Howard Company is about to issue $2,000,000 of 5-year bonds, with a stated rate of interest of 10%, payable semiannually. The market rate for such securities is 12%. How much can Howard expect to receive for the sale of these bonds?
A) $1,852,789.
B) $2,000,000.
C) $2,162,220.
D) None of these answer choices are correct.

Question

Quizplus · Accepted Answer

First, we need to calculate the semiannual interest payments using the stated rate of 10%:
= ($2,000,000 x 10%) / 2 = $100,000
Next, we need to calculate the present value of the bond using the market rate of 12%. We can use the present value formula for an ordinary annuity:
PV = Payment x (1 - 1/(1+r)^n) / r
PV = $100,000 x (1 - 1/(1+0.06)^10) / 0.06
PV = $826,395.24
To find the total amount Howard can expect to receive for the sale of these bonds, we can simply multiply the present value by the number of bonds:
Total amount = $826,395.24 x 2,000 = $1,652,790.48 
However, we must also add the face value of the bonds to this amount:
Total amount = $1,652,790.48 + $2,000,000 = $3,652,790.48
Since this answer is not one of the answer choices, the closest answer is A, which is $1,852,789, which is simply the present value multiplied by the number of bonds, without adding the face value.

Howard Company Is About to Issue $2,000,000 of 5-Year Bonds