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# CORP FINANCIAL MANAGEMENT FIN 315

ISU

GPA 3.95

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This 28 page Class Notes was uploaded by Delia McCullough on Monday October 12, 2015. The Class Notes belongs to FIN 315 at Idaho State University taught by J. Brookman in Fall. Since its upload, it has received 26 views. For similar materials see /class/222156/fin-315-idaho-state-university in Finance at Idaho State University.

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Date Created: 10/12/15

CHAPTER 3 FINANCIAL STATEMENTS ANALYSIS AND LONGTERM PLANNING Answers to Concept Questions 1 Time trend analysis gives a picture of changes in the company s nancial situation over time Comparing a rm to itself over time allows the nancial manager to evaluate whether some aspects of the rm s operations nances or investment activities have changed Peer group analysis involves comparing the nancial ratios and operating performance of a particular rm to a set of peer group rms in the same industry or line of business Comparing a rm to its peers allows the nancial manager to evaluate whether some aspects of the rm s operations nances or investment activities are out of line with the norm thereby providing some guidance on appropriate actions to take to adjust these ratios if necessary Both allow an investigation into what is different about a company from a nancial perspective but neither method gives an indication of whether the difference is positive or negative For example suppose a company s current ratio is increasing over time It could mean that the company had been facing liquidity problems in the past and is rectifying those problems or it could mean the company has become less efficient in managing its current accounts Similar arguments could be made for a peer group comparison A company with a current ratio lower than its peers could be more efficient at managing its current accounts or it could be facing liquidity problems Neither analysis method tells us whether a ratio is good or bad both simply show that something is different and tells us where to look If a company is growing by opening new stores then presumably total revenues would be rising Comparing total sales at two different points in time might be misleading Samestore sales control for this by only looking at revenues of stores open within a speci c period The reason is that ultimately sales are the driving force behind a business A rm s assets employees and in fact just about every aspect of its operations and nancing exist to directly or indirectly support sales Put differently a rm s future need for things like capital assets employees inventory and nancing are determined by its future sales level Two assumptions of the sustainable growth formula are that the company does not want to sell new equity and that nancial policy is xed If the company raises outside equity or increases its debt equity ratio it can grow at a higher rate than the sustainable growth rate Of course the company could also grow faster than its pro t margin increases if it changes its dividend policy by increasing the retention ratio or its total asset turnover increases The sustainable growth rate is greater than 20 percent because at a 20 percent growth rate the negative EFN indicates that there is excess nancing still available If the rm is 100 percent equity nanced then the sustainable and internal growth rates are equal and the internal growth rate would be greater than 20 percent However when the rm has some debt the internal growth rate is always less than the sustainable growth rate so it is ambiguous whether the internal growth rate would be greater than or less than 20 percent If the retention ratio is increased the rm will have more internal funding sources available and it will have to take on more debt to keep the debtequity ratio constant so the EFN will decline Conversely if the retention ratio is decreased the EFN will rise If the retention rate is zero both the internal and sustainable growth rates are zero and the EFN will rise to the change in total assets p A O p A p A p A N p A DJ p A J Commonsize nancial statements provide the nancial manager with a ratio analysis of the company The commonsize income statement can show for example that cost of goods sold as a percentage of sales is increasing The commonsize balance sheet can show a rm s increasing reliance on debt as a form of nancing Commonsize statements of cash ows are not calculated for a simple reason There is no possible denominator It would reduce the external funds needed If the company is not operating at full capacity it would be able to increase sales without a commensurate increase in xed assets Presumably not but of course if the product had been much less popular then a similar fate would have awaited due to lack of sales Since customers did not pay until shipment receivables rose The rm s NWC but not its cash increased At the same time costs were rising faster than cash revenues so operating cash ow declined The rm s capital spending was also rising Thus all three components of cash ow from assets were negatively impacted Financing possibly could have been arranged if the company had taken quick enough action Sometimes it becomes apparent that help is needed only when it is too late again emphasizing the need for planning All three were important but the lack of cash or more generally nancial resources ultimately spelled doom An inadequate cash resource is usually cited as the most common cause of small business failure Demanding cash upfront increasing prices subcontracting production and improving nancial resources via new owners or new sources of credit are some of the options When orders exceed capacity price increases may be especially bene cial ROE is a better measure of the company s performance ROE shows the percentage return for the year earned on shareholder investment Since the goal of a company is to maximize shareholder wealth this ratio shows the company s performance in achieving this goal over the period The EBITDAssets ratio shows the company s operating performance before interest depreciation and taxes This ratio would show how a company has controlled costs While taxes are a cost and interest and depreciation can be considered costs they are not as easily controlled by company management Conversely depreciation and amortization can be altered by accounting choices This ratio only uses revenue minus costs that are directly related to operations in the numerator As such it gives a better metric to measure management performance over a period than does ROA Solutions to Questions and Problems NOTE All end of chapter problems were solved using a spreadsheet Many problems require multiple steps Due to space and readability constraints when these intermediate steps are included in this solutions manual rounding may appear to have occurred However the final answerfor each problem is foundwithout rounding during any step in the problem m 1 Using the Du Pont identity the ROE is ROE 1970 or 1970 2 The equity multiplier is EM 185 One formula to calculate return on equity is ROE 1499 or 1499 ROE can also be calculated as ROE NI TE So net income is NT 112388 3 This is a multistep problem involving several ratios The ratios given are all part of the Du Pont identity The only Du Pont identity ratio not given is the pro t margin If we know the pro t margin we can nd the net income since sales are given So we begin with the Du Pont identity ROE 016 Solving the Du Pont identity for pro t margin we get PM 0463 or 463 P Now that we have the pro t margin we can use this number and the given sales gure to solve for net income NT 17600 An increase of sales to 31360 is an increase of Sales increase 12 or 12 Assuming costs and assets increase proportionally the pro forma nancial statements will look like this Pro forma income statement Pro forma balance sheet Sales 3136000 Assets 112336 Debt 2650000 Costs 2671200 Equity 76 55162 EBIT 464800 Total 112336 Total 10305162 Taxes 34 158032 Net income 306768 The payout ratio is constant so the dividends paid this year is the payout ratio from last year times net income or Dividends 31606 The addition to retained earnings is Addition to retained earnings 275162 And the new equity balance is Equity 7655162 So the EFN is EFN 928438 The maXimum percentage sales increase is the sustainable growth rate To calculate the sustainable growth rate we rst need to calculate the ROE which is ROE 1775 or 1775 The plowback ratio b is Now we can use the sustainable growth rate equation to get Sustainable growth rate 1418 or 1418 So the maximum dollar increase in sales is Maximum increase in sales 964480 We need to calculate the retention ratio to calculate the sustainable growth rate The retention ratio is b 80 Now we can use the sustainable growth rate equation to get Sustainable growth rate 1574 or 1574 We must rst calculate the ROE using the Du Pont ratio to calculate the sustainable growth rate The ROE is ROE 1435 or 1435 The plowback ratio is one minus the dividend payout ratio so b 60 Now we can use the sustainable growth rate equation to get Sustainable growth rate 0942 or 942 An increase of sales to 6360 is an increase of Sales increase 20 or 20 9 Assuming costs and assets increase proportionally the pro forma nancial statements will look like this Pro forma income statement Pro forma balance sheet Sales 6360 Assets 18960 Debt 2700 Costs 4608 Equ39 14 852 Net income g 1752 Total g 18960 Total g 17552 If no dividends are paid the equity account will increase by the net income so Equity 14852 So the EFN is EFN 1408 a First we need to calculate the current sales and change in sales The current sales are neXt year s sales divided by one plus the growth rate so Current sales 320000000 And the change in sales is Change in sales 48000000 We can now complete the current balance sheet The current assets xed assets and shortterm debt are calculated as a percentage of current sales The longterm debt and par value of stock are given The plug variable is the additions to retained earnings So m Liabilities and eguitv Current assets 64000000 Shortterm debt 48000000 Longterm debt 3 5000000 Fixed assets 288000000 Common stock 60000000 Accumulated RE 209000000 Total equity 269000000 Total assets 352000000 Total liabilities and equity 352000000 We can use the equation from the teXt to answer this question The assetssales and debtsales are the percentages given in the problem so EFN 23520000 The current assets xed assets and shortterm debt will all increase at the same percentage as sales The longterm debt and common stock will remain constant The accumulated retained earnings will increase by the addition to retained earnings for the year We can calculate the addition to retained earnings for the year as Net income 36800000 The addition to retained earnings for the year will be the net income times one minus the diVidend payout ratio which is Addition to retained earnings 22080000 So the new accumulated retained earnings will be Accumulated retained earnings 231080000 The pro forma balance sheet will be Assets Liabilities and equitv Current assets 73600000 Shortterm debt 55200000 Longterm debt 3 5000000 Fixed assets 331200000 Common stock 60000000 Accumulated RE 231080000 Total equity 292080000 Total assets 404800000 Total liabilities and equity 381280000 The EFN is EFN 23520000 p A p A The sustainable growth rate is Sustainable growth rate 0934 or 934 It is possible for the sustainable growth rate and the actual growth rate to differ If any of the actual parameters in the sustainable growth rate equation differs from those used to compute the sustainable growth rate the actual growth rate will differ from the sustainable growth rate Since the sustainable growth rate includes ROE in the calculation this also implies that changes in the pro t margin total asset turnover or equity multiplier will affect the sustainable growth rate 0 The company can increase its growth rate by doing any of the following Increase the debttoequity ratio by selling more debt or repurchasing stock Increase the pro t margin most likely by better controlling costs Decrease its total assetssales ratio in other words utilize its assets more efficiently Reduce the diVidend payout ratio Intermediate The solution requires substituting two ratios into a third ratio Rearranging DTA FirmA DTA 70 TAiETA 70 TA TA 7 E TA 70 17ETA70 FirmB D TA 60 TA 7E TA 60 TA TA 7 E TA 60 17ETA60 ETA30 ETA40 E 30TA E 40TA Rearranging ROA we nd NTTA10 NTTA15 NT 10TA NT 15TA Since ROE NT E we can substitute the above equations into the ROE formula which yields ROE 3333 or 3333 ROE 3750 or 3750 12 13 PM 71465 or 71465 As long as both net income and sales are measured in the same currency there is no problem in fact except for some market value ratios like EPS and BVPS none of the nancial ratios discussed in the teXt are measured in terms of currency This is one reason Why nancial ratio analysis is widely used in international nance to compare the business operations of rms andor divisions across national economic borders The net income in dollars is NT 74368185 a The equation for eXtemal funds needed is EFN 1556350 b The current assets xed assets and shortterm debt will all increase at the same percentage as sales The longterm debt and common stock will remain constant The accumulated retained earnings will increase by the addition to retained earnings for the year We can calculate the addition to retained earnings for the year as Net income 6519500 The addition to retained earnings for the year will be the net income times one minus the diVidend payout ratio which is Addition to retained earnings 4563650 So the new accumulated retained earnings will be Accumulated retained earnings 28563650 The pro forma balance sheet will be Assets Current assets 12390000 Fixed assets 3 5400000 Total assets 4737903000 The EFNis EFN 1556350 The sustainable growth is Liabilities and eguitv Shortterm debt Longterm debt Common stock Accumulated RE Total equity Total liabilities and equity Sustainable growth rate 1672 or 1672 167q000 zooopoo 300q000 28563650 531563650 4632333650 d With a lower dividend the company can meet its goals With a zero dividend EFN is Assets Current assets 12390000 Fixed assets 3 5400000 Total assets i47790000 The EFN is EFN 7399500 Liabilities and equitv Shortterm debt Longterm debt Common stock Accumulated retained earnings Total equity Total liabilities and equity 7670000 7000000 3000000 30 519 500 33 591 500 i49189500 If the dividend increase is not suf cient the company does have several other alternatives It can increase its asset utilization andor its pro t margin The company could also increase the debt in its capital structure This will decrease the equity account thereby increasing ROE 14 This is a multistep problem involving several ratios It is often easier to look backward to determine where to start We need receivables turnover to nd days sales in receivables To calculate receivables turnover we need credit sales and to nd credit sales we need total sales Since we are given the pro t margin and net income we can use these to calculate total sales as Sales 2032609 Credit sales 1524457 Now we can nd receivables turnover by Receivables turnover 957 times Days sales in receivables 3814 days 15 The solution to this problem requires a number of steps First remember that current assets plus xed assets equal total assets So if we nd the current assets and the total assets we can solve for net xed assets Using the numbers given for the current ratio and the current liabilities we solve for current assets Current assets 120250 Net income 54340 Total equity 282286 Longterm debt ratio 055 Inverting both sides gives LTD 345016 Total debt 437516 Total assets 719802 F gt1 Net xed assets 599552 This problem requires you to work backward through the income statement First recognize that EBT 1946970 EBIT 2328970 EBITD 2797970 Cash coverage ratio 732 times The only ratio given which includes cost of goods sold is the inventory turnover ratio so it is the last ratio used Inventory 56000 on COGS 358400 The commonsize balance sheet answers are found by dividing each category by total assets For example the cash percentage for 2007 is 0295 or 295 The commonbase year answers are found by dividing each category value for 2008 by the same category value for 2007 For example the cash commonbase year number is found by 9688 9453 10249 The commonsize and commonbase year balance sheets for the company are Common Common Common 2007 size 2008 size base year 1 Current assets Cash 9453 295 9688 282 10249 Accounts receivable 18635 582 19680 573 10561 Inventory 34807 1087 37976 1106 10910 Total 62895 1965 67344 1961 10707 Fixed assets Net plant and equipment 257190 8035 276050 8039 10733 Total assets 320085 100 343394 10000 10728 Liabilities and Owners39 Equim Current liabilities Accounts payable 27386 856 29186 850 10657 Notes payable 19543 611 20438 595 10458 Total 46929 1466 49624 1445 10574 Longterm debt 40000 1250 55000 1602 13750 Owners equity Common stock 25000 781 25000 728 10000 Accumulated RE 208156 6503 213770 6225 10270 Total 233156 7284 238770 6953 10241 Total LampE 320085 100 343394 10000 10728 19 N O To determine full capacity sales we divide the current sales by the capacity the company is currently using so Full capacity sales 679775 Maximum sales growth 1236 or 1236 To nd the new level of xed assets we need to nd the capital intensity ratio Doing so we nd Capital intensity ratio 08576 Total xed assets 626075 New xed assets 43075 Assuming costs vary with sales and a 20 percent increase in sales the pro forma income statement will look like this Pro Forrna Income Statement Sales 868800 Costs 681600 Other expenses 11520 EBIT 175680 Interest expense 19700 Taxable income 155980 Taxes 54 593 Net income 101387 The payout ratio is constant so the dividends paid this year is the payout ratio from last year times net income or Dividends 3294282355101387 Dividends 40555 N And the addition to retained earnings will be Addition to retained earnings 60832 New accumulated retained earnings 266232 The pro forma balance sheet will look like this Pro Forma Balance Sheet Assets Liabilities and Owners Equity Current assets Cash 24000 Accounts receivable 41280 Inventory 72960 Total 138240 Fixed assets Net plant and equipment 349440 Total assets 487680 So the EFN is EFN 10048 Full capacity sales 905000 Current liabilities Accounts payable 62400 Notes payable 7200 Total 69600 Longterm debt 124800 Owners equity Common stock and paidin surplus 17000 Retained earnings 266232 Total 283232 Total LampE 477632 First we need to calculate full capacity sales which is The capital intensity ratio at full capacity sales is Capital intensity ratio 32177 DJ The xed assets required at full capacity sales is the capital intensity ratio times the projected sales level Total xed assets 32177868000 279552 So EFN is EFN 759840 Note that this solution assumes that xed assets are decreased sold so the company has a 100 percent xed asset utilization If we assume xed assets are not sold the answer becomes EFN 748192 The DE ratio of the company is DE 082734 So the new total debt amount will be New total debt 234329 So the EFN is EFN 729881 An interpretation of the answer is not that the company has a negative EFN Looking back at Problem 21 we see that for the same sales growth the EFN is 10639 The negative number in this case means the company has too much capital There are two possible solutions First the company can put the excess funds in cash which has the effect of changing the current asset growth rate Second the company can use the excess funds to repurchase debt and equity To maintain the current capital structure the repurchase must be in the same proportion as the current capital structure Challenge 24 The pro forma income statements for all three growth rates will be Pro Forrna Income Statement 15 Sales 20 Sales 25 Sales Growth Growth Growth Sales 832600 868800 905000 Costs 653200 681600 710000 Other expenses 11040 11520 12000 EBIT 168360 175680 183000 Interest 19700 19700 19700 Taxable income 148660 155980 163300 Taxes 35 52031 54593 57155 Net income 96629 101387 106145 Dividends 38652 40555 42458 Add to RE 57977 60832 63687 We will calculate the EFN for the 15 percent growth rate rst Assuming the payout ratio is constant the dividends paid will be Dividends 38652 And the addition to retained earnings will be Addition to retained earnings 57977 The new accumulated retained earnings on the pro forma balance sheet will be New accumulated retained earnings 263377 The pro forma balance sheet will look like this 15 Sales Growth Pro Forma Balance Sheet Assets Liabilities and Owners Equity Current assets Current liabilities Cash 23000 Accounts payable 59800 Accounts receivable 39560 Notes payable 7200 Inventory 69920 Total 67000 Total 132480 Longterm debt 124800 Fixed assets Net plant and Owners equity equipment 334880 Common stock and paidin surplus 17000 Retained earnings 263377 Total 280377 Total assets 467360 Total LampE 472177 So the EFN is EFN 74817 At a 20 percent growth rate and assuming the payout ratio is constant the dividends paid will be Dividends 40555 And the addition to retained earnings will be Addition to retained earnings 60832 The new accumulated retained earnings on the pro forma balance sheet will be New accumulated retained earnings 266232 The pro forma balance sheet will look like this Pro Forrna Balance Sheet Assets Liabilities and Owners Equity Current assets Current liabilities Cash 24000 Accounts payable 62400 Accounts receivable 41280 Notes payable 7200 Inventory 72960 Total 69600 Total 138240 Longterm debt 124800 Fixed assets Net plant and Owners equity equipment 349440 Common stock and paidin surplus 17000 Retained earnings 266232 Total 283232 Total assets 487680 Total LampE 477632 So the EFN is EFN 10048 At a 25 percent growth rate and assuming the payout ratio is constant the dividends paid will be Dividends 42458 And the addition to retained earnings will be Addition to retained earnings 63687 The new accumulated retained earnings on the pro forma balance sheet will be New accumulated retained earnings 269087 The pro forma balance sheet will look like this 5 quot 25 Sales Growth Pro Forma Balance Sheet Assets Liabilities and Owners Equity Current assets Current liabilities Cash 25000 Accounts payable 65000 Accounts receivable 43000 Notes payable 7200 Inventory 76000 Total 72200 Total 144000 Longterm debt 124800 Fixed assets Net plant and Owners equity equipment 364000 Common stock and paidin surplus 17000 Retained earnings 269087 Total 286087 Total assets 508000 Total LampE 483087 So the EFN is EFN 24913 The pro forma income statements for all three growth rates will be Pro Forma Income Statement 20 Sales 30 Sales 35 Sales Growth Growth Growth Sales 868800 941200 977400 Costs 681600 738400 766800 Other expenses 11520 12480 12960 EBIT 175680 190320 197640 Interest 19700 19700 19700 Taxable income 155980 170620 177940 Taxes 35 54593 59717 62279 Net income 101387 110903 115661 Dividends 40555 44361 46264 Add to RE 60832 66542 69397 Under the sustainable growth rate assumption the company maintains a constant debtequity ratio The DE ratio of the company is DE 82734 At a 20 percent growth rate and assuming the payout ratio is constant the dividends paid will be Dividends 40555 And the addition to retained earnings will be Addition to retained earnings 60832 The new accumulated retained earnings on the pro forma balance sheet will be New accumulated retained earnings 266232 The new total debt will be New total debt 234329 So the new longterm debt will be the new total debt minus the new shortterm debt or New longterm debt 164729 The pro forma balance sheet will look like this Sales growth rate 20 and DebtEquity ratio 82 734 Pro Forrna Balance Sheet Assets Liabilities and Owners Equity Current assets Current liabilities Cash 24000 Accounts payable 62400 Accounts receivable 41280 Notes payable 7200 Inventory 72960 Total 69600 Total 138240 Longterm debt 164729 Fixed assets Net plant and Owners equity equipment 349440 Common stock and paidin surplus 17000 Retained earnings 266232 Total 283232 Total assets 487680 Total LampE 517561 So the EFN is EFN 729881 At a 30 percent growth rate and assuming the payout ratio is constant the dividends paid will be Dividends 44361 And the addition to retained earnings will be Addition to retained earnings 66542 The new accumulated retained earnings on the pro forma balance sheet will be New accumulated retained earnings 271942 The new total debt will be New total debt 239053 So the new longterm debt will be the new total debt minus the new shortterm debt or New longterm debt 164253 Sales growth rate 30 and debtequity ratio 82 734 Pro Forrna Balance Sheet Assets Liabilities and Owners Equity Current assets Current liabilities Cash 26000 Accounts payable 67600 Accounts receivable 44720 Notes payable 7200 Inventory 79040 Total 74800 Total 149760 Longterm debt 164253 Fixed assets Net plant and Owners equity equipment 378560 Common stock and paidin surplus 17000 Retained earnings 271942 Total 288942 Total assets 528320 Total LampE 527994 So the EFN is EFN 326 At a 35 percent growth rate and assuming the payout ratio is constant the dividends paid will be Dividends 46264 And the addition to retained earnings will be Addition to retained earnings 69397 The new accumulated retained earnings on the pro forma balance sheet will be New accumulated retained earnings 274797 The new total debt will be New total debt 241414 So the new longterm debt will be the new total debt minus the new shortterm debt or New longterm debt 164014 Sales growth rate 35 and debtequity ratio 82 734 Pro Forrna Balance Sheet Assets Liabilities and Owners Equity Current assets Current liabilities Cash 27000 Accounts payable 70200 Accounts receivable 46440 Notes payable 7200 Inventory 82080 Total 77400 Total 155520 Longterm debt 164014 Fixed assets Net plant and Owners equity equipment 393120 Common stock and paidin surplus 17000 Retained earnings 274797 Total 291797 Total assets 548640 Total LampE 533211 F gt1 So the EFN is EFN 15429 We must need the ROE to calculate the sustainable growth rate The ROE is ROE 0516 or 516 Now we can use the sustainable growth rate equation to nd the retention ratio as b 238 This implies the payout ratio is Payout ratio 7138 This is a negative dividend payout ratio of 138 percent which is impossible The growth rate is not consistent with the other constraints The lowest possible payout rate is 0 which corresponds to retention ratio of 1 or total earnings retention The maximum sustainable growth rate for this company is Maximum sustainable growth rate 0544 or 544 We know that EFN is EFN Increase in assets 7 Addition to retained earnings The increase in assets is the beginning assets times the growth rate so Increase in assets A x g The addition to retained earnings neXt year is the current net income times the retention ratio times one plus the growth rate so Addition to retained earnings NI x b1 g And rearranging the pro t margin to solve for net income we get N1 PMS on 0 Substituting the last three equations into the EFN equation we started with and rearranging we get EFN 7 PMSb A 7 PMSbg We start with the EFN equation we derived in Problem 27 and set it equal to zero EFN 0 7 PMSb A 7 PMSbg Substituting the rearranged pro t margin equation into the internal growth rate equation we have Internal growth rate PMSb A 7 PMSb Since ROANIA ROAPMSA We can substitute this into the internal growth rate equation and divide both the numerator and denominator by A This gives Internal growth rate PMSb A A 7 PMSb A Internal growth rate bROA l 7 bROA To derive the sustainable growth rate we must realize that to maintain a constant DE ratio with no eXtemal equity nancing EFN must equal the addition to retained earnings times the DE ratio EFN 7 DEPMSb1 g EFN 7 Ag 7 PMSbl g Solving for g and then dividing numerator and denominator by A Sustainable growth rate bROE l 7 bROE In the following derivations the subscript E refers to end of period numbers and the subscript B refers to beginning of period numbers TE is total equity and TA is total assets For the sustainable growth rate Sustainable growth rate NITEE X b l 7 NITEE X b We multiply this equation by TEE TEE Sustainable growth rate NI X b TEE 7 NT X b Recognize that the numerator is equal to beginning of period equity that is TEE 7N1 X b TEE Substituting this into the previous equation we get Sustainable rate NI X b TEE Which is equivalent to Sustainable rate NI TEE X b Since ROEB NI TEE The sustainable growth rate equation is Sustainable growth rate ROEB X b For the internal growth rate Internal growth rate NI TAE X b l 7 NT TAE X b We multiply this equation by TAE TAE Internal growth rate NI X b TAE 7 NT X b Recognize that the numerator is equal to beginning of period assets that is TAE 7N1 X b TAB Substituting this into the previous equation we get Internal growth rate NI X b TAB Which is equivalent to Internal growth rate NI TAB X b Since ROAB NI TAB The internal growth rate equation is Internal growth rate ROAB X b 30 Since the company issued no new equity shareholders equity increased by retained earnings Retained earnings for the year were Retained earnings 29000 So the equity at the end of the year was Ending equity 209000 The ROE based on the end of period equity is ROE 5024 or 5024 The plowback ratio is Plowback ratio 2762 or 2762 Using the equation presented in the teXt for the sustainable growth rate we get Sustainable growth rate 1611 or 1611 The ROE based on the beginning of period equity is ROE 5833 or 5833 Using the shortened equation for the sustainable growth rate and the beginning of period ROE we get Sustainable growth rate 1611 or 1611 Using the shortened equation for the sustainable growth rate and the end of period ROE we get Sustainable growth rate 1388 or 1388 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

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