Question

Cost of Trade Credit

Grunewald Industries sells on terms of 3/10, net 30. Gross sales last year were $4,964,000 and accounts receivable averaged $476,000. Half of Grunewald's customers paid on the 10th day and took discounts. What are the nominal and effective costs of trade credit to Grunewald's nondiscount customers? (Hint: Calculate daily sales based on a 365-day year, calculate the average receivables for discount customers, and then find the DSO for the nondiscount customers.) Do not round intermediate calculations. Round your answers to two decimal places.

Nominal cost of trade credit: _____ %

Effective cost of trade credit: _____ %

Answer 1

Grunewald Industries sells on terms of 3/10, net 30 means, those customers whole will pay within 10 days will get 3% discount. The customers who can't avail the discount have to pay within 30 days.

Total Sales =  $4,964,000

Therefore, Sales per day = $4,964,000 / 365 = $13,600

Half of the customers availed the discount offer.

Therfore, Discount sales amount per day = $13,600 * 0.5 = $6,800

Since the discount customers paid on the 10th day and availed discount.

Thus, the Accounts receivables attributable to the discount customers = $6,800 * 10 = $68,000

Total avaerage accounts receivable = $476,000

Therefore, the accounts receivable atrributable to non discount customers = (Total A/R - A/R attributable to discount customers) = $476,000 - $68,000 = $408,000

We know, Days Sales Outstanding (DSO) = (Accounts receivables / Net Credit sales) * No.of days

Here, Daily Sales = $13,600

Accounts receivables = $476,000

Hence, DSO = $476,000 / $13,600 = 35 days

Therefore. we can write as,

35 = 0.5 (10) + 0.5 (DSO_non-discount)

This means, the total DSO of 35 days include the half discount customers who paid within 10 days and half non discount customers, for whom the credit period is 30 days.

35 = 0.5 (10) + 0.5 (DSO_non-discount)

Or, 0.5 (DSO_non-discount) = 35 - 0.5 (10) = 35 - 5

Or,  0.5 (DSO_non-discount) = 30

Or, DSO_non-discount = 30 /0.5 = 60

Therefore, DSO for non-discount customers = 60 days.

This means, although as per the credit terms, the non discount customers are supposed to pay within 30 days, but they are actually paying on an average, in 60 days, (Since, the DSO for the non-discount customers is 60 days).

Nominal cost of trade credit for non-discount customers is given by the following formula :-

[Discount percentage / (100% - discount percentage)] * [365 / (full allowed payment days - discount period)]

Here, the given discount percentage = 3%

Discount period = 10 days

DSO for non-discount customers = 60 days

Therefore, Nominal cost of trade credit for non-discount customers =

[3% / (100% - 3%)] * [365/ (60 -10)]

= 3/97 * 365/50

=0.03092 * 7.3

= 0.2257 = 22.57%

Hence, Nominal cost of trade credit for non-discount customers = 22.57%

Effective cost of trade credit is given by the following formula :-

[1 + {Discount /(1- Discount)}]^{365 / days after the expiry of discount period} - 1

Therefore, Effective cost of trade credit =

[1 + (3 / 100 -3)]^{365 / (60 -10)} - 1

= (1 + 3/97)^365/50 - 1

= (1.03092)^7.3 - 1

=1.248942 - 1

= 0.248942 = 24.89%

Hence, the Effective cost of trade credit for the non - discount customers = 24.89%