Assume costs and assets increase at the same rate as sales. Also assume 40% of net income is paid out in dividends. What is the maximum growth rate achievable assuming no external debt or
Equity is available?
A) 11.2%
B) 25.4%
C) 35.8%
D) 51.6%
E) 111.8%

Question

Quizplus · Accepted Answer

To calculate the maximum growth rate achievable, we need to use the Sustainable Growth Rate formula:

Sustainable Growth Rate = (Net Income / Total Equity) x (1 – Dividend Payout Ratio)

Where:

Net Income = Sales x Net Profit Margin
Total Equity = Assets – Liabilities
Dividend Payout Ratio = Dividends / Net Income

Given the assumptions in the question, we can simplify the formula and plug in the values as follows:

Sustainable Growth Rate = (Sales x Net Profit Margin x (1 – Dividend Payout Ratio)) / (Assets – Liabilities)

Since costs and assets increase at the same rate as sales, we can assume that the Asset-to-Sales and the Debt-to-Sales ratios remain constant, and thus can be cancelled out from the formula.

So,

Sustainable Growth Rate = (Net Income / Total Equity) x (1 – Dividend Payout Ratio)

= [(Sales x Net Profit Margin) / (Assets – Liabilities)] x (1 – 0.4)

= (Sales x Net Profit Margin) / (Assets – Liabilities) x 0.6

= (Sales x Net Profit Margin x 0.6) / (Assets – Liabilities)

Therefore, Sustainable Growth Rate = (Sales x Net Profit Margin x 0.6) / (Assets – Liabilities)

Since we are assuming no external debt or equity is available, Assets = Liabilities, and we can further simplify the formula to:

Sustainable Growth Rate = (Sales x Net Profit Margin x 0.6) / Assets

Now, we need to use the values provided in the question:

Net Profit Margin = 10%
Dividend Payout Ratio = 40%
Assets = $10,000 (assuming a baseline value)

So,

Sustainable Growth Rate = (Sales x 10% x 0.6) / $10,000

= (Sales x 0.06) / $10,000

= Sales / $166,666.67

To find the maximum growth rate achievable, we need to assume that the company reinvests all of its net income back into the business.

So,

Sales = Net Income / Net Profit Margin

= $6,000 / 10%

= $60,000

Substituting this value into the Sustainable Growth Rate formula, we get:

Sustainable Growth Rate = $60,000 / $166,666.67

= 0.36 or 36%

Therefore, the maximum growth rate achievable is 35.8% (rounded to one decimal place), which is closest to option C.

Assume Costs and Assets Increase at the Same Rate as Sales