James Corporation is planning to issue bonds with a face value of $504,000 and a coupon rate of 6 percent

Determination of Issue Price of Bonds on January 1 of this year :-

Face Value of Bonds = $504,000  

Life of Bond (in years) = 7

Maturity amount of Bond $504,000  

Coupon rate = 6% per year payable semi annually i.e. 3% per semi annual

Semi annual Coupon Amount = $504,000 × 3%

= $15,120 This will be paid 14 times

n = 7 years i.e. 7 * 2 = 14 semi annuals

Case A : Market Interest Rate (annual) : 4 percent  

Market rate on similar bonds (r) = 4%  

= 2% semi annual  

PVAF(r, n) = Present Value Annuity factor at r% for n periods

Present Value of an Annuity of $1 at 2% for 14 periods = 12.1062488

PVIF(r, n) = Present Value interest factor at r% for n periods

Present Value of $1 at 2% at n= 14 periods = 0.7578750

Price of Bond = Coupon Amount * PVAF(r,n) + Redemption Amount * PVIF(r,n)

= $15120* 12.1062488 + $504000* 0.757875

= $183047 + $381969

= $565016

Case B : Market Interest Rate (annual) : 6 percent  

Market rate on similar bonds (r) = 6%  

= 3% semi annual  

PVAF(r, n) = Present Value Annuity factor at r% for n periods

Present Value of an Annuity of $1 at 3% for 14 periods = 11.296073

PVIF(r, n) = Present Value interest factor at r% for n periods

Present Value of $1 at 3% at n= 14 periods = 0.661118

Price of Bond = Coupon Amount * PVAF(r,n) + Redemption Amount * PVIF(r,n)

= $15120* 11.296073 + $504000* 0.661118

= $170797+ $333203

= $504000

Case C : Market Interest Rate (annual) : 8.5 percent  

Market rate on similar bonds (r) = 8.5%  

= 4.25% semi annual  

PVAF(r, n) = Present Value Annuity factor at r% for n periods

Present Value of an Annuity of $1 at 4.25% for 14 periods = 10.390900

PVIF(r, n) = Present Value interest factor at r% for n periods

Present Value of $1 at 4.25% at n= 14 periods = 0.558387

Price of Bond = Coupon Amount * PVAF(r,n) + Redemption Amount * PVIF(r,n)

= $15120* 10.390900 + $504000* 0.558387

= $157110 + $281427

= $438537