Maggie's Muffins, Inc., generated $2,000,000 in sales during 2015, and its year-end total assets were $1,400,000. Also, at year-end 2015, current liabilities were $1,000,000, consisting of $300,000 of notes payable, $500,000 of accounts payable, and $200,000 of accruals. Looking ahead to 2016, the company estimates that its assets must increase at the same rate as sales, its spontaneous liabilities will increase at the same rate as sales, its profit margin will be 7%, and its payout ratio will be 50%. Required:
How large a sales increase can the company achieve without having to raise funds externally; that is, what is its self-supporting growth rate?

The Sales will increase by $350,000 (2000,000 * 17.5%)

Explanation:

As we know that,

Self Supporting Growth Rate = Return on Equity * (1 - Payout Ratio) ...Eq1

Here

Payout ratio given is 50%

and

Return on Equity =  35% (Step 1)

By putting values in Eq1, we have:

Self Supporting Growth Rate = 35% * (1 - 50%)

Self Supporting Growth Rate = 17.5%

Which means that Sales will increase by $350,000 (2000,000 * 17.5%) which is 17.5%.

Step 1: Find Return on Equity

We know that:

Return on Equity = Net Income / Equity Eq2

As we are not given value of Net Income we can not calculate the value of return on equity. But there is another way that we can calculate by simply multiplying and dividing by sales on Left hand side of the Eq2 equation.

Return on Equity = Net Income / Equity          * Sales / Sales

By rearranging, we have:

Return on Equity = Net Income / Sales  *   Sales / Equity

Now here,

Net Income / Sales  = Profit Margin

By putting this in the above equation, we have:

Return on Equity = Profit Margin  * Sales / Equity

Here

Profit Margin is 7% given in the question.

Sales were $2,000,000

And  

Equity is $400,000 (Step 2)

By putting values, we have:

Return on Equity = 7%  * $2,000,000 / $400,000

Return on Equity = 35%

Step 2. Find Equity

Equity = Assets - Liabilities

Here,

Assets are worth $1,400,000

Liabilities are standing at $1,000,000 which includes only current liabilities because company doesn't have any long term borrowings

By putting the values, we have:

Equity = $1,400,000 - $1,000,000 = $400,000

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