A firm is considering relaxing credit standards, which will result in annual sales increasing from$1.5 million to $1.75 million, the cost of annual sales increasing from $1,000,000 to $1,125,000, andthe average collection period increasing from 40 to 55 days. The bad debt loss is expected to increase from 1 percent of sales to 1.5 percent of sales. The firm's required return on investments is20 percent. The firm's cost of marginal investment in accounts receivable is__________ .
A) $9,943
B) $5,556
C) $152,778
D) $12,153

Question

Quizplus · Accepted Answer

The cost of marginal investment in accounts receivable can be calculated using the following formula:

Cost of marginal investment in accounts receivable = (increase in bad debt loss - increase in annual cost of sales) / (increase in accounts receivable)

First, let's calculate the increase in bad debt loss:
Old bad debt loss = 1% of $1.5 million = $15,000
New bad debt loss = 1.5% of $1.75 million = $26,250
Increase in bad debt loss = $26,250 - $15,000 = $11,250

Next, let's calculate the increase in annual cost of sales:
Old cost of sales = $1,000,000
New cost of sales = $1,125,000
Increase in annual cost of sales = $1,125,000 - $1,000,000 = $125,000

Finally, let's calculate the increase in accounts receivable:
Old average collection period = 40 days
New average collection period = 55 days
Increase in average collection period = 55 days - 40 days = 15 days

Using a 365-day year, the increase in accounts receivable can be calculated as:
Increase in accounts receivable = (15 days / 365 days) x $1.75 million = $72,603

Plugging these values into the formula, we get:
Cost of marginal investment in accounts receivable = ($11,250 - $125,000) / $72,603 = -$1,943

Since the cost of marginal investment in accounts receivable is negative, it means that the firm should not relax its credit standards. The firm would actually lose money if it relaxed its credit standards. Therefore, the best choice is D, $12,153, which is not a valid option.

A Firm Is Considering Relaxing Credit Standards, Which Will Result