Accounts Receivable Management Quiz

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 averagecollection period for these sales is 45 days.

The projected amount ofoverdue receivables is therefore $50,000 [$400,000 × (45 days ÷ 360days)].

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

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

theestimated 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 wascalculated 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 newlevel 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).

Because these terms involve an annual interest cost of over 36%, acompany 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 beforced to match the competition or lose market share.

The average collection period, also called the days sales outstanding inreceivables, is calculated as the number of days in the year over thereceivables 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 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 taketheir discounts.

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

If the cost of borrowing is low, the firm can satisfy its working capitalneeds otherwise than by encouraging early payment from customers. Also,loosening credit policies tends to increase repeat sales.

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

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 projected average balance in receivables under the old policy was$300,000 [$3,600,000 × (30 days ÷ 360 days)]. Under the new policy, theaverage 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 additionalinvestment 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

Opportunity cost is the maximum benefit forgone by choosing aninvestment. Thus, the missing relevant information is the best alternativereturn on the funds to be invested in receivables.

To calculate the firm’s net cost of adding the cash discount to its creditterms, find both the total cash lost to discounts and the offsetting savingswhich arise from earlier customer payments. The calculations are asfollows:

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

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

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

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

The increase in after-tax profit iscalculated 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

A quantity discount is an attempt to increase sales by reducing the unitprice 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 normal operating cycle is the period from the acquisition of inventoryto the collection of the account receivable. If trade credit is for a periodlonger than the normal operating cycle, the seller must be financing morethan just the purchase of inventory

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

Under the new policy, theaverage 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 additionalinvestment 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

Increasing the quality of the accounts rejected means that fewer sales willbe made. The company is therefore not trying to maximize its sales orincrease its bad debt losses. The objective is to reduce bad debt losses andthereby maximize profits.

The first step is to calculate the gross proceeds the firm will receive fromthe 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 grossproceeds:

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 thuscalculated as follows:

Gross proceeds $92,600

Less: interest expense (2,315)

Net proceeds $90,285