maturity = 5% [10% x ½]

Maturity Period = 46 Years [23 Years x 2]

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

= $40[PVIFA 5%, 46 Years] + $1,000[PVIF 5%, 46 Years]

= [$40 x 17.88007] + [$1,000 x 0.10600]

= $715.20 + $106.00

= $821.20

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.