Chapter 4, Problem 27QP

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% to illustrate graphical representation between external financing needed and growth

Note: The below statement shows the pro forma statement at 15% sales growth rate

Pro forma statement at 15%sales growth rate:

Pro forma income statement
Particulars	Current Year Amount ($)	Amount ($) (15%)
Sales	$743,000	$854,450
Costs	$578,000	$664,700
Other expenses	$15,200	$17,480
Earnings Before Interest and Tax (EBIT)	$149,800	$172,270
Interest paid	$11,200	$12,880
Taxable income	$138,600	$159,390
Taxes (35%)	$48 510	$55,787
Net income	$90,090	$103,604

Hence, the net income is $103,604 when the sales growth rate is 15%.

Compute dividend and addition to retained earnings:

Note: The below calculation shows the dividend and addition to retained earnings for the rate of 15% sales growth.

$\begin{array}{c}\text{Dividend}=\frac{\text{Current dividend}}{\text{Current year's net income}}\times \text{Projected net income}\\ =\frac{\$27,027}{\$90,090}\times \$103,604\\ =\$31,081\end{array}$

$\begin{array}{c}\text{Addition to retained earnings}=\text{Net income}-\text{Dividend}\\ =\$103,604-\text{\$31,081}\\ =\text{\$72,523}\end{array}$

Hence, the dividend and addition to retained earnings is $31,081 and $72,523.

Compute total retained earnings:

$\begin{array}{c}\text{Total retained earnings}=\text{Existing retained earnings}+\text{Additional retained earnings}\\ =\text{\$146,720+\$72,523}\\ =\text{\$219,243}\end{array}$

Hence, the total retained earnings are $219,243.

Pro forma balance sheet after adjusting 15% of growth rate:

Pro forma balance sheet
Assets	Amount ($)	Liabilities	Amount ($)
Current assets:		Current liabilities:
Cash	$23,276	Accounts payable	$62,560
Accounts receivable	$37,444	Notes payable	$13,600
Inventory	$79,948	Total	$76,160
Total	$140,668	Long-term debt	$126,000
Fixed assets:		Owner's equity:
Net plant and equipment	$379,960	Common stock and paid in surplus	$112,000
		Retained earnings	$219,243
		Total Owner's equity	$331,243
Total	$520,628	Total	$533,403

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

$\begin{array}{c}\text{External financing needed}=\text{Total assets}-\text{Total liabilities and Owner's equity}\\ =\$520,628-\$533,403\\ =-\$12,775\end{array}$

Hence, the external financing needed at the rate of 15% growth rate is −$12,775.

Pro forma income statement at 20% growth rate:

Pro forma income statement
Particulars	Current year Amount ($)	Amount ($) (20%)
Sales	$743,000	$891,600
Costs	$578,000	$693,600
Other expenses	$15,200	$18,240
EBIT	$149,800	$179,760
Interest paid	$11,200	$13,440
Taxable income	$138,600	$166,320
Taxes (35%)	$48,510	$58,212
Net income	$90,090	$108,108

Hence, the net income is $108,108 when the sales growth rate is 20%.

Compute dividend and addition to retained earnings:

Note: The below calculation shows the dividend and addition to retained earnings for the rate of 20% sales growth.

$\begin{array}{c}\text{Dividend}=\frac{\text{Current dividend}}{\text{Current year's net income}}\times \text{Projected net income}\\ =\frac{\$27,027}{\$90,090}\times \$108,108\\ =\$32,432\end{array}$

$\begin{array}{c}\text{Addition to retained earnings}\text{= Net income}-\text{Dividend}\\ \text{=}\text{\$108,108}-\$32,432\\ =\$75,676\end{array}$

Hence, the dividend and addition to retained earnings is $32,432 and $75,676.

Compute total retained earnings:

$\begin{array}{c}\text{Total retained earnings}=\text{Existing retained earnings}+\text{Additional retained earnings}\\ =\text{\$146,720}+\text{\$75,676}\\ =\text{\$222,396}\end{array}$

Hence, the total retained earnings are $222,396.

Pro forma balance sheet after adjusting 20% of growth rate:

Pro forma balance sheet
Assets	Amount ($)	Liabilities	Amount ($)
Current assets:		Current liabilities:
Cash	$24,288	Accounts payable	$65,280
Accounts receivable	$39,072	Notes payable	$13,600
Inventory	$83,424	Total	$78,880
Total	$146,784	Long-term debt	$126,000
Fixed assets:		Owner's equity:
Net plant and equipment	$396,480	Common stock and paid in surplus	$112,000
		Retained earnings	$222,396
		Total Owner's equity	$334,396
Total	$543,264	Total	$539,276

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

$\begin{array}{c}\text{External financing needed}=\text{Total assets}-\text{Total liabilities and Owner's equity}\\ =\$543,264-\$539,276\\ =\$3,988\end{array}$

Hence, the external financing needed at the rate of 20% sales growth rate is $3,988.

Pro forma income statement at 25% growth rate

Pro forma income statement
Particulars	Current year Amount ($)	Amount ($) (25%)
Sales	$743,000	$928,750
Costs	$578,000	$722,500
Other expenses	$15,200	$19,000
EBIT	$149,800	$187,250
Interest paid	$11,200	$14,000
Taxable income	$138,600	$173,250
Taxes (35%)	$48,510	$60,638
Net income	$90,090	$112,613

Compute dividend and addition to retained earnings:

Note: The below calculation shows the dividend and addition to retained earnings for the rate of 25% sales growth.

$\begin{array}{c}\text{Dividend}=\frac{\text{Current dividend}}{\text{Current year's net income}}\times \text{Projected net income}\\ =\frac{\$27,027}{\$90,090}\times \$112,613\\ =\$33,784\end{array}$

$\begin{array}{c}\text{Addition to retained earnings}=\text{Net income}-\text{Dividend}\\ =\$112,613-\$33,784\\ =\$78,829\end{array}$

Hence, the dividend and retained earnings is $33,784 and $78,829.

Compute total retained earnings:

$\begin{array}{c}\text{Total retained earnings}=\text{Existing retained earnings}+\text{Additional retained earnings}\\ =\text{\$146,720}+\$78,829\\ =\$225,549\end{array}$

Hence, the total retained earnings are $225,549.

Pro forma balance sheet after adjusting 25% of growth rate:

Pro forma balance sheet
Assets	Amount ($)	Liabilities	Amount ($)
Current assets:		Current liabilities:
Cash	$25,300	Accounts payable	$68,000
Accounts receivable	$40,700	Notes payable	$13,600
Inventory	$86,900
Total	$152,900	Total	$81,600
Fixed assets:		Long-term debt	$126,000
Net plant and equipment	$413,000	Owner's equity:
		Common stock and paid in surplus	$112,000
		Retained earnings	$225,549
		Total Owner's equity	$337,549
Total	$565,900	Total	$545,149

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

$\begin{array}{c}\text{External financing needed}=\text{Total assets}-\text{Total liabilities and Owner's equity}\\ =\$565,900-\$545,149\\ =\$20,751\end{array}$

Hence, the external financing needed at the rate of 25% growth rate is $20,751.

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.