Gilmore inc, had equity of $195,000 at the beginning of the year. At the end of the year the company had a total assets of $350,000. During the year the company sold no new equity. Net income for the year was $41,000 and the dividends were $5,800.a. What is the sustainable growth rate for the company?b. what is the sustainable growth rate if you use the formula ROE x b and the beginning of the period equity. c. what is the sustainable growth rate if you use end of period equity in this formula.

a. 18.05%

b. 18.05%

c. 15.29%

Explanation:

The computation is shown below:

a. The  sustainable growth rate for the company is

Sustainable Growth rate = (Return on equity × retention ratio) ÷ (1 - return on equity × retention ratio)

where,

Return on equity = Net income ÷ ending equity

The net income is $41,000

And, the ending equity is

= Beginning equity + Net Income - Dividends

= $195,000 + $41,000 - $5,800

= $230,200

Now the return on equity is

= $41,000 ÷ $230,200

= 17.8106%

And, the retention ratio is

= 1 - dividend payout ÷ net income

= 0.8585

So, the Sustainable Growth rate is

= (17.8106% × 0.8585) ÷ (1 - 17.8106% × 0.8585)

= 18.05%

b. The sustainable growth rate at the beginning of the period is

= Return on equity × retention ratio

= $41,000 ÷ $195,000 × 0.8585

= 18.05%

c. The sustainable growth rate at the beginning of the period is

= Return on equity × retention ratio

= $41,000 ÷ $230,200 × 0.8585

= 15.29%

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