rossfcf8ce sm ch04

7/23/2019 RossFCF8ce SM Ch04

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CHAPTER 4

LONG-TERM FINANCIAL PLANNINGAND GROWTH

Learning Objectives

LO1 The objectives and goals of financial planning.

LO2 How to compute the external financing needed to fund a firms growth.

LO3 How to apply the percentage sales method.

LO4 The factors determining the growth of the firm.

LO5 How to compute the sustainable and internal growth rates.LO6 Some of the problems in planning for growth.

Answers to Concepts Review and Critical Thinking Questions

1. (LO1The reason is that, ultimately, sales are the driving force behind a business. A firms assets, employees,and, in fact, just about every aspect of its operations and financing exist to directly or indirectly support sales.Put differently, a firms future need for things like capital assets, employees, inventory, and financing aredetermined by its future sales level.

!. (LO1 Its probably more important for a capital intensive company because such companies must make largecash outlays long in advance of actual needs. or example, a ne! manufacturing facility might have to bestarted years before the planned output is needed.

". (LO!The internal gro!th rate is greater than "#$, because at a "#$ gro!th rate the negative %& indicatesthat there is excess internal financing. If the internal gro!th rate is greater than "#$, then the sustainablegro!th rate is certainly greater than "#$, because there is additional debt financing used in that case 'assumingthe firm is not "(($ e)uity*financed+. As the retention ratio is increased, the firm has more internal sources offunding, so the %& !ill decline. onversely, as the retention ratio is decreased, the %& !ill rise. If the firmpays out all its earnings in the form of dividends, then the firm has no internal sources of funding 'ignoring theeffects of accounts payable+- the internal gro!th rate is ero in this case and the %& !ill rise to the change intotal assets.

#. (LO!$ " The sustainable gro!th rate is greater than /($, because at a /($ gro!th rate the negative %&indicates that there is excess financing still available. If the firm is "(($ e)uity financed, then the sustainableand internal gro!th rates are e)ual and the internal gro!th rate !ould be greater than /($. 0o!ever, !hen the

firm has some debt, the internal gro!th rate is al!ays less than the sustainable gro!th rate, so it is ambiguous!hether the internal gro!th rate !ould be greater than or less than /($. If the retention ratio is increased, thefirm !ill have more internal funding sources available, and it !ill have to take on more debt to keep thedebt1e)uity ratio constant, so the %& !ill decline. onversely, if the retention ratio is decreased, the %& !illrise. If the retention rate is ero, both the internal and sustainable gro!th rates are ero, and the %& !ill rise tothe change in total assets.

%. (LO&Presumably not, but, of course, if the product had been muchless popular, then a similar fate !ould havea!aited due to lack of sales.


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&. (LO& 2ince customers did not pay until shipment, receivables rose. The firms &3, but not its cash,increased. At the same time, costs !ere rising faster than cash revenues, so operating cash flo! declined. Thefirms capital spending !as also rising. Thus, all three components of cash flo! from assets !ere negativelyimpacted.

'. (LO&Apparently not4 In hindsight, the firm may have underestimated costs and also underestimated the extrademand from the lo!er price.

. (LO&inancing possibly could have been arranged if the company had taken )uick enough action. 2ometimesit becomes apparent that help is needed only !hen it is too late, again emphasiing the need for planning.

). (LO&All three !ere important, but the lack of cash or, more generally, financial resources ultimately spelleddoom. An inade)uate cash resource is usually cited as the most common cause of small business failure.

1*. (LO& 5emanding cash up front, increasing prices, subcontracting production, and improving financialresources via ne! o!ners or ne! sources of credit are some of the options. 3hen orders exceed capacity, priceincreases may be especially beneficial.


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+olutions to Questions and ,roble-s

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 answer for each problem is found without rounding during anystep in the problem.

Basic

1. (LO3) It is important to remember that equity will not increase by the same percentage as the other assets. If

every other item on the income statement and balance sheet increases by 15 percent, the pro forma income

statement and balance sheet will look like this:

Pro forma income statement Pro forma balance sheet

Sales $ 26,450 Assets $ 18,170 Debt $ 5,980

Costs 19,205 Equity 12,190

Net income $ 7,245 Total $ 18,170 Total $ 18,170

In order for the balance sheet to balance, equity must be:

Equity = Total liabilities and equity Debt

Equity = $18,170 - $5,980

Equity = $12,190

Equity increased by:

Equity increase = $12,190 10,600

Equity increase = $1,590

Net income is $7,245 but equity only increased by $1,590; therefore, a dividend of:

Dividend = $7,245 1,590

= $5,655

must have been paid. Dividends paid is the plug variable.

2. (LO2, 3)Here we are given the dividend amount, so dividends paid is not a plug variable. If the company pays

out one-half of its net income as dividends, the pro forma income statement and balance sheet will look like

this:


Sales $ 26,450 Assets $ 18,170 Debt $ 5,200Costs 19,205 Equity 14,222.50

Net income $ 7,245 Total $ 18,170 Total $ 19,422.50

Dividends $3,622.50

Add. to RE 3,622.50

Note that the balance sheet does not balance. This is due to EFN. The EFN for this company is:


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EFN = Total assets Total liabilities and equity

EFN = $18,170 19,422.50

EFN = $1,252.50

3. (LO2) An increase of sales to $7,434 is an increase of:

Sales increase = ($7,434 6,300) / $6,300Sales increase = .18 or 18%

Assuming costs and assets increase proportionally, the pro forma financial statements will look like this:


Sales $ 7,434.00 Assets $ 21,594 Debt $ 12,400

Costs 4,590.20 Equity 8,743.80

Net income $ 2,843.80 Total $ 21,594 Total $ 21,143.80

If no dividends are paid, the equity account will increase by the net income, so:

Equity = $5,900 + 2,843.80Equity = $8,743.80

Note that the balance sheet does not balance. This is due to EFN. The EFN for this company is:


EFN = $21,594 21,1434 = -$450

4. (LO2)An increase of sales to $21,840 is an increase of:

Sales increase = ($21,840 19,500) / $19,500

Sales increase = .12 or 12%

Assuming costs and assets increase proportionally, the pro forma financial statements will look like this:


Sales $ 21,840 Assets $ 109,760 Debt $ 52,500

Costs 16,800 Equity 46,956

EBIT 5,040 Total $ 109,760 Total $ 99,456

Taxes (40%) 2,016

Net income $ 3,024

The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times net income,

or:

Dividends = ($1,400 / $2,700)($3,024)Dividends = $1,568

The addition to retained earnings is:

Addition to retained earnings = $3,024 1,568

Addition to retained earnings = $1,456

And the new equity balance is:


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Equity = $45,500 + 1,456

Equity = $46,956

So the EFN is:


EFN = $109,760 99,456

EFN = $10,304

5. (LO2)Assuming costs, assets and current liabilities increase proportionally, the pro forma financial statements

will look like this:


Sales $ 4,830.00 CA $ 4,140.00 CL $ 2,415.00

Costs 3795.00 FA 9085.00 LTD 3,650.00

Taxable income 1,035.00 Equity 6,159.86

Taxes (34%) 351.90 Total $13,225.00 Total $ 12,224.86Net income $ 683.10

The payout ratio is 40 percent, so dividends will be:

Dividends = 0.40($683.10)

Dividends = $273.24

The addition to retained earnings is:

Addition to retained earnings = $683.10 273.24

Addition to retained earnings = $409..86

So the EFN is:


EFN = $13,225 12,224.86

EFN = $1,000.14

6. (LO5)To calculate the internal growth rate, we first need to calculate the ROA, which is:

ROA = NI / TA

ROA = $2,262 / $39,150

ROA = .0577 or 5.77%

The retention ratio, R, is one minus the payout ratio, so:

R = 1 .30

R = .70

Now we can use the internal growth rate equation to get:

Internal growth rate = (ROA R) / [1 (ROA R)]

Internal growth rate = [0.0577(.70)] / [1 0.0577(.70)]

Internal growth rate = .04209 or 4.209%


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7. (LO5)To calculate the sustainable growth rate, we first need to calculate the ROE, which is:

ROE = NI / TE

ROE = $2,262 / $21,650

ROE = .1045 or 10.45%


R = 1 .30

R = .70

Now we can use the sustainable growth rate equation to get:

Sustainable growth rate = (ROE R) / [1 (ROE R)]

Sustainable growth rate = [0.1045(.70)] / [1 0.1045(.70)]

Sustainable growth rate = .0789 or 7.89%

8. (LO2)The maximum percentage sales increase is the sustainable growth rate. To calculate the sustainable

growth rate, we first need to calculate the ROE, which is:

ROE = NI / TE

ROE = $8,910 / $56,000

ROE = .159107142


R = 1 .30

R = .70



Sustainable growth rate = [.1591(.70)] / [1 .1591(.70)]


So, the maximum dollar increase in sales is:

Maximum increase in sales = $42,000(.125334083)

Maximum increase in sales = $5,264.03

9. (LO3)Assuming costs vary with sales and a 20 percent increase in sales, the pro forma income statement will

look like this:

Dartmoor CORPORATION

Pro Forma Income Statement

Sales $45,600.00

Costs 22,080.00

Taxable income $23,520.00

Taxes (34%) 7,996.80

Net income $ 15,523.20


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or:

Dividends = ($5,200/$12,936)($15,523.20)

Dividends = $6,240.00

And the addition to retained earnings will be:

Addition to retained earnings = $15,523.70 6,240

Addition to retained earnings = $9,283.20

10. (LO3)Below is the balance sheet with the percentage of sales for each account on the balance sheet. Notes

payable, total current liabilities, long-term debt, and all equity accounts do not vary directly with sales.


Balance Sheet

($) (%) ($) (%)

Assets Liabilities and Owners Equity

Current assets Current liabilities

Cash $ 3,050 8.02 Accounts payable $ 1,300 3.42

Accounts receivable 6,900 18.15 Notes payable 6,800 n/a

Inventory 7,600 20.00 Total $ 8,100 n/a

Total $ 17,550 46.18 Long-term debt 25,000 n/a

Fixed assets Owners equity

Net plant and Common stock and

equipment 34,500 90.79 paid-in surplus $ 15,000 n/a

Retained earnings 3,950 n/a

Total $ 18,950 n/aTotal liabilities and owners

Total assets $ 52,050 136.97 equity $ 52,050 n/a

11. (LO2, 3) Assuming costs vary with sales and a 15 percent increase in sales, the pro forma income statement

will look like this:


Pro Forma Income Statement

Sales $43,700.00

Costs 21,160.00

Taxable income $22,540.00

Taxes (34%) 7,663.60Net income $ 14,876.40


or:

Dividends = ($5,200/$12,936)($14,876.40)

Dividends = $5,980.00


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And the addition to retained earnings will be:

Addition to retained earnings = $14,876.40 5,980

Addition to retained earnings = $8,896.40

The new accumulated retained earnings on the pro forma balance sheet will be:

New accumulated retained earnings = $3,950 + 8,896.40

New accumulated retained earnings = $12,846.40


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The pro forma balance sheet will look like this:


Pro Forma Balance Sheet

Assets Liabilities and Owners Equity

Current assets Current liabilitiesCash $ 3,507.50 Accounts payable $ 1,495.00

Accounts receivable 7,935.00 Notes payable 6,800.00

Inventory 8,740.00 Total $ 8,295.00

Total $ 20,182.50 Long-term debt 25,000.00

Fixed assets

Net plant and Owners equity

equipment 39,675 Common stock and

paid-in surplus $ 15,000.00

Retained earnings 12,846.40

Total $ 27,846.40

Total liabilities and owners

Total assets $ 59,857.50 equity $ 61,141.40

So the EFN is:


EFN = $59,857.50 61,141.40

EFN = $1,283.90

12. (LO5)We need to calculate the retention ratio to calculate the internal growth rate. The retention ratio is:

R = 1 .2

R = .8

Now we can use the internal growth rate equation to get:

Internal growth rate = (ROA R) / [1 (ROA R)]

Internal growth rate = [.08(.8)] / [1 .08(.8)]

Internal growth rate = .0684 or 6.84%

13. (LO5) We need to calculate the retention ratio to calculate the sustainable growth rate. The retention ratio is:

R = 1 .25

R = .75


Sustainable growth rate = (ROE R) / [1 (ROE R)]Sustainable growth rate = [.15(.75)] / [1 .15(.75)]



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14. (LO5)We first must calculate the ROE using the DuPont ratio to calculate the sustainable growth rate. To do

this we must realize two other relationships. The total asset turnover is the inverse of the capital intensity ratio,

and the equity multiplier is 1 + D/E. Using these relationships, we get:

ROE = (PM)(TAT)(EM)

ROE = (.082)(1/.75)(1 + .40)

ROE = .1531 or 15.31%

The retention ratio is one minus the dividend payout ratio, so:

R = 1 ($12,000 / $43,000)

R = .7209





15. (LO5)We must first calculate the ROE using the DuPont ratio to calculate the sustainable growth rate. TheROE is:

ROE = (PM)(TAT)(EM)

ROE = (.078)(2.50)(1.80)

ROE = .351 or 35.1%

The retention ratio is one minus the dividend payout ratio, so:

R = 1 .60

R = .40





Intermediate

16. (LO3)To determine full capacity sales, we divide the current sales by the capacity the company is currently

using, so:

Full capacity sales = $550,000 / .95

Full capacity sales = $578,947.37

The maximum sales growth is the full capacity sales divided by the current sales, so:

Maximum sales growth = ($578,947.37 / $550,000) 1

Maximum sales growth = .0526 or 5.26%


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17. (LO3)To find the new level of fixed assets, we need to find the current percentage of fixed assets to full

capacity sales. Doing so, we find:

Fixed assets / Full capacity sales = $440,000 / $578,947.37

Fixed assets / Full capacity sales = .76

Next, we calculate the total dollar amount of fixed assets needed at the new sales figure.

Total fixed assets = .76($630,000)

Total fixed assets = $478,800

The new fixed assets necessary is the total fixed assets at the new sales figure minus the current level of fixed

assts.

New fixed assets = $478,800 440,000

New fixed assets = $38,800

1. (LO" 3e first need to determine full capacity sales. To do so !e divide the current sales by the capacity thecompany is currently using6

ull capacity sales 7 89#(,((( 1 .:(ull capacity sales 7 8#;9,999.99

The maximum sales gro!th is the full capacity sales divided by the current sales, so6

(+F 1 E" = B%'.>(+FB% 7 ."#9" or "#.9"$

&o! !e can use the 5uPont identity to find the profit margin as6

B% 7 P


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!1. (LO#3e have all the variables to calculate B% using the 5uPont identity except the e)uity multiplier.emember that the e)uity multiplier is one plus the debt*e)uity ratio. If !e find B%, !e can solve the 5uPontidentity for e)uity multiplier, then the debt*e)uity ratio. 3e can calculate B% from the sustainable gro!thrate e)uation. or this e)uation !e need the retention ratio, so6

7 " = .9( 7 .>(

Csing the sustainable gro!th rate e)uation and solving for B%, !e get6

2ustainable gro!th rate 7 'B% D + 1 E" = 'B% D +F.""# 7 EB%'.>(+F 1 E" = B%'.>(+FB% 7 ."@>9 or "@.>9$

&o! !e can use the 5uPont identity to find the e)uity multiplier as6

B% 7 P/ 1 .(#TAT 7 ".>@ times


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!". (LO%3e should begin by calculating the 51% ratio. 3e calculate the 51% ratio as follo!s6

Total debt ratio 7 .:# 7 T5 1 TA

Inverting both sides !e get6

" 1 .:# 7 TA 1 T5

&ext, !e need to recognie that

TA 1 T5 7 " G T% 1 T5

2ubstituting this into the previous e)uation, !e get6

" 1 .:# 7 " G T% 1T5

2ubtract " 'one+ from both sides and inverting again, !e get6

51% 7 " 1 E'" 1 .:#+ = "F

51% 7 ".;:

3ith the 51% ratio, !e can calculate the %< and solve for B% using the 5uPont identity6

B% 7 'P."@$

&o! !e can calculate the retention ratio as6

7 " = .9( 7 .>(

inally, putting all the numbers !e have calculated into the sustainable gro!th rate e)uation, !e get6

2ustainable gro!th rate 7 'B% D + 1 E" = 'B% D +F2ustainable gro!th rate 7 E.">"@'.>(+F 1 E" = .">"@'.>(+F2ustainable gro!th rate 7 ."9:9 or "9.:9$

!#. (LO!$ %To calculate the sustainable gro!th rate, !e first must calculate the retention ratio and B%. Theretention ratio is6

7 " = 8?,9(( 1 8">,#(( 7 .@:;:

And the B% is6

B% 7 8">,#(( 1 8#;,(((B% 7 .9("> or 9(.">$

2o, the sustainable gro!th rate is6

2ustainable gro!th rate 7 'B% D + 1 E" = 'B% D +F2ustainable gro!th rate 7 E.9(">'.@:;:+F 1 E" = .9(">'.@:;:+F2ustainable gro!th rate 7 .":@> or ":.@>$


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If the company gro!s at the sustainable gro!th rate, the ne! level of total assets is6

urrent TA 7 8;:,((( G #;,((( 7 8"@@,(((&e! TA 7 ".":@>'8"@@,(((+ 7 8":>,>":.;(

To find the ne! level of debt in the companys balance sheet, !e take the percentage of debt in the capitalstructure times the ne! level of total assets. The additional borro!ing !ill be the ne! level of debt minus thecurrent level of debt. 2o6

&e! T5 7 E5 1 '5 G %+F'TA+&e! T5 7 E8;:,((( 1 '8;:,((( G #;,(((+F'8":>,>":.;(+&e! T5 7 8"((,":@./(

And the additional borro!ing !ill be6

Additional borro!ing 7 8"((,":@./( = ;:,(((Additional borro!ing 7 8"@,":@./(

The gro!th rate that can be supported !ith no outside financing is the internal gro!th rate. To calculate the

internal gro!th rate, !e first need the BA, !hich is6

BA 7 8">,#(( 1 8"@@,(((BA 7 ."/"# or "/."#$

This means the internal gro!th rate is6

Internal gro!th rate 7 'BA D + 1 E" = 'BA D +FInternal gro!th rate 7 E."/"#'.@:;:+F 1 E" = ."/"#'.@:;:+FInternal gro!th rate 7 .(:(9; or :.(9;$

!%. (LO%2ince the company issued no ne! e)uity, shareholders e)uity increased by retained earnings. etainedearnings for the year !ere6

etained earnings 7 &I = 5ividendsetained earnings 7 8"?,((( = /,#((etained earnings 7 8":,#((

2o, the e)uity at the end of the year !as6

%nding e)uity 7 8"9#,((( G ":,#((%nding e)uity 7 8"#",#((

The B% based on the end of period e)uity is6

B% 7 8"?,((( 1 8"#",#((

B% 7 "/.#@$

The retention ratio is6

etention ratio 7 Addition to retained earnings1&Ietention ratio 7 8":,#(( 1 8"?,(((etention ratio 7 .;:;@ or ;:.;@$

Csing the e)uation presented in the text for the sustainable gro!th rate, !e get6


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2ustainable gro!th rate 7 'B% D + 1 E" = 'B% D +F2ustainable gro!th rate 7 E."/#@'.;:;@+F 1 E" = ."/#@'.;:;@+F2ustainable gro!th rate 7 ."/// or "/.//$

The B% based on the beginning of period e)uity is

B% 7 8"?,((( 1 8"9#,(((B% 7 ."@(> or "@.(>$

Csing the shortened e)uation for the sustainable gro!th rate and the beginning of period B%, !e get6

2ustainable gro!th rate 7 B% D 2ustainable gro!th rate 7 ."@(> D .;:;@2ustainable gro!th rate 7 ."/// or "/.//$

Csing the shortened e)uation for the sustainable gro!th rate and the end of period B%, !e get6

2ustainable gro!th rate 7 B% D 2ustainable gro!th rate 7 ."/#@ D .;:;@2ustainable gro!th rate 7 ."(;? or "(.;?$

Csing the end of period B% in the shortened sustainable gro!th rate results in a gro!th rate that is too lo!.This !ill al!ays occur !henever the e)uity increases. If e)uity increases, the B% based on end of periode)uity is lo!er than the B% based on the beginning of period e)uity. The B% 'and sustainable gro!th rate+in the abbreviated e)uation is based on e)uity that did not exist !hen the net income !as earned.

!&. (LO%The BA using end of period assets is6

BA 7 8"?,((( 1 8/#(,(((BA 7 .(>: or >.:

The beginning of period assets had to have been the ending assets minus the addition to retained earnings, so6

Heginning assets 7 %nding assets = Addition to retained earningsHeginning assets 7 8/#(,((( = '8"?,((( = /,#((+Heginning assets 7 8/99,#((

And the BA using beginning of period assets is6

BA 7 8"?,((( 1 8/99,#((BA 7 .(;"9>(@@? or .;."@$

Csing the internal gro!th rate e)uation presented in the text, !e get6

Internal gro!th rate 7 'BA D + 1 E" = 'BA D +FInternal gro!th rate 7 E.(>:'.;:;@+F 1 E" = .(>:'.;:;@+F

Internal gro!th rate 7 .(>(> or >.(>$

Csing the formula BA D , and end of period assets6

Internal gro!th rate 7 .(>: D .;:;@Internal gro!th rate 7 .(:#??;@ or :.:$

Csing the formula BA D , and beginning of period assets6

Internal gro!th rate 7 .(;"9>(@@? D .;:;@


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Internal gro!th rate 7 .(>(::/(?> or >.(>$


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!'. (LO!Assuming costs vary !ith sales and a /( percent increase in sales, the pro forma income statement !illlook like this6

0BPI&TB& TBC2 I&. Pro orma Income 2tatement

2ales 8 ",""@,;((osts ;:>,:((Bther expenses //,;((%HIT 8 //@,@((Interest "@,(((Taxable income 8 /"(,@((Taxes'9#$+ >9,:@(&et income 8 "9:,>:(

The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times net income,or6

5ividends 7 '899,>9#18""/,@#(+'8"9:,>:(+5ividends 7 8@",(/;

And the addition to retained earnings !ill be6

Addition to retained earnings 7 8"9:,>:( = @",(/;Addition to retained earnings 7 8?#,>9/

The ne! addition to retained earnings on the pro forma balance sheet !ill be6

&e! retained earnings 7 8";/,?(( G ?#,:?(&e! retained earnings 7 8/>;,#?(

The pro forma balance sheet !ill look like this6

0BPI&TB& TBC2 I&.

Pro orma Halance 2heet

Assets Jiabilities and B!ners %)uity

urrent assets urrent liabilitiesash 8 9(,9:( Accounts payable 8 ;",:((Accounts receivable @;,;@( &otes payable ">,(((Inventory "(@,/;( Total 8 ?;,:((

Total 8 ";9,@;( Jong*term debt "#;,(((ixed assets

&et plant and B!ners e)uitye)uipment @?#,:(( ommon stock and

paid*in surplus 8 "@(,(((

etained earnings />;,:9/Total 8 @";,:9/Total liabilities and o!ners

Total assets 8 :>?,(;( e)uity 8 :>#,/9/


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2o the %& is6

%& 7 Total assets = Total liabilities and e)uity%& 7 8:>?,(;( = :>#,/9/%& 7 9,;@;

!. (LO!irst, !e need to calculate full capacity sales, !hich is6

ull capacity sales 7 8?/?,((( 1 .;(ull capacity sales 7 8",":",/#(

The capital intensity ratio at full capacity sales is6

apital intensity ratio 7 ixed assets 1 ull capacity salesapital intensity ratio 7 8@"9,((( 1 8",":",/#(apital intensity ratio 7 .9##:#"/9>

The fixed assets re)uired at full capacity sales is the capital intensity ratio times the projected sales level6

Total fixed assets 7 .9##:#'8",""@,;((+ 7 89?:,@;(

2o, %& is6

%& 7 '8";9,@;( G 89?:,@;(+ = 8:>#,/9/ 7 =8?#,/>/

&ote that this solution assumes that fixed assets are decreased 'sold+ so the company has a "(( percent fixedasset utiliation. If !e assume fixed assets are not sold, the ans!er becomes6

%& 7 '8";9,@;( G @"9,(((+ = 8:>#,/9/ 7 =8>;,>#/

!). (LO!The 51% ratio of the company is6

51% 7 '8;#,((( G "#;,(((+ 1 89//,?((

51% 7 .>#/##

2o the ne! total debt amount !ill be6

&e! total debt 7 .>#/##'8@";,:9/+&e! total debt 7 89"#,(@9.#?

This is the ne! total debt for the company. iven that our calculation for %& is the amount that must beraised externally and does not increase spontaneously !ith sales, !e need to subtract the spontaneous increasein accounts payable. The ne! level of accounts payable !ill be, !hich is the current accounts payable timesthe sales gro!th, or6

2pontaneous increase in accounts payable 7 8:;,((('./(+

2pontaneous increase in accounts payable 7 8"9,:((


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This means that 8"9,:(( of the ne! total debt is not raised externally. 2o, the debt raised externally, !hich !ill bethe %& is6

%& 7 &e! total debt = 'Heginning JT5 = Heginning J = 2pontaneous increase in AP+%& 7 89"#,(@9.#? = E8"#;,((( G ':;,((( G ">,(((+F = "9,:(( 7 8#;,@@9.#?

The pro forma balance sheet !ith the ne! long*term debt !ill be6

0BPI&TB& TBC2 I&.Pro orma Halance 2heet



Total 8 ";9,@;( Jong*term debt /":,@@9.#?ixed assets

&et plant and B!ners e)uity

e)uipment @?#,:(( ommon stock andpaid*in surplus 8 "@(,(((etained earnings />;,:9/

Total 8 @";,:9/Total liabilities and o!ners

Total assets 8 :>?,(;( e)uity 8 >9",:>#.#?

The funds raised by the debt issue can be put into an excess cash account to make the balance sheet balance.The excess debt !ill be6

%xcess debt 7 8>9",:>#.#? = :>?,(;( 7 8#@,#?#.#?

To make the balance sheet balance, the company !ill have to increase its assets. 3e !ill put this amount in an

account called excess cash, !hich !ill give us the follo!ing balance sheet6



urrent assets urrent liabilitiesash 8 9(,9:( Accounts payable 8 ;",:((%xcess ash 54,595.59Accounts receivable @;,;@( &otes payable ">,(((Inventory "(@,/;( Total 8 ?;,:((

Total 8238,075.59 Jong*term debt /":,@@9.#?

ixed assets&et plant and B!ners e)uitye)uipment @?#,:(( ommon stock and

paid*in surplus 8 "@(,(((etained earnings />;,:9/


Total assets 8 >99,:>#.#? e)uity 8 >99,:>#.#?


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The excess cash has an opportunity cost that !e discussed earlier. Increasing fixed assets !ould also not be agood idea since the company already has enough fixed assets. A likely scenario !ould be the repurchase ofdebt and e)uity in its current capital structure !eights. The companys debt*assets and e)uity assets are6

5ebt*assets 7 .>#/## 1 '" G .>#/##+ 7 .@/?@%)uity*assets 7 " 1 '" G .>#/##+ 7 .#>(:

2o, the amount of debt and e)uity needed !ill be6

Total debt needed 7 .@/?@'8:>?,(;(+ 7 8/?",:((%)uity needed 7 .#>(:'8:>?,(;(+ 7 89;>,@;(

2o, the repurchases of debt and e)uity !ill be6

5ebt repurchase 7 '8?;,:(( G /":,@@9.#?+ = /?",:(( 7 823,443.59%)uity repurchase 7 8@";,:9/ = 9;>,@;( 7 89","#/

Assuming all of the debt repurchase is from long*term debt, and the e)uity repurchase is entirely from theretained earnings, the final pro forma balance sheet !ill be6




Total 8 ";9,@;( Jong*term debt "?9,(((ixed assets


paid*in surplus 8 "@(,(((etained earnings /@>,@;(

Total 8 9;>,@;(Total liabilities and o!ners

Total assets 8 :>?,(;( e)uity 8 :>?,(;(


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Challenge

"*. (LO!$ %The pro forma income statements for all three gro!th rates !ill be6

0BPI&TB& TBC2 I&.Pro orma Income 2tatement

15 % SalesGrowth

20% SalesGrowth

25% SalesGrowth

2ales 8",(:;,9#( 8",""@,;(( 8",":",/#(osts ;9",@#( ;:>,:(( ?(9,>#(Bther expenses /",;#( //,;(( /9,>#(%HIT 8 /"#,(#( 8 //@,@(( 8/99,>#(Interest "@,((( "@,((( "@,(((Taxable income 8 /(",(#( 8 /"(,@(( 8/"?,>#(Taxes '9#$+ >(,9:>.#( >9,:@( >:,?"/.#(&et income 8 "9(,:;/.#( 8 "9:,>:( 8"@/,;9>.#(

5ividends 8 9?,/(@.># 8 @",(/; 8@/,;#"./# Add to % ?",@>>.># ?#,9>/ ??,?;:./#

3e !ill calculate the %& for the "# percent gro!th rate first. Assuming the payout ratio is constant, thedividends paid !ill be6

5ividends 7 '899,>9#18""/,@#(+'8"9(,:;/.#(+5ividends 7 89?,/(@.>#


Addition to retained earnings 7 8"9(,:;/.#(Addition to retained earnings 7 8?",@>>.>#

The ne! retained earnings on the pro forma balance sheet !ill be6

&e! retained earnings 7 8";/,?(( G ?",@>>.>#&e! retained earnings 7 8/>@,9>>.>#


15% Sales Growth6 0BPI&TB& TBC2 I&.Pro orma Halance 2heet


urrent assets urrent liabilitiesash 8 /?,(?# Accounts payable 8 >;,/((

Accounts receivable @:,;(# &otes payable ">,(((Inventory ??,?9# Total 8 ?#,/((Total 8 ">#,;9# Jong*term debt "#;,(((

ixed assets&et plant and B!ners e)uitye)uipment @>@,?#( ommon stock and

paid*in surplus 8 "@(,(((etained earnings />@,9>>.>#

Total 8 @"@,9>>.>#Total liabilities and o!ners


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Total assets 8 :#(,>;# e)uity 8 ::>,#>>.>#

2o the %& is6

%& 7 Total assets = Total liabilities and e)uity%& 7 8:#(,>;# = ::>,#>>.>#%& 7 =8":,>?/.>#

At a /( percent gro!th rate, and assuming the payout ratio is constant, the dividends paid !ill be6

5ividends 7 ($33,735/$112,450)($136,760)5ividends 7 8@",(/;


Addition to retained earnings 7 8$136,760 41,028Addition to retained earnings 7 8?#,>9/


&e! retained earnings 7 $182,900 + 95,732&e! retained earnings 7 89/>;,:9/


20% Sales Growth6



urrent assets urrent liabilities

ash 8 9(,9:( Accounts payable 8 ;",:((Accounts receivable @;,;@( &otes payable ">,(((Inventory "(@,/;( Total 8 ?;,:((

Total 8 ";9,@;( Jong*term debt "#;,(((ixed assets




Total assets 8 :>?,(;( e)uity 8 :>#,/9/

2o the %& is6

%& 7 Total assets = Total liabilities and e)uity%& 7 8:>?,(;( = :>#,/9/%& 7 89,;@;

At a /# percent gro!th rate, and assuming the payout ratio is constant, the dividends paid !ill be6

5ividends 7 '99,>9#18""/,@#(+'8"@/,;9>.#(+5ividends 7 8@/,;#"./#


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Addition to retained earnings 7 8"@/,;9>.#( * 8@/,;#"./#Addition to retained earnings 7 8??,?;:./#


&e! retained earnings 7 8";/,?(( G ??,?;:./#&e! retained earnings 7 8/;/,;;:./#


25% Sales Growth60BPI&TB& TBC2 I&.Pro orma Halance 2heet


urrent assets urrent liabilities

ash 8 9",:/# Accounts payable 8 ;#,(((Accounts receivable #(,;># &otes payable ">,(((Inventory "(;,:/# Total 8 "(/,#((

Total 8 "?","/# Jong*term debt "#;,(((ixed assets

&et plant and B!ners e)uitye)uipment #":,/#( ommon stock and

paid*in surplus 8 "@(,(((etained earnings /;/,;;:./#

Total 8 @//,;;:./#Total liabilities and o!ners

Total assets 8 >(>,9># e)uity 8 :;/,;;:./#

2o the %& is6

%& 7 Total assets = Total liabilities and e)uity%& 7 8>(>,9># = :;/,;;:./#%& 7 824,488.75

Inspection of the plot sho!s that %& 7 ( at approximately ";$ gro!th rate. The formula for %& is6

%& 7 *'P


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2etting %& 7 ( gives 6

g 7 'P.#(&et income 8 "9:,>:( 8 "@;,?"# 8 "#@,??/.#(

5ividends 8 @",(/; 8 @@,:>@.#( 8 @:,@?>.># Add to % ?#,>9/ "(@,/@(.#( "(;,@?@.>#

Cnder the sustainable gro!th rate assumption, the company maintains a constant debt*e)uity ratio. The 51%ratio of the company is6

51% 7 '8"#;,((( G ;#,(((+ 1 89//,?((51% 7 .>#/##

At a /( percent gro!th rate, and assuming the payout ratio is constant, the dividends paid !ill be6

5ividends 7 '899,>9#18""/,@#(+'8"9:,>:(+5ividends 7 8@",(/;


Addition to retained earnings 7 8"9:,>:( = @",(/;Addition to retained earnings 7 8?#,>9/


&e! retained earnings 7 8";/,?(( G ?#,>9/&e! retained earnings 7 8/>;,:9/

The ne! total debt !ill be6

&e! total debt 7 .>#/##'8@";,:9/+&e! total debt 7 89"#,(@9.#?


25/32

2o, the ne! long*term debt !ill be the ne! total debt minus the ne! short*term debt, or6

&e! long*term debt 7 89"#,(@9.#? = ?;,:((&e! long*term debt 7 8/":,@@9.#?


Sales growth rate = 20% and Debt/Equit ratio = !"5225#




Total 8 ";9,@;( Jong*term debt /":,@@9.#?

ixed assets&et plant and B!ners e)uitye)uipment @?#,:(( ommon stock and



Total assets 8 :>?,(;( e)uity 8>9#,:>#.#?

2o the %& is6

%& 7 Total assets = Total liabilities and e)uity%& 7 8:>?,(;( = >9#,:>#.#?

%& 7 =8#@,#?#.#?

At a 9( percent gro!th rate, and assuming the payout ratio is constant, the dividends paid !ill be6

5ividends 7 '899,>9#18""/,@#(+'8"@;,?"#+5ividends 7 8@@,:>@.#(


Addition to retained earnings 7 8"@;,?"# = @@,:>@.#(Addition to retained earnings 7 8"(@,/@(.#(


&e! retained earnings 7 8";/,?(( G "(@,/@(.#(&e! retained earnings 7 8/;>,"@(.#(


&e! total debt 7 .>#/##'8@/>,"@(.#(+&e! total debt 7 89/",@@:.>"


26/32


&e! long*term debt 7 89/",@@:.>" = "(#,@((&e! long*term debt 7 8/":,(@:.>"

Sales growth rate = 30% and debt/equit ratio = !"5255#



urrent assets urrent liabilitiesash 8 9/,;?( Accounts payable 8 ;;,@((Accounts receivable #/,?"( &otes payable ">,(((Inventory ""/,?>( Total 8 "(#,@((

Total 8 "?;,>>( Jong*term debt /":,(@:.>"ixed assets

&et plant and B!ners e)uity

e)uipment #9:,?(( ommon stock andpaid*in surplus 8 "@(,(((.((etained earnings /;>,"@(.#(

Total 8 @/>,"@(.#(Total liabilities and o!ners

Total assets 8 >9#,:>( e)uity 8 >@;,#;>./"

2o the %& is6

%& 7 Total assets = Total liabilities and e)uity%& 7 8>9#,:>( = >@;,#;>./"%& 7 *"/,?">./"

At a 9# percent gro!th rate, and assuming the payout ratio is constant, the dividends paid !ill be6

5ividends 7 '899,>9#18""/,@#(+'8"#@,??/.#(+5ividends 7 8@:,@?>.>#


Addition to retained earnings 7 8"#@,??/.#( = @:,@?>.>#Addition to retained earnings 7 8"(;,@?@.>#

The retained earnings on the pro forma balance sheet !ill be6

&e! retained earnings 7 8";/,?(( G "(;,@?@.>#

&e! retained earnings 7 8/?",9?@.>#


&e! total debt 7 .>#/##'8@9",9?@.>#+&e! total debt 7 89/@,:@;./:


&e! long*term debt 7 89/@,:@;./: = "(;,;((


27/32

&e! long*term debt 7 8/"#,;@;./:


28/32

Sales growth rate = 35% and debt/equit ratio = !"5255#



urrent assets urrent liabilitiesash 8 9@,"## Accounts payable 8 ?",;((Accounts receivable #@,?@# &otes payable ">,(((Inventory "">,9"# Total 8 "(;,;((

Total 8 /(:,@"# Jong*term debt /"#,;@;./:ixed assets

&et plant and B!ners e)uitye)uipment ##>,##( ommon stock and

paid*in surplus 8 "@(,(((etained earnings /?",9?@.>#

Total 8 @9",9?@.>#Total liabilities and o!ners

Total assets 8 >:9,?:# e)uity 8 >#:,(@9.(",

2o the %& is6

%& 7 Total assets = Total liabilities and e)uity%& 7 8>:9,?:# = 756,043.01%& 7 7,921.99

Inspection of the plot sho!s that %& 7 ( at approximately 9;$ gro!th rate. The formula for %& is6

%& 7 *'P


29/32

"!. (LO#3e must have the B% to calculate the sustainable gro!th rate. The B% is6

B% 7 'P


30/32

The sustainable growth rateis the gro!th rate a firm can maintain given its debt capacity, B% and retention ratio.Assuming you !ish to maintain the same 51% ratio of the firm.

Therefore 51% 7 &e! Horro!ings1Additions to etained %arnings

&e! Horro!ings 7 51% ' P


31/32

2ustainable rate 7 '&I 1 T%H+ D b

2ince B%H7 &I 1 T%H

The sustainable gro!th rate e)uation is6

2ustainable gro!th rate 7 B%HD b

/or the internal growth rate3

Internal gro!th rate 7 'BA%D b+ 1 '" = BA%D b+Internal gro!th rate 7 '&I 1 TA%D b+ 1 '" = &I 1 TA%D b+

3e multiply this e)uation by6

'TA%1 TA%+

Internal gro!th rate 7 '&I 1 TA%D b+ 1 '" = &I 1 TA%D b+ D 'TA%1 TA%+Internal gro!th rate 7 '&I D b+ 1 'TA%= &I D b+

ecognie that the numerator is e)ual to beginning of period assets, that is6

'TA%= &I D b+ 7 TAH

2ubstituting this into the previous e)uation, !e get6

Internal gro!th rate 7 '&I D b+ 1 TAH

3hich is e)uivalent to6

Internal gro!th rate 7 '&I 1 TAH+ D b

2ince BAH7 &I 1 TAH

The internal gro!th rate e)uation is6

Internal gro!th rate 7 BAHD b


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rossfcf8ce sm ch04

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