Question

James Corporation is planning to issue bonds with a face value of $508,500 and a coupon rate of 6 percent. The bonds mature in 7 years and pay interest semiannually every June 30 and December 31. All of the bonds will be 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 answer to whole dollars.)

Required:

Compute the issue (sale) price on January 1 of this year for each of the following independent cases:

  

a. Case A: Market interest rate (annual): 4 percent.

Issue Price:

b. Case B: Market interest rate (annual): 6 percent.

Issue price:

c. Case C: Market interest rate (annual): 8.5 percent.

Issue price

Answer 1

The issue price of bond is equal to present value of coupon payment plus present value of par value of bond
Formula to calculate issue price of bond
Price of bond = Coupon amount*PVA(n,i) + Par value*PV(n,i)
Case A
Face value	$508,500
Number of payments (n)	14	7*2
Coupon rate semi annual	3%	6%/2
Coupon amount	$15,255	508500*3%
Market interest rate semi annual (i)	2%	4%/2
Price of bond	15255*PVA(i=2%,n=14) + 508500*PV(i=2%,n=14)
Price of bond	(15255*12.10625) + (508500*0.75788)
Price of bond	$570,060
PVA(i=2%, n=14)	(1-(1+r)^-n))/r
PVA(i=2%, n=14)	(1-(1.02^-14))/0.02
PVA(i=2%, n=14)	12.10625
PV(i=2%,n=14)	1/(1+r)^n
PV(i=2%,n=14)	1/(1.02^14)
PV(i=2%,n=14)	0.75788
The present value calculated based on above formula would be same as that of present value table.
The issue price of bond is $570,060
Case B
Price of bond	15255*PVA(i=3%,n=14) + 508500*PV(i=3%,n=14)
Price of bond	(15255*12.10625) + (508500*0.75788)
Price of bond	$508,500
PVA(i=2%, n=14)	(1-(1+r)^-n))/r
PVA(i=2%, n=14)	(1-(1.03^-14))/0.03
PVA(i=2%, n=14)	11.29607
PV(i=2%,n=14)	1/(1+r)^n
PV(i=2%,n=14)	1/(1.03^14)
PV(i=2%,n=14)	0.66112
The present value calculated based on above formula would be same as that of present value table.
The issue price of bond is $508,500
Case C
Price of bond	15255*PVA(i=4.25%,n=14) + 508500*PV(i=4.25%,n=14)
Price of bond	(15255*12.10625) + (508500*0.75788)
Price of bond	$442,453
PVA(i=2%, n=14)	(1-(1+r)^-n))/r
PVA(i=2%, n=14)	(1-(1.0425^-14))/0.0425
PVA(i=2%, n=14)	10.3909
PV(i=2%,n=14)	1/(1+r)^n
PV(i=2%,n=14)	1/(1.0425^14)
PV(i=2%,n=14)	0.55839
The present value calculated based on above formula would be same as that of present value table.
The issue price of bond is $442,453