Concept explainers
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?
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:
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:
Hence, dividend and addition to retained earnings are $47,251 and $95,936.
Compute new long-term debt, keeping debt equity constant:
Hence, debt equity ratio is 0.77616.
New long-term debt
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:
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%
Hence, dividend and addition to retained earnings is $49,179 and $99,850.
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
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:
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.
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.
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