CHAPTER 3 – 1
24. The pro forma income statements for all three growth rates will be:
MOOSE TOURS INC.
Pro Forma Income Statement
15 % Sales
Growth
20% Sales
Growth
25% Sales
Growth
Sales $865,375 $903,000 $940,625
Costs 673,440 702,720 732,000
Other expenses 17,710 18,480 19,250
We will calculate the EFN for the 15 percent growth rate first. Assuming the payout ratio is constant,
the dividends paid will be:
Dividends = ($27,331 / $91,104)($105,875)
Dividends = $31,762
And the addition to retained earnings will be:
The pro forma balance sheet will look like this:
15% Sales Growth:
MOOSE TOURS INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 24,877 Accounts payable $ 66,861
Accounts receivable 40,019 Notes payable 14,535
Inventory 85,445 Total $ 81,396
CHAPTER 3 – 2
So the EFN is:
EFN = Total assets – Total liabilities and equity
20% Sales Growth:
The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times
net income, or:
Dividends = ($27,331 / $91,104)($110,799)
Dividends = $32,239
And the addition to retained earnings will be:
The pro forma balance sheet will look like this:
20% Sales Growth:
MOOSE TOURS INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 25,958 Accounts payable $ 69,768
Accounts receivable 41,759 Notes payable 14,535
CHAPTER 3 – 3
So the EFN is:
EFN = Total assets – Total liabilities and equity
EFN = $580,621 – 573,039
EFN = $7,583
25% Sales Growth:
At a 25 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be:
The new retained earnings on the pro forma balance sheet will be:
New retained earnings = $161,176 + 81,006
New retained earnings = $242,182
The pro forma balance sheet will look like this:
25% Sales Growth:
MOOSE TOURS INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 27,040 Accounts payable $ 72,675
Accounts receivable 43,499 Notes payable 14,535
CHAPTER 3 – 4
25. The pro forma income statements for all three growth rates will be:
MOOSE TOURS INC.
Pro Forma Income Statement
20% Sales
Growth
30% Sales
Growth
35% Sales
Growth
Sales $903,000 $978,250 $1,015,875
Costs 702,720 761,280 790,560
Other expenses 18,480 20,020 20,790
At a 30 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be:
Dividends = ($27,331 / $91,104)($120,647)
Dividends = $36,194
And the addition to retained earnings will be:
The new total debt will be:
New total debt = .75197($360,629)
New total debt = $271,181
CHAPTER 3 – 5
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:
MOOSE TOURS INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 28,122 Accounts payable $ 75,582
Accounts receivable 45,239 Notes payable 14,535
Inventory 96,590 Total $ 90,117
So the excess debt raised is:
Excess debt = $631,809 – 629,006
Excess debt = $2,803
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 total debt will be:
CHAPTER 3 – 6
New total debt = .75197($364,075)
New total debt = $273,772
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 = .75197:
MOOSE TOURS INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 29,203 Accounts payable $ 78,489
Accounts receivable 46,979 Notes payable 14,535
Inventory 100,305 Total $ 93,024
So the excess debt raised is:
At a 35 percent growth rate, the firm will need funds in the amount of $15,351 in addition to the
external debt already raised. So, the EFN will be:
26. We need the ROE to calculate the sustainable growth rate. The ROE is:
ROE = (Profit margin)(Total asset turnover)(Equity multiplier)
ROE = (.041)(1 / .75)(1 + .35)
ROE = .0738, or 7.38%
Now, we can use the sustainable growth rate equation to find the retention ratio as:
Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]
CHAPTER 3 – 7
This is a dividend payout ratio of negative 45 percent, which is impossible. The growth rate is not
consistent with the other constraints. The lowest possible payout rate is 0, which corresponds to a
retention ratio of 1, or total earnings retention.
The maximum sustainable growth rate for this company is:
27. 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
Substituting the last three equations into the EFN equation we started with and rearranging, we get:
28. We start with the EFN equation we derived in Problem 27 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:
CHAPTER 3 – 8
Since:
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:
EFN = (D/E)[PM(S)b(1 + g)]
EFN = A(g) – PM(S)b(1 + g)
Solving for g and then dividing both the numerator and denominator by A:
29. 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 denominator is equal to beginning of period equity, that is:
(TEE – NI × b) = TEB
Substituting this into the previous equation, we get:
CHAPTER 3 – 9
The sustainable growth rate equation is:
Sustainable growth rate = ROEB × b
For the internal growth rate:
Recognize that the denominator is equal to beginning of period assets, that is:
(TAE – NI × b) = TAB
Substituting this into the previous equation, we get:
Internal growth rate = (NI × b) / TAB
Which is equivalent to:
30. Since the company issued no new equity, shareholders’ equity increased by retained earnings.
Retained earnings for the year were:
So, the equity at the end of the year was:
The ROE based on the end of period equity is:
CHAPTER 3 – 10
The plowback ratio is:
Plowback ratio = Addition to retained earnings/NI
Using the equation presented in the text for the sustainable growth rate, we get:
Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]
Sustainable growth rate = [.2747(.5733)] / [1 – .2747(.5733)]
Sustainable growth rate = .1870, or 18.70%
The ROE based on the beginning of period equity is
Using the shortened equation for the sustainable growth rate and the end of period ROE, we get:
Sustainable growth rate = ROE × b
Using the end of period ROE in the shortened sustainable growth rate results in a growth rate that is
too low. This will always occur whenever the equity increases. If equity increases, the ROE based on