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:
A)$205,607.
B)$194,492.
C)$200,000.
D)$22,032.
E)$172,460.

Question

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: 
A)$205,607. 
B)$194,492. 
C)$200,000. 
D)$22,032. 
E)$172,460.

Quizplus · Accepted Answer

First, we need to calculate the semi-annual interest payment:
$200,000 x 4% x 6/12 = $4,000
Next, we calculate the present value of the bond using the present value factor for a 3-year bond with a semi-annual interest rate of 2% (4%/2) at a market rate of 5%:
PV factor = 1/(1 + 0.05/2)^6 + 1/(1 + 0.05/2)^12 + 1/(1 + 0.05/2)^18 + 1/(1 + 0.05/2)^24
PV factor = 0.89000
Present value of bond = $4,000 x PV factor x 2 + $200,000 x PV factor
Present value of bond = $4,000 x 0.89000 x 2 + $200,000 x 0.89000 = $194,492
Therefore, the issue (selling) price of the bonds is $194,492, which is answer B.

On January 1,a Company Issues Bonds Dated January 1 with a Par