Question

Maggie's Muffins Bakery generated $2 million in sales during 2019, and its year-end total assets were $1.1 million. Also, at year-end 2019, current liabilities were $1 million, consisting of $300000 of notes payable, $500000 of accounts payable, and $200000 of accruals. Looking ahead to 2020, 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 75%. How large a sales increase can the company achieve without having to raise funds externally—that is, what is its self-supporting growth rate?

Answer 1

To find the self-supporting growth rate, we need to find the amount of increase in assets that can be funded by the increase in spontaneous liabilities and retained earnings, without requiring external financing.

First, let's calculate the company's profit margin:

Profit Margin = Net Income / Sales

0.07 = Net Income / 2,000,000

Solving for Net Income:

Net Income = 0.07 * 2,000,000 = 140,000

Next, let's calculate the amount of retained earnings that will be available for funding growth:

Retained Earnings = Net Income * (1 - Payout Ratio)

Retained Earnings = 140,000 * (1 - 0.75) = 35,000

Now, let's calculate the increase in assets that can be funded by spontaneous liabilities and retained earnings:

Increase in Assets = Self-Supporting Growth Rate * Total Assets

Increase in Assets = Self-Supporting Growth Rate * 1,100,000

Increase in Spontaneous Liabilities = Self-Supporting Growth Rate * Spontaneous Liabilities

Increase in Spontaneous Liabilities = Self-Supporting Growth Rate * (Notes Payable + Accounts Payable + Accruals)

Increase in Spontaneous Liabilities = Self-Supporting Growth Rate * (300,000 + 500,000 + 200,000) = Self-Supporting Growth Rate * 1,000,000

Since the increase in assets must equal the increase in spontaneous liabilities and retained earnings, we can set these two expressions equal to each other and solve for the self-supporting growth rate:

Self-Supporting Growth Rate * 1,100,000 = Self-Supporting Growth Rate * 1,000,000 + 35,000

Self-Supporting Growth Rate * 100,000 = 35,000

Self-Supporting Growth Rate = 0.35 or 35%

Therefore, the company can achieve a sales increase of up to 35% without requiring external financing, assuming its profit margin, payout ratio, and spontaneous liabilities remain constant.