Brown Company is about to issue $300,000 of 8-year bonds paying a 12% interest rate with interest payable semiannually. The effective interest rate for such securities is 10%. Below are available time value of money factors.
$\begin{array}{|l|l|l|l|l|}
\hline &8 \text { periods, } & 16 \text { periods, } & 8 \text { periods, } & 16 \text { periods, } \
&10 \% & 5 \% & 12 \% & 6 \%\
\hline \text { Present Value of 1 } & 0.46651 & 0.45811 & 0.40388 & 0.39365 \
\hline \text { Future Value of 1 } & 2.14359 & 2.18287 & 2.47596 & 2.54035 \
\hline \text { Present Value of an Annuity of 1 } & 5.33493 & 10.83777 & 4.96764 & 10.10590 \
\hline \text { Future Value of an Annuity of 1 } & 11.43589 & 23.65749 & 12.29969 & 25.67253\
\hline
\end{array}$

To the closest dollar, how much can Brown expect to receive for the sale of these bonds?
A)$319,339
B)$229,371
C)$332,513
D)$540,000

Question

Brown Company is about to issue $300,000 of 8-year bonds paying a 12% interest rate with interest payable semiannually. The effective interest rate for such securities is 10%. Below are available time value of money factors.
$\begin{array}{|l|l|l|l|l|}
\hline &8 \text { periods, } & 16 \text { periods, } & 8 \text { periods, } & 16 \text { periods, } \
&10 \% & 5 \% & 12 \% & 6 \%\
\hline \text { Present Value of 1 } & 0.46651 & 0.45811 & 0.40388 & 0.39365 \
\hline \text { Future Value of 1 } & 2.14359 & 2.18287 & 2.47596 & 2.54035 \
\hline \text { Present Value of an Annuity of 1 } & 5.33493 & 10.83777 & 4.96764 & 10.10590 \
\hline \text { Future Value of an Annuity of 1 } & 11.43589 & 23.65749 & 12.29969 & 25.67253\
\hline
\end{array}$

To the closest dollar, how much can Brown expect to receive for the sale of these bonds?
A)$319,339
B)$229,371
C)$332,513
D)$540,000

Quizplus · Accepted Answer

To calculate the selling price of the bonds we need to find the present value of the future cash flows, which include the semi-annual coupon payments and the principal payment at maturity.

Step 1: Calculate the semi-annual coupon payment 
Coupon rate = 12%
Face value of bonds = $300,000

Semi-annual coupon payment = (12% x $300,000)/2 = $18,000

Step 2: Calculate the number of semi-annual periods 
Number of years = 8 
Number of semi-annual periods = 8 x 2 = 16

Step 3: Calculate the present value of the coupon payments 
PMT = $18,000 
i = 5% (effective semi-annual interest rate = 10% / 2) 
n = 16

Present value of coupon payments = PMT x [(1 - (1 + i)^-n) / i] 
Present value of coupon payments = $18,000 x [(1 - (1 + 5%)^-16) / 5%] 
Present value of coupon payments = $218,240

Step 4: Calculate the present value of the principal payment 
FV = $300,000 
i = 5% (effective semi-annual interest rate = 10% / 2) 
n = 16

Present value of principal payment = FV / (1 + i)^n 
Present value of principal payment = $300,000 / (1 + 5%)^16 
Present value of principal payment = $114,273

Step 5: Calculate the selling price of the bonds 
Selling price of bonds = Present value of coupon payments + Present value of principal payment 
Selling price of bonds = $218,240 + $114,273 
Selling price of bonds = $332,513

Therefore, the closest dollar amount that Brown can expect to receive for the sale of these bonds is $332,513, which is answer choice C.

Brown Company Is About to Issue $300,000 of 8-Year Bonds