Chapter 4, Problem 27QP

EFN and Internal Growth [LO2, 3] Redo Problem 24 using sales growth rates of 15 and 25 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 internal growth rate different from that found by using the equation in the text?

Summary Introduction

To determine: The grow rate at which external financing needed is zero.

Introduction:

Using the graphical presentation for external financing needed and growth rate, the relationship between the both can be determined. The rate at which the EFN is zero can be determined using this representation.

Answer to Problem 27QP

The growth rate at which the external financing needed is zero is 15%.

Explanation of Solution

Given information:

The various sales growth rates in addition to 20% are given as 15% and 25%.

Compute pro forma income statement at the rates of 15%, 20%, 25%:

The graphical relationship between external financing needed and growth rate:

Pro forma statement at 15% growth rate

Pro forma income statement
Particulars	Current year Amount ($)	Amount ($) (15%)
Sales	$891,600	$1,025,340
Costs	$693,600	$797,640
Other expenses	$18,240	$20,976
EBIT	$179,760	$206,724
Interest paid	$13,400	$13,400
Taxable income	$166,360	$193,324
Taxes (35%)	$58226	$67,663
Net income	$108,134	$125,661

Hence, net income increased at the rate of 15%.

Compute dividend and addition to retained earnings:

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

$\begin{array}{c}\text{Dividend}=\frac{\text{Current dividend}}{\text{Current year's net income}}\times \text{Projected net income}\\ =\frac{\$35,684}{\$108,134}\times \$125,661\\ =\$41,468\end{array}$

$\begin{array}{c}\text{Addition to retained earnings}=\text{Net income}-\text{Dividend}\\ =\text{\$125,661}-\text{\$41,468}\\ =\text{\$84,193}\end{array}$

Hence, dividend and addition to retained earnings is $41,468 and $84,193.

Pro forma balance sheet after adjusting 15% of growth rate

Pro forma balance sheet
Assets	Amount ($)	Liabilities	Amount ($)
Current assets:		Current liabilities:
Cash	$27,922	Accounts payable	$74,980
Accounts receivable	$42,631	Notes payable	$16,320
Inventory	$95,910
Total	$166,463	Total	$91,300
Fixed assets:		Long-term debt	$155,000
Net plant and equipment	$455,975	Owner's equity:
		Common stock and paid in surplus	$130,000
		Retained earnings	$258,923
		Total owner’s equity	$388,923
Total	$622,438	Total	$635,223

The difference between the total assets and the total liabilities and owner’s equity is termed as external financing needed.

$\begin{array}{c}\text{External financing needed}=\text{Total assets}-\text{Total liabilities and Owner's equity}\\ =\text{\$649,500}-\text{\$642,397}\\ =\text{\$622,438}-\text{635,223}\\ =\boxed{-\$12,785}\end{array}$

Hence, external financing needed at the rate of 15% growth rate is -$12,785.

Pro forma income statement at 20% growth rate

Pro forma income statement
Particulars	Current Year Amount ($)	Amount ($) (20%)
Sales	$891,600	$1,069,920
Costs	$693,600	$832,320
Other expenses	$18,240	$21,888
EBIT	$179,760	$215,712
Interest paid	$13,400	$13,400
Taxable income	$166,360	$202,312
Taxes (35%)	$58226	$70,809
Net income	$108,134	$131,503

Hence, the income increased at the rate of 20%.

Dividend and addition to retained earnings for the rate of 20% sales growth:

$\begin{array}{c}\text{Dividend}=\frac{\text{Current dividend}}{\text{Current year's net income}}\times \text{Projected net income}\\ =\frac{\$41,468}{\$125,661}\times \$131,503\\ =\$43,396\end{array}$

$\begin{array}{c}\text{Addition to retained earnings}=\text{Net income}-\text{Dividend}\\ =\$131,503-\$43,396\\ =\$88,107\end{array}$

Hence, dividend and addition to retained earnings is $43,396 and $88,107.

Pro forma balance sheet after adjusting 20% of growth rate

Pro forma balance sheet
Assets	Amount ($)	Liabilities	Amount ($)
Current assets:		Current liabilities:
Cash	$29,136	Accounts payable	$78,240
Accounts receivable	$44,484	Notes payable	$16,320
Inventory	$100,080
Total	$173,700	Total	$94,560
Fixed assets:		Long-term debt	$155,000
Net plant and equipment	$475,800	Owner's equity:
		Common stock and paid in surplus	$130,000
		Retained earnings	$262,837
		Total owner’s equity	$392,837
Total	$649,500	Total	$642,397

The external financing needed is determined by the difference of the total assets and the total liabilities and owner’s equity.

$\begin{array}{c}\text{External financing needed}=\text{Total assets}-\text{Total liabilities and Owner's equity}\\ =\$676,563-\$649,571\\ =\$26,992\end{array}$

Hence, external financing needed at the rate of 20% growth rate is $7,103.

Pro forma income statement at 25% growth rate

Pro forma income statement
Particulars	Current Year Amount ($)	Amount ($) (25%)
Sales	$891,600	$1,114,500
Costs	$693,600	$867,000
Other expenses	$18,240	$22,800
EBIT	$179,760	$224,700
Interest paid	$13,400	$13,400
Taxable income	$166,360	$211,300
Taxes (35%)	$58226	$73,955
Net income	$108,134	$137,345

Dividend and addition to retained earnings for the rate of 25% sales growth:

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

$\begin{array}{c}\text{Dividend}=\frac{\$43,396}{\$131,503}\times \$137,345\\ =\$45,324\end{array}$

$\begin{array}{c}\text{Addition to retained earnings}=\text{Net income}-\text{Dividend}\\ =\$137,345-\$45,324\\ =\$92,021\end{array}$

Hence, dividend and retained earnings is $45,324 and $92,021.

Pro forma balance sheet after adjusting 25% of growth rate

Pro forma balance sheet
Assets	Amount ($)	Liabilities	Amount ($)
Current assets:		Current liabilities:
Cash	$30,350	Accounts payable	$81,500
Accounts receivable	$46,338	Notes payable	$16,320
Inventory	$104,250
Total	$180,938	Total	$97,820
Fixed assets:		Long-term debt	$155,000
Net plant and equipment	$495,625	Owner's equity:
		Common stock and paid in surplus	$130,000
		Retained earnings	$266,751
		Total owner’s equity	$396,751
Total	$676,563	Total	$649,571

The external financing needed is determined by the difference of the total assets and the total liabilities and owner’s equity.

$\begin{array}{c}\text{External financing needed}=\text{Total assets}-\text{Total liabilities and Owner's equity}\\ =\$676,563-\$649,571\\ =\boxed{\$26,992}\end{array}$

Hence, external financing needed at the rate of 25% growth rate is $26,992.

Summary Introduction

To discuss: The relationship between external financing and growth rate.

Explanation of Solution

The relationship of external financing and growth rate is a primary element in the area of financial planning.

• The firm maintains 100% capacity utilization to make the things easy and simple.
• When growth rate is at 15% the EFN is negative, this shows the company has more funds.
• When growth rate at 20% and 25% the EFN is positive, this indicates the company needs additional financing for the upcoming period.

Summary Introduction

To determine: The rate at which EFN is zero.

Explanation of Solution

The rate at which external financing needed is zero at 15% growth rate. As the difference of total assets and total liabilities of external financing needed at the rate of 15% growth rate is -$12,785 this shows that EFN is zero since it exceeds the liabilities.

Summary Introduction

To discuss: Reason for the difference of internal growth using graphical method and equation method.

Explanation of Solution

The (ROA x b) is the element which is used throughout the text. This is based on the ROA using ending balance sheet numbers of assets and beginning balance sheet number of assets whereas the internal growth rate and ROA calculated by the equations on a abbreviated form is based on the assets which will not exists once the net income earned.

Conclusion

Thus, the rate 15% at which the company external financing needed is negative. Negative external financing needed indicates that the company has more funds which can be used to reduce current liabilities, debts etc. Thus, these are the graphical relationship between external financing needed and growth rates.