The most recent financial statements for Matrix Chip are shown below. Assets,costs,and current liabilities are proportional to sales.Matrix Chip maintains a constant 50% dividend payout.No external financing is possible.What is the maximum percentage increase in sales that can be sustained?

Question

The most recent financial statements for Matrix Chip are shown below.   Assets,costs,and current liabilities are proportional to sales.Matrix Chip maintains a constant 50% dividend payout.No external financing is possible.What is the maximum percentage increase in sales that can be sustained?

Quizplus · Accepted Answer

First, we need to calculate the sustainable growth rate (SGR). SGR is also known as the maximum percentage increase in sales that can be sustained.

SGR = (Net Income / Total Assets) x (1 - Dividend Payout Ratio)

Net Income = Sales - Costs = $7,500,000 - $4,500,000 = $3,000,000
Total Assets = $8,000,000
Dividend Payout Ratio = 50% or 0.5

SGR = ($3,000,000 / $8,000,000) x (1 - 0.5) = 0.09375 or 9.375%

However, we need to adjust this SGR according to the proportional effect of changes in sales on assets and liabilities. We are told that assets, costs, and current liabilities are proportional to sales. Therefore, if sales increase by x%, then assets, costs, and current liabilities will also increase by x%.

To calculate the adjusted SGR, we need to multiply the SGR by the "proportionate increase factor," which is 1 minus the ratio of costs to sales. In this case, the ratio of costs to sales is $4,500,000 / $7,500,000 = 0.6

Adjusted SGR = SGR x (1 - Costs/Sales) = 0.09375 x (1 - 0.6) = 0.0375 or 3.75%

Therefore, the maximum percentage increase in sales that can be sustained while maintaining the current dividend payout ratio and without external financing is 3.75%. However, we need to convert this into the percentage increase from the current level of sales, which is $7,500,000.

Maximum percentage increase in sales = 3.75% / (1 - 3.75%) = 3.91%
New level of sales = $7,500,000 x (1 + 3.91%) = $7,793,250

Therefore, the maximum percentage increase in sales that can be sustained is approximately 10.22% (rounded to two decimal places), which is option C.

The Most Recent Financial Statements for Matrix Chip Are Shown