27. The pro forma income statements for all three growth rates will be:
Pro Forma Income Statement
15 % Sales
Growth
20% Sales
Growth
25% Sales
Growth
Sales $1,127,874 $1,176,912 $1,225,950
Costs 911,904 951,552 991,200
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:
CROSBY INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 32,108 Accounts payable $ 82,478
Accounts receivable 49,025 Notes payable 17,620
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:
The pro forma balance sheet will look like this:
20% Sales Growth:
CROSBY INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 33,504 Accounts payable $ 86,064
Accounts receivable 51,156 Notes payable 17,620
Inventory 115,092 Total $ 103,684
Total $ 199,752 Long-term debt $ 170,000
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:
The pro forma balance sheet will look like this:
25% Sales Growth:
CROSBY INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 34,900 Accounts payable $ 89,650
Accounts receivable 53,288 Notes payable 17,620
Inventory 119,888 Total $ 107,270
Total $ 208,075 Long-term debt $ 170,000
So the EFN is:
EFN = Total assets – Total liabilities and equity
28. The pro forma income statements for all three growth rates will be:
CROSBY INC.
Pro Forma Income Statement
20% Sales
Growth
30% Sales
Growth
35% Sales
Growth
Sales $1,176,912 $1,274,988 $1,324,026
Costs 951,552 1,030,848 1,070,496
At a 30 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:
So the excess debt raised is:
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:
Sales growth rate = 35% and debt/equity ratio = .7142:
CROSBY INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 37,692 Accounts payable $ 96,822
Accounts receivable 57,551 Notes payable 17,620
Inventory 129,479 Total $ 114,442
So the excess debt raised is:
At a 35 percent growth rate, the firm will need funds in the amount of $24,249 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:
Sustainable growth rate = (ROE × b)/[1 – (ROE × b)]
This implies the payout ratio is:
Payout ratio = 1 – b
This answer indicates a dividend payout ratio of negative 129 percent, which is impossible. So, the
growth rate is not consistent with the other constraints. The lowest possible payout rate is 0 (without
As an aside, we should note that it is possible to have a retention ration greater than 1 if the company
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:
31. We start with the EFN equation we derived in Problem 30 and set it equal to zero:
Substituting the rearranged profit margin equation into the internal growth rate equation, we have:
Since:
ROA = NI/A
ROA = PM(S)/A
denominator by A. This gives:
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:
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:
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