internal growth rate we first need the ROA which is ROA 17500 144000 ROA 1215

# Internal growth rate we first need the roa which is

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internal growth rate, we first need the ROA, which is: ROA = \$17,500 / \$144,000 ROA = .1215 or 12.15% This means the internal growth rate is: Internal growth rate = (ROA × R) / [1 – (ROA × R)] Internal growth rate = [.1215(.4686)] / [1 – .1215(.4686)] Internal growth rate = .06038 or 6.038% 25. (LO5) Since the company issued no new equity, shareholders’ equity increased by retained earnings. Retained earnings for the year were: Retained earnings = NI – Dividends Retained earnings = \$19,000 – 2,500 Retained earnings = \$16,500 So, the equity at the end of the year was: Ending equity = \$135,000 + 16,500 Ending equity = \$151,500 The ROE based on the end of period equity is: ROE = \$19,000 / \$151,500 ROE = 12.54% The retention ratio is: Retention ratio = Addition to retained earnings/NI Retention ratio = \$16,500 / \$19,000 Retention ratio = .8684 or 86.84% Using the equation presented in the text for the sustainable growth rate, we get:
Sustainable growth rate = (ROE × R) / [1 – (ROE × R)] Sustainable growth rate = [.1254(.8684)] / [1 – .1254(.8684)] Sustainable growth rate = .1222 or 12.22% The ROE based on the beginning of period equity is ROE = \$19,000 / \$135,000 ROE = .1407 or 14.07% Using the shortened equation for the sustainable growth rate and the beginning of period ROE, we get: Sustainable growth rate = ROE × R Sustainable growth rate = .1407 × .8684 Sustainable growth rate = .1222 or 12.22% Using the shortened equation for the sustainable growth rate and the end of period ROE, we get: Sustainable growth rate = ROE × R Sustainable growth rate = .1254 × .8684 Sustainable growth rate = .1089 or 10.89% Using the end of period ROE in the shortened sustainable growth rate results in a growth rate that is too low. This will always occur whenever the equity increases. If equity increases, the ROE based on end of period equity is lower than the ROE based on the beginning of period equity. The ROE (and sustainable growth rate) in the abbreviated equation is based on equity that did not exist when the net income was earned. 26. (LO5) The ROA using end of period assets is: ROA = \$19,000 / \$250,000 ROA = .076 or 7.6 The beginning of period assets had to have been the ending assets minus the addition to retained earnings, so: Beginning assets = Ending assets – Addition to retained earnings Beginning assets = \$250,000 – (\$19,000 – 2,500) Beginning assets = \$233,500 And the ROA using beginning of period assets is: ROA = \$19,000 / \$233,500 ROA = .081370449 or .8.14% Using the internal growth rate equation presented in the text, we get: Internal growth rate = (ROA × R) / [1 – (ROA × R)] Internal growth rate = [.076(.8684)] / [1 – .076(.8684)] Internal growth rate = .0707 or 7.07% Using the formula ROA × R, and end of period assets: Internal growth rate = .076 × .8684 Internal growth rate = .0659984 or 6.6% Using the formula ROA × R, and beginning of period assets: Internal growth rate = .081370449 × .8684
Internal growth rate = .070662097 or 7.07%
27. (LO2) Assuming costs vary with sales and a 20 percent increase in sales, the pro forma income statement will look like this: HOPINGTON TOURS INC. Pro Forma Income Statement Sales \$ 1,114,800 Costs 867,600 Other expenses 22,800 EBIT \$ 224,400 Interest 14,000 Taxable income \$ 210,400 Taxes(35%) 73,640 Net income \$ 136,760 The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times net income, or: Dividends = (\$33,735/\$112,450)(\$136,760) Dividends = \$41,028 And the addition to retained earnings will be: Addition to retained earnings = \$136,760 – 41,028 Addition to retained earnings = \$95,732

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