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CHAPTER 3 B - 1
24. The pro forma income statements for all three growth rates will be:
RETRO MACHINE INC.
Pro Forma Income Statement
15 % Sales
Growth
20% Sales
Growth
25% Sales
Growth
Sales
$683,790
$713,520
$743,250
Costs
532,105
555,240
578,375
Other expenses
14,030
14,640
15,250
EBIT
$137,655
$143,640
$149,625
Interest
8,960
8,960
8,960
Taxable income
$128,695
$134,680
$140,665
Taxes (35%)
45,043
47,138
49,233
Net income
$ 83,652
$ 87,542
$ 91,432
Dividends
$33,460
$35,016
$36,572
Add to RE
50,192
52,526
54,860
We will calculate the EFN for the 15 percent growth rate first. Assuming the payout ratio is constant,
the dividends paid will be:
Dividends = ($28,792/$71,981)($83,652)
Dividends = $33,460
And the addition to retained earnings will be:
Addition to retained earnings = $83,652 – 33,460
15% Sales Growth:
RETRO MACHINE INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 19,631 Accounts payable $ 52,785
Accounts receivable 28,244 Notes payable 11,480
equipment 320,597 Common stock and
paid-in surplus $ 95,000
Retained earnings 170,782
Total $ 265,872
Total liabilities and owners’
Total assets $ 435,919 equity $ 436,137
So the EFN is:
EFN = Total assets – Total liabilities and equity
The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times net
income, or:
Dividends = ($28,792/$71,981)($87,542)
Dividends = $35,016
And the addition to retained earnings will be:
Addition to retained earnings = $87,542 – 35,016
Addition to retained earnings = $52,526
The new retained earnings on the pro forma balance sheet will be:
New retained earnings = $120,680 + 52,526
20% sales growth:
RETRO MACHINE INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 20,484 Accounts payable $ 55,080
Accounts receivable 29,472 Notes payable 11,480
Inventory 70,380 Total $ 66,560
paid-in surplus $ 95,000
Retained earnings 173,206
Total $ 268,206
Total liabilities and owners’
CHAPTER 3 B - 3
Total assets $ 454,872 equity $ 440,766
So the EFN is:
EFN = Total assets – Total liabilities and equity
Dividends = ($28,792/$71,981)($94,432)
Dividends = $36,572
And the addition to retained earnings will be:
Addition to retained earnings = $91,432 – 36,572
Addition to retained earnings = $54,860
The new retained earnings on the pro forma balance sheet will be:
New retained earnings = $164,810 + 79,989
New retained earnings = $244,799
The pro forma balance sheet will look like this:
25% Sales Growth:
RETRO MACHIINE INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 21,338 Accounts payable $ 57,375
Accounts receivable 30,700 Notes payable 11,480
Inventory 73,313 Total $ 68,855
Total $ 125,350 Long-term debt $ 106,000
Fixed assets
Net plant and Owners’ equity
equipment 348,475 Common stock and
paid-in surplus $ 95,000
Retained earnings 175,540
Total $ 270,540
Total liabilities and owners’
Total assets $ 636,638 equity $ 445,395
So the EFN is:
CHAPTER 3 B - 4
25. The pro forma income statements for all three growth rates will be:
RETRO MACHINE INC.
Pro Forma Income Statement
20% Sales
Growth
30% Sales
Growth
35% Sales
Growth
Sales
$713,520
$772,980
$1,003,320
Costs
555,240
601,510
780,840
Other expenses
14,640
15,860
20,520
EBIT
$143,640
$155,610
$201,960
Interest
8,960
8,960
11,200
Taxable income
$134,680
$146,650
$190,760
Taxes (35%)
47,138
51,328
66,766
Net income
$87,542
$95,323
$123,994
Dividends
$35,016
$38,128
$37,198
Add to RE
52,526
57,194
86,796
Pro Forma Balance Sheet
CHAPTER 3 B - 5
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 22,191 Accounts payable $ 59,760
Accounts receivable 31,928 Notes payable 11,480
Inventory 76,245 Total $ 71,150
Total $ 130,364 Long-term debt 135,555
Fixed assets
Net plant and Owners’ equity
equipment 362,414 Common stock and
paid-in surplus $ 95,000
Retained earnings 177,874
Total $ 272,874
Total liabilities and owners’
Total assets $ 492,778 equity $ 479,579
So the excess debt raised is:
Excess debt = $479,579 – 492,778
Excess debt = –$13,199
At a 30 percent growth rate, the firm will need funds in the amount of $13,199 in addition to the
external debt already raised. So, the EFN will be:
RETRO MACHIINE INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 23,045 Accounts payable $ 61,695
Accounts receivable 33,156 Notes payable 11,480
Inventory 79,178 Total $ 73,445
Total $ 135,378 Long-term debt $ 135,028
Fixed assets
Net plant and Owners’ equity
equipment 376,353 Common stock and
paid-in surplus $ 95,000
Retained earnings 180,208
Total $ 275,208
Total liabilities and owners’
Total assets $ 511,731 equity $ 483,681
So the excess debt raised is:
Excess debt = $483,681 – 511,731
Excess debt = –$28,050
ROE = (PM)(TAT)(EM)
ROE = (.072)(1/2.25)(1 + .40)
ROE = .0448, or 4.48%
Now, we can use the sustainable growth rate equation to find the retention ratio as:
Sustainable growth rate = (ROE × b)/[1 – (ROE × b)]
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:
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]
Since:
ROA = NI/A
Internal growth rate = {[PM(S)b]/A}/{[A – PM(S)b]/A}
For the sustainable growth rate:
Sustainable growth rate = (ROEE × b)/(1 – ROEE × b)
Sustainable growth rate = (NI/TEE × b)/(1 – NI/TEE × b)
We multiply this equation by:
(TEE/TEE)
Sustainable growth rate = (NI/TEE × b)/(1 – NI/TEE × b) × (TEE/TEE)
Sustainable growth rate = (NI × b)/(TEE – NI × b)
Recognize that the denominator is equal to beginning of period equity, that is:
(TEE – NI × b) = TEB
CHAPTER 3 B - 9
We multiply this equation by:
(TAE/TAE)
Internal growth rate = (NI/TAE × b)/(1 – NI/TAE × b) × (TAE/TAE)
Internal growth rate = (NI × b)/(TAE – NI × b)
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:
Retained earnings = NI – Dividends
Retained earnings = $75,000 – 32,000
Retained earnings = $43,000
So, the equity at the end of the year was:
Ending equity = $265,000 + 43,000
Ending equity = $308,000
The ROE based on the end of period equity is:
ROE = $75,000/$308,000
CHAPTER 3 B - 10
Sustainable growth rate = (ROE × b)/[1 – (ROE × b)]
Sustainable growth rate = [.2435(.5733)]/[1 – .2435(.5733)]
Sustainable growth rate = .1623, or 16.23%
The ROE based on the beginning of period equity is:
ROE = $75,000/$265,000
ROE = .2830, or 28.30%
Using the shortened equation for the sustainable growth rate and the beginning of period ROE, we get:
Sustainable growth rate = ROE × b
