If possible could you show your work so I can apply it to ot

If possible could you show your work so I can apply it to other problems thanks!

(12-14. 16, 17,21,22) 100 points Problem 4-22 Sustainable Growth Rate [LO3] Inc., had equity af $190,000 at the beginning of the year At the end of the year the company had total assers of $345,000 During the year the company sold no new equity Net income for the year was $40,000 and dividends were $5,600 What is the sustainable growth rate for the company? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16) Sustanable growth rate What is the sustainable growth rate if you use the formula ROE * b and beginning of period equity? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Beginning of peniod equity What is the sustainable growth rate if you use end of period equity in this formula? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)

Solution

Sustainable Growth rate = ROE * (1 - Dividend Payout Ratio) = ROE * Retention Ratio (Retention ratio is shown as \'b\' in question)

where ROE = Net Income/Average Equity; Dividend Payout Ratio = Dividend Paid/Net Income

Part a) Using the above mathematical relations,

Average Equity = (Beginning Equity + Ending Equity)/2

Beginning Equity = $190,000

Ending Equity = Beginning Equity + Retained Earnings, where Retained Earnings = Net Income - Dividend

Ending Equity = 190,000 + (40,000 - 5,600) = $224,400

Average Equity = (190,000 + 224,400)/2 = $207,200

ROE = 40,000/207,200 = 19.305%

Retention Ratio = 1 - (5600/40000) = 86%

Therefore, Sustainable Growth rate = 19.305% * 86% = 16.60% --> Answer to a

b) ROE needs to be calculated here using beginning equity only.

ROE = 40,000/190,000 = 21.0526%

Sustainable Growth rate = 21.0526% * 86% = 18.11%--> Answer to b

c) ROE needs to be calculated here using ending equity only.

ROE = 40,000/224,400 = 17.8253%

Sustainable Growth rate = 17.8253% * 86% = 15.33%--> Answer to c