Grunewald Industries sells on terms of 2/10, net 40. Gross sales last year were $4,380,000 and accounts receivable averaged $493,500. 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

Nominal 24.83%

Effective 27.86%

Explanation:

Terms 2/10, n/40 means there is a discount of 2% is available on payment of due amount within discount period of 10 days after sale with net credit period of 40 days.

Gross Sales = $4,380,000

Received within 10 days = $2,190,000

As $2,190,000 of Gross sales payments are made within discount period, discount will be availed on this value.

Discount = $2,190,000 x 2% = $43,800

Nominal Cost of trade = 2%

Effective cost of Trade

Nominal Cost of trade  = 2% / (1 - 2%) x (365 / (40 -10 )

Nominal Cost of trade  = 24.83%

Effective cost of Trade = ( 2%/(1-2%) )^(365/(40-10)) - 1

Effective cost of Trade =   27.86%

Nominal cost = 17.7 %.

Effective cost = 19.2 %

Explanation:

Calculate daily sales based on a 365-day year,

calculate the average receivables for discount customers,

find the DSO for the nondiscount customers

Sales per day = $4,380,000 / 365 days = $12,000

Discounted sales = 0.50 ($12,000) = $6,000

Accounts receivable attributable to discount customers = 10 * $6,000 = $60,000

Accounts receivable attributable to non-discount customers = $493,500 - $60,000 = $433,500

Alternatively

$493,500 / $12,000 = 41.13 days i.e. 41 days

41 days = 0.50 (10) + .50 * DSO nondiscount

Non discount = 36/.50 = 72 days

Non discount are require to pay in 40 days but they are paying in 72 days

Effective cost = (1 + 2/98 ) ^ (365 / 42) - 1

1.192 - 1 = 0.192 = 19.2 %

Nominal cost = 2/98*365/42 = 0.177 = 17.7 %.