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CHAPTER 3
LONG-TERM FINANCIAL PLANNING
AND GROWTH
Answers to Concepts Review and Critical Thinking Questions
1. Time trend analysis gives a picture of changes in the company’s financial situation over time.
Comparing a firm to itself over time allows the financial manager to evaluate whether some aspects
of the firm’s operations, finances, or investment activities have changed. Peer group analysis
involves comparing the financial ratios and operating performance of a particular firm to a set of
peer group firms in the same industry or line of business. Comparing a firm to its peers allows the
financial manager to evaluate whether some aspects of the firm’s operations, finances, or investment
2. If a company is growing by opening new stores, then presumably total revenues would be rising.
3. The reason is that, ultimately, sales are the driving force behind a business. A firm’s assets,
employees, and, in fact, just about every aspect of its operations and financing exist to directly or
4. Two assumptions of the sustainable growth formula are that the company does not want to sell new
equity, and that financial policy is fixed. If the company raises outside equity, or increases its debt–
5. The sustainable growth rate is greater than 20 percent, because at a 20 percent growth rate the
negative EFN indicates that there is excess financing still available. If the firm is 100 percent equity
financed, then the sustainable and internal growth rates are equal and the internal growth rate would
be greater than 20 percent. However, when the firm has some debt, the internal growth rate is always
less than the sustainable growth rate, so it is ambiguous whether the internal growth rate would be
6. Common-size financial statements provide the financial manager with a ratio analysis of the
company. The common-size income statement can show, for example, that cost of goods sold as a
7. It would reduce the external funds needed. If the company is not operating at full capacity, it would
8. ROE is a better measure of the company’s performance. ROE shows the percentage return for the
9. The EBITD/Assets ratio shows the company’s operating performance before interest, taxes, and
depreciation. This ratio would show how a company has controlled costs. While taxes are a cost, and
depreciation and amortization can be considered costs, they are not as easily controlled by company
10. Long-term liabilities and equity are investments made by investors in the company, either in the
form of a loan or ownership. Return on investment is intended to measure the return the company
earned from these investments. Return on investment will be higher than the return on assets for a
11. Presumably not, but, of course, if the product had been much less popular, then a similar fate would
12. Since customers did not pay until shipment, receivables rose. The firm’s NWC, but not its cash,
increased. At the same time, costs were rising faster than cash revenues, so operating cash flow
13. Financing possibly could have been arranged if the company had taken quick enough action.
14. All three were important, but the lack of cash or, more generally, financial resources, ultimately
15. Demanding cash up front, increasing prices, subcontracting production, and improving financial
Solutions to Questions and Problems
NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Basic
1. Using the DuPont identity, the ROE is:
ROE = (Profit margin)(Total asset turnover)(Equity multiplier)
2. The equity multiplier is:
One formula to calculate return on equity is:
ROE = (ROA)(Equity multiplier )
ROE can also be calculated as:
ROE = Net income / Total equity
So, net income is:
3. This is a multi-step problem involving several ratios. The ratios given are all part of the DuPont
Identity. The only DuPont Identity ratio not given is the profit margin. If we know the profit margin,
we can find the net income since sales are given. So, we begin with the DuPont Identity:
ROE = .15 = (Profit margin)(Total asset turnover)(Equity multiplier)
Now that we have the profit margin, we can use this number and the given sales figure to solve for
net income:
4. An increase of sales to $45,426 is an increase of:
Sales increase = ($45,426 – 40,200) / $40,200
Sales increase = .1300, or 13.00%
Assuming costs and assets increase proportionally, the pro forma financial statements will look like
this:
Pro forma income statement Pro forma balance sheet
The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times
net income, or:
The addition to retained earnings is:
And the new equity balance is:
Equity = $106,000 + 5,665.82
5. The maximum percentage sales increase without issuing new equity is the sustainable growth rate.
To calculate the sustainable growth rate, we first need to calculate the ROE, which is:
ROE = NI / TE
ROE = $14,190 / $83,000
ROE = .1710
The plowback ratio, b, is one minus the payout ratio, so:
Now we can use the sustainable growth rate equation to get:
So, the maximum dollar increase in sales is:
6. We need to calculate the retention ratio to calculate the sustainable growth rate. The retention ratio
is:
b = 1 – .15
b = .85
Now we can use the sustainable growth rate equation to get:
7. We must first calculate the ROE using the DuPont ratio to calculate the sustainable growth rate. The
ROE is:
ROE = (PM)(TAT)(EM)
ROE = (.059)(2.85)(1.70)
ROE = .2859, or 28.59%
The plowback ratio is one minus the dividend payout ratio, so:
8. An increase of sales to $9,006 is an increase of:
Sales increase = ($9,006 – 7,900) / $7,900
Sales increase = .14, or 14%
Assuming costs and assets increase proportionally, the pro forma financial statements will look like
this:
Pro forma income statement Pro forma balance sheet
If no dividends are paid, the equity account will increase by the net income, so:
9. a. First, we need to calculate the current sales and change in sales. The current sales are next
year’s sales divided by one plus the growth rate, so:
Current sales = Next year’s sales / (1 + g)
We can now complete the current balance sheet. The current assets, fixed assets, and short-term
debt are calculated as a percentage of current sales. The long-term debt and par value of stock
are given. The plug variable is the additions to retained earnings. So:
Assets Liabilities and equity
Current assets $65,454,545 Short-term debt $49,090,909
b. We can use the equation from the text to answer this question. The assets/sales and debt/sales
are the percentages given in the problem, so:
EFN =
(
Assets
Sales
)
× ΔSales –
(
Debt
Sales
)
× ΔSales – (PM × Projected sales) × (1 – d)
EFN = (.20 + .75) × $32,727,273 – (.15 × $32,727,273) – [(.09 × $360,000,000) × (1 – .30)]
EFN = $3,501,818
c. The current assets, fixed assets, and short-term debt will all increase at the same percentage as
sales. The long-term debt and common stock will remain constant. The accumulated retained
earnings will increase by the addition to retained earnings for the year. We can calculate the
addition to retained earnings for the year as:
Net income = Profit margin × Sales
The addition to retained earnings for the year will be the net income times one minus the
dividend payout ratio, which is:
So, the new accumulated retained earnings will be:
The pro forma balance sheet will be:
Assets Liabilities and equity
Current assets $72,000,000 Short-term debt $54,000,000
Long-term debt $105,000,000
The EFN is:
EFN = Total assets – Total liabilities and equity
10. a. The sustainable growth is:
Sustainable growth rate =
ROE ×b
1 - ROE ×b
where:
b = Retention ratio = 1 – Payout ratio = .75
So:
.114 ×. 75
1 – . 114 ×.75
b. It is possible for the sustainable growth rate and the actual growth rate to differ. If any of the
actual parameters in the sustainable growth rate equation differs from those used to compute
the sustainable growth rate, the actual growth rate will differ from the sustainable growth rate.
c. The company can increase its growth rate by doing any of the following:
- Increase the debt-to-equity ratio by selling more debt or repurchasing stock.
Intermediate
11. The solution requires substituting two ratios into a third ratio. Rearranging D/TA:
Firm A Firm B
D / TA = .25 D / TA = .40
(TA – E) / TA = .25 (TA – E) / TA = .40
Rearranging ROA, we find:
NI / TA = .08 NI / TA = .07
NI = .08(TA) NI = .07(TA)
12. Profit margin = Net income / Sales
Profit margin = –£26,832 / £294,813
Profit margin = –.0910, or 9.10%
As long as both net income and sales are measured in the same currency, there is no problem; in fact,
except for some market value ratios like EPS and BVPS, none of the financial ratios discussed in the
13. a. The equation for external funds needed is:
EFN =
(
Assets
Sales
)
× ΔSales –
(
Debt
Sales
)
× ΔSales – (PM × Projected sales) × (1 – d)
where:
Assets / Sales = $24,800,000 / $25,380,000 = .98
ΔSales = Current sales × Sales growth rate = $25,380,000(.15) = $3,807,000
so:
b. The current assets, fixed assets, and short-term debt will all increase at the same percentage as
sales. The long-term debt and common stock will remain constant. The accumulated retained
earnings will increase by the addition to retained earnings for the year. We can calculate the
addition to retained earnings for the year as:
Net income = Profit margin × Sales
The addition to retained earnings for the year will be the net income times one minus the
dividend payout ratio, which is:
Addition to retained earnings = Net income(1 – d)
So, the new accumulated retained earnings will be:
Accumulated retained earnings = $12,079,633
The pro forma balance sheet will be:
Assets Liabilities and equity
Current assets $8,280,000 Short-term debt $5,980,000
Long-term debt $6,000,000
The EFN is:
EFN = Total assets – Total liabilities and equity
c. The sustainable growth is:
Sustainable growth rate =
ROE ×b
1 - ROE ×b
where:
d. The company cannot just cut its dividends to achieve the forecast growth rate. As shown below,
even with a zero dividend policy, the EFN will still be $355,950.
Assets Liabilities and equity
Current assets $8,280,000 Short-term debt $5,980,000
Long-term debt $6,000,000
The company does have several alternatives. It can increase its asset utilization and/or its profit
margin. The company could also increase the debt in its capital structure. This will decrease the
equity account, thereby increasing ROE.
