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.

Short answer

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

Step-by-step solution

Definition of the bonds

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

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

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