Question

Determining the present value of bonds payable and journalizingusing the effective-interest amortization methodRelaxation, Inc. is authorized to issue 7%, 10-year bonds payable. On January 1, 2018,when the market interest rate is 12%, the company issues $300,000 of the bonds. Thebonds pay interest semiannually.

Requirements

1. How much cash did the company receive upon issuance of the bonds payable?(Round to the nearest dollar.)

2. Prepare an amortization table for the bond using the effective-interest method,through the first two interest payments (Round to the nearest dollar.)

3. Journalize the issuance of the bonds on January 1, 2018, and the first and secondpayments of the semiannual interest amount and amortization of the bonds onJune 30, 2018, and December 31, 2018. Explanations are not required.

Short answer

The present value of the principal is $93,540.

Step-by-step solution

Definition of bonds

The bonds are a long-term liability that the company issues to fulfill the need for a large amount of money.

Calculation of cash received upon the issuance

To calculate the cash acquired upon the issuance of the bonds, all the present value of the principal and the current value of the interest are calculated.

$\begin{array}{c}\mathrm{Present}\hspace{0.17em}\hspace{0.17em}\mathrm{Value}\hspace{0.17em}\hspace{0.17em}\mathrm{of}\hspace{0.17em}\hspace{0.17em}\mathrm{principal}=\hspace{0.17em}\mathrm{Face}\hspace{0.17em}\hspace{0.17em}\mathrm{Value}\times \hspace{0.17em}\mathrm{PVIF}(6\mathrm{\%},20)\hspace{0.17em}\\ =\mathrm{\$}300,000\times \hspace{0.17em}0.31180\\ =\mathrm{\$}93,540\\ \\ \mathrm{Present}\hspace{0.17em}\hspace{0.17em}\mathrm{Value}\hspace{0.17em}\hspace{0.17em}\mathrm{of}\hspace{0.17em}\hspace{0.17em}\mathrm{Interest}=\hspace{0.17em}\hspace{0.17em}\mathrm{Interest}\hspace{0.17em}\hspace{0.17em}\mathrm{Amount}\hspace{0.17em}\times \hspace{0.17em}\mathrm{PVAF}(6\%,20)\hspace{0.17em}\\ =\$10,500\times \hspace{0.17em}11.46992\\ =\$120,434.16\\ \\ \mathrm{Cash}\hspace{0.17em}\hspace{0.17em}\mathrm{Received}\hspace{0.17em}=\hspace{0.17em}\mathrm{Present}\hspace{0.17em}\hspace{0.17em}\mathrm{Value}\hspace{0.17em}\hspace{0.17em}\mathrm{of}\hspace{0.17em}\hspace{0.17em}\mathrm{Interest}+\hspace{0.17em}\mathrm{Present}\hspace{0.17em}\hspace{0.17em}\mathrm{Value}\hspace{0.17em}\hspace{0.17em}\mathrm{of}\hspace{0.17em}\hspace{0.17em}\mathrm{Principal}\\ =\hspace{0.17em}\mathrm{\$}120,434.16+\hspace{0.17em}\mathrm{\$}93,540\\ =\mathrm{\$}213,974\end{array}$

Hence, the cash received on the issue of the bonds is $213,974.

Preparation of amortization schedule

Date	Interest Expense	Cash Paid	Amortization Amount	Carrying Amount
01-01-2018				$213,974
30-06-2018	$12,838	$10,500	$2,338	$216,912
31-12-2018	$12,979	$10,500	$2,479	$218,791

Necessary journal entries

Date	Particulars	Debit	Credit
January 1, 2018	Cash	$213,974
	Discount on Bonds Payable	$86,026
	Bonds Payable		$300,000
	(Being entry for the issue of the bonds)
June 30, 2018	Interest Expense	$12,838
	Discount on Bonds Payable		$2,338
	Cash		$10,500
	(Being entry for the payment of interest)
December 31, 2018	Interest Expense	$12,979
	Discount on Bonds Payable		$2,479
	Cash		$10,500
	(Being entry for the payment of interest)