Moore Money Inc. has a proﬁt margin of 11% and a retention ratio of 70%. Last year, the ﬁrm had sales of $500 and total assets of $1,000. What is the internal growth rate?
A) 1.7%
B) 2.6%
C) 3.7%
D) 4.0%
E) 5.9%

Question

Quizplus · Accepted Answer

The internal growth rate formula is: 
Internal Growth Rate = Retention Ratio x Return on Assets

We are given: 
Profit Margin = Return on Assets - Retention Ratio
Profit Margin = 0.11
Retention Ratio = 0.70
Sales = $500
Total Assets = $1,000

We need to find the return on assets first:
Return on Assets = Profit Margin + Retention Ratio
Return on Assets = 0.11 + 0.70
Return on Assets = 0.81

Now we can calculate the internal growth rate:
Internal Growth Rate = Retention Ratio x Return on Assets
Internal Growth Rate = 0.70 x 0.81
Internal Growth Rate = 0.567 or 56.7%

However, we are given that the firm had sales of $500 last year and total assets of $1,000. To calculate the maximum possible internal growth rate, we need to assume that the total assets grow by the retention rate.

New Total Assets = Total Assets x (1 + Retention Ratio)
New Total Assets = $1,000 x (1 + 0.70)
New Total Assets = $1,700

Now we can recalculate the internal growth rate with the new total assets:
Return on Assets = Profit Margin + Retention Ratio
Return on Assets = 0.11 + 0.70
Return on Assets = 0.81

Internal Growth Rate = Retention Ratio x Return on Assets
Internal Growth Rate = 0.70 x 0.81
Internal Growth Rate = 0.567 or 56.7%

Internal Growth Rate = (Net Income / Total Assets) x (1 - Dividend Payout Ratio)
We are given Net Income = Profit Margin x Sales
Net Income = 0.11 x $500
Net Income = $55

Dividend Payout Ratio = 1 - Retention Ratio
Dividend Payout Ratio = 1 - 0.70
Dividend Payout Ratio = 0.30

Internal Growth Rate = ($55 / $1,000) x (1 - 0.30)
Internal Growth Rate = 0.039 or 3.9%

Therefore, the internal growth rate is 3.9%, which is closest to option D (4.0%).