Accounts Receivable Management Quiz

The firm has daily sales of $45,000 consisting of 150 units at $300 each.

For 30 days, sales total $1,350,000. Of these sales, 40%, or $540,000 ($1,350,000 × 40%), will be uncollected because customers do not take their discounts.

The remaining $810,000 ($1,350,000 × 60%) will be paid within the discount period.

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

The total amount of sales overdue at any time during the year is $400,000 ($2,000,000 gross credit sales × 20% received after 30 days). The average collection period for these sales is 45 days.

The projected amount of overdue receivables is therefore $50,000 [$400,000 × (45 days ÷ 360 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

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.

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).

The additional annual income (loss) from using the lockbox service is the excess (deficit) of interest earned on the early deposits over (under) the
cost of the service.

If the plan is adopted, the firm’s average cash balance will increase by $3,000,000 ($600 value per check × 2,500 checks received
per day × 2 days).

Benefit (loss) = Interest earned – Cost. Thus, the loss of $45,500 is calculated from the interest earned of $210,000 ($3,000,000 ×
7%) minus the cost of $255,500 ($0.28 per check × 2,500 checks per day × 365 days in a year)

Expected discounts taken under the new credit policy can be calculated as follows:

Total sales $20,000,000

Times: percentage on credit × 80%

= Credit sales $16,000,000

Times: subject to discount × 60%

= Sales subject to discount $9,600,000

Times: discount percentage × 3%

= Expected discounts taken $288,000

The company can calculate expected discounts taken under the new credit policy as follows:

Total sales $24,000,000

Times: percentage on credit × 90%

= Credit sales $21,600,000

Times: subject to discount × 50%

= Sales subject to discount $10,800,000

Times: discount percentage × 2%

= Expected discounts taken $ 216,000

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.

Opportunity cost is the maximum benefit forgone by choosing an investment. Thus, the missing relevant information is the best alternative return on the funds to be invested in receivables.

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.

Average collection period equals average receivables divided by daily sales. The corporation’s average daily sales were $51,666 ($18,600,000 ÷ 360).

The average collection period was thus 26.7 days ($1,380,000 ÷ $51,666).

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%)

A firm’s average gross receivables balance can be calculated by multiplying average daily sales by the average collection period (days’sales outstanding).

lternatively, annual credit sales can be divided by the accounts-receivable turnover (net credit sales ÷ average accounts receivable) to obtain the average balance in receivables.

The first step is to calculate the gross proceeds the firm will receive from the factoring transaction:

Amount of receivable $100,000

Less: reserve ($100,000 × 6%)= (6,000)

Less: factor fee ($100,000 × 1.4%) =(1,400)

= Gross proceeds $ 92,600

This amount must be reduced by the interest charged on the gross proceeds:

Gross proceeds $92,600

Times: annual finance charge × 15%

Annualized interest expense $13,890

Times: portion of year (60 days ÷ 360 days) × 16.7%

Interest expense $ 2,315

The actual cash the firm will receive from this factoring transaction is thus calculated as follows:

Gross proceeds $92,600

Less: interest expense (2,315)

Net proceeds $90,285

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

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