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WEEK 3TUTORIAL QUESTIONS

Chapter 4

Question 2.

Sales $10,000 Assets $5,000 Debt $2,500Costs $9,000 Equity $2,500Net profit $1,000 Total $5,000 Total $5,000

BALANCE SHEET (20XX) $INCOME STATEMENT

Swimming Pool has predicted a sales increase of 20 per cent. It has also predicted that every item on the Balance Sheet will increase by 20 per cent as well. Create the pro-forma statements and reconcile them. What is the plug variable here?


INCOME STATEMENT BALANCE SHEET (20XX) $

Net profit is $1 200, but equity only increased by $500; therefore, a dividend of $700 must have been paid. Dividends paid is the plug variable.

Question3.

In the previous question, assume that Swimming Pool pays out half of net profit in the form of a cash dividend. Costs and assets vary with sales, but debt and equity do not. Prepare the pro-forma statements and determine the external financing needed.



Dividends $600 Retained Profits $600EFN = 6 000 – 5 600 = $400

Question 4.

What are the advantages and disadvantages of the percentage of sales approach? In particular, is the assumption that many of the firm's costs and assets are directly proportional to sales a reasonable assumption? Does your answer depend on the time horizon being considered?

One advantage is that it is easy to implement. A big disadvantage is that the relationships between factors are assumed to be static, at least within each scenario. It is probably true that sales, costs and asset needs are closely associated over the long term, but in the short term, they need not be.Question 6.

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The most recent financial statements for Small Fry Ltd are shown below.

Sales $2,620 CA $1,000 Debt $8,300Costs $1,420 NCA $12,300 Equity $5,000

$1,200 Total $13,300 Total $13,300Less tax $360Net profit $840


Assets and costs are proportional to sales. Debt is not. Small Fry maintains a constant 15 per cent dividend payout. No external financing is possible

a) What is the sustainable growth rate?

Let g = sustainable growthEFN = 0p = profit margin = 840/2,620 = 0.3206R = retention = 1 – 0.15 = 0.850 = –0.3206(2 620)(0.85) + [13 300 – 0.3206 (2 620)(0.85)]g0 = –713.98 + 12 586.02gg = 713.98/12 586.02g = 0.0567 = 5.67%

Net Profit $840Sales $2,620

Retention Rate = 1 -= 1 -= 0.85

= = 0.320611

Payout Ratio0.15

=Profit Margin

Profit Retention Total Profit RetentionMargin Rate Assets Margin Rate

- 0.320611 x $2,620 x 0.85 + $13,300 0.320611 x $2,620 x 0.85 x g

= + x gg = 0.057

x x g-

-$714.00 $12,586

Sales x + - x Salesx

b) If the government were to reduce company tax by 3 per cent, what would be the new sustainable growth rate?

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$1,200 Total $13,300 Total $13,300Less tax $324Net profit $876


Net Profit $876Sales $2,620


= = 0.334351

Payout Ratio0.15

=Profit Margin


- 0.334351 x $2,620 x 0.85 + $13,300 0.334351 x $2,620 x 0.85 x g

= + x gg = 0.059

x x g-

-$744.60 $12,555

Sales x + - x Salesx

Question 7.

Consider the following Income Statement for Poppins Ltd:

Sales $400Costs $300

$100Less tax $30Net profit $70Dividends $12.6

INCOME STATEMENT

Pay-out ratio .18

A 10% per cent growth rate is projected. Prepare a pro-forma Income Statement assuming that costs vary with sales and the dividend pay-out ratio is constant. What is the projected addition to retained profit?


$110Less tax $33Net profit $77Dividends $13.86Ret Earnings $63.14

INCOME STATEMENT

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Question 8 & 9.

The Balance Sheet for Poppins Ltd is shown below. Based on this information and the Income Statement apply the percentage of sales approach. Assume that accounts payable vary with sales while notes payable do not.

Tax rate 0.30Growth Rate 0.10Payout Ratio 0.18


$110Less tax $33Net profit $77Dividends $13.9

$63.14

INCOME STATEMENT

C Assets LiabilitiesCash $50.00 Creditors $200.00Debtors $100.00 Notes Payable $100.00Inventory $100.00 $300.00

$250.00 L-Term Debt $100.00NC Assets EquityPP&E $300.00 Share Capital $50.00

Retained Profits $100.00$550.00 $550.00

BALANCE SHEET

Prepare a partial pro-forma Balance Sheet showing EFN, assuming a 10 per cent increase in sales




Total $605.00 Total $633.14

BALANCE SHEET

EFN = 605 – 633.14 = –$28.14

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Question 10.

From the previous question, assuming that non-current debt is the plug, prepare the completed pro-forma Balance Sheet. What is the projected ROE?




Total $605.00 Total $533.14$71.86

BALANCE SHEET




Total $605.00 Total $605.00

BALANCE SHEET

Question 11.

The most recent financial statements for Redflower Ltd are shown below.

Tax rate 0.30

Sales $50,000 CA $53,200 LT Debt $130,000Costs $40,000 NCA $199,800 Equity $123,000

$10,000 Total $253,000 Total $253,000Less tax $3,000Net profit $7,000


Assets and costs are proportional to sales. Redflower maintains a constant 30 per cent dividend pay-out and a constant debt-to-equity ratio. What is the maximum increase in sales that can be sustained assuming no new equity is issued?

ROE = 7 000/123 000 = 0.0569

6

R = 1 – 0.3 = 0.7g* = 0.0569(0.7)/[1 – 0.0569(0.7)] = 0.0415 = 4.15%Maximum increase in sales = 50 000(0.0415) = $2 075

Net Profit $7,000Equity $123,000


Payout Ratio0.3

Return on Equity = = = 0.056911

RetentionRate

RetentionRate

0.0569 x 0.71 - 0.0569 x 0.7

= g*

=0.04149

ROE x

ROE-1 x

Question 12.

The most recent financial statements for Tropicana Ltd are shown below.

Growth in Sales 0.10Tax rate 0.00Payout Ratio 0

Sales $5,000 CA $13,000 LT Debt $8,000Costs $2,000 NCA $0 Equity $5,000

$3,000 Total $13,000 Total $13,000Less tax $0Net profit $3,000


Assets and costs are proportional to sales. Debt is not. No dividends are paid. Next year's sales are projected to be $5,500. What are the external funds needed (EFN)?


$3,300 Total $14,300 Total $16,300Less tax $0Net profit $3,300


EFN = 14 300 – 16 300 = –$2 000. No external financing is needed. There is a surplus of cash, so either debt can be retired or dividends can be paid after all.

Question 13.

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The most recent financial statements for Frangipani Pty Ltd are shown below.

Growth in Sales 0.15Tax rate 0.30Payout Ratio 0.762


Sales $80,000 CA $240,000 LT Debt $150,00

0Costs $20,000 NCA $0 Equity $90,000

$60,000 Total $240,000 Total $240,00

0Less tax $18,000 Net profit $42,000Dividend $32,000

Assets and costs are proportional to sales. Debt is not. A dividend of $32,000 was paid, and Frangipani wishes to maintain a constant pay-out. Next year's sales are projected to be $92,000. What are the EFN (external funds needed)?


$69,000 Total $276,000 Total $251,500Less tax $20,700Net profit $48,300 EFNDividend $36,800

$24,500


Question 14.

The most recent financial statements for Big Winners Ltd are shown below.


Sales $5,000 CA $4,000 C Debt $2,000Costs $4,400 NCA $8,000 NC Debt $2,000

$600 Equity $8,000Less tax $180 Total $12,000 $12,000Net profit $420Dividend $294


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Assets, costs and current liabilities are proportional to sales. Non-current debt is not. Big Winners maintains a constant 70 per cent dividend pay-out. Next year's sales are projected to be $6400. What are the external funds needed (EFN)?

Sales $6,400 CA $5,120 C Debt $2,560Costs $5,632 NCA $10,240 NC Debt $2,000

$768 Equity $8,161Less tax $230 Total $15,360 $12,721Net profit $538Dividend $376

$2,639


Question 15.

Assuming a firm does not wish to sell new equity, what are the four determinants of growth? Explain how an increase in each of these affects the firm's growth rate. If these four elements are taken as fixed and no new equity will be issued, then what must be true?

Profit margin: As the profit margin increases, the firm’s sustainable growth rate increases.Dividend payout: As the dividend payout increases, the firm’s sustainable growth rate decreases.Debt/equity ratio: As the debt/equity ratio increases, the firm’s sustainable growth rate increases.Total asset turnover: As the total asset turnover increases, the firm’s sustainable growth rate increases.If these are fixed and no new equity will be issued, then there is only one growth rate which is possible, and that is the sustainable growth rate.

Question 16.

Assuming that the following ratios are constant, what is the sustainable growth rate?

Total assets/sales = 1.0Net profit/sales = 0.05Debt/equity = 0.5Dividends/net profit = 0.6

R = 1 – 0.6 = 0.4ROE = 0.05(1/1)(1 + 0.5) = 0.075g* = (ROE × i) / (1 – ROE × i)= 0.075(0.4)/[1 – 0.075(0.4)] = 0.0309 = 3.09%

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Total Assets 100000Total Sales 100000Total assets/sales 1Total Sales 100000Costs 95000Net Profit 5000Net profit/sales 0.05Total Debt 5000Total Equity 5000Total Debt + Equity 10000Debt/equity 0.5Dividend Payout 0.6Retention Ratio 0.4

Net Profit Total Sales DebtSales Total Assets Equity

5000 100000 5000100000 100000 10000

= 0.05 x 1 x 1 + 0.5

= 0.075

+

ROE = x x 1 +

ROE = x x 1

Net Profit 1 Debt/EquityMargin Assets Ratio

Sales

1100000100000

0.075 = 0.05 x 1 x 1 + 0.5

0.5ROE = 0.05 x x 1 +

= x x 1 +ROE

RetentionRate

RetentionRate

0.0750 x 0.41 - 0.0750 0.4

x

x

ROE

0.030928 =

ROE xg* =

1 -

Question 17.

Based on the following information, calculate the sustainable growth rate:

Profit margin = 5%Capital intensity ratio = 2Debt/equity ratio = 0.5Net profit = $10,000Dividends = $3,000What is the ROE here?

Retained earnings = 10 000 – 3 000 = 7 000

R = 7 000/10 000 = 0.7

ROE = 0.05(1/2)(1 + 0.5) = 0.0375 = 3.75%

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g* = (ROE × R) / (1 – ROE × i)

= 0.0375(0.7)/[1 – 0.0375(0.7)] = 0.02695 = 2.695%

Capital Intensity Ratio 2Total Assets 400000Total Sales 200000 Net Profit Total Sales DebtTotal assets/sales 2 Sales Total Assets EquityTotal Sales 200000Costs 190000 10000 200000 5000Net Profit 10000 200000 400000 10000Net profit/sales 0.05Total Debt 5000 = 0.05 x 0.5 x 1 + 0.5Total Equity 5000Total Debt + Equity 10000 = 0.0375Debt/equity 0.5Dividend 3000Dividend Payout 0.3Retention Ratio 0.7

1 +

ROE = x x 1 +

ROE = x x

Net Profit 1 Debt/EquityMargin Assets Ratio

Sales

1400000200000

0.0375 = 0.05 x 0.5 x 1 + 0.5

0.5= 0.05 x x 1 +

ROE = x x 1 +

ROE

RetentionRate

RetentionRate

0.0375 x 0.71 - 0.0375 0.7

ROE x

0.026958 =x

ROE xg* =

1 -

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Question 18, 19 & 20.

Regina Stone operates a mining firm and she has a tax rate of 30 per cent. Her accountant has provided the following financial statements:


Sales $5,250 CA $1,200 C Debt $800Costs $4,200 NCA $2,550 NC Debt $1,800

$1,050 Equity $1,150Less tax $315 Total $3,750 $3,750Net profit $735Dividend $294


Assume the firm is operating at full capacity and that Regina Stone will draw a salary as a constant percentage of profit. Sales are predicted to grow at 10 per cent. Use the percentage of sales approach to calculate the EFN. Assume current liabilities and assets grow at the same rate as that of sales.

Sales $5,775 CA $1,320 C Debt $880Costs $4,620 NCA $2,805 NC Debt $1,800

$1,155 Equity $1,635Less tax $347 Total $4,125 $4,315Net profit $809Dividend $323Add to RE $485


-$190.10

What is the EFN if capacity is 60 per cent for fixed assets? If the capacity is 95 per cent?

Full-capacity sales are equal to current sales divided by the capacity utilisation.

Sales $5,250Percentage of Capacity 0.60Full Capacity Sales 8750.00

Full Sales 5250Capacity --------------------- = ---------- = 8750

Sales Percentage of Capacity 0.60

66.67% without the addition of new fixed assets

=

Therefore sales can increase

At 60% capacity: $5 250/0.60 = $8 750

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With forecast sales of $5 775 well below full-capacity sales, no net new fixed assets will be needed. In solution 17, it was estimated that fixed assets would increase by $255 ($2 805 – $2 550); however, this investment is not needed as sales are below capacity. The new EFN will be –$190.10 (from solution 17) plus –$255, which is a negative $445.10. A surplus exists and no external financing is needed in this case.

At 95% capacity, full capacity is $5 250/0.95 = $5 526.The ratio of non-current assets to full capacity sales is $2 550/$5 526 = 0.46157. Therefore, at the forecast sales level of $5 775, we will need $5 775 × 0.46157 = $2 665 in net fixed assets, an increase of $115. This is $140 less than predicted in solution 17 ($255 – $115 = $140). The EFN is now –$190.10 – $140 = –$330.10, which is a surplus. Therefore, no additional financing is needed.

What growth can Regina Store maintain if no external financing is used? What is the sustainable growth rate?

Regina Stone retains R = 1 – 0.4 = 0.6, 60% of net profit. The return on assets is $735/$3 750 = 0.196, or 19.6%.The internal growth rate is:(ROA × R)/(1 – ROA × R ) = (0.196 × 0.6)/(1 – 0.196 × 0.6)= 0.1176/0.8824= 0.1333 or 13.33%

$735 Net Profit$3,750 Debt + Equity

Return on Retention Growth Assets Rate

Rate Return on Retention Assets Rate

GrowthRate

0.600

0.6000.13327

x=

1 - x

0.196

0.196

Return on Assets =0.196

x

x1 -=

Return on equity for Regina Stone is $735/$1 150 = 0.6391, or 63.91%, so we calculate sustainable growth as:

(ROE × R)/(1 – ROE × R ) = (0.6391 × 0.6)/(1 – 0.6391 × 0.6)= 0.3835/0.6165 = 0.6221 or 62.21%

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$735 Net Profit$1,150 Equity

Sustainable Return on x Retention Growth = Equity Rate

Rate 1 - Return on x Retention Rquity Rate

Sustainable 0.63913 x 0.600Growth 0.622 =

Rate 1 - 0.63913 x 0.600

Return on Equity 0.63913 =

Question 21.

Assuming the following ratios are constant, what is the sustainable growth rate?

Sales/total assets = 0.6Net profit/sales = 0.1Debt/total assets = 0.5Retained profit/net profit = 0.8

D/E = 0.5/0.5 = 1

ROE = 0.1(0.6)(1 + 1) = 0.12

g* = (ROE × R)/(1 – ROE × R)

= 0.12(0.8)/[1 – 0.12(0.8)] = 0.1062 = 10.62%

Capital Intensity Ratio 1.666667Total Assets 100000Total Sales 60000Total assets/sales 1.666667Total Sales/Assets 0.6Total Sales 60000 $6,000 Net ProfitCosts 54000 $50,000 EquityNet Profit 6000Net profit/sales 0.1 Sustainable Return on x Retention Total Debt 50000 Growth = Equity RateTotal Equity 50000 Rate 1 - Return on x Retention Total Debt + Equity 100000 Rquity RateDebt/equity 0.5Debt/Total Assets 0.5 Sustainable 0.12 x 0.800Dividend Payout 0.2 Growth 0.10619 =Retention Ratio 0.8 Rate 1 - 0.12 x 0.800

SUSTAINABLE GROWTH RATE


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Question 22.

Preference Ltd wishes to maintain a growth rate of 10 per cent per year and a dividend pay-out of 20 per cent. The ratio of total assets to sales is constant at 2, and profit margin is 10 per cent.

What must the debt/equity ratio be?

g* = 0.1R = 1 – payout ratio = 1 - 0.2 = 0.8p = 0.1A/S = 2 so that S/A = ½ = 0.5g*= [p(S/A) (1 + D/E) R]/(1 – [p(S/A) (1+ D/E) R ])0.1 = (0.1)(0.5)(1 + D/E) 0.8/[1 – (0.1)(0.5)(1 + D/E)0.8]0.1 = 0 .05 (1 + D/E)/(1 – 0.05 (1 + D/E))D/E = 1.2744

Growth Rate 0.1Capital Intensity Ratio 2Total Assets 100000Total Sales 50000Total assets/sales 2Total Sales/Assets 0.5Total Sales 50000Costs 45000Net Profit 5000Net profit/sales 0.1Total Debt 50000Total Equity 50000Total Debt + Equity 100000Debt/equity 0.5Debt/Total Assets 0.5Dividend Payout 0.2Retention Ratio 0.8

Net Profit Total Sales Debt RetentionSales Total Assets Equity Rate


5000 5000050000 100000

5000 5000050000 100000

0.1 x 0.5 x 1 + 1.274 x 0.8

1 - 0.1 x 0.5 x 1 + 1.274 x 0.8

x x 0.8

1 - x x 0.8

0.05 x 1.81921 - 0.05 x 1.8192

0.09 =

0.1

0.05

0.05

0.1 =

0.1 =

0.1

x x

x x1 -

+

x

x

x 0.8

+

+

1.00

=

x 0.81.274

1.274x x 1 +

1 - x x 1

0.09

1

1

=

2.274

2.274

0.090960.909040.1 =

Question 23.

Mansions Ltd wishes to maintain a growth rate of 5 per cent per year, a debt-to-equity ratio of 0.5, and a dividend payout of 60 per cent. The ratio of total assets to sales is constant at 2 . What profit margin must it achieve?

R = 1 – payout ratio = 1 – 0.6 = 0.4 A/S = 2 so that S/A = ½ = 0.5i* =[p(i) (1 + D/E) R]/(1 – [p(S/A)(1+ D/E) R])0.05 = [p(0.5)(1.5)0.4]/[1 – [p(0.5)(1.5)0.4]0.05 = [0.3p]/[1 – 0.3p]

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0.05*(1 – 0.3p) = 0.3p0.05 – 0.015p = 0.3p0.05= 0.3p + 0.015pp = 0.1587 = 15.87%

Growth Rate 0.05Capital Intensity Ratio 2Total Assets 106974Total Sales 53487Total assets/sales 2Total Sales/Assets 0.5Total Sales 53487Costs 45000Net Profit 8487Net profit/sales 0.1587Total Debt 53487Total Equity 53487Total Debt + Equity 106974Debt/equity 0.5Debt/Total Assets 0.5Dividend Payout 0.6Retention Ratio 0.4



8487 5348753487 106974

8487 5348753487 106974

0.15867407 x 0.5 x 1 + 0.500 x 0.4

1 - 0.15867407 x 0.5 x 1 + 0.500 x 0.4

x x 0.4

1 - x x 0.4

0.07933704 x 0.61 - 0.07933704 x 0.6

0.0476 = 0.0476

1.000

1.500

0.079337035 1.500

0.05 =0.0476022210.952397779

0.05 =

0.05 = 0.079337035

0.4

0.05 =

1 - x x 1 + 0.500 x 0.4

x

x x 1 + 0.500 x

- x x 1 +

0.05 =

1

x x 1 + x

Question 24.

Based on the following information, calculate the sustainable growth rate and the ROA:Profit margin = 4%Total asset turnover = 2Total debt ratio = 0.5Payout ratio = 60%

g*=[p(S/A)(1 + D/E)R]/1 – [p(S/A)(1+ D/E)R]= 0.04(2)(2)(0.4)/[1 – 0.04(2)(2)(0.4)] = 0.0684 = 6.84%ROA = 0.04(2) = 0.08 = 8%

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Capital Intensity Ratio 0.5Total Assets 30000Total Sales 60000Total assets/sales 0.5Total Sales/Assets 2Total Sales 60000 $2,400 Net ProfitCosts 57600 $15,000 EquityNet Profit 2400Net profit/sales 0.0400 Sustainable Return on x Retention Total Debt 15000 Growth = Equity RateTotal Equity 15000 Rate 1 - Return on x Retention Total Debt + Equity 30000 Rquity RateDebt/equity 0.5Debt/Total Assets 0.5 Sustainable 0.16 x 0.400Dividend Payout 0.6 Growth 0.06838 =Retention Ratio 0.4 Rate 1 - 0.16 x 0.400



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Qu estion 25.

Postal Note Ltd has $50 000 in total assets. The retention ratio is 0.50, the debt/equity ratio is 1, and the profit margin is 5 per cent. Sales for the year just ended were $20 000. If sales are to rise by 10 per cent, what is the EFN?

EFN = –(0.05)(20 000)(0.5) + [50 000 – (0.05)(20 000)(0.5)](0.1)= $4 450


0.05 $1,000 Total $50,000 Total $50,000Less tax $0Net profit $1,000


Net Profit $1,000Sales $20,000


Payout Ratio0.5

Profit Margin = = = 0.05


- 0.05 x $20,000 x 0.5 + $50,000 0.05 x $20,000 x 0.5 x 0.100

= + x 0.100g = 4,450.000

x Sales x x g

-$500.00 $49,500

- x Sales x + -

Question 26.

In the previous question, what is the general relationship between growth in sales and EFN? What growth rate can be supported with no external financing? What would happen if growth were zero? How do you interpret this?

EFN = –500 + 495g0 = –500 + 495gg = 0.0101 = 1.01%If growth is 0, then there is a $500 surplus in funds that could be used to retire debt or pay a larger dividend.

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Question 27.

In the previous question, what is the sustainable growth rate?

ROE = 0.05(20 000/50 000)(1 + 1) = 0.04g* = 0.04(0.5)/[1 – (0.04)(0.5)] = 0.0204 = 2.04%

Capital Intensity Ratio 2.5Total Assets $50,000Total Sales $20,000Total assets/sales 2.5Total Sales/Assets 0.4Total Sales 20000 $1,000 Net ProfitCosts $19,000 $25,000 EquityNet Profit 1000Net profit/sales 0.0500 Sustainable Return on x Retention Total Debt $25,000 Growth = Equity RateTotal Equity $25,000 Rate 1 - Return on x Retention Total Debt + Equity 50000 Rquity RateDebt/equity 0.5Debt/Total Assets 0.5 Sustainable 0.04 x 0.500Dividend Payout 0.5 Growth 0.02041 =Retention Ratio 0.5 Rate 1 - 0.04 x 0.500



Question 28.

Beanie Ltd wishes to maintain a growth rate of 4 per cent per year, a debt-to-equity ratio of 0.5, and a dividend payout of 80 per cent. If the profit margin is 8 per cent and next year's sales are projected at $1500, what is the total asset projection?

R + 1 – 0.8 + 0.2 g* = [p(S/A)(1 + D/E)R]/1 – [p(S/A)(1+ D/E)R]0.04 = (0.08)(1500/A)(1.5)(0.2)/[1 – (0.08)(1500)/A)(1.5)(0.2)]A = $936

Question 29.

If a firm has a 20 per cent ROE and a 35 per cent payout ratio, what is its sustainable growth rate?

R = 1 – 0.35 = 0.65g* = 0.2(0.65)/[1 – 0.2(0.65)] = 0.1494 = 14.94%

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