27. The pro forma income statements for all three growth rates will be:
FLEURY INC.
Pro Forma Income Statement
15 % Sales
Growth
20% Sales
Growth
25% Sales
Growth
Sales $1,025,340 $1,069,920 $1,114,500
Costs 797,640 832,320 867,000
We will calculate the EFN for the 15 percent growth rate first. Assuming the payout ratio is constant,
the dividends paid will be:
And the addition to retained earnings will be:
The new retained earnings on the pro forma balance sheet will be:
The pro forma balance sheet will look like this:
15% Sales Growth:
FLEURY INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 27,922 Accounts payable $ 74,980
Accounts receivable 42,631 Notes payable 16,320
CHAPTER 4 – 2
Fixed assets
So the EFN is:
EFN = Total assets – Total liabilities and equity
At a 20 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be:
And the addition to retained earnings will be:
The new retained earnings on the pro forma balance sheet will be:
CHAPTER 4 – 3
The pro forma balance sheet will look like this:
20% Sales Growth:
FLEURY INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 29,136 Accounts payable $ 78,240
Fixed assets
Net plant and Owners’ equity
So the EFN is:
EFN = Total assets – Total liabilities and equity
At a 25 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be:
And the addition to retained earnings will be:
The new retained earnings on the pro forma balance sheet will be:
CHAPTER 4 – 4
The pro forma balance sheet will look like this:
25% Sales Growth:
FLEURY INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 30,350 Accounts payable $ 81,500
Fixed assets
Net plant and Owners’ equity
So the EFN is:
EFN = Total assets – Total liabilities and equity
28. The pro forma income statements for all three growth rates will be:
FLEURY INC.
Pro Forma Income Statement
20% Sales
Growth
30% Sales
Growth
35% Sales
Growth
Sales $1,069,920 $1,159,080 $1,203,660
Costs 832,320 901,680 936,360
Dividends $43,396 $47,251 $49,179
Add to RE 88,107 95,936 99,850
At a 30 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be:
CHAPTER 4 – 5
And the addition to retained earnings will be:
The new addition to retained earnings on the pro forma balance sheet will be:
The new total debt will be:
So, the new long-term debt will be the new total debt minus the new short-term debt, or:
The pro forma balance sheet will look like this:
FLEURY INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 31,564 Accounts payable $ 84,760
Fixed assets
Net plant and Owners’ equity
equipment 515,450 Common stock and
paid-in surplus $ 130,000
So the excess debt raised is:
CHAPTER 4 – 6
And the EFN is:
At a 35 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be:
And the addition to retained earnings will be:
The new retained earnings on the pro forma balance sheet will be:
The new total debt will be:
So, the new long-term debt will be the new total debt minus the new short-term debt, or:
CHAPTER 4 – 7
Sales growth rate = 35% and debt/equity ratio = .7762:
FLEURY INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 32,778 Accounts payable $ 88,020
Fixed assets
Net plant and Owners’ equity
So the excess debt raised is:
At a 35 percent growth rate, the firm will need funds in the amount of $12,088 in addition to the
external debt already raised. So, the EFN will be:
29. We need the ROE to calculate the sustainable growth rate. The ROE is:
ROE = (PM)(TAT)(EM)
Now we can use the sustainable growth rate equation to find the retention ratio as:
This implies the payout ratio is:
Payout ratio = 1 – b
CHAPTER 4 – 8
This is a dividend payout ratio of negative 134 percent, which is impossible. The growth rate is not
The maximum sustainable growth rate for this company is:
Maximum sustainable growth rate = (ROE × b) / [1 – (ROE × b)]
30. We know that EFN is:
EFN = Increase in assets – Addition to retained earnings
The increase in assets is the beginning assets times the growth rate, so:
Increase in assets = A g
The addition to retained earnings next year is the current net income times the retention ratio, times
one plus the growth rate, so:
31. We start with the EFN equation we derived in Problem 30 and set it equal to zero:
EFN = 0 = – PM(S)b + [A – PM(S)b]g
Substituting the rearranged profit margin equation into the internal growth rate equation, we have:
Internal growth rate = [PM(S)b ] / [A – PM(S)b]
CHAPTER 4 – 9
To derive the sustainable growth rate, we must realize that to maintain a constant D/E ratio with no
external equity financing, EFN must equal the addition to retained earnings times the D/E ratio:
Solving for g and then dividing numerator and denominator by A:
Sustainable growth rate = PM(S)b(1 + D/E) / [A – PM(S)b(1 + D/E )]
32. In the following derivations, the subscript “E” refers to end of period numbers, and the subscript “B”
refers to beginning of period numbers. TE is total equity and TA is total assets.
For the sustainable growth rate:
We multiply this equation by:
(TEE / TEE)
Recognize that the numerator is equal to beginning of period equity, that is:
Substituting this into the previous equation, we get:
Which is equivalent to:
The sustainable growth rate equation is:
For the internal growth rate:
CHAPTER 4 – 10
We multiply this equation by:
(TAE / TAE)
Recognize that the numerator is equal to beginning of period assets, that is:
Substituting this into the previous equation, we get:
Which is equivalent to:
The internal growth rate equation is:
Internal growth rate = ROAB × b