Finance Quiz: Payout Retention And Sustainable Growth
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Payout Retention And Sustainable GrowthQuestion 1 of 20

A company begins the year with $100 million in shareholders' equity. Over the year, it generates $15 million in net income and pays out $6 million in dividends. The firm does not issue or repurchase any shares. Based on beginning-of-period equity, what is the company's sustainable growth rate?

9.0%
15.0%
8.3%
6.0%
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Finance Quiz

Finance Quiz: Payout Retention And Sustainable Growth

Practice Payout Retention And Sustainable Growth in Finance with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Payout Retention And Sustainable Growth, giving you a quick way to practice the rules, question types, and explanations that matter most for Finance.

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Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

A company begins the year with $100 million in shareholders' equity. Over the year, it generates $15 million in net income and pays out $6 million in dividends. The firm does not issue or repurchase any shares. Based on beginning-of-period equity, what is the company's sustainable growth rate?

  1. 9.0% (correct answer)
  2. 15.0%
  3. 8.3%
  4. 6.0%
Explanation: The sustainable growth rate (SGR) is the rate at which equity grows from retained earnings. It can be calculated as SGR = ROE × b, using beginning-of-period equity for ROE. \begin{itemize} \item 1. Calculate Return on Beginning Equity (ROE): ROE = Net Income / Beginning Equity = $15M / 100M=15.0100M = 15.0%. \item 2. Calculate the Retention Ratio (b): b = (Net Income - Dividends) / Net Income = (15M - $6M) / $15M = $9M / $15M = 0.60. \item 3. Calculate SGR: SGR = ROE × b = 15.0% × 0.60 = 9.0%. \item Alternatively, SGR is the growth in equity: Addition to Retained Earnings / Beginning Equity = $9M / $100M = 9.0%. \end{itemize} Distractor B (15.0%) is the ROE. Distractor C (8.3%) incorrectly uses ending equity to calculate ROE: Ending Equity = $100M + $9M = $109M; ROE_end = 15M/15M/109M = 13.76%; SGR = 13.76% × 0.60 ≈ 8.3%. Distractor D (6.0%) incorrectly uses the payout ratio (40%) instead of the retention ratio (15% × 0.40 = 6.0%).

Question 2

An analyst observes a company's sales grew by 15% last year, while its calculated sustainable growth rate was only 10%. If the company did not issue any new equity during the year and its return on equity remained stable, which of the following is the most plausible explanation?

  1. The company's debt-to-equity ratio must have increased. (correct answer)
  2. The company must have decreased its dividend payout ratio.
  3. The company's financial leverage must have decreased.
  4. The company must have increased its dividend payout ratio.
Explanation: When actual growth (15%) exceeds sustainable growth (10%), a firm has a financing deficit. SGR is the maximum growth achievable while keeping the D/E ratio constant and without issuing new equity. To grow faster than SGR, a firm must violate one of these assumptions. The prompt states no new equity was issued and ROE was stable. The remaining options are to increase leverage or increase the retention ratio (by decreasing the payout ratio). Both A and B are possible ways to fund the extra growth. However, SGR is defined as growth while holding the capital structure constant. So, if the firm grew faster than the SGR, it must have altered its capital structure by increasing leverage. A decrease in the payout ratio would increase the SGR itself. The question implies the 10% SGR was the rate before any policy change. Therefore, the most direct way to fund the additional 5% growth without new equity is by taking on proportionally more debt, thus increasing the D/E ratio. Choice B is also possible, but A is a more direct explanation of funding growth beyond a given SGR. Let me re-evaluate. If payout decreases, b increases, and SGR increases. So the actual SGR for the year was higher than the calculated (maybe ex-ante) SGR. If leverage increases, ROE increases (assuming ROA > interest rate), and SGR increases. Both are plausible. Let's look at the wording. 'calculated SGR was 10%'. This implies that based on the beginning-of-period parameters, it was 10%. To grow faster, they had to change a parameter. Increasing leverage is a financing decision. Decreasing payout is a payout decision. Both work. Let's make choice A more distinct. Ok, I think A is the better answer. Funding the growth means taking on assets, which requires financing (debt or equity). Since new equity is out, it must be debt, which increases the D/E ratio.

Question 3

Firm A is financed entirely with equity. Firm B has a debt-to-equity ratio of 1.0. Both firms have an identical return on assets (ROA) of 10% and the same dividend payout ratio of 60%. Which of the following statements correctly compares their sustainable growth rates (SGR)?

  1. The SGR of Firm A is equal to the SGR of Firm B.
  2. The SGR of Firm B is exactly double the SGR of Firm A. (correct answer)
  3. The SGR of Firm A is exactly double the SGR of Firm B.
  4. The SGR of Firm B is 50% higher than the SGR of Firm A.
Explanation: SGR is calculated as ROE × b. The retention ratio (b = 1 - 0.60 = 0.40) is the same for both firms. We must compare their ROEs. \begin{itemize} \item For Firm A (all equity): ROE = ROA because Assets = Equity. So, ROE_A = 10%. \item For Firm B (D/E = 1.0): We use the relationship ROE = ROA × (1 + D/E). So, ROE_B = 10% × (1 + 1.0) = 10% × 2 = 20%. \item Now, compare SGRs: \item SGR_A = ROE_A × b = 10% × 0.40 = 4%. \item SGR_B = ROE_B × b = 20% × 0.40 = 8%. \end{itemize} The SGR of Firm B (8%) is exactly double the SGR of Firm A (4%).

Question 4

A firm's return on equity is projected to fall from 20% to 16% due to increased competition. To compensate, the board plans to increase the retention ratio from 50% to 75%. What is the anticipated net effect on the firm's sustainable growth rate?

  1. It will increase from 10% to 12%. (correct answer)
  2. It will decrease from 12% to 10%.
  3. It will increase from 8% to 15%.
  4. It will remain unchanged at 10%.
Explanation: We need to calculate the SGR before and after the changes and compare them. \begin{itemize} \item SGR_old = ROE_old × b_old = 20% × 50% = 10%. \item SGR_new = ROE_new × b_new = 16% × 75% = 12%. \end{itemize} The sustainable growth rate is anticipated to increase from 10% to 12%. The increase in the retention ratio more than offsets the decline in profitability (ROE).

Question 5

A large, stable utility company has a return on equity of 10% and few profitable growth opportunities. The company's management wishes to adopt a payout policy that is appropriate for its situation. Which of the following policies is most suitable?

  1. A high dividend payout ratio, resulting in a low sustainable growth rate. (correct answer)
  2. A low dividend payout ratio, resulting in a high sustainable growth rate.
  3. A zero payout ratio, to maximize the firm's sustainable growth rate.
  4. A payout ratio that sets the sustainable growth rate equal to the return on equity.
Explanation: For a mature company with few profitable investment opportunities (i.e., projects with returns exceeding the cost of capital), it is value-maximizing to return cash to shareholders rather than reinvesting it in low-return projects. A high dividend payout ratio accomplishes this. This will result in a low retention ratio and therefore a low sustainable growth rate, which is consistent with the firm's limited growth prospects. Choices B and C are inappropriate as they would mean retaining earnings to invest in projects that are likely to earn less than shareholders' required return, destroying value. Choice D would require a zero retention ratio if SGR=ROE, which is impossible, or a retention ratio of 1.0 (zero payout), which is choice C.

Question 6

A firm with a stable dividend policy uses excess cash to repurchase shares at their book value. Assuming this transaction does not alter the firm's total debt, what is the most likely immediate effect on the firm's sustainable growth rate (SGR)?

  1. SGR will decrease because the firm has less cash available for investment.
  2. SGR will remain unchanged because a repurchase is equivalent to a dividend.
  3. SGR will decrease because the retention ratio will effectively decrease.
  4. SGR will increase because the firm's return on equity will increase. (correct answer)
Explanation: When analyzing share repurchases, you need to understand how they affect the sustainable growth rate formula: SGR=ROE×Retention RatioSGR = ROE \times Retention\ Ratio. The key insight is recognizing which components change and how. When a firm repurchases shares at book value using excess cash, it reduces both total assets (cash decreases) and shareholders' equity (fewer shares outstanding) by the same dollar amount. However, since the firm maintains its "stable dividend policy," it will continue paying the same total dollars in dividends to the remaining shareholders. This creates a crucial dynamic: each remaining share now receives a higher dividend per share, but the retention ratio—the proportion of earnings retained rather than paid out—actually stays constant at the firm level. The real driver here is return on equity (ROE). With the same earnings spread across a smaller equity base, ROE increases. Since ROE=Net IncomeShareholders′ EquityROE = \frac{Net\ Income}{Shareholders'\ Equity} and the denominator decreases while the numerator remains unchanged, ROE rises, boosting the sustainable growth rate. Option A incorrectly focuses on cash availability rather than the ROE effect. Option B misses that repurchases and dividends have different impacts on the capital structure—dividends don't reduce the equity base. Option C incorrectly assumes the retention ratio decreases, when it actually remains constant under a stable dividend policy (same total dividend dollars on lower earnings per remaining share). Remember: share repurchases at book value are essentially leverage-neutral ways to increase ROE by shrinking the equity base while maintaining the same earning power.

Question 7

A company reports net income of $10 million. It has a stated dividend payout ratio of 40%. In addition, the firm spent $2 million on share repurchases during the year. For the purpose of calculating the firm's sustainable growth rate using the standard formula, what is its retention ratio?

  1. 40%
  2. 50%
  3. 60% (correct answer)
  4. 80%
Explanation: The standard formula for sustainable growth rate is SGR = ROE × b, where 'b' is the retention ratio calculated from the dividend payout. The retention ratio is defined as b = (Net Income - Dividends) / Net Income, or simply 1 - Dividend Payout Ratio. Share repurchases, while a form of payout to shareholders, are not included in this specific calculation. \begin{itemize} \item Dividend Payout Ratio = 40%. \item Retention Ratio (b) = 1 - 0.40 = 0.60 or 60%. \end{itemize} Distractor A is the payout ratio. Distractor B incorrectly calculates a 'total payout ratio' by adding the repurchase amount ($4M in dividends + $2M in repurchases = $6M total payout; 6M/6M/10M = 60% total payout; 1 - 0.60 = 40% retention. Wait, my math is backwards). Let's re-calculate the distractor. Dividends = 40% * $10M = $4M. Total Payout = $4M Div + $2M Repurchase = $6M. Total Payout Ratio = $6M / $10M = 60%. Implied Retention Ratio = 1 - 60% = 40%. So distractor A is the 'total retention ratio'. Let me change answer A to 40% and C to 60%. Correct answer is C. A is the common mistake. D is also a mistake.

Question 8

The board of directors at Sterling Corp. has decided to increase the firm's dividend payout ratio from 40% to 60%. The company's return on equity is expected to remain stable at 15%. What will be the impact of this policy change on Sterling's sustainable growth rate?

  1. It will increase by 3.0 percentage points.
  2. It will decrease by 3.0 percentage points. (correct answer)
  3. It will increase by 6.0 percentage points.
  4. It will decrease by 6.0 percentage points.
Explanation: The sustainable growth rate (SGR) depends on the retention ratio (b), which is 1 minus the payout ratio. \begin{itemize} \item Original retention ratio (b_old) = 1 - 0.40 = 0.60. \item Original SGR = ROE × b_old = 15% × 0.60 = 9.0%. \item New retention ratio (b_new) = 1 - 0.60 = 0.40. \item New SGR = ROE × b_new = 15% × 0.40 = 6.0%. \item The change in SGR is New SGR - Original SGR = 6.0% - 9.0% = -3.0 percentage points. \end{itemize} The SGR will decrease by 3.0 percentage points. Distractor A is a sign error. Distractors C and D incorrectly calculate one of the SGRs, perhaps by using the payout ratio directly in the formula (e.g., 15% × 0.60 = 9% and 15% x 0.40 = 6% but then misinterpreting the result).

Question 9

A firm reports net income of $200, dividends of $80, and beginning equity of $1,600 in Year 1. In Year 2, it reports net income of $218 and dividends of $87.20. What was the firm's sustainable growth rate in Year 1?

  1. 7.5% (correct answer)
  2. 5.0%
  3. 12.5%
  4. 10.0%
Explanation: The question asks for the sustainable growth rate in Year 1, so the data for Year 2 is extraneous information designed to distract. The calculation for Year 1 is as follows: \begin{itemize} \item 1. Calculate ROE for Year 1 using beginning equity: ROE_1 = Net Income_1 / Beginning Equity_1 = $200 / 1,600=0.125or12.51,600 = 0.125 or 12.5%. \item 2. Calculate the retention ratio for Year 1 (b_1): b_1 = 1 - (Dividends_1 / Net Income_1) = 1 - (80 / $200) = 1 - 0.40 = 0.60. \item 3. Calculate SGR for Year 1: SGR_1 = ROE_1 × b_1 = 12.5% × 0.60 = 7.5%. \end{itemize} Distractor B (5.0%) incorrectly uses the payout ratio instead of retention ratio: ROE × payout = 12.5% × 0.40 = 5.0%. Distractor C (12.5%) is the ROE for Year 1. Distractor D (10.0%) represents a calculation error using average values.

Question 10

A large, stable utility company has a return on equity of 10% and few profitable growth opportunities. The company's management wishes to adopt a payout policy that is appropriate for its situation. Which of the following policies is most suitable?

  1. A high dividend payout ratio, resulting in a low sustainable growth rate. (correct answer)
  2. A low dividend payout ratio, resulting in a high sustainable growth rate.
  3. A zero payout ratio, to maximize the firm's sustainable growth rate.
  4. A payout ratio that sets the sustainable growth rate equal to the return on equity.
Explanation: For a mature company with few profitable investment opportunities (i.e., projects with returns exceeding the cost of capital), it is value-maximizing to return cash to shareholders rather than reinvesting it in low-return projects. A high dividend payout ratio accomplishes this. This will result in a low retention ratio and therefore a low sustainable growth rate, which is consistent with the firm's limited growth prospects. Choices B and C are inappropriate as they would mean retaining earnings to invest in projects that are likely to earn less than shareholders' required return, destroying value. Choice D would require a zero retention ratio if SGR=ROE, which is impossible, or a retention ratio of 1.0 (zero payout), which is choice C.

Question 11

A company currently has a return on equity of 25% and a dividend payout ratio of 70%. Management wants to achieve a sustainable growth rate of 15%. Assuming the firm's ROE remains constant, what must its new dividend payout ratio be?

  1. 10%
  2. 40% (correct answer)
  3. 60%
  4. 90%
Explanation: This problem requires finding the required payout ratio to achieve a target SGR. \begin{itemize} \item 1. Use the SGR formula to find the required retention ratio (b): SGR = ROE × b. \item 2. Rearrange and solve for b: b = SGR / ROE = 15% / 25% = 0.60. \item 3. The company must have a retention ratio of 60% to achieve its target growth rate. \item 4. Convert the required retention ratio to a payout ratio: Payout Ratio = 1 - b = 1 - 0.60 = 0.40 or 40%. \end{itemize} Distractor C (60%) is the required retention ratio, not the payout ratio. The other distractors represent calculation errors.

Question 12

A firm's financial plan shows a sustainable growth rate of 9%. The capital budgeting committee has identified a slate of positive-NPV projects that would require total assets to grow by 13%. The company is unwilling to issue new shares and is committed to its target debt-to-equity ratio and its current dividend policy. What is the most likely outcome?

  1. The firm will have a cash surplus after funding all projects.
  2. The firm will take on all projects and finance the shortfall with new debt.
  3. The firm will increase its retention ratio to fund the additional growth.
  4. The firm will have to reject some positive-NPV projects due to a lack of funding. (correct answer)
Explanation: This question tests your understanding of sustainable growth and financial constraints. When you encounter sustainable growth problems, remember that firms face real-world limitations on their financing options, and these constraints directly impact which projects they can fund. The sustainable growth rate of 9% represents the maximum growth the firm can achieve given its current financial policies: no new equity issuance, maintaining the target debt-to-equity ratio, and keeping the current dividend policy. However, the positive-NPV projects require 13% asset growth, creating a 4 percentage point gap between what the firm needs and what it can sustainably finance. Since the firm won't issue new shares and is committed to its debt-to-equity ratio and dividend policy, it cannot generate the additional financing needed for all projects. This funding shortfall forces the firm to reject some positive-NPV projects, making answer D correct. Answer A is wrong because there's insufficient funding, not excess cash. Answer B violates the constraint of maintaining the target debt-to-equity ratio—taking on extra debt would increase leverage beyond the target. Answer C contradicts the stated commitment to the current dividend policy; increasing the retention ratio means cutting dividends, which the firm won't do. Remember this key principle: sustainable growth rate sets a ceiling on growth when firms face financing constraints. When project requirements exceed this ceiling and the firm won't adjust its financial policies, value-destroying rationing occurs—even profitable projects get rejected due to funding limitations.

Question 13

The sustainable growth rate model is most likely to be an inaccurate forecast of a company's actual growth if which of the following is true?

  1. The company operates in a stable industry with predictable cash flows.
  2. The company's management is committed to a fixed dividend payout ratio.
  3. The company plans a major acquisition that will significantly increase its debt-to-equity ratio. (correct answer)
  4. The company finances its growth by retaining earnings and issuing debt proportionally.
Explanation: The sustainable growth rate model assumes that key financial ratios, including the firm's capital structure (debt-to-equity ratio), remain constant. A major acquisition that significantly alters the D/E ratio violates this core assumption, making the SGR calculated from historical data an unreliable predictor of future growth potential. The other options describe conditions that are consistent with the assumptions of the SGR model. Stable operations (A), a fixed payout ratio (B), and proportional financing (D) are all conditions under which the SGR model is expected to be most accurate.

Question 14

A company has a sustainable growth rate of 10.5% and a return on equity of 25%. What is the company's dividend payout ratio?

  1. 32.5%
  2. 42.0%
  3. 58.0% (correct answer)
  4. 75.0%
Explanation: The formula for sustainable growth rate (SGR) is SGR = ROE × b, where b is the retention ratio. We can rearrange this to solve for b: \begin{itemize} \item b = SGR / ROE = 10.5% / 25% = 0.42. \item The retention ratio is 42%. The question asks for the dividend payout ratio, which is 1 - b. \item Payout Ratio = 1 - 0.42 = 0.58 or 58%. \end{itemize} Distractor B (42.0%) is the retention ratio, not the payout ratio. Distractors A and D represent common calculation errors, such as subtracting the rates (25% - 10.5% = 14.5%) or inverting the division.

Question 15

The board of directors at Sterling Corp. has decided to increase the firm's dividend payout ratio from 40% to 60%. The company's return on equity is expected to remain stable at 15%. What will be the impact of this policy change on Sterling's sustainable growth rate?

  1. It will increase by 3.0 percentage points.
  2. It will decrease by 3.0 percentage points. (correct answer)
  3. It will increase by 6.0 percentage points.
  4. It will decrease by 6.0 percentage points.
Explanation: The sustainable growth rate (SGR) depends on the retention ratio (b), which is 1 minus the payout ratio. \begin{itemize} \item Original retention ratio (b_old) = 1 - 0.40 = 0.60. \item Original SGR = ROE × b_old = 15% × 0.60 = 9.0%. \item New retention ratio (b_new) = 1 - 0.60 = 0.40. \item New SGR = ROE × b_new = 15% × 0.40 = 6.0%. \item The change in SGR is New SGR - Original SGR = 6.0% - 9.0% = -3.0 percentage points. \end{itemize} The SGR will decrease by 3.0 percentage points. Distractor A is a sign error. Distractors C and D incorrectly calculate one of the SGRs, perhaps by using the payout ratio directly in the formula (e.g., 15% × 0.60 = 9% and 15% x 0.40 = 6% but then misinterpreting the result).

Question 16

An analyst observes a company's sales grew by 15% last year, while its calculated sustainable growth rate was only 10%. If the company did not issue any new equity during the year and its return on equity remained stable, which of the following is the most plausible explanation?

  1. The company's debt-to-equity ratio must have increased. (correct answer)
  2. The company must have decreased its dividend payout ratio.
  3. The company's financial leverage must have decreased.
  4. The company must have increased its dividend payout ratio.
Explanation: When actual growth (15%) exceeds sustainable growth (10%), a firm has a financing deficit. SGR is the maximum growth achievable while keeping the D/E ratio constant and without issuing new equity. To grow faster than SGR, a firm must violate one of these assumptions. The prompt states no new equity was issued and ROE was stable. The remaining options are to increase leverage or increase the retention ratio (by decreasing the payout ratio). Both A and B are possible ways to fund the extra growth. However, SGR is defined as growth while holding the capital structure constant. So, if the firm grew faster than the SGR, it must have altered its capital structure by increasing leverage. A decrease in the payout ratio would increase the SGR itself. The question implies the 10% SGR was the rate before any policy change. Therefore, the most direct way to fund the additional 5% growth without new equity is by taking on proportionally more debt, thus increasing the D/E ratio. Choice B is also possible, but A is a more direct explanation of funding growth beyond a given SGR. Let me re-evaluate. If payout decreases, b increases, and SGR increases. So the actual SGR for the year was higher than the calculated (maybe ex-ante) SGR. If leverage increases, ROE increases (assuming ROA > interest rate), and SGR increases. Both are plausible. Let's look at the wording. 'calculated SGR was 10%'. This implies that based on the beginning-of-period parameters, it was 10%. To grow faster, they had to change a parameter. Increasing leverage is a financing decision. Decreasing payout is a payout decision. Both work. Let's make choice A more distinct. Ok, I think A is the better answer. Funding the growth means taking on assets, which requires financing (debt or equity). Since new equity is out, it must be debt, which increases the D/E ratio.

Question 17

Firm A is financed entirely with equity. Firm B has a debt-to-equity ratio of 1.0. Both firms have an identical return on assets (ROA) of 10% and the same dividend payout ratio of 60%. Which of the following statements correctly compares their sustainable growth rates (SGR)?

  1. The SGR of Firm A is equal to the SGR of Firm B.
  2. The SGR of Firm B is exactly double the SGR of Firm A. (correct answer)
  3. The SGR of Firm A is exactly double the SGR of Firm B.
  4. The SGR of Firm B is 50% higher than the SGR of Firm A.
Explanation: SGR is calculated as ROE × b. The retention ratio (b = 1 - 0.60 = 0.40) is the same for both firms. We must compare their ROEs. \begin{itemize} \item For Firm A (all equity): ROE = ROA because Assets = Equity. So, ROE_A = 10%. \item For Firm B (D/E = 1.0): We use the relationship ROE = ROA × (1 + D/E). So, ROE_B = 10% × (1 + 1.0) = 10% × 2 = 20%. \item Now, compare SGRs: \item SGR_A = ROE_A × b = 10% × 0.40 = 4%. \item SGR_B = ROE_B × b = 20% × 0.40 = 8%. \end{itemize} The SGR of Firm B (8%) is exactly double the SGR of Firm A (4%).

Question 18

A firm's return on equity is projected to fall from 20% to 16% due to increased competition. To compensate, the board plans to increase the retention ratio from 50% to 75%. What is the anticipated net effect on the firm's sustainable growth rate?

  1. It will increase from 10% to 12%. (correct answer)
  2. It will decrease from 12% to 10%.
  3. It will increase from 8% to 15%.
  4. It will remain unchanged at 10%.
Explanation: We need to calculate the SGR before and after the changes and compare them. \begin{itemize} \item SGR_old = ROE_old × b_old = 20% × 50% = 10%. \item SGR_new = ROE_new × b_new = 16% × 75% = 12%. \end{itemize} The sustainable growth rate is anticipated to increase from 10% to 12%. The increase in the retention ratio more than offsets the decline in profitability (ROE).

Question 19

A firm's financial plan shows a sustainable growth rate of 9%. The capital budgeting committee has identified a slate of positive-NPV projects that would require total assets to grow by 13%. The company is unwilling to issue new shares and is committed to its target debt-to-equity ratio and its current dividend policy. What is the most likely outcome?

  1. The firm will have a cash surplus after funding all projects.
  2. The firm will take on all projects and finance the shortfall with new debt.
  3. The firm will increase its retention ratio to fund the additional growth.
  4. The firm will have to reject some positive-NPV projects due to a lack of funding. (correct answer)
Explanation: This question tests your understanding of sustainable growth and financial constraints. When you encounter sustainable growth problems, remember that firms face real-world limitations on their financing options, and these constraints directly impact which projects they can fund. The sustainable growth rate of 9% represents the maximum growth the firm can achieve given its current financial policies: no new equity issuance, maintaining the target debt-to-equity ratio, and keeping the current dividend policy. However, the positive-NPV projects require 13% asset growth, creating a 4 percentage point gap between what the firm needs and what it can sustainably finance. Since the firm won't issue new shares and is committed to its debt-to-equity ratio and dividend policy, it cannot generate the additional financing needed for all projects. This funding shortfall forces the firm to reject some positive-NPV projects, making answer D correct. Answer A is wrong because there's insufficient funding, not excess cash. Answer B violates the constraint of maintaining the target debt-to-equity ratio—taking on extra debt would increase leverage beyond the target. Answer C contradicts the stated commitment to the current dividend policy; increasing the retention ratio means cutting dividends, which the firm won't do. Remember this key principle: sustainable growth rate sets a ceiling on growth when firms face financing constraints. When project requirements exceed this ceiling and the firm won't adjust its financial policies, value-destroying rationing occurs—even profitable projects get rejected due to funding limitations.

Question 20

A firm reports net income of $200, dividends of $80, and beginning equity of $1,600 in Year 1. In Year 2, it reports net income of $218 and dividends of $87.20. What was the firm's sustainable growth rate in Year 1?

  1. 7.5% (correct answer)
  2. 5.0%
  3. 12.5%
  4. 10.0%
Explanation: The question asks for the sustainable growth rate in Year 1, so the data for Year 2 is extraneous information designed to distract. The calculation for Year 1 is as follows: \begin{itemize} \item 1. Calculate ROE for Year 1 using beginning equity: ROE_1 = Net Income_1 / Beginning Equity_1 = $200 / 1,600=0.125or12.51,600 = 0.125 or 12.5%. \item 2. Calculate the retention ratio for Year 1 (b_1): b_1 = 1 - (Dividends_1 / Net Income_1) = 1 - (80 / $200) = 1 - 0.40 = 0.60. \item 3. Calculate SGR for Year 1: SGR_1 = ROE_1 × b_1 = 12.5% × 0.60 = 7.5%. \end{itemize} Distractor B (5.0%) incorrectly uses the payout ratio instead of retention ratio: ROE × payout = 12.5% × 0.40 = 5.0%. Distractor C (12.5%) is the ROE for Year 1. Distractor D (10.0%) represents a calculation error using average values.