Question

Trew Company plans to issue bonds with a face value of $908,500 and a coupon rate of 6 percent. The bonds will mature in 10 years and pay interest semiannually every June 30 and December 31. All of the bonds are sold on January 1 of this year. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use the appropriate factor(s) from the tables provided. Round your final answers to nearest whole dollar amount.)

   

Determine the issuance price of the bonds assuming an annual market rate of interest of 7.5 percent.

Answer 1

Issue Price of the Bond

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

Par Value of the bond = $908,500

Semi-annual Coupon Amount = $27,255 [$908,500 x 6.00% x ½]

Semi-annual Yield to Maturity = 3.75% [7.50% x ½]

Maturity Period = 20 Years [10 Years x 2]

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

= $27,255[PVIFA 3.75%, 20 Years] + $908,500[PVIF 3.75%, 20 Years]

= [$27,255 x 3.89620] + [$908,500 x .47889]

= $378,741 + $435,072

= $813,813

“Therefore, the Issue Price of the Bond will be $813,813”

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.