Question

Sourstone, Inc., had total assets of $299,000 and equity of $190,000 at the beginning of the year. At the end of the year, the company had total assets of $324,000. During the year, the company sold no new equity. Net income for the year was $104,000 and dividends were $50,000.

  

What is the sustainable growth rate if you calculate ROE based on the end-of-period equity? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

What is the sustainable growth rate if you calculate ROE based on the beginning-of-period equity? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

Answer 1

What is the sustainable growth rate if you calculate ROE based on the end-of-period equity?

Net income for the year = $104,000

Dividends = $50,000

Therefore retained earnings = Net income – Dividends = $104,000 - $50,000 = $54,000

And

Return on Equity (ROE) = Net income / Total equity   

Where net income = $104,000

Total equity on the end-of-period = Total equity on the beginning of the year + retained earnings

=$190,000 + $54,000

= $244,000

Therefore

Return on Equity (ROE) = $104,000 / $244,000 = 0.4262 or 42.62%

Sustainable Growth rate = Retention rate * ROE / (1- Retention rate * ROE)

Where, retention rate = (1- payout rate)

Where payout rate = dividend paid / net income = $50,000/$104,000 =0.4808 or 48.08%

Therefore, retention rate = (1- payout rate) = (1-0.4808) =0.5192 or 51.92%

Therefore,

Sustainable Growth rate =0.5192 * 42.62%/ (1- 0.5192 *42.62%) = 0.2213/0.7787

= 0.2842 or 28.42%

What is the sustainable growth rate if you calculate ROE based on the beginning-of-period equity?

Net income for the year = $104,000

Dividends = $50,000

Therefore retained earnings = Net income – Dividends = $104,000 - $50,000 = $54,000

And

Return on Equity (ROE) = Net income / Total equity   

Where net income = $104,000

Total equity on the beginning of the year = $190,000

Therefore

Return on Equity (ROE) = $104,000 / $190,000 = 0.5474 or 54.74%

Sustainable Growth rate = Retention rate * ROE / (1- Retention rate * ROE)

Where, retention rate = (1- payout rate)

Where payout rate = dividend paid / net income = $50,000/$104,000 =0.4808 or 48.08%

Therefore, retention rate = (1- payout rate) = (1-0.4808) =0.5192 or 51.92%

Therefore,

Sustainable Growth rate =0.5192 * 54.74%/ (1- 0.5192 *54.74%) = 0.2842/0.7158

= 0.3971 or 39.71%