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Sustainable Growth Rate - Corporate Finance

  1. A firm has a net profit margin of 8%, asset turnover of 1.5, and a debt-to-equity ratio of 0.5. Its dividend payout ratio is 40%. The firm plans to change its capital structure by increasing its debt-to-equity ratio to 1.0. Assuming profitability and asset turnover remain unchanged, what will be the new sustainable growth rate?
    Answer: 14.4% This problem uses the DuPont framework to see how a change in leverage affects SGR. 1. Calculate the retention ratio (b), which is constant: b=1−0.40=0.60b = 1 - 0.40 = 0.60. 2. Find the old Equity Multiplier (EM): EMold=1+D/E=1+0.5=1.5EM_{old} = 1 + D/E = 1 + 0.5 = 1.5. 3. Find the new Equity Multiplier: EMnew=1+D/E=1+1.0=2.0EM_{new} = 1 + D/E = 1 + 1.0 = 2.0. 4. Calculate the new ROE using the DuPont identity: ROEnew=Profit Margin×Asset Turnover×EMnew=8%×1.5×2.0=24%ROE_{new} = \text{Profit Margin} \times \text{Asset Turnover} \times EM_{new} = 8\% \times 1.5 \times 2.0 = 24\%. 5. Calculate the new SGR: SGRnew=ROEnew×b=24%×0.60=14.4%SGR_{new} = ROE_{new} \times b = 24\% \times 0.60 = 14.4\%.
  2. Two companies, Firm A and Firm B, have the same return on assets (ROA) of 10% and the same dividend payout ratio of 30%. Firm A has a debt-to-assets ratio of 0.2, while Firm B has a debt-to-assets ratio of 0.5. Which of the following statements is most accurate regarding their sustainable growth rates (SGR)?
    Answer: Firm B has a higher SGR than Firm A. SGR depends on ROE, not ROA. We must convert ROA to ROE using the equity multiplier (EM = Assets/Equity). EM can be found from the debt-to-assets ratio (D/A) as EM=1/(1−D/A)EM = 1 / (1 - D/A). 1. Both firms have a retention ratio b=1−0.30=0.70b = 1 - 0.30 = 0.70. 2. For Firm A: EMA=1/(1−0.2)=1.25EM_A = 1 / (1 - 0.2) = 1.25. ROEA=ROA×EMA=10%×1.25=12.5%ROE_A = ROA \times EM_A = 10\% \times 1.25 = 12.5\%. SGRA=12.5%×0.70=8.75%SGR_A = 12.5\% \times 0.70 = 8.75\%. 3. For Firm B: EMB=1/(1−0.5)=2.0EM_B = 1 / (1 - 0.5) = 2.0. ROEB=ROA×EMB=10%×2.0=20%ROE_B = ROA \times EM_B = 10\% \times 2.0 = 20\%. SGRB=20%×0.70=14.0%SGR_B = 20\% \times 0.70 = 14.0\%. Since Firm B has higher leverage, it has a higher ROE and therefore a higher SGR.
  3. A firm reports net income of $100 million. Its balance sheet shows total common equity of $500 million and preferred stock of $100 million. The firm paid $8 million in preferred dividends and $36.8 million in common dividends during the year. What is its sustainable growth rate?
    Answer: 11.04% SGR should be calculated based on the returns and retention available to common shareholders. 1. Calculate Earnings Available to Common: Net Income - Preferred Dividends = $100M - $8M = $92M. 2. Calculate Return on Common Equity (ROCE): Earnings Available to Common / Common Equity = $92M / $500M = 18.4%. 3. Calculate Retention Ratio (b) for common shareholders: b = (Earnings Available to Common - Common Dividends) / Earnings Available to Common = ($92M - $36.8M) / $92M = $55.2M / $92M = 0.60. 4. Calculate SGR: SGR = ROCE × b = 18.4% × 0.60 = 11.04%.
  4. A stable, mature company adheres to a policy of paying out 40% of its earnings as dividends and maintains a constant debt-to-equity ratio. The company's return on equity (ROE) is consistently 15%. Assuming these policies continue, what is the expected long-term growth rate of its dividends per share?
    Answer: 9.0% For a firm with a constant dividend payout ratio, the growth rate of dividends per share will be equal to the growth rate of earnings per share. The sustainable growth rate (SGR) represents the rate at which earnings can grow while maintaining constant financial policies (profitability, dividend policy, and leverage). Therefore, the expected long-term dividend growth rate is the SGR. 1. Retention ratio (b) = 1 - 0.40 = 0.60. 2. SGR = ROE × b = 15% × 0.60 = 9.0%.
  5. An analyst is comparing two firms in the same industry. Firm A has an SGR of 12% with ROE of 20% and retention ratio of 60%. Firm B has an SGR of 12% with ROE of 16% and retention ratio of 75%. If both firms want to reduce their growth rates to 8% while maintaining their current ROEs, which firm will be able to offer higher dividends to shareholders?
    Answer: Firm A will offer higher dividends because it can increase its payout ratio to 60% while Firm B can only increase to 50% When you encounter sustainable growth rate (SGR) problems involving changes in growth targets, you need to understand the relationship between SGR, ROE, and retention ratio: SGR=ROE×Retention RatioSGR = ROE \times \text{Retention Ratio} To find which firm can offer higher dividends when reducing growth to 8%, you must calculate their new retention ratios and corresponding payout ratios (since Payout Ratio = 1 - Retention Ratio). For Firm A: If SGR drops to 8% while ROE stays at 20%, the new retention ratio becomes 8%20%=40%\frac{8\%}{20\%} = 40\%. This means Firm A can now pay out 60% of earnings as dividends (compared to its current 40% payout ratio). For Firm B: If SGR drops to 8% while ROE stays at 16%, the new retention ratio becomes 8%16%=50%\frac{8\%}{16\%} = 50\%. This means Firm B can pay out 50% of earnings as dividends (compared to its current 25% payout ratio). Choice A is incorrect because the firms achieve different payout ratios (60% vs 50%), not identical 50% ratios. Choice B contains faulty logic—lower ROE doesn't create "more efficient dividend distribution." Choice D reverses the calculations, incorrectly stating that Firm B achieves 55% while Firm A achieves 45%. Choice C correctly identifies that Firm A can increase its payout ratio to 60% while Firm B can only reach 50%. Study tip: Remember that firms with higher ROEs need lower retention ratios to achieve the same growth rate, which means they can afford higher dividend payouts. Always work backward from the target SGR to find the required retention ratio.
  6. A company's current sustainable growth rate is 10%, supported by a 25% return on equity. The company plans to improve its operating efficiency, which is expected to increase its ROE to 30%, with no change to its dividend policy. What will be the new sustainable growth rate?
    Answer: 12.0% This is a multi-step problem. First, determine the current dividend policy (retention ratio), then apply it to the new ROE. 1. Find the current retention ratio (b) using the SGR formula: SGR=ROE×b  ⟹  b=SGRROE=10%25%=0.40SGR = ROE \times b \implies b = \frac{SGR}{ROE} = \frac{10\%}{25\%} = 0.40. 2. Since the dividend policy is unchanged, the retention ratio remains 0.40. 3. Calculate the new SGR with the new ROE: New SGR = New ROE × b = 30% × 0.40 = 12.0%.
  7. A firm has maintained a steady 9% sustainable growth rate for three years with an ROE of 15% and a 40% dividend payout ratio. This year, the firm's ROE increased to 18% due to operational improvements, but management wants to maintain the same 9% growth rate. What should management do with the dividend policy, and what are the implications?
    Answer: Increase the payout ratio to 50% to maintain 9% growth, providing higher dividends to shareholders while maintaining steady growth This question tests your understanding of the sustainable growth rate formula and how changes in profitability affect dividend policy decisions. The sustainable growth rate formula is: g=ROE×(1−dividend payout ratio)g = ROE \times (1 - \text{dividend payout ratio}), where the retention ratio is (1−dividend payout ratio)(1 - \text{dividend payout ratio}). Let's verify the initial situation: with ROE of 15% and 40% payout ratio, the growth rate was 0.15×(1−0.40)=0.15×0.60=9%0.15 \times (1 - 0.40) = 0.15 \times 0.60 = 9\%. Now with ROE at 18%, if management wants to maintain 9% growth, you need to solve: 0.09=0.18×(1−payout ratio)0.09 = 0.18 \times (1 - \text{payout ratio}). This gives us: 1−payout ratio=0.09/0.18=0.501 - \text{payout ratio} = 0.09/0.18 = 0.50, so the new payout ratio should be 50%. This increase allows shareholders to benefit from the improved profitability through higher dividends while maintaining the desired growth trajectory. Answer A is wrong because the sustainable growth formula absolutely requires adjustment when ROE changes if you want to maintain the same growth rate. Answer B incorrectly calculates the required payout ratio - decreasing it to 30% would actually increase growth to 0.18×0.70=12.6%0.18 \times 0.70 = 12.6\%, overshooting the target. Answer D misses the point entirely - eliminating dividends would maximize growth at 18%, far exceeding the 9% target and ignoring shareholder income needs. Remember: when a company's profitability improves but wants steady growth, it can "share the wealth" by increasing dividends while maintaining its growth target. Always work backwards from your desired growth rate using the sustainable growth formula.
  8. A firm calculates its sustainable growth rate to be 9%. The board of directors has set a corporate growth target of 12% for the upcoming year, without any plans to alter its current profitability or dividend policy. To achieve this target while maintaining its dividend and profitability profile, the company will most likely need to:
    Answer: issue new equity or increase its debt-to-equity ratio beyond the current level. The sustainable growth rate (SGR) is the maximum growth rate a firm can achieve without external equity financing, while maintaining a constant debt-to-equity ratio. If the firm wants to grow faster than its SGR (12% > 9%) and its profitability (ROE) and dividend policy (retention ratio) are fixed, it must obtain additional capital. This can be achieved by either issuing new shares (external equity) or by increasing its debt-to-equity ratio (taking on proportionally more debt than assumed by the SGR).
  9. A firm has a sales forecast of $2 billion, a net profit margin of 6%, total assets of $1.5 billion, and a debt-to-equity ratio of 0.50. If the firm maintains a dividend payout ratio of 40%, what is its sustainable growth rate?
    Answer: 7.20% To find the SGR, we first need to calculate Return on Equity (ROE) and the retention ratio (b). 1. Net Income (NI) = Sales × Net Profit Margin = $2B × 0.06 = $120M. 2. Equity = Total Assets / (1 + Debt/Equity Ratio) = $1.5B / (1 + 0.50) = $1.5B / 1.5 = $1B. 3. ROE = NI / Equity = $120M / $1,000M = 12.0%. 4. Retention Ratio (b) = 1 - Payout Ratio = 1 - 0.40 = 0.60. 5. SGR = ROE × b = 12.0% × 0.60 = 7.20%.
  10. A corporation reports net income of $50 million, total shareholders' equity of $400 million, and pays out $15 million in common dividends. Assuming the firm does not issue new equity, what is its sustainable growth rate (SGR)?
    Answer: 8.75% The sustainable growth rate (SGR) is calculated as the Return on Equity (ROE) multiplied by the retention ratio (b). 1. Calculate ROE: ROE=Net IncomeShareholders’ Equity=$50M$400M=12.5%ROE = \frac{\text{Net Income}}{\text{Shareholders' Equity}} = \frac{\text{\$50M}}{\text{\$400M}} = 12.5\% 2. Calculate the retention ratio (b): b=1−payout ratio=1−DividendsNet Income=1−$15M$50M=1−0.30=0.70b = 1 - \text{payout ratio} = 1 - \frac{\text{Dividends}}{\text{Net Income}} = 1 - \frac{\text{\$15M}}{\text{\$50M}} = 1 - 0.30 = 0.70 3. Calculate SGR: SGR=ROE×b=12.5%×0.70=8.75%SGR = ROE \times b = 12.5\% \times 0.70 = 8.75\%
  11. A financial analyst calculates a company's sustainable growth rate to be 12%. The company's return on equity is 20%. If the company's net income for the year is $10 million, how much is it retaining for future growth?
    Answer: $6.0 million The question asks for the dollar amount of retained earnings. This requires first finding the retention ratio. 1. Use the SGR formula to find the retention ratio (b): SGR=ROE×b  ⟹  b=SGRROE=12%20%=0.60SGR = ROE \times b \implies b = \frac{SGR}{ROE} = \frac{12\%}{20\%} = 0.60. 2. The amount retained for growth is the net income multiplied by the retention ratio. 3. Retained Earnings = Net Income × b = $10 million × 0.60 = $6.0 million.
  12. For the past three years, a company has achieved an actual sales growth rate of 15% annually. An analyst calculates that the company's sustainable growth rate over the same period was consistently around 11%. Which of the following is the most plausible explanation for this discrepancy?
    Answer: The company has been steadily increasing its financial leverage. When actual growth exceeds the sustainable growth rate (SGR), it means the firm is growing faster than it can support with just retained earnings and a proportional increase in debt. This implies that one of the SGR's underlying assumptions is being violated. A steady increase in financial leverage (debt-to-equity ratio) would increase ROE each year, allowing the firm to support a higher growth rate than the SGR calculated using a constant leverage assumption.
  13. A company's board is debating whether to pursue a 14% growth rate when the calculated sustainable growth rate is 11%. The CFO argues this is feasible for 2-3 years, while the treasurer warns of long-term risks. Given that the company's current ROE is 22% and retention ratio is 50%, what is the most accurate assessment of this situation?
    Answer: The 14% growth rate is achievable short-term through increased borrowing, but will gradually reduce ROE and create financial strain unless operational improvements occur Current SGR = 22% × 50% = 11%. To achieve 14% growth while maintaining the same retention ratio and ROE, the company must use external financing (likely debt). This will increase assets faster than equity, reducing ROE over time due to higher interest expenses and leverage. The CFO is correct that it's temporarily feasible, but the treasurer is right about long-term risks. Choice A is wrong - growth above SGR is possible with external financing. Choice C ignores that changing retention to 64% would require 14% = 22% × 64%, which gives 64% ≈ 64%, but this doesn't address the external financing implications. Choice D incorrectly mandates equity financing.
  14. During a period of continuously rising inventory costs, a company changes its inventory accounting method from LIFO to FIFO. Assuming the company's dividend payout ratio and financial leverage remain constant, what is the most likely impact on its calculated sustainable growth rate for the year of the change?
    Answer: It will increase because reported return on equity will be higher. In a period of rising prices, switching from LIFO to FIFO results in a lower Cost of Goods Sold (COGS), which leads to higher reported gross profit and net income. While ending inventory (assets) and therefore equity also increase, the percentage increase in net income is typically larger than the percentage increase in equity. This leads to a higher calculated Return on Equity (ROE). Since SGR=ROE×bSGR = ROE \times b and b is assumed constant, an increase in ROE will directly lead to an increase in the calculated SGR.
  15. A company's ROE has been declining from 20% to 16% over the past year, but management has maintained a constant sustainable growth rate of 12% by adjusting dividend policy. What was the company's dividend payout ratio at the beginning of the year, and what is it now?
    Answer: Payout ratio decreased from 40% at the beginning to 25% currently to maintain constant growth SGR = ROE × (1 - payout ratio) = 12%. Beginning: 12% = 20% × (1 - payout ratio), so (1 - payout ratio) = 0.60, meaning payout ratio = 40%. Currently: 12% = 16% × (1 - payout ratio), so (1 - payout ratio) = 0.75, meaning payout ratio = 25%. The payout ratio decreased from 40% to 25%. Choice B incorrectly suggests the payout ratio increased. Choice C incorrectly assumes constant payout ratio. Choice D uses incorrect initial calculations.
  16. A company has a target sustainable growth rate of 8.4% and a firm policy of maintaining a 30% dividend payout ratio. To achieve its target growth rate, what return on equity (ROE) must the company generate?
    Answer: 12.0% This question requires rearranging the SGR formula to solve for ROE. 1. First, determine the retention ratio (b): b=1−payout ratio=1−0.30=0.70b = 1 - \text{payout ratio} = 1 - 0.30 = 0.70. 2. The SGR formula is SGR=ROE×bSGR = ROE \times b. 3. Rearrange to solve for ROE: ROE=SGRb=8.4%0.70=12.0%ROE = \frac{SGR}{b} = \frac{8.4\%}{0.70} = 12.0\%.
  17. A firm currently retains 70% of its earnings and has an ROE of 18%. If the firm's actual growth rate exceeds its sustainable growth rate, which of the following scenarios most likely explains this situation and its implications?
    Answer: The firm is operating above its sustainable growth rate temporarily by increasing financial leverage, but this cannot continue indefinitely without affecting capital structure When you encounter questions about growth rates exceeding sustainable levels, you're dealing with the fundamental relationship between a firm's growth capacity and its financing constraints. The sustainable growth rate represents the maximum growth a company can achieve without issuing new equity, calculated as: SGR=ROE×Retention RatioSGR = ROE \times \text{Retention Ratio} In this case, the firm's sustainable growth rate is 18%×0.70=12.6%18\% \times 0.70 = 12.6\%. When actual growth exceeds this rate, the firm must find additional financing sources beyond retained earnings. Answer D correctly identifies that the firm is likely increasing financial leverage (taking on more debt) to fund growth beyond what retained earnings can support. This strategy works temporarily but creates rising debt-to-equity ratios that eventually become unsustainable, as excessive leverage increases financial risk and borrowing costs. Answer A incorrectly assumes the firm must immediately adjust its retention ratio. While reducing retention could help, firms often prefer maintaining dividend policies and seeking alternative financing first. Answer B misunderstands the problem. The ROE calculation isn't necessarily wrong—the issue is that even with an 18% ROE, the current retention rate cannot sustain the higher growth rate through internal financing alone. Answer C completely misses the constraint. The retention ratio doesn't support "any" growth rate—it specifically limits sustainable growth based on available retained earnings. Study tip: Remember that sustainable growth rate represents a financing constraint, not an operational limit. When actual growth exceeds SGR, look for external financing sources, particularly increased leverage, as the temporary solution.
  18. A company with a return on equity of 25% and a dividend payout ratio of 80% is seeking to increase its sustainable growth rate. Which of the following single changes would have the greatest positive impact on its SGR?
    Answer: Decreasing the dividend payout ratio from 80% to 60%. First, calculate the current SGR. Then, calculate the new SGR under each scenario to find the largest increase. * Current State: Retention ratio b=1−0.80=0.20b = 1 - 0.80 = 0.20. SGR=ROE×b=25%×0.20=5.0%SGR = ROE \times b = 25\% \times 0.20 = 5.0\%. * Choice A: New SGR = 30% × 0.20 = 6.0%. (Increase of 1.0%) * Choice B: New b=1−0.70=0.30b = 1 - 0.70 = 0.30. New SGR = 25% × 0.30 = 7.5%. (Increase of 2.5%) * Choice C: New b=1−0.60=0.40b = 1 - 0.60 = 0.40. New SGR = 25% × 0.40 = 10.0%. (Increase of 5.0%) * Choice D: New SGR = 28% × 0.20 = 5.6%. (Increase of 0.6%) Decreasing the dividend payout ratio from 80% to 60% results in the largest increase in the SGR.
  19. A company with a current ROE of 18% and a dividend payout ratio of 40% is considering reducing its payout ratio to 25% to support faster growth. If the company maintains its current capital structure and operating efficiency, what will be the change in its sustainable growth rate?
    Answer: The sustainable growth rate will increase by 2.7 percentage points from 10.8% to 13.5% Sustainable growth rate = ROE × (1 - payout ratio). Current SGR = 18% × (1 - 0.40) = 18% × 0.60 = 10.8%. New SGR = 18% × (1 - 0.25) = 18% × 0.75 = 13.5%. The increase is 13.5% - 10.8% = 2.7 percentage points. Choice B incorrectly calculates the new retention ratio as 0.85 instead of 0.75. Choice C uses the wrong initial payout ratio of 60% instead of 40%. Choice D makes an arithmetic error in the initial calculation.
  20. The sustainable growth rate (SGR) model is most reliable as a forward-looking tool when which of the following underlying assumptions about the firm's future policies are expected to hold true?
    Answer: The firm will maintain a constant debt-to-equity ratio and dividend payout ratio. The SGR model is built on a foundation of stable financial policies. The key assumptions are that the firm will maintain a constant capital structure (i.e., a constant debt-to-equity ratio), a constant dividend payout ratio (which implies a constant retention ratio), and stable profitability (constant ROE). If these ratios are not held constant, the calculated SGR will not be an accurate measure of sustainable growth.

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