Question

Mansfield Corporation had 20X1 sales of \(100 million. The balance sheet items that vary directly with sales and the profit margin are as follows:

	Percent
Cash	5%
Accounts receivable	15
Inventory	20
Net fixed assets	40
Accounts payable	15
Accruals	10
Profit margin after tax	10%

The dividend payout rate is 50 percent of earnings, and the balance in retained earnings at the end of 20X1 was \)33 million. Notes payable are currently \(7 million. Long-term bonds and common stock are constant at \)5 million and $10 million, respectively.

a. How much additional external capital will be required for next year if sales

increase 15 percent? (Assume that the company is already operating at full

capacity.)

Short answer

The additional external capital required by the company amounts to $2.50 million.

Step-by-step solution

Change in sales

$\begin{array}{rcl}\mathrm{Change}\mathrm{in}\mathrm{sales}& =& \mathrm{Existing}\mathrm{sales}\times \mathrm{Growth}\mathrm{ratio}\\ & =& \$100\mathrm{million}\times 15\%\\ & =& \$15\mathrm{million}\end{array}$

Assets to sales ratio

$\begin{array}{rcl}\mathrm{Assets}\mathrm{to}\mathrm{sales}\mathrm{ratio}& =& \mathrm{Cash}+\mathrm{Accounts}\mathrm{receivables}+\mathrm{Inventory}+\mathrm{Net}\mathrm{fixed}\mathrm{assets}\\ & =& 5\%+15\%+20\%+40\%\\ & =& 80\%\end{array}$

Liabilities to sales ratio

$\begin{array}{rcl}\mathrm{Liabilities}\mathrm{to}\mathrm{sales}\mathrm{ratio}& =& \mathrm{Accounts}\mathrm{payable}+\mathrm{Accruals}\\ & =& 15\%+10\%\\ & =& 25\%\end{array}$

New sales level

$\begin{array}{rcl}\mathrm{New}\mathrm{sales}\mathrm{level}& =& \mathrm{Existing}\mathrm{sales}+\mathrm{Increase}\mathrm{in}\mathrm{sales}\\ & =& \$100\mathrm{million}+\$15\mathrm{million}\\ & =& \$115\mathrm{million}\end{array}$

Required new funds

$\begin{array}{rcl}\mathrm{Required}\mathrm{new}\mathrm{funds}& =& \left(\mathrm{Assets}\mathrm{to}\mathrm{sales}\mathrm{ratio}\times \mathrm{Change}\mathrm{in}\mathrm{sales}\right)-\left(\mathrm{Liabilities}\mathrm{to}\mathrm{sales}\mathrm{ratio}\times \mathrm{Chnage}\mathrm{in}\mathrm{sales}\right)-\left(\mathrm{Profit}\mathrm{margin}\times \mathrm{New}\mathrm{sales}\mathrm{level}\right)\left(1-\mathrm{Dividend}\mathrm{payout}\mathrm{ratio}\right)\\ & =& \left(0.80\times \$15\mathrm{million}\right)-\left(0.25\times \$15\mathrm{million}\right)-\left(0.10\times \$115\mathrm{million}\right)\left(1-0.50\right)\\ & =& \$12\mathrm{million}-\$3.75\mathrm{million}-\$6.75\mathrm{million}\\ & =& \$2.50\mathrm{million}\end{array}$