Finance Quiz: Growth Payout And Valuation
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Growth Payout And ValuationQuestion 1 of 20

An analyst is valuing a company using a two-stage dividend discount model. The company just paid a dividend (D₀) of $1.50. Dividends are expected to grow at 15% per year for three years, after which the growth rate will fall to a stable 4% per year indefinitely. If the required rate of return is 11%, the company's value per share is closest to:

$34.33
$36.51
$38.04
$41.18
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Finance Quiz

Finance Quiz: Growth Payout And Valuation

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

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

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Question 1

An analyst is valuing a company using a two-stage dividend discount model. The company just paid a dividend (D₀) of $1.50. Dividends are expected to grow at 15% per year for three years, after which the growth rate will fall to a stable 4% per year indefinitely. If the required rate of return is 11%, the company's value per share is closest to:

  1. $34.33
  2. $36.51 (correct answer)
  3. $38.04
  4. $41.18
Explanation: This valuation requires discounting the dividends from the high-growth phase and the terminal value.
  1. Calculate dividends for the high-growth phase (Years 1-3):
    • D₁ = D₀ × (1 + g₁) = $1.50 × (1.15) = $1.725
    • D₂ = D₁ × (1 + g₁) = $1.725 × (1.15) = $1.984
    • D₃ = D₂ × (1 + g₁) = $1.984 × (1.15) = $2.281
  2. Calculate the terminal value at the end of Year 3 (P₃):
    • First, find the dividend for Year 4: D₄ = D₃ × (1 + g₂) = $2.281 × (1.04) = $2.372
    • P₃ = D₄ / (k - g₂) = $2.372 / (0.11 - 0.04) = $2.372 / 0.07 = $33.886
  3. Discount the dividends and terminal value back to today (Year 0):
    • PV(D₁) = $1.725 / (1.11)¹ = $1.554
    • PV(D₂) = $1.984 / (1.11)² = $1.610
    • PV(D₃) = $2.281 / (1.11)³ = $1.668
    • PV(P₃) = $33.886 / (1.11)³ = $24.778
  4. Sum the present values to find the stock price:
    • P₀ = $1.554 + $1.610 + $1.668 + $24.778 = $36.51
Distractors arise from common errors, such as miscalculating the terminal value (e.g., using D₃ instead of D₄) or making an off-by-one error in discounting.

Question 2

A company with a constant ROE of 16% and a cost of equity of 14% currently has a dividend payout ratio of 50%. The company's management is considering two mutually exclusive proposals: (1) increase the payout ratio to 60%, or (2) decrease the payout ratio to 40%. Which of the following statements best describes the valuation impact of these proposals?

  1. Proposal 2 creates more value due to higher sustainable growth rates from increased retention.
  2. Proposal 1 creates more value as higher dividend payments outweigh the reduced growth benefits.
  3. Both proposals decrease value since the current payout ratio is optimal for this company.
  4. Proposal 2 creates more value because the company earns returns exceeding its cost of capital. (correct answer)
Explanation: The key insight is that ROE (16%) > cost of equity (14%), meaning the company creates value by retaining and reinvesting earnings.
  • Current State: b = 50%, g = 0.50 × 16% = 8%. P/E = 0.50 / (0.14 - 0.08) = 8.33x
  • Proposal 1 (Increase Payout to 60%): New b = 40%, New g = 0.40 × 16% = 6.4%. New P/E = 0.60 / (0.14 - 0.064) = 7.89x. This decreases value.
  • Proposal 2 (Decrease Payout to 40%): New b = 60%, New g = 0.60 × 16% = 9.6%. New P/E = 0.40 / (0.14 - 0.096) = 9.09x. This increases value.
Since ROE > k, retaining more earnings creates value through positive NPV reinvestment opportunities.

Question 3

An analyst is using the DuPont model to analyze a company. The company has a net profit margin of 5%, total asset turnover of 1.2x, and financial leverage (assets/equity) of 2.5x. It maintains a dividend payout ratio of 30% and has a required rate of return of 12%. Based on these fundamentals, the company's justified leading P/E ratio is closest to:

  1. 4.0x
  2. 5.1x
  3. 22.1x
  4. 20.0x (correct answer)
Explanation: This question tests your understanding of how DuPont analysis connects to equity valuation through the justified P/E ratio. When you see DuPont components alongside required return and payout ratios, you're being asked to link fundamental analysis to valuation metrics. First, calculate the company's Return on Equity (ROE) using the DuPont formula: ROE = Net Profit Margin × Asset Turnover × Financial Leverage = 5% × 1.2 × 2.5 = 15%. Next, determine the growth rate using the retention ratio: Growth rate = ROE × (1 - Payout ratio) = 15% × (1 - 0.30) = 10.5%. Finally, apply the justified P/E formula: P/E = Payout ratio ÷ (Required return - Growth rate) = 0.30 ÷ (0.12 - 0.105) = 0.30 ÷ 0.015 = 20.0x. Answer choice A (4.0x) likely results from incorrectly using the reciprocal of ROE without considering growth or payout ratios. Answer choice B (5.1x) appears to stem from using the wrong denominator, possibly confusing the required return with ROE. Answer choice C (22.1x) might come from arithmetic errors in the growth calculation or using an incorrect payout ratio in the final computation. The correct answer is D) 20.0x. Study tip: Master the connection between DuPont analysis and valuation models. Practice the sequence: DuPont → ROE → Growth rate → Justified P/E. This framework appears frequently on finance exams and is essential for equity analysis.

Question 4

An analyst determines that a company has a sustainable growth rate of 7.2% and a return on equity of 16%. The company's cost of equity is 11%. Based on this information, what is the company's justified leading P/E ratio?

  1. 11.5x
  2. 14.5x (correct answer)
  3. 17.1x
  4. 27.8x
Explanation: This question requires you to first solve for the payout ratio and then use it to calculate the P/E ratio.
  1. Solve for the retention ratio (b):
    • We know g = b × ROE.
    • 0.072 = b × 0.16
    • b = 0.072 / 0.16 = 0.45 or 45%.
  2. Solve for the payout ratio (1-b):
    • Payout ratio = 1 - b = 1 - 0.45 = 0.55 or 55%.
  3. Calculate the justified leading P/E ratio:
    • P₀/E₁ = (1 - b) / (k - g)
    • P₀/E₁ = 0.55 / (0.11 - 0.072) = 0.55 / 0.038 = 14.47x, which is closest to 14.5x.
Distractor A (11.5x) incorrectly uses the retention ratio (0.45) in the numerator. Distractor C (17.1x) results from a sign error in the denominator (k+g). Distractor D (27.8x) incorrectly uses ROE in place of k in the denominator.

Question 5

A company has a required return on equity of 10%. It currently pays a dividend of $2 per share (D₀) and its stock trades for $52.50. The company's ROE is 15%. What dividend payout ratio is implied by the current market price, assuming the constant growth model holds?

  1. 30%
  2. 40%
  3. 60% (correct answer)
  4. 70%
Explanation: This problem requires working backward from the price to find the growth rate, then the retention ratio, and finally the payout ratio.
  1. Calculate D₁ and use the Gordon Growth Model to solve for the implied growth rate (g):
    • First, we need to express D₁ in terms of D₀ and g: D₁ = D₀(1 + g) = $2.00(1 + g)
    • P₀ = D₁ / (k - g)
    • $52.50 = $2.00(1 + g) / (0.10 - g)
    • $52.50 × (0.10 - g) = $2.00(1 + g)
    • $5.25 - $52.50g = $2.00 + $2.00g
    • $3.25 = $54.50g
    • g = $3.25 / $54.50 = 0.0596 or approximately 6%
  2. Use the sustainable growth formula to solve for the retention ratio (b):
    • g = b × ROE
    • 0.06 = b × 0.15
    • b = 0.06 / 0.15 = 0.40 or 40%
  3. Calculate the implied dividend payout ratio:
    • Payout ratio = 1 - b = 1 - 0.40 = 0.60 or 60%

Question 6

An analyst is evaluating a company and has compiled the following forecasts for the upcoming year: Earnings per share (E₁) of $5.00, a retention ratio (b) of 60%, a return on equity (ROE) of 15%, and a required rate of return (k) of 11%. Based on these forecasts, what is the company's Present Value of Growth Opportunities (PVGO)?

  1. $45.45
  2. $54.55 (correct answer)
  3. $100.00
  4. $104.55
Explanation: The Present Value of Growth Opportunities (PVGO) is the difference between the stock's price with growth and its no-growth value. The formula is PVGO = P₀ - (E₁/k).
  1. Calculate the no-growth value of the stock:
    • No-Growth Value = E₁ / k = $5.00 / 0.11 = $45.45.
  2. Calculate the stock's price with growth (P₀) using the Gordon Growth Model:
    • First, find the growth rate (g): g = b × ROE = 0.60 × 0.15 = 0.09 or 9%.
    • Next, find the dividend per share (D₁): D₁ = E₁ × (1 - b) = $5.00 × (1 - 0.60) = $2.00.
    • Now, calculate the price: P₀ = D₁ / (k - g) = $2.00 / (0.11 - 0.09) = $2.00 / 0.02 = $100.00.
  3. Calculate PVGO:
    • PVGO = P₀ - (E₁/k) = $100.00 - $45.45 = $54.55.
Distractor A is the no-growth value. Distractor C is the stock's price with growth. Distractor D results from incorrectly using retained earnings instead of dividends in the GGM.

Question 7

A company can be valued using the formula P₀ = E₁/k + PVGO. If a company's return on equity (ROE) is equal to its required rate of return (k), the company's valuation is most accurately described by which of the following?

  1. The stock price P₀ will be equal to E₁/k, because PVGO will be zero. (correct answer)
  2. The stock price P₀ will be greater than E₁/k, because growth is still positive.
  3. The stock price P₀ will be less than E₁/k, because growth opportunities are not profitable.
  4. The stock price cannot be determined because the payout ratio is unknown.
Explanation: PVGO (Present Value of Growth Opportunities) represents the value added by reinvesting earnings in projects that earn more than the cost of capital. A project's net present value (NPV) is positive only if its return exceeds the discount rate. In this context, ROE is the return on reinvested earnings, and k is the discount rate. When ROE = k, the investments earn exactly the required rate of return. This means the NPV of these growth opportunities is zero. Therefore, PVGO is zero. The valuation formula P₀ = E₁/k + PVGO simplifies to P₀ = E₁/k. The company is a 'no-growth' company in terms of value creation, even if its earnings are growing.

Question 8

A company's cost of equity increases due to a rise in market risk. The company's ROE, which is currently higher than the original cost of equity, and its dividend payout ratio remain unchanged. What is the most likely impact on the company's sustainable growth rate (g) and its justified P/E multiple?

  1. g is unchanged; P/E multiple increases.
  2. g is unchanged; P/E multiple decreases. (correct answer)
  3. g decreases; P/E multiple decreases.
  4. g increases; P/E multiple is unchanged.
Explanation: Let's analyze the impact on each component:
  1. Sustainable Growth Rate (g): The formula is g = b × ROE. The problem states that both the retention ratio (b, implied by the constant payout ratio) and ROE are unchanged. Therefore, the sustainable growth rate (g) remains unchanged.
  2. Justified P/E Multiple: The formula is P/E = (1-b) / (k-g). We know that the numerator (1-b) is unchanged and the growth rate (g) in the denominator is unchanged. However, the cost of equity (k) has increased. An increase in k will increase the denominator (k-g), which in turn will cause the P/E multiple to decrease.
Therefore, the sustainable growth rate is unchanged, and the P/E multiple decreases.

Question 9

A company is projected to have a return on equity (ROE) that declines linearly over the next four years from its current 18% to a long-run stable level of 12%, which equals the cost of equity (k). The company currently maintains a constant 40% dividend payout ratio. To maximize shareholder value over the long term, the company's payout ratio should most likely:

  1. be held constant at 40% to maintain a predictable dividend stream for investors.
  2. gradually decrease as the ROE falls to fund projects in an attempt to restore ROE.
  3. gradually increase as the ROE falls, approaching 100% as ROE approaches the cost of equity. (correct answer)
  4. immediately increase to 100% because the future ROE is not expected to exceed the cost of equity.
Explanation: A firm creates value by retaining earnings only when its ROE is greater than its cost of equity (k). As the company's ROE declines and the spread between ROE and k narrows, the value created by reinvesting earnings diminishes. When ROE = k, there is no value created by retaining earnings (PVGO = 0), and the P/E ratio is simply 1/k regardless of the payout ratio. As ROE approaches k, the optimal strategy is to return more capital to shareholders. Therefore, the payout ratio should gradually increase as ROE falls. Once ROE falls below k, the optimal payout ratio would be 100%.

Question 10

Two companies, Firm A and Firm B, are identical in every respect (including ROE and cost of equity) except for their dividend payout policies. Both firms have an ROE of 20% and a cost of equity of 16%. Firm A has a payout ratio of 30%, while Firm B has a payout ratio of 60%. Which of the following is the most likely consequence of this difference?

  1. Firm A will have a higher stock price and a higher P/E ratio than Firm B. (correct answer)
  2. Firm A will have a higher stock price but a lower P/E ratio than Firm B.
  3. Firm B will have a higher stock price and a higher P/E ratio than Firm A.
  4. Firm B will have a higher stock price but a lower P/E ratio than Firm A.
Explanation: Since both firms have ROE > k (20% > 16%), the firm that retains more earnings will create more value and have a higher valuation multiple. Firm A:
  • Payout = 30%, Retention (b) = 70%
  • g = 0.70 × 20% = 14%
  • P/E = (1-b) / (k-g) = 0.30 / (0.16 - 0.14) = 15.0x
Firm B:
  • Payout = 60%, Retention (b) = 40%
  • g = 0.40 × 20% = 8%
  • P/E = (1-b) / (k-g) = 0.60 / (0.16 - 0.08) = 7.5x
Firm A has a higher P/E ratio. Since earnings are identical for both firms, a higher P/E ratio implies a higher stock price. Therefore, Firm A will have both a higher stock price and a higher P/E ratio than Firm B.

Question 11

A stable firm's Chief Financial Officer is evaluating the company's dividend payout policy. The company's return on equity (ROE) is projected to be 11% indefinitely, while its required rate of return on equity (k) is 14%. To maximize the company's intrinsic stock value, the CFO should recommend a policy that:

  1. sets the retention ratio to the level that maximizes the firm's sustainable growth rate.
  2. sets the dividend payout ratio as close to 100% as is prudently possible. (correct answer)
  3. matches the dividend payout ratio to the industry average to maintain a comparable P/E multiple.
  4. reduces the dividend payout ratio to increase investment in the company's operations.
Explanation: The core principle of value creation is that a company should only retain earnings if it can reinvest them at a rate of return higher than its cost of capital. In this case, the company's ROE (11%) is less than its required rate of return on equity (k) of 14%. This means that every dollar of earnings retained and reinvested in the company's operations destroys shareholder value, as shareholders could earn a higher return (14%) elsewhere on a similar-risk investment. Therefore, to maximize shareholder value, the company should return as much capital as possible to shareholders by increasing its dividend payout ratio towards 100%.

Question 12

A firm has a market value of equity of $500 million and 100 million shares outstanding. The company has $50 million in excess cash, which it intends to distribute to shareholders. If the firm repurchases shares at the prevailing market price, what is the most likely effect on the wealth of a shareholder who does not sell any shares?

  1. Wealth increases because their ownership percentage of the firm increases.
  2. Wealth decreases because the firm's total assets are reduced by the cash spent.
  3. Wealth remains unchanged as the share price remains the same after the repurchase. (correct answer)
  4. Wealth remains unchanged, but the share price decreases to reflect the cash distribution.
Explanation: In an efficient market without taxes or transaction costs, a share repurchase does not change the wealth of a non-selling shareholder or the stock price.
  1. Initial State:
    • Market Value = $500 million (This includes the $50M excess cash).
    • Shares Outstanding = 100 million.
    • Price per share = $500M / 100M = $5.00.
  2. Share Repurchase:
    • The firm uses $50 million to buy back shares at $5.00/share.
    • Number of shares repurchased = $50M / $5.00 = 10 million shares.
  3. Post-Repurchase State:
    • The firm's value is reduced by the cash spent: New Market Value = $500M - $50M = $450 million.
    • The number of shares outstanding is reduced: New Shares Outstanding = 100M - 10M = 90 million.
    • New share price = New Market Value / New Shares Outstanding = $450M / 90M = $5.00.
Since the share price remains $5.00, the wealth of a shareholder who did not sell is unchanged. Their number of shares is the same, and the price per share is the same.

Question 13

A firm adopts a total payout policy, returning capital to shareholders through a combination of dividends and share repurchases. For valuation purposes using a dividend discount model framework, the dividend per share should be adjusted to reflect the total payout. If a company has net income of $200 million, a dividend payout ratio of 20%, and uses an additional $80 million for share repurchases, what is the effective payout ratio an analyst should use to calculate the growth rate assuming the retention ratio drives growth?

  1. 40%
  2. 50%
  3. 60% (correct answer)
  4. 80%
Explanation: The question asks for the effective payout ratio for calculating the growth rate, which is based on the retention of earnings in the business. Growth is funded by retained earnings, not total payouts.
  1. Calculate total dollars paid out:
    • Dividends paid = Net Income × payout ratio = $200M × 20% = $40M.
    • Share repurchases = $80M.
    • Total Payout = $40M + $80M = $120M.
  2. Calculate total dollars retained:
    • Retained Earnings = Net Income - Total Payout = $200M - $120M = $80M.
  3. Calculate the retention ratio (b):
    • b = Retained Earnings / Net Income = $80M / $200M = 0.40 or 40%.
  4. Calculate the effective payout ratio for growth calculation:
    • The question is asking for the payout ratio that corresponds to the retention ratio driving growth. This is the total payout ratio.
    • Total Payout Ratio = Total Payout / Net Income = $120M / $200M = 0.60 or 60%.
The retention ratio used to calculate growth (g = b * ROE) would be 40%. The corresponding total payout ratio is 60%.

Question 14

An analyst is calculating the terminal value for a company at Year 5 (TV₅) using the Gordon Growth Model. The initial calculation used a terminal dividend (D₆) of $3.00, a cost of equity (k) of 12%, and a terminal retention ratio (b) of 40%, with a terminal ROE of 15%. Upon review, the analyst revises only the terminal retention ratio to 60%, believing the company will have more profitable reinvestment opportunities. What is the percentage change in the calculated terminal value (TV₅) as a result of this revision?

  1. A decrease of 33.3%
  2. An increase of 25.0%
  3. An increase of 33.3% (correct answer)
  4. An increase of 50.0%
Explanation: This multi-step problem requires calculating the terminal value under both scenarios and finding the percentage change. A key step is realizing that the earnings base (E₆) remains constant when the payout assumption changes.
  1. Analyze the initial calculation:
    • b_old = 40%, Payout_old = 60%
    • g_old = b_old × ROE = 0.40 × 15% = 6%
    • D₆ = $3.00
    • TV₅_old = D₆ / (k - g_old) = $3.00 / (0.12 - 0.06) = $3.00 / 0.06 = $50.00
  2. Determine the constant earnings base (E₆):
    • D₆ = E₆ × Payout_old
    • $3.00 = E₆ × 0.60
    • E₆ = $3.00 / 0.60 = $5.00
  3. Analyze the revised calculation:
    • b_new = 60%, Payout_new = 40%
    • g_new = b_new × ROE = 0.60 × 15% = 9%
    • D₆_new = E₆ × Payout_new = $5.00 × 0.40 = $2.00
    • TV₅_new = D₆_new / (k - g_new) = $2.00 / (0.12 - 0.09) = $2.00 / 0.03 = $66.67
  4. Calculate the percentage change:
    • % Change = (TV₅_new - TV₅_old) / TV₅_old
    • % Change = ($66.67 - $50.00) / $50.00 = $16.67 / $50.00 = 0.333 or 33.3%

Question 15

A company with an ROE greater than its cost of equity decides to increase its retention ratio. Which of the following outcomes is least likely to occur as a direct result of this policy change?

  1. The company's sustainable growth rate will increase.
  2. The company's stock price will increase.
  3. The company's Present Value of Growth Opportunities (PVGO) will increase.
  4. The company's dividend per share in the next period (D₁) will increase. (correct answer)
Explanation: When you encounter questions about retention ratios and ROE, focus on how reinvesting earnings affects both growth and current dividends. The key insight here is that retention ratio decisions create a direct trade-off between current dividends and future growth. Since the company's ROE exceeds its cost of equity, reinvesting earnings creates value. When the retention ratio increases, the company keeps more earnings to reinvest rather than paying them out as dividends. This directly reduces the dividend per share in the next period (D₁), making option D correct – it's the least likely positive outcome because it's actually a negative outcome. Let's examine why the other options would indeed occur: Option A is wrong because sustainable growth rate equals ROE×retention ratioROE \times \text{retention ratio}. With higher retention and ROE > cost of equity, sustainable growth rate definitely increases. Option B is wrong because when a company profitably reinvests earnings (ROE > cost of equity), the stock price should rise as the market recognizes the value creation. Option C is wrong because PVGO represents the value of profitable future investments. Since the company can earn above its cost of equity, retaining more earnings to fund these opportunities increases PVGO. The trap here is assuming all outcomes from a value-creating decision are positive. While increasing retention creates long-term value when ROE exceeds the cost of equity, it necessarily reduces near-term dividends. Remember: retention ratio decisions always involve this fundamental trade-off between current income and future growth, even when the decision creates overall value.

Question 16

A stable firm's Chief Financial Officer is evaluating the company's dividend payout policy. The company's return on equity (ROE) is projected to be 11% indefinitely, while its required rate of return on equity (k) is 14%. To maximize the company's intrinsic stock value, the CFO should recommend a policy that:

  1. sets the retention ratio to the level that maximizes the firm's sustainable growth rate.
  2. sets the dividend payout ratio as close to 100% as is prudently possible. (correct answer)
  3. matches the dividend payout ratio to the industry average to maintain a comparable P/E multiple.
  4. reduces the dividend payout ratio to increase investment in the company's operations.
Explanation: The core principle of value creation is that a company should only retain earnings if it can reinvest them at a rate of return higher than its cost of capital. In this case, the company's ROE (11%) is less than its required rate of return on equity (k) of 14%. This means that every dollar of earnings retained and reinvested in the company's operations destroys shareholder value, as shareholders could earn a higher return (14%) elsewhere on a similar-risk investment. Therefore, to maximize shareholder value, the company should return as much capital as possible to shareholders by increasing its dividend payout ratio towards 100%.

Question 17

An analyst is valuing a company using a two-stage dividend discount model. The company just paid a dividend (D₀) of $1.50. Dividends are expected to grow at 15% per year for three years, after which the growth rate will fall to a stable 4% per year indefinitely. If the required rate of return is 11%, the company's value per share is closest to:

  1. $34.33
  2. $36.51 (correct answer)
  3. $38.04
  4. $41.18
Explanation: This valuation requires discounting the dividends from the high-growth phase and the terminal value.
  1. Calculate dividends for the high-growth phase (Years 1-3):
    • D₁ = D₀ × (1 + g₁) = $1.50 × (1.15) = $1.725
    • D₂ = D₁ × (1 + g₁) = $1.725 × (1.15) = $1.984
    • D₃ = D₂ × (1 + g₁) = $1.984 × (1.15) = $2.281
  2. Calculate the terminal value at the end of Year 3 (P₃):
    • First, find the dividend for Year 4: D₄ = D₃ × (1 + g₂) = $2.281 × (1.04) = $2.372
    • P₃ = D₄ / (k - g₂) = $2.372 / (0.11 - 0.04) = $2.372 / 0.07 = $33.886
  3. Discount the dividends and terminal value back to today (Year 0):
    • PV(D₁) = $1.725 / (1.11)¹ = $1.554
    • PV(D₂) = $1.984 / (1.11)² = $1.610
    • PV(D₃) = $2.281 / (1.11)³ = $1.668
    • PV(P₃) = $33.886 / (1.11)³ = $24.778
  4. Sum the present values to find the stock price:
    • P₀ = $1.554 + $1.610 + $1.668 + $24.778 = $36.51
Distractors arise from common errors, such as miscalculating the terminal value (e.g., using D₃ instead of D₄) or making an off-by-one error in discounting.

Question 18

Two companies, Firm A and Firm B, are identical in every respect (including ROE and cost of equity) except for their dividend payout policies. Both firms have an ROE of 20% and a cost of equity of 16%. Firm A has a payout ratio of 30%, while Firm B has a payout ratio of 60%. Which of the following is the most likely consequence of this difference?

  1. Firm A will have a higher stock price and a higher P/E ratio than Firm B. (correct answer)
  2. Firm A will have a higher stock price but a lower P/E ratio than Firm B.
  3. Firm B will have a higher stock price and a higher P/E ratio than Firm A.
  4. Firm B will have a higher stock price but a lower P/E ratio than Firm A.
Explanation: Since both firms have ROE > k (20% > 16%), the firm that retains more earnings will create more value and have a higher valuation multiple. Firm A:
  • Payout = 30%, Retention (b) = 70%
  • g = 0.70 × 20% = 14%
  • P/E = (1-b) / (k-g) = 0.30 / (0.16 - 0.14) = 15.0x
Firm B:
  • Payout = 60%, Retention (b) = 40%
  • g = 0.40 × 20% = 8%
  • P/E = (1-b) / (k-g) = 0.60 / (0.16 - 0.08) = 7.5x
Firm A has a higher P/E ratio. Since earnings are identical for both firms, a higher P/E ratio implies a higher stock price. Therefore, Firm A will have both a higher stock price and a higher P/E ratio than Firm B.

Question 19

A company is projected to have a return on equity (ROE) that declines linearly over the next four years from its current 18% to a long-run stable level of 12%, which equals the cost of equity (k). The company currently maintains a constant 40% dividend payout ratio. To maximize shareholder value over the long term, the company's payout ratio should most likely:

  1. be held constant at 40% to maintain a predictable dividend stream for investors.
  2. gradually decrease as the ROE falls to fund projects in an attempt to restore ROE.
  3. gradually increase as the ROE falls, approaching 100% as ROE approaches the cost of equity. (correct answer)
  4. immediately increase to 100% because the future ROE is not expected to exceed the cost of equity.
Explanation: A firm creates value by retaining earnings only when its ROE is greater than its cost of equity (k). As the company's ROE declines and the spread between ROE and k narrows, the value created by reinvesting earnings diminishes. When ROE = k, there is no value created by retaining earnings (PVGO = 0), and the P/E ratio is simply 1/k regardless of the payout ratio. As ROE approaches k, the optimal strategy is to return more capital to shareholders. Therefore, the payout ratio should gradually increase as ROE falls. Once ROE falls below k, the optimal payout ratio would be 100%.

Question 20

A company can be valued using the formula P₀ = E₁/k + PVGO. If a company's return on equity (ROE) is equal to its required rate of return (k), the company's valuation is most accurately described by which of the following?

  1. The stock price P₀ will be equal to E₁/k, because PVGO will be zero. (correct answer)
  2. The stock price P₀ will be greater than E₁/k, because growth is still positive.
  3. The stock price P₀ will be less than E₁/k, because growth opportunities are not profitable.
  4. The stock price cannot be determined because the payout ratio is unknown.
Explanation: PVGO (Present Value of Growth Opportunities) represents the value added by reinvesting earnings in projects that earn more than the cost of capital. A project's net present value (NPV) is positive only if its return exceeds the discount rate. In this context, ROE is the return on reinvested earnings, and k is the discount rate. When ROE = k, the investments earn exactly the required rate of return. This means the NPV of these growth opportunities is zero. Therefore, PVGO is zero. The valuation formula P₀ = E₁/k + PVGO simplifies to P₀ = E₁/k. The company is a 'no-growth' company in terms of value creation, even if its earnings are growing.