If beginning-of-period common equity is $200,000 and end-of-period common equity is $300,000, the sustainable growth rate is:
A)33%
B)40%
C)50%
D)67%

Question

Quizplus · Accepted Answer

Sustainable growth rate = (ROE x Retention ratio)
ROE = (Net income / Beginning-of-period common equity) 
Retention ratio = (End-of-period common equity - Dividends) / End-of-period common equity

Plugging in the given values: 
ROE = (Net income / Beginning-of-period common equity) = (X / $200,000) 
Retention ratio = (End-of-period common equity - Dividends) / End-of-period common equity = ($300,000 - Y) / $300,000

Thus, Sustainable growth rate = (X / $200,000) x [($300,000 - Y) / $300,000]

The problem does not give values for net income or dividends, so we cannot determine a specific percentage for the sustainable growth rate. However, we can determine which answer choice is closest to being mathematically possible by using the maximum potential values for ROE and retention ratio based on the given information:

ROE would be highest if net income is equal to end-of-period common equity (since that would result in the highest return on the equity). Plugging in this value, we get: 
ROE = ($300,000 / $200,000) = 1.5 or 150%

Retention ratio would be highest if no dividends were paid during the period. Plugging in this value, we get: 
Retention ratio = ($300,000 / $300,000) = 1 or 100%

Thus, the highest possible sustainable growth rate based on the given information would be: 
Sustainable growth rate = (1.5 x 1) = 1.5 or 150%

Looking at the answer choices, we can see that C is the closest to 150%, so that is the best choice.

If Beginning-Of-Period Common Equity Is $200,000 and End-Of-Period Common Equity