Question

net income		million	increase
total asset turnover		times	faster
Equity multiplier		times	more
ROA		%	increase
ROE		%	increase

You are considering investing in Dakota’s Security Services. You have been able to locate the following information on the firm: Total assets are $33.6 million, accounts receivable are $4.56 million, ACP is 25 days, net income is $4.80 million, and debt-to-equity is 1.2 times. All sales are on credit. Dakota’s is considering loosening its credit policy such that ACP will increase to 30 days. The change is expected to increase credit sales by 5 percent. Any change in accounts receivable will be offset with a change in debt. No other balance sheet changes are expected. Dakota’s profit margin will remain unchanged. How will this change in accounts receivable policy affect Dakota’s net income, total asset turnover, equity multiplier, ROA, and ROE? (Do not round intermediate calculations. Enter your answer in millions of dollars. Round your answers to 2 decimal places. Use 365 days a year.)

Answer 1

• Total assets = $33.6 million
• accounts receivable = $4.56 million
• ACP = 25 days
• net income = $4.80 million
• debt-to-equity = 1.2
• All sales are on credit.
• ACP is changing to 30 days
• The change in ACP is expected to increase credit sales by 5%
• Any change in receivable will be off set by change in debt
• profit margin will remain same

Calculation of sales:

average accounts receivable turnover = 365/ accounts receivable turnover ratio

25 = 365/ accounts receivable turnover ratio

accounts receivable turnover ratio = 365/ 25 = 14.6

accounts receivable turnover ratio = net credit sales/ average accounts receivable

14.6 = net credit sales/ $4.56 million

net credit sales = 14.6 * $4.56 million = $66.576 million

Therefore sales = $66.576 million

Calculation of Profit margin:

Profit margin = net income/ sales

= $4.80 million/ $66.576 million = 7.21%

Profit margin = 7.21%

Calculation of total debt and total equity:

Debt to equity ratio = total debt/ total equity

1.2 = total debt/ total equity

1.2 = total debt/ (total assets - total debt)

1.2 (total assets - total debt) = total debt

1.2 ($33.6 million - total debt) = total debt

$40.32 million - 1.2 total debt = total debt

$40.32 million = total debt + 1.2 total debt =2.2 total debt

2.2 total debt = $40.32 million

total debt = $40.32 million/ 2.2 =$18.3273 million

total debt =$18.3 million

Therefore, total equity = total assets - total debt = $33.6 million - $18.3 million = $15.3 million

total equity = $15.3 million

Change in sales because of change in ACP:

Sales = $66.576 million

increase in sales = 5%

New sales = $66.576 million * 105% = $69.9048 million = $69.9 million

New profit = new sales * profit margin = = $69.9 million * 7.21% = $5.039 million = $5.04 million

average accounts receivable turnover = 365/ accounts receivable turnover ratio

30= 365/ accounts receivable turnover ratio

accounts receivable turnover ratio = 365/ 30 = 12.166

accounts receivable turnover ratio = new credit sales/ new average accounts receivable

12.166 = $69.9 million/ new average accounts receivable

new average accounts receivable= $69.9 million/ 12.166

new average accounts receivable = $5.75 million

Change in average accounts receivable = new average accounts receivable - old average accounts receivable

= $5.75 million - $4.56 million = $1.19 million

New debt = old debt + Change in average accounts receivable = $18.3 million + $1.19 million = $19.49 million

Now after finding the above things coming to the main question

New net income = $5.04 million

New total assets turnover = new sales/ average total assets = $69.9 million/ $33.4 million = 2.09

Equity multiplier = total assets/ total equity = $33.4 million/ $15.3 million = 2.18

Return on assets = net income/ total assets = $5.04 million/ $33.4 million = 15.09%

Return on equity = net income/ total equity = $5.04 million/ $15.3 million =32.94%