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:

Question

Quizplus · Accepted Answer

Step 1: Calculate the semiannual interest payment
Par Value x Contract rate = $200,000 x 4% = $8,000
Semiannual interest payment = $8,000/2 = $4,000

Step 2: Calculate the present value of principal
PV of $1 at 5% for 6 periods = 0.74726
PV of principal = $200,000 x 0.74726 = $149,452

Step 3: Calculate the present value of interest payments
PV of annuity of $1 at 5% for 6 periods = 5.21667
PV of interest payments = $4,000 x 5.21667 = $20,866.68

Step 4: Calculate the total present value
Total present value = PV of principal + PV of interest payments = $149,452 + $20,866.68 = $170,318.68

Step 5: Calculate the issue price
Issue price = total present value / PV factor of $1 at issue date for 6 periods at 5% = $170,318.68 / 0.87589 = $194,492.

Therefore, the best choice is (B) $194,492.

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