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14. We first must calculate the ROE to calculate the sustainable growth rate. To do this we must realize
two other relationships. The total asset turnover is the inverse of the capital intensity ratio, and the
equity multiplier is 1 + D/E. Using these relationships, we get:
ROE = (PM)(TAT)(EM)
The plowback ratio is one minus the dividend payout ratio, so:
Now we can use the sustainable growth rate equation to get:
Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]
15. We must first calculate the ROE using the DuPont ratio to calculate the sustainable growth rate. The
ROE is:
ROE = (PM)(TAT)(EM)
The plowback ratio is one minus the dividend payout ratio, so:
Now we can use the sustainable growth rate equation to get:
Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]
Intermediate
16. To determine full capacity sales, we divide the current sales by the capacity the company is currently
using, so:
The maximum sales growth is the full capacity sales divided by the current sales, so:
CHAPTER 27 - 2
17. To find the new level of fixed assets, we need to find the current percentage of fixed assets to full
capacity sales. Doing so, we find:
Next, we calculate the total dollar amount of fixed assets needed at the new sales figure.
The new fixed assets necessary is the total fixed assets at the new sales figure minus the current level
of fixed assts.
18. We have all the variables to calculate ROE using the DuPont identity except the profit margin. If we
find ROE, we can solve the DuPont identity for profit margin. We can calculate ROE from the
sustainable growth rate equation. For this equation we need the retention ratio, so:
Using the sustainable growth rate equation and solving for ROE, we get:
Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]
Now we can use the DuPont identity to find the profit margin as:
ROE = PM(TAT)(EM)
19. We are given the profit margin. Remember that:
ROA = PM(TAT)
We can calculate the ROA from the internal growth rate formula, and then use the ROA in this
equation to find the total asset turnover. The retention ratio is:
CHAPTER 27 - 3
Using the internal growth rate equation to find the ROA, we get:
Internal growth rate = (ROA × b) / [1 – (ROA × b)]
Plugging ROA and PM into the equation we began with and solving for TAT, we get:
ROA = (PM)(TAT)
20. We should begin by calculating the D/E ratio. We calculate the D/E ratio as follows:
Inverting both sides we get:
Next, we need to recognize that
TA / TD = 1 + TE / TD
Substituting this into the previous equation, we get:
Subtract 1 (one) from both sides and inverting again, we get:
With the D/E ratio, we can calculate the EM and solve for ROE using the DuPont identity:
ROE = (PM)(TAT)(EM)
Now we can calculate the retention ratio as:
Finally, putting all the numbers we have calculated into the sustainable growth rate equation, we get:
Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]
CHAPTER 27 - 4
21. To calculate the sustainable growth rate, we first must calculate the retention ratio and ROE. The
retention ratio is:
And the ROE is:
So, the sustainable growth rate is:
Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]
If the company grows at the sustainable growth rate, the new level of total assets is:
To find the new level of debt in the company’s balance sheet, we take the percentage of debt in the
capital structure times the new level of total assets. The additional borrowing will be the new level of
debt minus the current level of debt. So:
New TD = [D / (D + E)](TA)
And the additional borrowing will be:
The growth rate that can be supported with no outside financing is the internal growth rate. To
calculate the internal growth rate, we first need the ROA, which is:
This means the internal growth rate is:
Internal growth rate = (ROA × b) / [1 – (ROA × b)]
CHAPTER 27 - 5
22. Since the company issued no new equity, shareholders’ equity increased by retained earnings.
Retained earnings for the year were:
Retained earnings = NI – Dividends
So, the equity at the end of the year was:
The ROE based on the end of period equity is:
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)]
The ROE based on the beginning of period equity is
Using the shortened equation for the sustainable growth rate and the beginning of period ROE, we
get:
Sustainable growth rate = ROE × b
Using the shortened equation for the sustainable growth rate and the end of period ROE, we get:
Sustainable growth rate = ROE × b
CHAPTER 27 - 6
Using the end of period ROE in the shortened sustainable growth rate equation results in a growth
23. The ROA using end of period assets is:
The beginning of period assets had to have been the ending assets minus the addition to retained
earnings, so:
Beginning assets = Ending assets – Addition to retained earnings
And the ROA using beginning of period assets is:
Using the internal growth rate equation presented in the text, we get:
Internal growth rate = (ROA × b) / [1 – (ROA × b)]
Using the formula ROA × b, and beginning of period assets:
Using the formula ROA × b, and end of period assets:
Using the end of period ROA in the shortened internal growth rate equation results in a growth rate
CHAPTER 27 - 7
24. Assuming costs vary with sales and a 20 percent increase in sales, the pro forma income statement
will look like this:
FLEURY INC.
Pro Forma Income Statement
Sales $ 1,069,920
Costs 832,320
The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times
net income, or:
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:
FLEURY INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 29,136 Accounts payable $ 78,240
Accounts receivable 44,484 Notes payable 16,320
CHAPTER 27 - 8
So the EFN is:
EFN = Total assets – Total liabilities and equity
25. First, we need to calculate full capacity sales, which is:
The full capacity ratio at full capacity sales is:
Full capacity ratio = Fixed assets / Full capacity sales
The fixed assets required at the projected sales figure is the full capacity ratio times the projected
sales level:
So, EFN is:
Note that this solution assumes that fixed assets are decreased (sold) so the company has a 100
percent fixed asset utilization. If we assume fixed assets are not sold, the answer becomes:
26. The D/E ratio of the company is:
So the new total debt amount will be:
This is the new total debt for the company. Given that our calculation for EFN is the amount that
CHAPTER 27 - 9
This means that $13,040 of the new total debt is not raised externally. So, the debt raised externally,
which will be the EFN is:
EFN = New total debt – (Beginning LTD + Beginning CL + Spontaneous increase in AP)
The pro forma balance sheet with the new long-term debt will be:
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
The funds raised by the debt issue can be put into an excess cash account to make the balance sheet
balance. The excess debt will be:
To make the balance sheet balance, the company will have to increase its assets. We will put this
amount in an account called excess cash, which will give us the following balance sheet:
CHAPTER 27 - 10
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
equipment 475,800 Common stock and
paid-in surplus $ 130,000
The excess cash has an opportunity cost that we discussed earlier. Increasing fixed assets would also
not be a good idea since the company already has enough fixed assets. A likely scenario would be the
repurchase of debt and equity in its current capital structure weights. The company’s debt-assets and
equity-assets are:
So, the amount of debt and equity needed will be:
So, the repurchases of debt and equity will be:
Assuming all of the debt repurchase is from long-term debt, and the equity repurchase is entirely
from the retained earnings, the final pro forma balance sheet will be:
CHAPTER 27 - 11
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
Challenge
