Chapter 13, Problem 23E

1.

To determine

Calculate the value of the impaired loan on December 31, 2016.

Explanation of Solution

Annuity: An annuity is referred as a sequence of payment of fixed amount of cash flows that occurs over the equal intervals of time.  Cash flow occurs during the first day of each time period is known as an annuity due, whereas cash flow occurs during the last day of each time period is known as an ordinary annuity.

Present Value:  The value of today’s amount expected to be paid or received in the future at a compound interest rate is called as present value.

Calculate the value of the impaired loan on December 31, 2016.

$\begin{array}{c}\text{Impaired loan = Present value of principal +Present value of interest}\\ \text{=\$313,706+\$106,103}\text{.43}\\ \text{=\$419,809}\text{.43}\end{array}$

Working note (1):

Calculate the present value of principal.

$\begin{array}{c}\text{Present value of principal = }\left[\begin{array}{l}\text{Loan principal }\times \text{Present value of}\\ \text{single sum for 8 years at 6\%}\end{array}\right]\\ =\$500,000\times {\text{p}}_{\text{n=8,i=6\%}}\\ =\$500,000\times 0.627412\\ =\$313,706.00\end{array}$

Note:

Present value of $1: n = 8, i =6% is taken from the table value (Table 3 at the end of the time value money module).

Working note (2):

Calculate the amount of interest.

$\begin{array}{c}\text{Interest = Loan amount }\times \text{Rate of interest}\\ \text{=\$500,000}\times 6\text{\%}\\ \text{=\$30,000}\end{array}$

Working note (3):

Calculate the present value of interest.

$\begin{array}{c}\text{Present value of interest=}\left[\begin{array}{l}\text{Amount of interest}\times \text{Present value}\\ \text{of ordinary annuity for 5 years at 6\%}\times \\ \text{Present value for 3 years deferred period}\end{array}\right]\\ =\$30,000\times 4.212364\times 0.839619\\ =\$106,103.43\end{array}$

Note:

Present value of ordinary annuity of $1: n =5, i =6% is taken from the table value (Table 4 at the end of the time value money module).

Present value of $1: n = 3, i =6% is taken from the table value (Table 3 at the end of the time value money module).

Conclusion

Thus, the value of impaired loan on December 31, 2016 is $419,809.43.

2.

To determine

Prepare journal entries in the books of ON Bank.

Explanation of Solution

Record the amount of accrued interest as on December 31, 2016.

Date	Account Title and Explanation	Debit	Credit
December 31, 2016	Cash	$30,000.00
	Interest income		$30,000.00
	(To record the interest accrued)

Table (1)

• Cash is an asset. It is increased. Therefore cash account is debited.
• Interest income is an income, it increases the equity. Therefore interest income account is credited.

Recognize the impairment.

Date	Account Title and Explanation	Debit	Credit
December 31, 2016	Bad debt expense (4)	$80,190.57
	Allowance for doubtful notes		$80,190.57
	(To recognize the impairment)

Table (2)

Working note (4):

Calculate the amount of impairment.

$\begin{array}{c}\text{Impairment=Loan principal}-\text{Present value of imapired loan}\\ \text{=\$500,000}-\$419,809.43\\ =\$80,190.57\end{array}$

• Bad debt expense is an expense, it decreases the equity. Therefore Bad debt expense account is debited.
• Allowance for doubtful notes is a contra-asset, it is increased. Therefore it is credited.

Record the interest income at December 31, 2017.

Date	Account Title and Explanation	Debit	Credit
December 31, 2017	Allowance for doubtful notes	$25,188.57
	Interest income (5)		$25,188.57
	(To record the interest income)

Table (3)

Working note (5):

Calculate the amount of interest income.

$\begin{array}{c}\text{Interest income = Present value of impaired loan}\times \text{Interest rate}\\ \text{=\$419,809}\text{.43}\times \text{6\%}\\ \text{=\$25,188}\text{.57}\end{array}$

• Allowance for doubtful notes is a contra-asset, it is decreased. Therefore it is debited.
• Interest income is an income, it is increased. Therefore it is credited.

Record the interest income at December 31, 2018.

Date	Account Title and Explanation	Debit	Credit
December 31, 2018	Allowance for doubtful notes	$26,699.88
	Interest income (6)		$26,699.88
	(To record the interest income)

Table (4)

Working note (6):

Calculate the amount of interest income.

$\begin{array}{c}\text{Interest income =}\left(\begin{array}{l}\text{Present value of impaired loan+}\\ \text{Interest income earned in 2017}\end{array}\right)\times \text{Interest rate}\\ \text{=}\left(\text{\$419,809}\text{.43+\$25,188}\text{.57}\right)\times \text{6\%}\\ \text{=\$26,699}\text{.88}\end{array}$

• Allowance for doubtful notes is a contra-asset, it is decreased. Therefore it is debited.
• Interest income is an income, it is increased. Therefore it is credited.

Record the bad debt expense.

Date	Account Title and Explanation	Debit	Credit
December 31, 2019	Allowance for doubtful notes	$28,302.12
	Bad debt expense (7)		$28,302.12
	(To reverse the bad debt expense, as the interest is expected to be paid on due date)

Table (5)

Working note (7):

Determine the decrease in bad debt expense.

$\begin{array}{c}\text{Bad debt expense = Face value}-\text{Current carrying value}\\ \text{=\$500,000}-\left[\$419,809.43+\$25,188.57+\$26,699.88\right]\\ =\text{\$500,000}-\$471,697.88\\ =\$28,302.12\end{array}$

Record the interest income at December 31, 2019 through 2024.

Date	Account Title and Explanation	Debit	Credit
December 31, 2019	Cash	$30,000.00
	Interest income		$30,000.00
	(To record the interest income)
December 31, 2020	Cash	$30,000.00
	Interest income		$30,000.00
	(To record the interest income)
December 31, 2021	Cash	$30,000.00
	Interest income		$30,000.00
	(To record the interest income)
December 31, 2022	Cash	$30,000.00
	Interest income		$30,000.00
	(To record the interest income)
December 31, 2023	Cash	$30,000.00
	Interest income		$30,000.00
	(To record the interest income)
December 31, 2024	Cash	$30,000.00
	Interest income		$30,000.00
	(To record the interest income)

Table (6)

• Cash is an asset. It is increased. Therefore cash account is debited.
• Interest income is an income, it increases the equity. Therefore interest income account is credited.

Record the collection of cash on note.

Date	Account Title and Explanation	Debit	Credit
December 31, 2024	Cash	$500,000.00
	Notes receivable		$500,000.00
	(To record the collection of note)

Table (7)

• Cash is an asset. It is increased. Therefore cash account is debited.
• Notes receivable is an asset. It is decreased. Therefore notes receivable account is credited.