Chapter 4, Problem 28QP

EFN and Sustainable Growth [LO2, 3] Redo Problem 26 using sales growth rates of 30 and 35 percent in addition to 20 percent. Illustrate graphically the relationship between EFN and the growth rate, and use this graph to determine the relationship between them. At what growth rate is the EFN equal to zero? Why is this sustainable growth rate different from that found by using the equation in the text?

Summary Introduction

To determine:

• The relationship between external financing needed and growth rate
• The growth rate at which EFN is zero
• Reason for the difference between internal growth rates using graphical method and equation method

Introduction:

By using the graphical representation, the relationship between external financing needed and growth rate can be determined.

Answer to Problem 28QP

The growth rate at which the external financing is zero

Explanation of Solution

Given information:

The various growth rates in addition to 20% are 30% and 35%

Formulae:

$\text{Dividend}=\frac{\text{Current dividend}}{\text{Current year's net income}}\times \text{Projected net income}$

$\text{Addition to retained earnings}=\text{Net income}-\text{Dividend}$

$\text{New long term debt}=\text{Total debt}-\text{Total current liabilities}$

$\text{EFN}=\text{New longterm debt}-\text{Old debt}$

Compute pro forma income statement at the rates of 20%, 30%, 35%:

Pro forma statement at 30% growth rate

Pro forma income statement
Particulars	CurrentyearAmount($)	Amount($)(30%)
Sales	$891,600	$1,159,080
Costs	$693,600	$901,680
Other expenses	$18,240	$23,712
EBIT	$179,760	$233,688
Interest paid	$13,400	$13,400
Taxable income	$166,360	$220,288
Taxes (35%)	$58226	$77,101
Net income	$108,134	$143,187

Hence, the current year’s net income increases at 30% growth rate.

Compute dividend and addition to retained earnings:

Dividend and addition to retained earnings for the rate of 15%growth:

$\begin{array}{c}\text{Dividend}=\frac{\text{Current dividend}}{\text{Current year's net income}}\times \text{Projected net income}\\ =\frac{\$35,684}{\$108,134}\times \$143,187\\ =\$47,251\end{array}$

$\begin{array}{c}\text{Addition to retained earnings}=\text{Net income}-\text{Dividend}\\ =\text{\$143,187}-\text{\$47,251}\\ =\text{\$95,936}\end{array}$

Hence, dividend and addition to retained earnings are $47,251 and $95,936.

Compute new long-term debt, keeping debt equity constant:

$\begin{array}{c}\text{New debt}=\text{Debt equity ratio}\times \text{Total equity}\\ \text{Debt equity ratio}=\frac{\text{Current laibilities}+\text{Longterm Debt}}{\text{Total equity}}\\ =\frac{\$81,520+\$155,000}{\$304,730}\\ =\frac{\$236,520}{\$304,730}\\ =0.77616\end{array}$

Hence, debt equity ratio is 0.77616.

$\begin{array}{c}\text{New debt}=\text{ Debt equity ratio}\times \text{Total equity}\\ =0.77616\times \$400,666\\ =310,981\end{array}$

New long-term debt

$\begin{array}{c}\text{New long term debt}=\text{Total debt}-\text{Total current liabilities}\\ =\text{\$310,982}-\text{101,080}\\ =\text{\$209,902}\end{array}$

Hence, new long-term debt is $209,902.

Pro forma balance for the growth rate of 30%

Pro forma balance sheet
Assets	Amount($)	Liabilities	Amount($)
Current assets:		Current liabilities:
Cash	$31,564	Accounts payable	$84,760
Accounts receivable	$48,191	Notes payable	$16,320
Inventory	$108,420
Total	$188,175	Total	$101,080
Fixed assets:		Long-term debt	$209,902
Net plant and equipment	$4515,450	Owner's equity:
		Common stock and paid in surplus	$130,000
		Retained earnings	$270,666
		Total Owner's equity	$400,666
Total	$703,625	Total	$711,648

Therefore, the excess debt raised is $8022($711648-$703,625)

Compute external financing needed:

$\begin{array}{c}\text{EFN}=\text{New longterm debt}-\text{Old debt}\\ =\text{\$209,902}-\text{\$155,000}\\ =\text{\$54,902}\end{array}$

Hence, external financing needed at the grow rate of 30% is $54,902.

Pro forma income statement at the rate of 35% growth rate

Pro forma income statement
Particulars	CurrentyearAmount($)	Amount($)(35%)
Sales	$891,600	$1,203,660
Costs	$693,600	$ 936,360
Other expenses	$18,240	$24,624
EBIT	$179,760	$242,676
Interest paid	$13,400	$13,400
Taxable income	$166,360	$229,276
Taxes (35%)	$58226	$80,247
Net income	$108,134	$149,029

Hence, net income increased at the rate of 35%

Compute external financing needed at the growth rate of 35%

Compute dividend and addition to retained earnings for the rate of 35%

$\begin{array}{c}\text{Dividend}=\frac{\text{Current dividend}}{\text{Current year's net income}}\times \text{Projected net income}\\ =\frac{\$35,684}{\$108,134}\times \$149,029\\ =\$49,179\end{array}$

$\begin{array}{c}\text{Addition to retained earnings}=\text{Net income}-\text{Dividend}\\ =\text{\$149,029}-\text{\$49,179}\\ =\text{\$99,850}\end{array}$

Hence, dividend and addition to retained earnings is $49,179 and $99,850.

$\begin{array}{c}\text{New retained earnings}=\text{\$99,850+\$174,730}\\ =\text{\$274,580}\end{array}$

Hence, total retained earnings are $274,580.

Compute new long-term debt:

The new long term debt can be determined by using the below formula

$\begin{array}{c}\text{New debt}=\text{ Debt equity ratio}\times \text{Total equity}\\ =0.77616\times \$404,580\\ =314,020\end{array}$

$\begin{array}{c}\text{New long term debt}=\text{Total debt}-\text{Total current liabilities}\\ =\text{\$314,020}-\text{104,340}\\ =\text{\$209,680}\end{array}$

Hence, new long-term debt is $209,680

Pro forma balance for the growth rate of 35%

Pro forma balance sheet
Assets	Amount($)	Liabilities	Amount($)
Current assets:		Current liabilities:
Cash	$32,778	Accounts payable	$88,020
Accounts receivable	$50,045	Notes payable	$16,320
Inventory	$112,590
Total	$195,413	Total	$104,340
Fixed assets:		Long-term debt	$209,680
Net plant and equipment	$535,275	Owner's equity:
		Common stock and paid in surplus	$130,000
		retained earnings	$274,580
		Total Owner's equity	$404,580
Total	$730,688	Total	$718,600

Therefore, the excess debt raised is ($718,600-$730,688) is $-12088

Note: At 35% growth rate, the firm needs $12088 addition to external debt. Thus, existing financial need of $54,680 is added to $12,088.

Compute external financing needed:

$\begin{array}{c}\text{External financing needed}=\$54,680+\$12088\\ =\boxed{\$66,767}\end{array}$

Hence, external financing needed at the growth rate of 30% is $66,767.

The rate at which EFN is zero:

The rate at which external financing needed is zero at 30% growth rate

The internal growth rate differs from the calculated by using equation in the text:

The (ROE x b) is the element which is used throughout the text. This is based on the ROE using ending balance sheet of equity and beginning balance sheet equity whereas the sustainable growth rate and ROE calculated by using abbreviated equation is based on the equity that do not exist when the net income is earned.

Conclusion

Thus, negative external financing needed indicates that the company has more funds which can be used to reduce current liabilities, debts etc. Thus, these represents the relationship between external financing needed and growth rates.