All questions
Question 1
A company reports net income of $200 million. It declares and pays $50 million in cash dividends. Additionally, it spends $30 million repurchasing its own stock on the open market. What is the company's retention ratio for the period?
- 25%
- 40%
- 60% (correct answer)
- 75%
Explanation: The retention ratio is the proportion of earnings that is NOT returned to shareholders. The total amount returned to shareholders is the sum of dividends and share repurchases. Total Payout = $50M + $30M = $80M. The amount of earnings retained is Net Income - Total Payout = $200M - $80M = $120M. The retention ratio is Retained Earnings / Net Income = $120M / 200M=0.60,or60200M-50M)/200M = 75%. Question 2
Stellar Corp. reported net income of $50 million. The company's beginning-of-year retained earnings were $200 million and its end-of-year retained earnings were $230 million. The board of directors is targeting a sustainable growth rate for the upcoming year and assumes the company's return on equity will be 15%. Based on the past year's retention ratio, what is the company's implied sustainable growth rate?
- 6.0%
- 9.0% (correct answer)
- 12.0%
- 15.0%
Explanation: This is a multi-step problem. First, calculate the amount of earnings retained. Retained Earnings for the year = Ending RE - Beginning RE = $230M - $200M = $30M. Second, calculate the retention ratio (b). Retention Ratio = Retained Earnings / Net Income = $30M / $50M = 0.60 or 60%. Third, calculate the sustainable growth rate (g). Sustainable Growth Rate = Retention Ratio × Return on Equity = 0.60 × 15% = 9.0%.
Question 3
An analyst is comparing two companies in the same industry. Both companies have a cost of equity of 10%.
- Company G has a retention ratio of 70% and a return on equity (ROE) of 15%.
- Company M has a retention ratio of 20% and a return on equity (ROE) of 12%.
Which of the following statements is the most accurate assessment of their payout policies?
- Company M's policy is superior because its retention ratio is lower, returning more cash to shareholders.
- Company G's policy is superior because it is reinvesting a larger portion of earnings in projects earning more than the cost of equity.
- Both companies are creating value for shareholders, but Company G's policy results in a higher sustainable growth rate. (correct answer)
- Both companies are destroying value for shareholders because their payout ratios are too low relative to their ROE.
Explanation: Shareholder value is created when a company retains earnings and reinvests them in projects that earn a return higher than the cost of capital. For both companies, ROE > cost of equity (15% > 10% for G, and 12% > 10% for M), so both retention policies are creating value. We can also calculate the sustainable growth rate (g = b × ROE) for each. Company G's growth rate is 0.70 × 15% = 10.5%. Company M's growth rate is 0.20 × 12% = 2.4%. Therefore, both are creating value, and Company G's policy leads to a higher growth rate.
Question 4
A firm with $100 million in net income and 50 million shares outstanding decides to distribute $60 million to shareholders. It pays $20 million in dividends and uses $40 million to repurchase shares. Which of the following correctly describes the firm's retention and total payout ratios?
- Retention ratio is 80% and total payout ratio is 20%.
- Retention ratio is 60% and total payout ratio is 40%.
- Retention ratio is 40% and total payout ratio is 60%. (correct answer)
- Retention ratio is 20% and total payout ratio is 80%.
Explanation: The total payout to shareholders includes both dividends and share repurchases. Total Payout = $20M (dividends) + $40M (repurchases) = $60M. The Total Payout Ratio = Total Payout / Net Income = $60M / $100M = 60%. The retention ratio is the proportion of earnings not paid out. Retention Ratio = 1 - Total Payout Ratio = 1 - 0.60 = 40%. Alternatively, Retained Earnings = Net Income - Total Payout = $100M - $60M = $40M. Retention Ratio = $40M / $100M = 40%.
Question 5
The management of Apex Manufacturing wants to achieve a sustainable growth rate of 8.4%. The company has consistently generated a return on equity of 14%. To achieve its target growth rate, what dividend payout ratio must the company maintain?
- 30%
- 40% (correct answer)
- 60%
- 70%
Explanation: This problem requires working backwards from the sustainable growth rate (g) formula: g = retention ratio (b) × ROE. First, solve for the required retention ratio: b = g / ROE = 8.4% / 14% = 0.60. The retention ratio is 60%. The dividend payout ratio is 1 minus the retention ratio. Payout Ratio = 1 - b = 1 - 0.60 = 0.40, or 40%.
Question 6
A firm expects to generate earnings per share (EPS) of $4.00 next year and has a return on equity (ROE) of 20% and a cost of equity of 14%. The company currently has a retention ratio of 60%. If the company were to decrease its retention ratio to 40%, what would be the expected impact on its stock price, assuming the ROE and cost of equity remain constant?
- The price would increase to $60.00.
- The price would decrease from $80.00 to $40.00. (correct answer)
- The price would decrease from $53.33 to $34.29.
- The price would remain unchanged because the firm's ROE is greater than its cost of equity.
Explanation: This requires applying the constant-growth DDM (Gordon Growth Model) for both scenarios. The formula is P₀ = D₁ / (kₑ - g), where D₁ = E₁(1-b) and g = b × ROE.
Original Policy (b=60%):
g = 0.60 × 20% = 12%
D₁ = $4.00 × (1 - 0.60) = $1.60
P₀ = $1.60 / (0.14 - 0.12) = $80.00
New Policy (b=40%):
g = 0.40 × 20% = 8%
D₁ = $4.00 × (1 - 0.40) = $2.40
P₀,new = $2.40 / (0.14 - 0.08) = $2.40 / 0.06 = $40.00
Since the company's ROE (20%) is greater than its cost of equity (14%), retaining earnings creates value. Reducing the retention ratio from 60% to 40% reduces the firm's investment in value-creating projects, thus lowering the stock price.
Question 7
A firm's board of directors commits to a policy of maintaining a 30% retention ratio. The firm's chief economist projects that the company's return on equity (ROE) will increase from 10% to 15% over the next three years due to operational efficiencies. Assuming the policy is maintained, what is the most direct implication for the company's dividends?
- The dividend payout ratio will decrease.
- The dividend per share amount will remain constant.
- The growth rate of dividends per share will increase. (correct answer)
- The dividend payout ratio will increase to 70%.
Explanation: The growth rate of dividends is assumed to be the company's sustainable growth rate (g), which is calculated as g = retention ratio (b) × ROE. The company's retention ratio is fixed at b = 30%. As ROE increases from 10% to 15%, the sustainable growth rate will increase from g = 0.30 × 10% = 3% to g = 0.30 × 15% = 4.5%. Since the dividend growth rate is increasing, the dividends per share will grow at a faster rate.
Question 8
A company follows a stable dividend policy, aiming to increase its dividend per share by a consistent 3% each year. The company operates in a cyclical industry, causing its net income to be highly volatile. Which of the following statements correctly describes the company's dividend payout ratio?
- The dividend payout ratio will be counter-cyclical, rising during recessions and falling during expansions. (correct answer)
- The dividend payout ratio will remain stable over the business cycle.
- The dividend payout ratio will be pro-cyclical, falling during recessions and rising during expansions.
- The dividend payout ratio will be consistently higher than the industry average.
Explanation: When you encounter dividend policy questions, focus on the relationship between dividend payout ratio and earnings volatility. The dividend payout ratio equals dividends per share divided by earnings per share, so when one component stays stable while the other fluctuates, the ratio moves inversely.
Here's the key insight: A stable dividend policy means the company commits to steady, predictable dividend payments regardless of earnings fluctuations. Since this company increases dividends by exactly 3% annually, the numerator (dividends per share) grows smoothly. However, the denominator (earnings per share) swings dramatically due to the cyclical industry nature.
During economic expansions, earnings rise while dividends continue their modest 3% growth, causing the payout ratio to fall. During recessions, earnings plummet while dividends maintain their steady increase, forcing the payout ratio to spike. This creates a counter-cyclical pattern where the payout ratio moves opposite to the business cycle.
Answer A correctly identifies this counter-cyclical behavior. Answer B is wrong because the ratio cannot remain stable when earnings fluctuate while dividends stay on a fixed growth path. Answer C incorrectly suggests pro-cyclical movement, which would only occur if dividends fluctuated more than earnings. Answer D makes an unsupported comparison to industry averages, which isn't determinable from the given information about the company's specific policy and industry volatility.
Study tip: Remember that stable dividend policies create inverse relationships between earnings volatility and payout ratios. When companies prioritize dividend stability over payout ratio stability, expect counter-cyclical payout patterns in volatile industries.
Question 9
During a period of rising inventory costs, a U.S. company changes its inventory accounting method from FIFO to LIFO. The company's board decides to keep the total dollar amount of dividends paid to shareholders constant. What is the most likely effect of this accounting change on the company's reported dividend payout ratio?
- The payout ratio will increase, because net income will be lower. (correct answer)
- The payout ratio will decrease, because cost of goods sold will be lower.
- The payout ratio will remain unchanged, because the cash flow from operations is not affected.
- The payout ratio will remain unchanged, because dividends paid are constant.
Explanation: This question tests your understanding of how inventory accounting methods affect financial ratios during periods of changing costs. The dividend payout ratio is calculated as Net IncomeDividends Paid, so you need to consider how the FIFO-to-LIFO change affects both components.
When inventory costs are rising, switching from FIFO to LIFO increases the cost of goods sold because LIFO assigns the most recent (higher) costs to items sold. Higher COGS reduces gross profit and ultimately net income. Since the board keeps dividend payments constant in dollar terms, the numerator of the payout ratio stays the same while the denominator (net income) decreases. This makes the ratio larger.
Looking at the wrong answers: Option B incorrectly states that COGS will be lower under LIFO during rising costs—it's actually higher. Option C misses the point entirely by focusing on cash flow from operations, which isn't part of the payout ratio calculation. Option D makes a logical error by assuming that keeping dividends constant means the ratio stays constant, but this ignores that net income changes when you switch accounting methods.
Answer A correctly identifies that the payout ratio increases because net income decreases while dividends remain constant.
Study tip: Remember that inventory accounting changes are purely accounting adjustments—they don't affect actual cash flows or dividend payments, but they do impact reported earnings. When analyzing ratio effects, always identify which components of the ratio change and which stay constant. Question 10
A company has a cost of equity of 11%. For the past several years, it has maintained a high retention ratio of 90% while consistently generating a return on equity of exactly 11%. Which statement best describes the impact of this retention policy on shareholder wealth?
- It has significantly increased shareholder wealth due to the high sustainable growth rate of 9.9%.
- It has significantly decreased shareholder wealth because of the low dividend payout.
- It has had a neutral impact on shareholder wealth. (correct answer)
- It has increased shareholder wealth, but less than if the payout ratio were 100%.
Explanation: The net present value of growth opportunities (NPVGO) is positive only when the return on equity (ROE) is greater than the cost of equity (k_e). When ROE = k_e, the investments are earning exactly their required rate of return. This means the NPV of these growth opportunities is zero. While the firm is growing (g = 0.90 × 11% = 9.9%), this growth is not adding value beyond what shareholders could achieve by investing the dividends themselves at the required rate of return. Therefore, the policy has a neutral impact on wealth; it neither creates nor destroys value.
Question 11
A company that has historically maintained a retention ratio of 80% to fund its rapid expansion announces it will decrease its retention ratio to 40%. The company's return on equity is expected to remain well above its cost of equity. What is the most likely market interpretation of this strategic shift?
- The company is experiencing a decline in sales and profitability.
- The company is signaling a transition from a growth phase to a maturity phase. (correct answer)
- The company is attempting to artificially inflate its earnings per share through share repurchases.
- The company anticipates a significant increase in its cost of equity capital.
Explanation: A significant and permanent reduction in the retention ratio (and thus an increase in the payout ratio) signals that the company has fewer high-return investment opportunities. This is characteristic of a firm moving from a high-growth phase, where it needs to reinvest most of its earnings, to a more mature phase, where it can return more capital to shareholders. The company's ROE remains high, which contradicts the idea of declining profitability.
Question 12
During a severe recession, a manufacturing firm reports a net loss of $20 million. Despite the loss, the board of directors decides to maintain its long-standing policy and pays a cash dividend of $10 million. How should an analyst interpret the firm's payout and retention ratios for this period?
- The payout ratio is -50% and the retention ratio is 150%.
- The payout ratio is positive, and the retention ratio is negative.
- The payout ratio is 50% and the retention ratio is 50%, based on absolute values.
- Both ratios are not meaningful because net income is negative. (correct answer)
Explanation: Financial ratio analysis becomes problematic when dealing with negative earnings, and this question tests your understanding of when traditional ratios lose their meaning. The payout ratio typically measures dividends as a percentage of net income, while the retention ratio shows what percentage of earnings is retained in the business.
When a company has negative net income but still pays dividends, the mathematical calculations produce misleading results. With a $20 million loss and 10millionindividends,youmightcalculateapayoutratioof−5010M ÷ -$20M), but this negative percentage has no practical interpretation. You can't meaningfully say a company is paying out "negative 50%" of its earnings.
Answer A correctly calculates the mathematical result (-50% payout, 150% retention) but incorrectly suggests these numbers are interpretable. Answer B recognizes the signs would be opposite but still implies the ratios have meaning. Answer C attempts to use absolute values to force the ratios to make sense, but this approach ignores the fundamental issue that you cannot meaningfully express dividend payments as a percentage of losses.
Answer D correctly identifies that both ratios become meaningless when net income is negative. During loss periods, analysts should focus on different metrics: cash flow coverage of dividends, debt levels, liquidity ratios, and the sustainability of dividend payments from retained earnings or borrowing.
Study tip: Remember that many traditional financial ratios break down or become misleading when companies report losses. Always check whether the denominator in your ratio calculations makes economic sense before interpreting the results. Question 13
A company's board is debating between two dividend policies: Policy A is to maintain a constant dividend payout ratio of 40% of net income. Policy B is to adopt a stable dividend policy where the dividend per share is increased by a small, fixed amount each year. The company's earnings are known to be cyclical. How would the company's retention ratio behave under each policy during an economic expansion?
- Policy A: Stable; Policy B: Increase. (correct answer)
- Policy A: Stable; Policy B: Stable.
- Policy A: Decrease; Policy B: Decrease.
- Policy A: Decrease; Policy B: Increase.
Explanation: When analyzing dividend policies, you need to understand how retention ratio responds to earnings changes. The retention ratio equals (1 - payout ratio), representing the percentage of earnings retained for reinvestment.
Under Policy A's constant 40% payout ratio, the retention ratio remains fixed at 60% regardless of earnings levels. Even during economic expansion when net income increases, the company still pays out exactly 40% as dividends and retains exactly 60%. The retention ratio stays stable because it's mechanically tied to the payout ratio.
Under Policy B's stable dividend policy, the company commits to paying a fixed dollar amount per share (plus small annual increases). During economic expansion, net income rises significantly due to cyclical earnings growth, but the dividend payment remains relatively constant. This means dividends represent a smaller percentage of the higher earnings, so the payout ratio decreases. Consequently, the retention ratio (1 - payout ratio) increases as more earnings are automatically retained.
Choice A correctly identifies this pattern: Policy A keeps retention stable, while Policy B causes retention to increase during expansion. Choice B incorrectly assumes Policy B's retention stays stable, missing how fixed dividends interact with rising earnings. Choice C wrongly suggests both policies decrease retention, perhaps confusing expansion effects. Choice D incorrectly claims Policy A's retention decreases, misunderstanding how constant payout ratios work.
Remember: constant payout ratios create stable retention ratios, while stable dollar dividends create variable retention ratios that move inversely with earnings cycles.
Question 14
For the past 20 years, a utility company has maintained a dividend payout ratio of approximately 90%, attracting a large base of income-seeking investors. The board is now considering reducing the payout ratio to 50% to fund a major capital project. According to the clientele effect, what is the most likely immediate consequence of this change?
- A rapid increase in the stock price as the market prices in higher future growth from the new project.
- A temporary drop in the stock price as the current income-seeking investors sell their shares. (correct answer)
- No significant impact on the stock price, as the dividend reduction is offset by expected future earnings.
- A permanent shift in the firm's beta as the new project increases its systematic risk.
Explanation: The clientele effect suggests that companies attract investors whose preferences match their payout policies. A company with a long history of high payouts will have a 'clientele' of income-seeking investors (e.g., retirees). A sudden, large cut in the dividend will not meet the needs of this clientele, leading them to sell their shares. This selling pressure is likely to cause a short-term drop in the stock price until a new clientele of growth-oriented investors is attracted to the stock.
Question 15
A company with no debt generated unusually high free cash flow this year. It decides to distribute the entire excess amount as a one-time special dividend. How should analysts interpret the company's payout ratio for this year?
- The high payout ratio indicates a permanent shift in policy towards higher shareholder returns.
- The high payout ratio signals management's belief that the company's growth phase is over.
- The payout ratio for this year should be viewed as the new target for future dividend policies.
- The payout ratio should be ignored as it is artificially inflated by a non-recurring event. (correct answer)
Explanation: When evaluating dividend policy, you need to distinguish between recurring patterns and one-time events that don't reflect ongoing management strategy. The payout ratio—dividends divided by earnings—is most meaningful when it represents sustainable, repeatable behavior rather than exceptional circumstances.
Answer D is correct because a special dividend funded by unusually high free cash flow creates an artificially inflated payout ratio that doesn't represent the company's normal dividend policy. Since this is explicitly described as a one-time distribution of excess cash, the resulting payout ratio tells you nothing about management's ongoing dividend strategy or the company's sustainable dividend capacity. Analysts should exclude such non-recurring events when evaluating dividend policy trends.
Answer A incorrectly assumes that one exceptional year signals a permanent policy change. Companies regularly clarify that special dividends don't indicate new ongoing dividend levels. Answer B misinterprets the situation—distributing excess cash doesn't necessarily mean growth opportunities have disappeared; it often means management found no immediate value-creating investments for surplus funds. Answer C makes the dangerous assumption that an unusually high payout ratio should become the new baseline, which would likely be unsustainable since it was funded by exceptional rather than typical cash generation.
Study tip: When analyzing dividend ratios, always ask whether the dividend payment represents normal operations or a special circumstance. Look for keywords like "special," "extraordinary," or "one-time" that signal you should treat the payout ratio as non-representative of ongoing policy.
Question 16
A company has maintained a stable retention ratio for the past five years. However, an analyst notes that its sustainable growth rate has been steadily declining. Which of the following is the most likely explanation for this trend?
- The company has been issuing new equity to fund projects.
- The company's cost of equity has been increasing.
- The company's dividend payout ratio has been increasing.
- The company's return on equity (ROE) has been decreasing. (correct answer)
Explanation: When you encounter questions about sustainable growth rate trends, focus on the fundamental formula: SGR=ROE×Retention Ratio. Since the company has maintained a stable retention ratio over five years, any change in sustainable growth rate must come from changes in ROE.
The declining sustainable growth rate with a constant retention ratio can only be explained by a decreasing return on equity. ROE measures how effectively a company generates profits from shareholders' equity, and if this efficiency is declining while the company retains the same proportion of earnings, the sustainable growth rate will naturally fall.
Looking at the incorrect options: Choice A is wrong because issuing new equity would actually increase the company's financial capacity and wouldn't necessarily decrease sustainable growth rate. Choice B incorrectly focuses on cost of equity, which affects firm valuation but isn't a direct component of the sustainable growth formula. Choice C contradicts the given information—if the retention ratio is stable, then the dividend payout ratio (which equals 1 minus retention ratio) must also be stable, not increasing.
The key insight is that ROE can decline due to deteriorating profit margins, slower asset turnover, or reduced financial leverage, any of which would hurt the company's ability to generate growth from retained earnings.
Study tip: Memorize the sustainable growth formula and remember that with a constant retention ratio, SGR moves in lockstep with ROE. This relationship appears frequently on corporate finance exams. Question 17
A firm's management is considering two mutually exclusive uses for its earnings: 1) increase its retention ratio to invest in a project with an expected ROE of 12%, or 2) increase its dividend payout. The firm's cost of equity is 15%. Which action will most likely maximize shareholder wealth?
- Increase the retention ratio, as this leads to higher future earnings growth.
- The choice is irrelevant as both options will have the same net effect on the firm's value.
- Increase the dividend payout, as the proposed investment earns less than the cost of equity. (correct answer)
- Increase the retention ratio, as long as the ROE is positive.
Explanation: Shareholder wealth is increased when a company reinvests earnings in projects that have a return on equity (ROE) greater than the cost of equity (k_e). In this case, the project's ROE is 12%, while the cost of equity is 15%. Since ROE < k_e, reinvesting earnings in this project would destroy shareholder value. Therefore, the value-maximizing decision is to return the earnings to shareholders by increasing the dividend payout.
Question 18
A technology company has enjoyed a return on equity (ROE) of 25% for several years, well above its 10% cost of equity. However, due to increased competition, its ROE on new projects is forecast to decline to 8%. To maximize shareholder value, how should the company adjust its retention ratio?
- Increase the retention ratio to signal confidence in future prospects.
- Increase the retention ratio to invest in R&D to combat the increased competition.
- Keep the retention ratio constant to maintain a stable growth rate.
- Decrease the retention ratio, as reinvesting earnings will now destroy shareholder value. (correct answer)
Explanation: When evaluating investment decisions, you must compare the return on investment to the cost of capital. If projects earn less than the cost of equity, reinvesting destroys shareholder value – it's better to return cash to shareholders who can invest elsewhere at higher returns.
Here, the company's new projects will earn only 8% ROE while shareholders require a 10% return. This means every dollar retained and reinvested actually reduces shareholder wealth by 2 cents in present value terms. The company should decrease its retention ratio and pay out more dividends, allowing shareholders to invest that cash in opportunities that meet or exceed their 10% required return.
Option A is wrong because signaling confidence doesn't change the underlying economics – you can't create value by retaining cash for poor investments, regardless of market perception. Option B falls into the common trap of assuming all R&D is value-creating. While R&D might be necessary long-term, if it only generates 8% returns against a 10% cost of equity, it destroys value in the short run. Option C ignores the fundamental principle that growth only creates value when returns exceed the cost of capital – maintaining stable growth with sub-par returns actually accelerates value destruction.
The key insight is that growth isn't always good. Only profitable growth (where ROE > cost of equity) benefits shareholders. When this condition isn't met, returning cash to shareholders maximizes value.
Study tip: Always compare project returns to the cost of capital first. High retention ratios only make sense when ROE exceeds the required return.
Question 19
A mature company consistently generates free cash flow to equity (FCFE) that significantly exceeds its net income. However, it maintains a very low dividend payout ratio and rarely engages in share repurchases, leading to a large and growing cash balance on its balance sheet. From a corporate governance perspective, this combination of factors is most likely to be a sign of:
- an agency problem where management retains cash for personal benefits or empire-building activities. (correct answer)
- a conservative financial policy designed to weather economic downturns and maintain financial flexibility.
- a strategic signal that the company is preparing for a large, value-enhancing acquisition opportunity.
- an efficient tax-minimization strategy designed to optimize long-term shareholder value and tax efficiency.
Explanation: This question tests your understanding of agency problems in corporate finance, specifically the conflict between managers and shareholders over cash distribution policies. When you see scenarios involving excess cash accumulation despite strong cash flows, think about whether management's actions align with shareholder interests.
The correct answer is A because this scenario exhibits classic signs of an agency problem. When a mature company generates FCFE that significantly exceeds net income (indicating strong operational cash generation), yet maintains minimal dividend payouts, avoids share repurchases, and accumulates large cash balances, it suggests management is hoarding cash rather than returning it to shareholders. This behavior often stems from managerial preferences for empire-building, maintaining personal job security through financial "cushions," or pursuing pet projects that may not maximize shareholder value.
Answer B is incorrect because while conservative policies involve maintaining some cash reserves, the described pattern goes beyond prudent financial management—it represents excessive cash hoarding without clear strategic purpose. Answer C fails because the scenario describes a pattern of consistent cash accumulation over time, not preparation for a specific acquisition. If management were truly preparing for value-enhancing acquisitions, they would typically communicate this strategy to shareholders. Answer D is wrong because retaining cash instead of distributing it to shareholders generally creates tax inefficiency, as corporate cash earns lower after-tax returns than shareholders could achieve through diversified investments.
Study tip: On corporate finance exams, remember that mature companies with limited growth opportunities should typically return excess cash to shareholders. When they don't, suspect agency problems unless there's clear strategic justification.
Question 20
NovaTech's CFO is analyzing the relationship between payout policy and growth. The company currently has a 35% payout ratio, ROE of 16%, and debt-to-equity ratio of 0.4. If management wants to increase the sustainable growth rate by 2 percentage points without changing the capital structure or issuing new equity, by how many percentage points must the retention ratio increase?
- 12.5 percentage points to achieve the growth target (correct answer)
- 8.7 percentage points for the required adjustment
- 15.2 percentage points given the constraint parameters
- 10.4 percentage points considering the ROE limitation
Explanation: Current retention ratio = 65%. Current sustainable growth rate = ROE × retention = 16% × 65% = 10.4%. Target growth rate = 10.4% + 2% = 12.4%. Required retention ratio = 12.4%/16% = 77.5%. Increase needed = 77.5% - 65% = 12.5 percentage points. Choice B uses an incorrect base calculation. Choice C overstates the requirement. Choice D uses a flawed methodology for the constraint analysis.