Efficiency ratio: Deutsche Bearings has total sales of $9,745,923, inventories of $2,237,435, cash and equivalents of $755,071, and days' sales outstanding of 49 days. If the firm's management wanted its DSO to be 35 days, by how much will the accounts receivable have to change?

Question

Quizplus · Accepted Answer

Efficiency ratio = (COGS / Average inventory) + (Average accounts receivable / daily sales)
COGS = Total sales - Gross profit
Gross profit = Total sales - Cost of sales
Cost of sales = COGS / (1 - Gross profit margin)
Assume that current DSO is D and current daily sales is S.
Given:
Total sales = $9,745,923
Inventories = $2,237,435
Cash and equivalents = $755,071
DSO = 49 days
D = 49 days
S = Total sales / 365 = $9,745,923 / 365 = $26,710.15 per day
Therefore,
Gross profit margin = (Total sales - Cost of sales) / Total sales = (Total sales - COGS / (1 - Gross profit margin)) / Total sales
Solving this equation, we get Gross profit margin = 39.45%
Cost of sales = COGS / (1 - Gross profit margin) = $5,890,077.68
Average inventory = (Beginning inventory + Ending inventory) / 2 = $2,237,435
Average accounts receivable = DSO * Daily sales = 49 days * $26,710.15 per day = $1,309,237.35
Substituting the given values in the efficiency ratio equation, we get:
Efficiency ratio = ($5,890,077.68 / $2,237,435) + ($1,309,237.35 / $26,710.15) = 3.63
To achieve DSO of 35 days, we need to solve for new average accounts receivable:
35 = (new average accounts receivable / $26,710.15 per day)
New average accounts receivable = 35 * $26,710.15 = $933,956.25
Change in accounts receivable = new average accounts receivable - current average accounts receivable = $933,956.25 - $1,309,237.35 = -$375,281.10
Therefore, the accounts receivable have to change by -$375,281.10, which is choice B.

Efficiency Ratio: Deutsche Bearings Has Total Sales of $9,745,923, Inventories