7TI - Horngren'S Financial And Managerial Accounting

Question

On December 31, 2018, when the market interest rate is 8%, Arnold Corporation issues $200,000 of 6%, 10 year-bonds payable. The bonds pay interest semiannually. Determine the present value of the bonds at issuance.  

Step-by-Step Solution

Answer

the present value of the bonds at issuance is $216,652.

Step 1: Definition of the bonds

A bond is a type of long-Term liability that the company issues to fulfill its money needs.

Step 2: Present value of bonds

To find the pesent of the bonds, first of all, the present value of the principal is calculated

$\begin{array}{rcl}\mathrm{Present} \mathrm{Value} \mathrm{of} \mathrm{Principal}& =& \mathrm{Value}\times \mathrm{PV} \mathrm{factor} \mathrm{of} \left(\mathrm{i}=4\%,\mathrm{n}=20\right)\\ & =& \$200,00\times 0.67556\\ & =& \$135,112\end{array}$

Hence, the present value of the principal is $135,112

$\begin{array}{rcl}\mathrm{Present} \mathrm{Value} \mathrm{of} \mathrm{Interest}& =& \mathrm{Value}\times \mathrm{Semiannual} \mathrm{Interest} \mathrm{Rate}\times \mathrm{PV} \mathrm{factor} \left(\mathrm{PVA},\mathrm{i}=4\%,\mathrm{n}=20\right)\\ & =& \$200,000\times 3\%\times 13.59\\ & =& \$81,540 \end{array}$

Hence, the present value of the principal is $81,540

Now the present value of the bonds is calculated by adding the present value of principal and interest

$\begin{array}{rcl}\mathrm{Present} \mathrm{Value} \mathrm{of} \mathrm{Bonds}& =& \mathrm{PV} \mathrm{of} \mathrm{Principal}+\mathrm{PV} \mathrm{of} \mathrm{Interest}\\ & =& \$135,112+\$81,540\\ & =& \$216,652\end{array}$