Accounts Receivable Management Quiz

A quantity discount is an attempt to increase sales by reducing the unit price on bulk purchases. It concerns only the price term of an agreement, not the credit term, and thus is unrelated to credit and collection policy.

The company’s manufacturing and selling costs exclusive of bad debts equal 75% of sales. Hence, the gross profit on the $150,000 increase in sales will be $37,500 ($150,000 × 25%).

The increase in after-tax profit is calculated as follows:

Increase in gross profit = $37,500

Less: uncollectible accounts ($150,000 × 16%) = (24,000)

Less: collection costs  ($150,000 × 4%) = (6,000)

Increase in pre-tax income = $ 7,500

Less: income tax expense = ($7,500 × 38%) = (2,850)

Increase in after-tax income= $ 4,650

The projected average balance in receivables under the old policy was $383,333 [$4,600,000 × (30 days ÷ 360 days)].

Under the new policy, the average balance will be $482,222 [$4,960,000 × (35 days ÷ 360 days)].

Hence, the average balance is $98,889 higher under the new policy ($482,222 – $383,333).

The pre-tax cost of carrying the additional investment in receivables can be calculated as follows:

Increased investment in receivables -- gross $98,889

Times: variable cost ratio × 50%

Increased investment in receivables -- net = $49,444

Times: opportunity cost of funds × 11%

Incremental cost of new credit plan = $ 5,439

The increase in estimated gross profit is $32,000 ($80,000 × 40%).

The incremental bad debt loss is $4,800 ($80,000 × 6%). Accordingly,

the estimated net increase in operating income is $27,200 ($32,000 – $4,800).

The before-tax return on sales is 34% ($27,200 ÷ $80,000).

Projected credit sales for the year under the old credit policy were $35 million ($50,000,000 × 70%). The level of average receivables was calculated as follows:

Receivables turnover = Days in year ÷ Average collection period
                                            = 360 days ÷ 75 days
                                            = 4.8 times per year

Average receivables= Net credit sales ÷ Receivables turnover
                                        = $35,000,000 ÷ 4.8 times
                                        = $7,291,667

Under the new policy, total sales will be $47.5 million ($50,000,000 × 95%), and credit sales will be $28.5 million ($47,500,000 × 60%).

The new level of average receivables is calculated as follows: 

Receivables turnover = Days in year ÷ Average collection period
                                           = 360 days ÷ 50 days
                                            = 7.2 times per year

Average receivables = Net credit sales ÷ Receivables turnover
                                         = $28,500,000 ÷ 7.2 times
                                        = $3,958,333

The average receivables balance will therefore be reduced by $3,333,334 ($7,291,667 – $3,958,333).

To calculate the firm’s net cost of adding the cash discount to its credit terms, find both the total cash lost to discounts and the offsetting savings which arise from earlier customer payments. The calculations are as follows:

Cash to be discounted = $5,000,000 × 60% = $3,000,000

Cost of discount = $3,000,000 × 2% = $60,000

Average daily sales = $5,000,000 ÷ 365 days = $13,698.63 per day

Cost of A/R for 60 days = $13,698.63 × 60 days × 12% = $98,630.14

Cost of A/R for 30 days = $13,698.63 × 30 days × 12% = $49,315.07

Savings from discount = $98,630.14 – $49,315.07 = $49,315.07

Net cost of discount = $60,000 (cost) – $49,315 (savings) = $10,685

Increasing the quality of the accounts rejected means that fewer sales will be made. The company is therefore not trying to maximize its sales or increase its bad debt losses. The objective is to reduce bad debt losses and thereby maximize profits.

All factors should be considered that differ between the two policies. Factors that do not differ, such as the current bad debt experience, are not relevant. The company must estimate the expected bad debt losses under each new policy.

The average collection period, also called the days sales outstanding in receivables, is calculated as the number of days in the year over the receivables turnover ratio. The firm’s can be thus calculated as follows:

Average collection period = Days in year ÷ Accounts receivable turnover

                                                    = 365 ÷ (Net credit sales ÷ Average net receivables)

                                                     = 365 ÷ [(20,000 × $25,000) ÷ $30,000,000]

                                                    = 365 ÷ ($500,000,000 ÷ $30,000,000)

                                                    = 365 ÷ 16.667

                                                    = 21.9 days

The company’s manufacturing and selling costs exclusive of bad debts equal 70% of sales. Hence, the gross profit on the $100,000 increase in sales will be $30,000 ($100,000 × 30%).

The increase in after-tax profit is calculated as follows:

Increase in gross profit =  $30,000

Less: uncollectible accounts  ($100,000 × 15%) = (15,000)

Less: collection costs  ($100,000 × 5%) = (5,000)

Increase in pre-tax income = $10,000

Less: income tax expense  ($10,000 × 40%) = (4,000)

Increase in after-tax income =$ 6,000

Changing its credit terms to encourage earlier payment by customers increases the firm’s cash flow and decreases the need for short-term borrowing.

If the change is adopted, the company’s average balance in receivables will increase by $450,000 {$27,000,000 × [(34 days – 28 days) ÷ 360 days]}.

The minimum savings that Best must experience to justify the change is therefore $36,000 ($450,000 × 8%)

The average collection period measures the number of days between the date of sale and the date of collection. It should be related to a firm’s credit terms. For example, a firm that allows terms of 2/15, net 30, should have an average collection period of somewhere between 15 and 30 days.

The projected average balance in receivables under the old policy was $300,000 [$3,600,000 × (30 days ÷ 360 days)]. Under the new policy, the average balance will be $396,000 [$3,960,000 × (36 days ÷ 360 days)].

Hence, the average balance is $96,000 higher under the new policy ($396,000 – $300,000). The pre-tax cost of carrying the additional investment in receivables can be calculated as follows:

Increased investment in receivables -- gross =  $96,000

Times: variable cost ratio × 60%

Increased investment in receivables -- net =$57,600

Times: opportunity cost of funds × 10%

Incremental cost of new credit plan = $ 5,760

The purpose of an aging of receivables is to classify receivables by due date. Those that are current (not past due) are listed in one column, those less than 30 days past due in another column, etc.

The amount in each category can then be multiplied by an estimated bad debt percentage that is based on a company’s credit experience and other factors. The theory is that the oldest receivables are the least likely to be collectible.

Aging the receivables and estimating the uncollectible amounts is one method of arriving at the appropriate balance sheet valuation of the accounts receivable account.

Because these terms involve an annual interest cost of over 36%, a company would not offer them unless it desperately needed cash. Also, credit terms are typically somewhat standardized within an industry. Thus, if most companies in the industry offer similar terms, a firm will likely be forced to match the competition or lose market share.

If the change is adopted, Hest’s average balance in receivables will increase by $625,000 {$45,000,000 [(35 days – 30 days ) ÷ 360 days]}.

The company’s additional required investment in receivables is therefore $375,000 ($625,000 × 60% variable cost ratio), and the incremental pretax
cost of this investment is $22,500 ($375,000 × 6%).

Accordingly, the collection costs must be reduced by a pretax minimum of $22,500 to offset the cost of the increased investment in receivables.

The company can calculate the net benefit (loss) from the proposed change in credit policy as follows:

Increase in sales $720,000

Times: variable cost ratio × 80%

Increase in variable costs $576,000

Increased investment in receivables = $576,000 × (75 days ÷ 360 days) = $120,000

Increased investment in receivables $120,000

Times: opportunity cost of funds × 20%

Cost of new credit plan $ 24,000

Increase in sales $720,000

Times: contribution margin ratio × 20%

Increase in contribution margin $144,000

Less: cost of new credit plan (24,000)

Benefit of new credit plan $120,000