Solutions to Questions and Problems
6. We need to calculate the retention ratio to calculate the sustainable growth rate. The retention ratio is:
b = 1 – .30 b = .70
Now we can use the sustainable growth rate equation to get:
Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]
Sustainable growth rate = [.18(.70)] / [1 – .18(.70)]
Sustainable growth rate = .1442 or 14.42%
7. We must first calculate the ROE using the Du Pont ratio to calculate the sustainable growth rate. The ROE is:
ROE = (PM)(TAT)(EM) ROE = (.076)(1.40)(1.50) ROE = 15.96%
The plowback ratio is one minus the dividend payout ratio, so:
b = 1 – .25 b = .75
Now, we can use the sustainable growth rate equation to get:
Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]
Sustainable growth rate = [.1596(.75)] / [1 – .1596(.75)]
Sustainable growth rate = 13.60%
8. An increase of sales to $5,192 is an increase of:
Sales increase = ($5,192 – 4,400) / $4,400 Sales increase = .18 or 18%
Assuming costs and assets increase proportionally, the pro forma financial statements will look like this:
Pro forma income statement Pro forma balance sheet
Sales $ 5,192 Assets $ 15,812 Debt $ 9,100
Costs 3,168 Equity 6,324
Net income $ 2,024 Total $ 15,812 Total $ 15,424
If no dividends are paid, the equity account will increase by the net income, so:
Equity = $4,300 + 2,024 Equity = $6,324
So the EFN is:
EFN = Total assets – Total liabilities and equity EFN = $15,812 – 15,424 = $388
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) Current sales = ¥440,000,000 / (1 + .10) Current sales = ¥400,000,000
And the change in sales is:
Change in sales = ¥440,000,000 – 400,000,000 Change in sales = ¥40,000,000
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 ¥80,000,000 Short-term debt ¥60,000,000
Long-term debt ¥145,000,000
Fixed assets 560,000,000 Common stock ¥60,000,000
Accumulated retained earnings 375,000,000
Total equity ¥435,000,000
Total assets ¥640,000,000 Total liabilities and equity ¥640,000,000
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 =
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 Net income = .12(¥440,000,000) Net income = ¥52,800,000
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) Addition to retained earnings = ¥52,800,000(1 – .40) Addition to retained earnings = ¥31,680,000
So, the new accumulated retained earnings will be:
Accumulated retained earnings = ¥375,000,000 + 31,680,000 Accumulated retained earnings = ¥406,680,000
The pro forma balance sheet will be:
Assets Liabilities and equity
Current assets ¥88,000,000 Short-term debt ¥66,000,000
Long-term debt ¥145,000,000
Total assets ¥704,000,000 Total liabilities and equity ¥677,680,000 The EFN is:
EFN = Total assets – Total liabilities and equity EFN = ¥704,000,000 – 677,680,000
EFN = ¥26,320,000
10. a. The sustainable growth is:
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.
Since the sustainable growth rate includes ROE in the calculation, this also implies that changes in the profit margin, total asset turnover, or equity multiplier will affect 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 - Increase the profit margin, most likely by better controlling costs.
- Decrease its total assets/sales ratio; in other words, utilize its assets more efficiently.
- Reduce the dividend payout ratio.
Intermediate
11. The solution requires substituting two ratios into a third ratio. Rearranging D/TA:
Firm A Firm B
Since ROE = NI / E, we can substitute the above equations into the ROE formula, which yields:
ROE = .20(TA) / .40(TA) = .20 / .40 = 50% ROE = .30(TA) / .60 (TA) = .30 / .60 = 50%
12. PM = NI / S = –£13,156 / £147,318 = –8.93%
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 text are measured in terms of currency. This is one reason why financial ratio analysis is widely used in international finance to compare the business operations of firms and/or divisions across national economic borders. The net income in dollars is:
NI = PM × Sales
NI = –0.0893($267,661) = –$23,903
13. a. The equation for external funds needed is:
EFN =
Assets/Sales = ¥31,000,000/¥38,000,000 = 0.82
∆Sales = Current sales × Sales growth rate = ¥38,000,000(.20) = ¥7,600,000 Debt/Sales = ¥8,000,000/¥38,000,000 = .2105
p = Net income/Sales = ¥2,990,000/¥38,000,000 = .0787
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 Net income = .0787(¥45,600,000) Net income = ¥3,588,000
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) Addition to retained earnings = ¥3,588,000(1 – .40) Addition to retained earnings = ¥2,152,800
So, the new accumulated retained earnings will be:
Accumulated retained earnings = ¥13,000,000 + 2,152,800 Accumulated retained earnings = ¥15,152,800
The pro forma balance sheet will be:
Assets Liabilities and equity
Total assets ¥37,200,000 Total liabilities and equity ¥34,752,800 The EFN is:
EFN = Total assets – Total liabilities and equity EFN = ¥37,200,000 – 34,752,800
EFN = ¥2,447,200
c. The sustainable growth is:
Sustainable growth rate =
ROE = Net income/Total equity = ¥2,990,000/¥17,000,000 = .1759
b = Retention ratio = Retained earnings/Net income = ¥1,794,000/¥2,990,000 = .60 So:
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 ¥1,012,000.
Assets Liabilities and equity
Current assets ¥10,800,000 Short-term debt ¥9,600,000
Long-term debt ¥6,000,000
Fixed assets 26,400,000 Common stock ¥4,000,000
Accumulated retained earnings 16,588,000
Total equity ¥20,588,000
Total assets ¥37,200,000 Total liabilities and equity ¥36,188,000 The EFN is:
EFN = Total assets – Total liabilities and equity EFN = ¥37,200,000 – 36,188,000
EFN = ¥1,012,000
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.
14. This is a multi-step problem involving several ratios. It is often easier to look backward to determine where to start. We need receivables turnover to find days’ sales in receivables. To calculate receivables turnover, we need credit sales, and to find credit sales, we need total sales. Since we are given the profit margin and net income, we can use these to calculate total sales as:
PM = 0.086 = NI / Sales = NZ$173,000 / Sales; Sales = NZ$2,011,628 Credit sales are 70 percent of total sales, so:
Credit sales = NZ$2,011,628(0.70) = NZ$1,408,140 Now we can find receivables turnover by:
Receivables turnover = Sales / Accounts receivable = NZ$1,408,140 / NZ$143,200 = 9.83 times Days’ sales in receivables = 365 days / Receivables turnover = 365 / 9.833 = 37.12 days
15. The solution to this problem requires a number of steps. First, remember that CA + NFA = TA. So, if we find the CA and the TA, we can solve for NFA. Using the numbers given for the current ratio and the current liabilities, we solve for CA:
CR = CA / CL
CA = CR(CL) = 1.20(Rs.850,000) = Rs.1,020,000
To find the total assets, we must first find the total debt and equity from the information given. So, we find the sales using the profit margin:
PM = NI / Sales
NI = Profit margin × Sales = .095(Rs.4,310,000) = Rs.409,450
We now use the sales figure as an input into ROE to find the total equity:
ROE = NI / TE
TE = NI / ROE = Rs.409.45 / .215 = Rs.1,904,420
Next, we need to find the long-term debt. The long-term debt ratio is:
Long-term debt ratio = 0.70 = LTD / (LTD + TE) Inverting both sides gives:
1 / 0.70 = (LTD + TE) / LTD = 1 + (TE / LTD)
Substituting the total equity into the equation and solving for long-term debt gives the following:
1 + Rs.1,904,420 / LTD = 1.429
LTD = Rs.1,904,420 / .429 = Rs.4,443,640 Now, we can find the total debt of the company:
TD = CL + LTD = Rs.850,000 + 4,443,640 = Rs.5,293,640
And, with the total debt, we can find the TD&E, which is equal to TA:
TA = TD + TE = Rs.5,293,640 + 1,904,420 = Rs.7,198,060 And finally, we are ready to solve the balance sheet identity as:
NFA = TA – CA = Rs.7,198,060 – 1,020,000 = Rs.6,178,060
16. This problem requires you to work backward through the income statement. First, recognize that Net income = (1 – tC)EBT. Plugging in the numbers given and solving for EBT, we get:
EBT = $7,850 / 0.66 = $11,893.94
Now, we can add interest to EBIT to get EBIT as follows:
EBIT = EBT + Interest paid = $11,893.94 + 2,108 = $14,001.94
To get EBITD (earnings before interest, taxes, and depreciation), the numerator in the cash coverage ratio, add depreciation to EBIT:
EBITD = EBIT + Depreciation = $14,001.94 + 1,687 = $15,688.94 Now, simply plug the numbers into the cash coverage ratio and calculate:
Cash coverage ratio = EBITD / Interest = $15,688.94 / $2,108 = 7.44 times
17. The only ratio given which includes cost of goods sold is the inventory turnover ratio, so it is the last ratio used. Since current liabilities are given, we start with the current ratio:
Current ratio = 3.3 = CA / CL = CA / €340,000 CA = €1,122,000
Using the quick ratio, we solve for inventory:
Quick ratio = 1.8 = (CA – Inventory) / CL = (€1,122,000 – Inventory) / €340,000 Inventory = CA – (Quick ratio × CL)
Inventory = €1,122,000 – (1.8 × €340,000) Inventory = €510,000
Inventory turnover = 4.2 = COGS / Inventory = COGS / €510,000 COGS = €2,142,000
The common-size balance sheet answers are found by dividing each category by total assets. For example, the cash percentage for 2005 is:
£10,168 / £400,802 = .0254 or 2.54%
This means that cash is 2.54% of total assets.
The common-base year answers are found by dividing each category value for 2006 by the same category value for 2005. For example, the cash common-base year number is found by:
£10,683 / £10,168 = 1.0506
19. To determine full capacity sales, we divide the current sales by the capacity the company is currently