GMAT Corporation is planning to issue bonds with a face value of $254,500 and a

Question

GMAT Corporation is planning to issue bonds with a face value of $254,500 and a coupon rate of 6 percent. The bonds mature in 5 years and pay interest semiannually every June 30 and December 31. All of the bonds were sold on January 1 of this year. Determine the issuance price of the bonds assuming an annual market rate of interest of 8.0 percent. (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 answer to whole dollars.)

Explanation / Answer

the following is the calculation of bond price.

[present value annuity factor * interest payment] + [present value factor * face value]

here,

present value of annuity factor = [1 -(1+r)^(-n])/r

here,

r = 8% per annum =>4% for six months =>0.04.

n = 5 years * 2 semi annual periods =>10 periods.

now,

[1 -(1.04)^(-10)]/0.04

=>[0.3244358 /0.04]

=>8.110895.

interest amount = face value * coupon rate * 6/12

=>$254,500 * 6% *6/12

=>$7,635.

present value factor = 1 /(1+r)^n

=>1 /(1.04)^10

=>0.67556417.

facevalue = $254,500.

now,

issue price = [8.110895 *$7,635] + [0.67556417 * $254,500]

=> $61,926.6833 +$171,931.081

=>$233,858....(rounded to whole dollar)

therefore ISSUE PRICE = $233,858.

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