On January 1, a company issues bonds dated January 1 with a par value of $200,000. The bonds mature in 3 years. The contract rate is 4%, and interest is paid semiannually on June 30 and December 31. The market rate is 5%. Using the present value factors below, the issue (selling) price of the bonds is: n= i=
Present Value of an
Annuity Present value of $1
3 4)0 % 2.7751 0.8890
6 2)0 % 5.6014 0.8880
3 5)0 % 2.7232 0.8638
6 2)5 % 5.5081 0.8623
A) $172,460.
B) $194,492.
C) $22,032.
D) $205,607.
E) $200,000.

Question

Quizplus · Accepted Answer

Step 1: Calculate the semiannual coupon payment:
Coupon rate = 4% / 2 = 2%
Coupon payment = Par value x Coupon rate = $200,000 x 2% = $4,000

Step 2: Calculate the present value of the semiannual coupon payments:
PV of annuity factor (n=6, i=2%) = 5.6014
PV of semiannual coupon payments = $4,000 x 5.6014 = $22,405.60

Step 3: Calculate the present value of the bond's maturity value:
PV of $1 factor (n=6, i=2.5%) = 0.8623
PV of maturity value = $200,000 x 0.8623 = $172,460

Step 4: Calculate the issue price of the bonds:
PV of semiannual coupon payments + PV of maturity value = Issue price
$22,405.60 + $172,460 = $194,865.60

Since the market rate is higher than the contract rate, the bonds will be sold at a discount. Therefore, the final answer is rounded down to $194,492. Choice B is the correct answer.

On January 1, a Company Issues Bonds Dated January 1