On January 1, 2014, Broker Corp. issued $3,000,000 par value 12%, 10 year bonds which pay interest each December 31. If the market rate of interest was 14%, what was the issue price of the bonds? (The present value factor for $1 in 10 periods at 12% is .3220 and at 14% is .2697. The present value of an annuity of $1 factor for 10 periods at 12% is 5.6502 and at 14% is 5.2161.)
A) $3,339,084.
B) $2,843,172.
C)$3,000,000.
D)$2,686,896.

Question

Quizplus · Accepted Answer

To calculate the issue price of the bonds, we need to calculate the present value of future cash flows (principal and interest) discounted at the market rate of interest.

Step 1: Calculate the present value of $3,000,000 par value using the present value factor for $1 in 10 periods at 14%:
Present value of $3,000,000 = $3,000,000 x 0.2697 = $809,100

Step 2: Calculate the present value of annual interest payments of $360,000 (12% of $3,000,000) using the present value of an annuity of $1 factor for 10 periods at 14%:
Present value of annuity of $1 for 10 periods at 14% = 5.2161
Present value of interest payments = $360,000 x 5.2161 = $1,876,596

Step 3: Add the present values of the principal and interest payments to get the issue price:
Issue price = $809,100 + $1,876,596 = $2,685,696

Therefore, the answer is D) $2,686,896.