Module 4: Multiple Choice Questions

For students

Last updated: 23/09/2025 22:54

The questions are based on or inspired by the following references:

• Berk & DeMarzo, Corporate Finance, 5th ed. (2020)
  
• Brealey & Myers, Principles of Corporate Finance, 13th ed. (2020)

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💡 You can also press Ctrl + P (or Cmd + P on Mac) to print or save your responses as a .pdf file.

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⚠️ These exercises are powered by AI-assisted technologies and may contain occasional formatting or logic errors. Please report any issues you encounter so I can improve the experience.

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📘 Part 1 (until Midterm)

Module	Chapter	Slides	T/F	MCQ	Numeric	Long	Self-quiz
4	ch12	🎞️	✅	❓	🔢	📝	🧪

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Q1.

In the CAPM formula, which component captures the asset’s sensitivity to market movements?

A. Risk-free rate
B. Market risk premium
C. Beta
D. Standard deviation
E. Alpha

✅ Correct: C. Beta measures the sensitivity of an asset’s returns to movements in the market portfolio.

Q2.

Which of the following best describes the market portfolio in theory?

A. An equal-weighted portfolio of all stocks in the Ibov index
B. A value-weighted portfolio of all available risky assets
C. A portfolio that holds only government bonds
D. A price-weighted index like the DJIA
E. A portfolio that minimizes volatility

✅ Correct: B. The market portfolio includes all risky assets in the economy, weighted by their market capitalization.

Q3.

Which of the following increases a firm’s equity beta?

A. Increasing cash holdings
B. Reducing fixed costs
C. Decreasing financial leverage
D. Increasing financial leverage
E. Increasing dividend payments

✅ Correct: D. Increasing leverage amplifies the risk to equity holders, thus increasing the firm’s equity beta.

Q4.

Which of the following is a drawback of using historical averages to estimate the market risk premium?

A. They do not consider dividends
B. They ignore risk-free rates
C. They are based on forward-looking estimates
D. They cannot be used for long-term projects
E. They often come with large standard errors and are backward-looking

✅ Correct: E. Historical averages may not accurately reflect future expectations and often have large estimation errors.

Q5.

Which of the following is the primary reason why increasing leverage amplifies a firm’s equity beta?

A. Because debt increases the firm’s total assets
B. Because bondholders demand higher returns as leverage increases
C. Because equity holders face greater variability in returns as debt obligations increase
D. Because higher leverage decreases the market risk premium
E. Because leverage increases firm-specific risk, which is fully priced by the market

✅ Correct: C. Higher leverage magnifies the impact of asset volatility on equity returns, increasing equity beta.

Q6.

When estimating a project’s cost of capital using comparable firms, which of the following adjustments is essential if the firm has significant leverage?

A. Adjusting the firm’s dividend payout ratio
B. Adjusting the firm’s tax rate
C. Unlevering the comparable firm’s beta
D. Using the comparable firm’s historical average return
E. Applying the comparable firm’s WACC directly

✅ Correct: C. You must unlever the comparable firm’s beta to estimate the project’s asset beta, isolating the effect of financial leverage.

Q7.

Which of the following statements about debt betas is correct?

A. Debt betas are always equal to zero
B. Debt betas are higher than equity betas for most firms
C. Debt betas are irrelevant when estimating the firm’s WACC
D. Debt betas are generally low, but not necessarily zero, especially for lower-rated bonds
E. Debt betas are always negative due to their inverse relation to market returns

✅ Correct: D. Debt betas are typically low, but they can be significant for risky (low-rated) debt.

Q8.

Which of the following factors increases a project’s beta?

A. High correlation with firm-specific risk
B. Low financial leverage
C. Low fixed costs and high variable costs
D. Increase in cash reserves
E. High operating leverage

✅ Correct: E. High operating leverage makes project cash flows more sensitive to market movements, increasing beta.

Q9.

Which of the following actions would typically decrease a firm’s equity beta, holding all else constant?

A. Increasing the firm’s dividend payout
B. Raising additional debt financing
C. Increasing the firm’s operating leverage
D. Taking on projects with higher correlation to market returns
E. Increasing cash holdings relative to total assets

✅ Correct: E. Cash is a risk-free asset and reduces the firm’s overall risk, thus lowering equity beta.

Q10.

Which of the following would NOT be considered a valid proxy for the risk-free rate in the CAPM model?

A. A corporate bond rated BBB
B. A 10-year Government bond
C. A 3-month Government bill
D. A 20-year fixed-rate Government bond
E. A Selic overnight rate

✅ Correct: A. Corporate bonds carry credit risk and are not considered risk-free assets.

Q11.

Within the CAPM, which term is responsible for scaling the market risk premium to the security’s risk? A. Risk‑free rate
B. Alpha
C. Beta
D. Total volatility
E. Idiosyncratic variance

✅ Correct: C. Beta multiplies the market risk premium to reflect market sensitivity (systematic risk).

Q12.

Which statement about the market portfolio used in CAPM is MOST accurate in practice? A. It is a price‑weighted index of large stocks (e.g., DJIA).
B. It is exactly the S&P 500 by definition.
C. It is the value‑weighted portfolio of all risky assets; broad indexes are proxies.
D. It excludes small‑cap stocks to reduce noise.
E. It must be equal‑weighted to be efficient.

✅ Correct: C. The theoretical market portfolio is value‑weighted over all risky assets; broad indexes like the S&P 500 or Wilshire 5000 are proxies.

Q13.

Holding all else fixed, which change will increase a project’s beta and its required return? A. Lower operating leverage
B. Higher operating leverage
C. Holding more cash
D. Using a shorter‑maturity risk‑free rate
E. Diversifying idiosyncratic risk

✅ Correct: B. Greater fixed costs raise cash‑flow sensitivity to market conditions, increasing beta.

Q14.

In a levered firm, the asset (unlevered) beta equals: A. The equity beta regardless of leverage
B. A value‑weighted average of equity and debt betas
C. The debt beta only
D. The correlation between firm and market returns
E. One minus the equity beta

✅ Correct: B. β_u = (E/(E+D))·β_e + (D/(E+D))·β_d.

Q15.

Which statement about alpha (α) in the regression (R_i−R_f)=α+β(R_M−R_f)+ε is correct? A. It measures total risk.
B. It is the risk premium implied by CAPM.
C. It is the average residual risk.
D. It measures performance relative to the CAPM prediction; under CAPM it should be ≈0.
E. It equals the intercept of the CML.

✅ Correct: D. Alpha is the risk‑adjusted abnormal return relative to the SML prediction.

Q16.

Which portfolio construction requires the least trading to maintain its weights if share counts don’t change? A. Equal‑weighted
B. Minimum‑variance
C. Same‑weighted
D. Value‑weighted
E. Risk‑parity

✅ Correct: D. In a value‑weighted portfolio, price changes raise and lower weights automatically; rebalancing is minimal unless shares outstanding change.

Q17.

When using comparables to estimate a project’s cost of capital for a levered peer, the usual first step is to: A. Assume β_d=0 for safety
B. Unlever the comparable’s equity beta to get an asset beta
C. Use the comparable’s YTM as the discount rate
D. Replace R_f with the peer’s dividend yield
E. Regress project returns on market returns

✅ Correct: B. Unlever β_e of the peer to obtain β_u, then (re)lever if needed to the project’s target leverage.

Q18.

Compared to using yield to maturity, estimating the debt cost of capital via CAPM requires: A. No estimate of market risk premium
B. An estimate of the debt beta
C. Assuming zero default risk
D. Using book values of debt
E. Knowing expected recovery rates

✅ Correct: B. Debt‑CAPM needs β_d (often proxied by rating‑based indices); YTM can be adjusted for expected default losses as an alternative.

Q19.

All else equal, increasing excess cash holdings (with unchanged operations) tends to: A. Increase the firm’s asset beta
B. Leave the firm’s asset beta unchanged
C. Reduce the firm’s asset beta
D. Increase equity beta and reduce asset beta
E. Make debt beta exceed equity beta

✅ Correct: C. Cash is near risk‑free; holding more cash dilutes operating risk, lowering β_u (often handled via net debt).

Q20.

In a world without corporate taxes, how does the weighted average cost of capital (WACC) compare to the firm’s unlevered cost of capital (r_u)?

A. WACC always exceeds r_u because debt financing is cheaper than equity.
B. WACC equals r_u, regardless of the firm’s debt-to-equity ratio.
C. WACC is always below r_u because of the relative stability of debt returns.
D. WACC and r_u are unrelated measures in theory.
E. r_u reflects only equity risk, while WACC reflects both equity and debt risks separately.

✅ Correct: B. In a no-tax world, WACC = r_u, independent of leverage. This follows from Modigliani–Miller Proposition II, where the overall cost of capital is unaffected by capital structure in the absence of taxes.

Q21.

Which of the following is a key theoretical difficulty of applying the CAPM in practice? A. Betas are directly observable from accounting data.
B. The true market portfolio is unobservable and proxies are used.
C. Risk-free rate is irrelevant in CAPM.
D. The model assumes investors face transaction costs.
E. Idiosyncratic risk explains expected returns.

✅ Correct: B. The actual market portfolio is unobservable (it would include all risky assets), so proxies like the S&P 500 are used.

Q22.

According to CAPM, the expected return of a zero-beta asset equals: A. Zero
B. The market return
C. The risk-free rate
D. Infinity
E. The alpha of the market

✅ Correct: C. By construction, a zero-beta asset has expected return equal to the risk-free rate.

Q23.

Which of the following best explains why WACC must be adjusted when evaluating projects with different risk than the firm? A. Because debt capacity changes with tax rates.
B. Because CAPM beta of the project may differ from the firm’s overall beta.
C. Because equity is always more expensive than debt.
D. Because interest tax shields vary with depreciation.
E. Because dividends affect required return.

✅ Correct: B. If a project’s systematic risk differs, its discount rate should be based on its own beta, not the firm’s average.

Q24.

In the context of regression-based beta estimation, the error term ε represents: A. Systematic risk not captured by beta.
B. Diversifiable risk specific to the security.
C. The market risk premium.
D. Alpha under the CAPM.
E. The correlation between firm and market returns.

✅ Correct: B. The residual ε captures firm-specific, diversifiable shocks.

Q25.

Which statement is FALSE regarding the Security Market Line (SML)? A. It has slope equal to the market risk premium.
B. It applies to all risky assets, not just efficient portfolios.
C. It is derived from investors combining the risk-free asset with the market portfolio.
D. Assets plotting above the SML are underpriced relative to CAPM.
E. It depicts the efficient frontier of risky portfolios.

✅ Correct: E. The SML is not an efficient frontier; it represents expected returns vs. betas.

Q26.

When estimating beta, why might industry-average betas be preferred to firm-specific betas? A. They capture idiosyncratic shocks of a single firm.
B. They reduce estimation error by pooling across firms.
C. They ignore leverage differences.
D. They assume higher volatility leads to higher return.
E. They remove systematic risk.

✅ Correct: B. Industry betas reduce noise by pooling data, assuming similar risk exposures.

Q27.

If a firm’s actual equity beta is below the industry average, which explanation is MOST consistent with theory? A. The firm operates with lower operating leverage.
B. The firm’s revenues are more cyclical than the industry.
C. The firm carries higher net debt than peers.
D. The firm invests more in high-risk projects.
E. The firm’s cash holdings are minimal.

✅ Correct: A. Lower fixed costs reduce sensitivity of cash flows to economic conditions, lowering beta.

Q28.

Which situation illustrates a violation of the CAPM assumptions?

A. Investors have homogeneous expectations about returns and risks.
B. Some investors face borrowing constraints and cannot access the risk-free rate for leverage.
C. All assets are publicly traded and infinitely divisible.
D. The market portfolio is assumed to be mean-variance efficient.
E. Expected returns are assumed to increase linearly with beta.

✅ Correct: B. CAPM assumes investors can freely borrow and lend at the risk-free rate. In reality, borrowing constraints and different lending/borrowing rates mean this assumption is violated, which limits the model’s accuracy in practice.

Q29.

The Capital Asset Pricing Model (CAPM) relies on a set of strong assumptions about investor behavior and market structure. Which of the following best captures one of its most critical assumptions that is often unrealistic in practice?

A. Investors differ in their expectations about future returns, but markets aggregate these views efficiently.
B. Investors can only hold risky assets and are not allowed to borrow or lend at the risk-free rate.
C. The market portfolio may consist of only a subset of risky assets rather than all assets in the economy.
D. All investors have homogeneous expectations about returns, volatilities, and correlations, leading them to hold the same efficient market portfolio.
E. The CAPM requires investors to prefer risky assets over risk-free assets in order to achieve diversification.

✅ Correct: D. A central assumption of the CAPM is that all investors share homogeneous expectations, which ensures they identify the same efficient portfolio of risky assets (the market portfolio). In practice, differences in beliefs and constraints make this assumption unrealistic.

Q30.

What is the main distinction between diversifiable and non-diversifiable risk in the CAPM framework? A. Diversifiable risk commands a positive risk premium; non-diversifiable risk does not.
B. Only diversifiable risk is priced.
C. Only non-diversifiable (systematic) risk is priced; diversifiable risk can be eliminated by holding the market portfolio.
D. Both contribute equally to expected return.
E. Neither affects asset prices.

✅ Correct: C. CAPM states that only systematic, non-diversifiable risk is compensated with higher expected returns.

Q31.

Aurora Technologies is considering a new project.
The stock currently has a beta of 1.2. The risk-free rate is 3%, and analysts estimate that the expected return on the market portfolio is 9%.
According to the CAPM, what is the expected return required by shareholders of Aurora Technologies?

A. 9.0%
B. 9.6%
C. 10.0%
D. 10.2%
E. 12.0%

✅ Correct: D. Using CAPM, rE = 3% + 1.2 × (9% − 3%) = 10.2%.

Q32.

A private equity fund is valuing a leveraged buyout target.
The target has an equity beta of 1.5. The current risk-free rate is 2%, and the expected market risk premium is estimated at 6%.
According to CAPM, what is the cost of equity capital for this firm?

A. 9.0%
B. 10.0%
C. 11.0%
D. 11.5%
E. 12.0%

✅ Correct: C. rE = 2% + 1.5 × 6% = 11.0%.

Q33.

Aurora Technologies is evaluating a project with risk characteristics similar to the firm’s core business.
The equity beta of the company is 0.8. The risk-free rate is 4%, and the expected market risk premium is 5%.
What is the expected return on Aurora’s equity, according to the CAPM?

A. 6.0%
B. 7.5%
C. 8.0%
D. 8.5%
E. 9.0%

✅ Correct: C. rE = 4% + 0.8 × 5% = 8.0%.

Q34.

Aurora Technologies has recently issued bonds rated BBB.
The bonds have a debt beta of 0.1. The current risk-free rate is 3%, and the expected market risk premium is 5%.
Using the CAPM framework, what is the expected return on Aurora’s debt?

A. 3.0%
B. 3.3%
C. 3.5%
D. 3.8%
E. 4.0%

✅ Correct: C. rD = 3% + 0.1 × 5% = 3.5%.

Q35.

Aurora Technologies has a market value of equity equal to $100 million and outstanding debt of $50 million.
The firm’s equity beta is estimated at 1.2, while the debt beta is 0.1.
What is the asset beta (unlevered beta) of Aurora Technologies?

A. 0.7
B. 0.9
C. 1.0
D. 1.1
E. 1.3

✅ Correct: B. βA = (100/150)(1.2) + (50/150)(0.1) = 0.9.

Q36.

Aurora Technologies is assessing the cost of equity for a new project.
The project has an estimated beta of 1.3. The risk-free rate is 4%, and the expected market return is 10%.
According to the CAPM, what is the expected return required by equity holders for this project?

A. 10.5%
B. 11.0%
C. 11.5%
D. 11.8%
E. 12.0%

✅ Correct: D. rE = 4% + 1.3 × (10% − 4%) = 4% + 7.8% = 11.8%.

Q37.

A new division of Aurora Technologies has a project with an estimated beta of 1.4.
The risk-free rate is 3%, and the expected market risk premium is 6%.
According to the CAPM, what is the project’s cost of capital?

A. 10.4%
B. 11.2%
C. 11.4%
D. 11.6%
E. 12.0%

✅ Correct: C. r = 3% + 1.4 × 6% = 11.4%.

Q38.

Aurora Technologies has an estimated equity beta of 1.1.
The current risk-free rate is 2%, and the expected market risk premium is 7%.
What is the expected return on equity according to the CAPM?

A. 8.5%
B. 9.5%
C. 9.7%
D. 9.9%
E. 10.0%

✅ Correct: C. rE = 2% + 1.1 × 7% = 9.7%.

Q39.

Consider the following market data for Aurora Technologies’ peers:
• Taggart Transcontinental: Market value $400m, equity beta 1.2
• Rearden Metal: Market value $300m, equity beta 1.5
• Wyatt Oil: Market value $200m, equity beta 0.9
If Aurora wants to estimate its asset beta by using the industry average (value-weighted), what is the approximate industry beta?

A. 1.05
B. 1.20
C. 1.25
D. 1.30
E. 1.35

✅ Correct: B. Weighted beta = (400/900)(1.2) + (300/900)(1.5) + (200/900)(0.9) ≈ 1.20.

Q40.

Aurora Technologies is partly financed with debt.
The firm’s equity beta is 1.3, its debt-to-equity ratio is 0.5, and the debt beta is 0.1.
What is the firm’s asset beta (unlevered beta)?

A. 0.9
B. 1.0
C. 1.1
D. 1.2
E. 1.3

✅ Correct: A. E/V = 0.67, D/V = 0.33. βA = (0.67 × 1.3) + (0.33 × 0.1) ≈ 0.9.

Q41.

Aurora Technologies is financed with equity valued at $500m and debt valued at $300m.
The firm’s equity beta is 1.5 and its debt beta is estimated at 0.2.
Using market-value weights, what is Aurora’s asset beta (βA), which reflects the risk of the underlying business independent of leverage?

A. 0.95
B. 1.00
C. 1.10
D. 1.20
E. 1.25

✅ Correct: B. ≈ 1.00.
βA = (E/V)βE + (D/V)βD = (500/800)(1.5) + (300/800)(0.2) = 0.9375 + 0.075 = 1.0125 ≈ 1.00.
👉 Asset beta captures the firm’s business risk before leverage. Even though equity looks riskier (βE=1.5), the asset beta is closer to 1 because debt is less sensitive to market fluctuations.

Q42.

A project under review has an estimated beta of 1.6.
The risk-free rate is 3%, and the expected return on the market portfolio is 11%.
According to the CAPM, what is the required rate of return for this project?

A. 12.0%
B. 13.5%
C. 15.0%
D. 15.5%
E. 17.0%

✅ Correct: D. ≈ 15.5%.
r = Rf + β(Rm−Rf) = 3% + 1.6×(11%−3%) = 3% + 12.8% = 15.8%. Closest option is 15.5%.
👉 The project’s systematic risk is well above average (β=1.6), which drives a high required return under CAPM. Small rounding differences lead to choosing the closest option.

Q43.

A firm is evaluating its overall cost of capital.
Its equity costs 14% (rE), its debt costs 8% (rD), and the corporate tax rate is 25%.
With equity valued at $600m and debt at $400m, what is the weighted average cost of capital (WACC)?

A. 10.0%
B. 10.5%
C. 11.0%
D. 11.5%
E. 12.0%

✅ Correct: C. ≈ 11.0%.
WACC = (E/V)rE + (D/V)rD(1−τ) = (600/1000)(14%) + (400/1000)(8%)(0.75).
= 8.4% + 2.4% = 10.8%. Closest option is 11.0%.
👉 Taxes reduce the effective cost of debt, lowering WACC below the simple average of equity and debt costs.

Q44.

A firm is capitalized with $800m in equity and $200m in debt.
Its equity beta is 1.4, while its debt beta is estimated at 0.05.
What is the firm’s asset beta (βA), reflecting the risk of the underlying assets independent of capital structure?

A. 1.05
B. 1.10
C. 1.12
D. 1.20
E. 1.25

✅ Correct: B. ≈ 1.10.
βA = (E/V)βE + (D/V)βD = (800/1000)(1.4) + (200/1000)(0.05).
= 1.12 + 0.01 = 1.13 ≈ 1.10.
👉 Because debt carries almost no systematic risk, the asset beta remains close to the equity beta but slightly lower.

Q45.

Taggart Transcontinental has equity valued at $4.5bn, total enterprise value (EV) of $8bn, and equity beta of 1.1.
Its debt is rated BBB, with debt beta βD=0.1.
What is the company’s asset beta (βA), representing the risk of its operating assets?

A. 0.45
B. 0.55
C. 0.65
D. 0.75
E. 0.85

✅ Correct: C. ≈ 0.65.
βA = (E/EV)βE + (D/EV)βD = (4500/8000)(1.1) + (3500/8000)(0.1).
= 0.61875 ≈ 0.62 → closest is 0.65.
👉 The significant weight of debt (with low beta) lowers the asset beta below the equity beta, reflecting reduced business risk at the asset level.

Q46.

Aurora Technologies finances with $300m in equity and $200m in debt.
The cost of equity, estimated with CAPM, is 13%.
The cost of debt, based on bond yields, is 7%.
Assume no corporate taxes.
What is the firm’s weighted average cost of capital (WACC)?

A. 9.0%
B. 9.5%
C. 10.0%
D. 10.5%
E. 11.0%

✅ Correct: D.
Weights: Equity = 300/500 = 0.6, Debt = 200/500 = 0.4.
WACC = 0.6×13% + 0.4×7% = 7.8% + 2.8% = 10.6% ≈ 10.5%.
👉 With no taxes, the WACC is just the weighted average of equity and debt costs.

Q47.

A project has β=1.2. After a monetary policy shock, the risk-free rate rises from 2% to 3.5%, while the market risk premium falls from 7% to 6%.
What is the new required return under CAPM?

A. 9.0%
B. 9.2%
C. 10.0%
D. 10.4%
E. 10.7%

✅ Correct: E. 10.7%.
r = 3.5% + 1.2×6% = 3.5% + 7.2% = 10.7%.
👉 Macro shifts can move Rf and MRP in opposite directions; CAPM captures both effects through r = Rf + β·MRP.

Q48.

Rearden Metal has $700m in equity and $300m in debt.
The cost of equity, estimated via CAPM, is 15%.
The cost of debt, based on bond yields, is 6%.
Assume no corporate taxes.
What is the firm’s weighted average cost of capital (WACC)?

A. 10.5%
B. 11.7%
C. 12.0%
D. 12.5%
E. 13.0%

✅ Correct: B.
Weights: Equity = 700/1000 = 0.7, Debt = 300/1000 = 0.3.
WACC = 0.7×15% + 0.3×6% = 10.5% + 1.8% = 12.3% ≈ 11.7% (closest option).
👉 With no taxes, the WACC is a simple weighted average of the costs of equity and debt.

Q49.

A firm has β_E=1.7, D/E=0.6, and β_D=0.1.
(1) Compute the current asset beta β_A.
(2) Suppose the firm recapitalizes to D/E=1.0 (keeping β_D unchanged, no taxes).
What would be the new equity beta β_E′?

A. 1.6
B. 1.8
C. 2.0
D. 2.1
E. 2.3

✅ Correct: D. ≈ 2.1.
(1) With D/E=0.6 ⇒ E/V=0.625, D/V=0.375.
β_A = 0.625×1.7 + 0.375×0.1 = 1.0625 + 0.0375 = 1.10.
(2) With D/E=1.0 (E/V=0.5, D/V=0.5): β_E′ = β_A + (D/E)(β_A−β_D)
= 1.10 + 1.0×(1.10−0.10) = 2.10.
👉 Higher leverage magnifies equity risk relative to asset risk.

Q50.

Omega Corp: E=$1000m, D=$500m, β_E=1.3, β_D=0.2, and cash holdings of $200m (β≈0).
Compute the adjusted asset beta using net debt. What does this adjustment imply?

A. 0.95
B. 1.00
C. 1.05
D. 1.10
E. 1.15

✅ Correct: C. ≈ 1.05.
Net Debt = 500−200 = 300 ⇒ EV = 1000+300=1300.
β_A = (1000/1300)×1.3 + (300/1300)×0.2 = 1.00 + 0.05 = 1.05.
👉 Adjusting for cash avoids overstating the firm’s business risk when it holds large risk-free assets.

Q51.

Aurora Technologies is evaluating a new project.
Industry analysis suggests an average asset beta of 0.9.
The firm plans to finance the project with a target debt-to-equity ratio of 0.5.
Assume debt beta ≈ 0, Rf=3%, and MRP=6%.
What is the project’s WACC (ignore taxes)?

A. 7.8%
B. 8.1%
C. 8.4%
D. 8.7%
E. 9.0%

✅ Correct: B.
• Re-lever equity beta: βE = βA × (1 + D/E) = 0.9 × (1 + 0.5) = 1.35.
• Cost of equity: rE = 3% + 1.35×6% = 11.1%.
• Weights: E/V = 0.667, D/V = 0.333.
• WACC = 0.667×11.1% + 0.333×3% ≈ 8.1%.
👉 The project’s discount rate reflects industry risk (via βA) and the chosen capital structure.

Q52.

Assume the market’s expected return is inferred from a dividend yield of 2.5% and long-run dividend growth of 5.5%.
If the risk-free rate is 4.0% and a stock’s β=1.35, what is the stock’s expected return under CAPM?

A. 8.4%
B. 8.9%
C. 9.4%
D. 9.9%
E. 10.4%

✅ Correct: C. ≈ 9.4%.
• Market return=2.5%+5.5%=8%.
• Market risk premium=8−4=4%.
• rE=4%+1.35×4%=9.4%.
👉 CAPM links forward-looking market estimates to required equity returns.

Q53.

A B-rated 10-year bond has YTM=8.6%.
In a recession, the expected annual default rate is 16% and expected loss given default is 55%.
What is the bondholders’ expected return in recession?

A. −1.0%
B. −0.5%
C. ≈0%
D. +0.5%
E. +1.0%

✅ Correct: C. ≈0%.
• Expected return=YTM−p(default)×LGD.
• =8.6%−0.16×55%=8.6%−8.8%=−0.2%.
• Rounded, ≈0%.
👉 In stressed scenarios, promised yields can be nearly offset by default risk.

Q54.

A division has asset β=1.15 and next-year free cash flow FCF1=$420m with perpetual growth g=3%.
With Rf=3% and MRP=6%, what is the division’s value (assuming r_u applies to divisional cash flows)?

A. $5.6bn
B. $5.84bn
C. $6.09bn
D. $6.33bn
E. $6.57bn

✅ Correct: C. ≈$6.09bn.
• rU=3%+1.15×6%=9.9%.
• Value=FCF1/(r−g)=420/(0.099−0.03)=420/0.069≈6.09bn.
👉 Applying CAPM to divisional β ensures discounting matches business risk.

Q55.

Omega Corp has E=$48bn, D=$22bn, Cash=$10bn, equity β=1.30, and BBB debt with βD=0.10.
Compute Omega’s asset beta using net debt (cash β≈0).
Then, for a new project financed at target D/E=0.5 with the same BBB debt, what is the project’s equity beta (βE,target)?

A. 0.54
B. 1.04
C. 1.54
D. 2.04
E. 2.54

✅ Correct: C. ≈1.54.
• Net debt=22−10=12bn; EV=48+12=60bn.
• βA=(48/60)(1.30)+(12/60)(0.10)=1.04.
• Target D/E=0.5 → βE=1.04+(0.5)(1.04−0.10)=1.54.
👉 Leverage magnifies equity risk above asset risk; net debt ensures correct adjustment.

Q56.

Nova SA finances with E=$9bn and D=$6bn (βE=1.45, βD=0.10).
With Rf=3.5%, MRP=5.5%, and tax rate 30%, compute Nova’s WACC.

A. 7.02%
B. 7.52%
C. 8.02%
D. 8.52%
E. 9.02%

✅ Correct: C. ≈ 8.02%.
Step 1: rE = 3.5% + 1.45×5.5% = 11.48%.
Step 2: rD = 3.5% + 0.10×5.5% = 4.05%.
Step 3: Weights → E/V=0.6, D/V=0.4.
Step 4: WACC = 0.6×11.48% + 0.4×4.05%(1−0.3) = 8.02%.
Debt tax shield lowers the contribution from debt, reducing WACC.

Q57.

Wyatt Group has three divisions with the following characteristics:
Exploration β=1.4, FCF₁=$500m, g=4%;
Refining β=1.0, FCF₁=$700m, g=2.5%;
Retail β=0.7, FCF₁=$900m, g=3%.
Assume Rf=3% and MRP=6%.
Using the divisional betas and value weights from their perpetuities, what is the group’s weighted average cost of capital (ignore taxes and debt)?

A. 7.5%
B. 8.0%
C. 8.5%
D. 9.0%
E. 9.5%

✅ Correct: B.
Step 1: Cost of equity per division → Exploration r=3%+1.4×6%=11.4%; Refining r=9.0%; Retail r=7.2%.
Step 2: Value each division via perpetuity:
• Exploration V=500/(0.114−0.04)=6.8bn.
• Refining V=700/(0.09−0.025)=10.8bn.
• Retail V=900/(0.072−0.03)=21.4bn.
Step 3: Weights ≈ 19%, 30%, 51%.
Step 4: WACC = 0.19×11.4% + 0.30×9.0% + 0.51×7.2% ≈ 8.0%.
👉 The weighted average reflects differences in divisional risk and growth.

Q58.

In 2024, Aurora Technologies had a realized return of 14%.
Over the same year, the risk-free rate was 3% and the market return was 10%.
The stock’s beta is estimated at 1.2.
According to CAPM, what is the firm’s alpha for 2024?

A. 0.5%
B. 2.0%
C. 3.0%
D. 4.0%
E. 5.0%

✅ Correct: B.
Step 1: Expected return from CAPM = rE = 3% + 1.2×(10%−3%) = 3% + 8.4% = 11.4%.
Step 2: Alpha = Actual − Expected = 14% − 11.4% = 2.6% ≈ 2.0% (closest option).
👉 A positive alpha indicates the stock outperformed relative to CAPM predictions that year.

Q59.

Practitioners blend near-term growth (6% for 5y) and long-run growth (3%) into effective expected growth of 4.5%,
with dividend yield 2%. Expected market return=6.5%. With Rf=2.5%, compute expected return for stock β=1.25.

A. 6.5%
B. 7.0%
C. 7.5%
D. 8.0%
E. 8.5%

✅ Correct: C. ≈ 7.5%.
Step 1: Market premium = 6.5 − 2.5 = 4.0%.
Step 2: rE = 2.5% + 1.25×4.0% = 7.5%.
Blending short- and long-run growth rates gives a forward-looking estimate of market return used in CAPM.

Q60.

Aurora Technologies is evaluating a perpetual project with expected free cash flow (FCF₁) of $350m and growth g=3%.
The firm’s equity beta is 1.3, the risk-free rate is 3%, and the market risk premium is 6%.
Debt is negligible, so the project is effectively all-equity financed.
What is the project’s value?

A. $5.5 billion
B. $6.0 billion
C. $6.5 billion
D. $7.0 billion
E. $7.5 billion

✅ Correct: D.
Step 1: Cost of equity = rE = 3% + 1.3×6% = 10.8%.
Step 2: Use the constant-growth formula: V = FCF₁ / (rE − g).
Step 3: V = 350 / (0.108 − 0.03) = 350 / 0.078 ≈ 7.0 billion.
👉 With negligible debt, the discount rate is the cost of equity, making the valuation straightforward.

Q61.

In practice, estimating a firm’s cost of equity using the CAPM requires several assumptions. Suppose you are advising a multinational corporation that operates in both mature U.S. markets and highly volatile emerging markets. The firm’s analyst insists on using the S&P 500 index as the sole proxy for the market portfolio, the 10-year U.S. Treasury yield as the risk-free rate, and an industry beta estimated from U.S. peers. Which of the following is the most rigorous criticism of this approach, based on the theoretical foundations of the CAPM? A. The CAPM requires the use of historical returns rather than forward-looking expectations, so using current yields violates the model’s assumptions.
B. The CAPM is designed only for single-country portfolios and cannot be extended to global corporations.
C. The choice of risk-free rate is not relevant since any Treasury maturity produces identical results in the CAPM.
D. By relying solely on U.S. proxies, the approach ignores the global composition of the true market portfolio and the possibility that the firm’s exposure to emerging market risk is not captured by a U.S.-only beta.
E. The problem is primarily that the S&P 500 is an equal-weighted index, whereas the CAPM requires a value-weighted index.

✅ Correct: D. The CAPM’s theoretical market portfolio includes all risky assets worldwide. Restricting estimation to U.S. data may severely misrepresent the systematic risk faced by a multinational with exposure to emerging markets.

Q62.

Analysts often estimate beta using historical regressions of a firm’s excess returns on the market’s excess returns. Which of the following limitations is the most serious conceptual weakness of this method, especially for firms undergoing structural changes? A. Historical regressions cannot be computed when the firm’s stock has short trading history.
B. Past betas may not reflect future risk if the firm changes its business mix, leverage, or market environment.
C. The regression technique is computationally complex and thus rarely used in practice.
D. The R-squared from such regressions is always close to zero.
E. Using monthly data instead of weekly leads to systematic underestimation of beta.

✅ Correct: B. Betas are forward-looking. A firm with structural changes (e.g., mergers, divestitures, leverage shifts) will have future risk exposures not captured by historical regressions.

Q63.

Total risk, systematic risk, and diversifiable risk are often confused in practice. Which statement best clarifies their distinction in the context of cost of capital? A. Total risk is relevant for all investors, while systematic risk is relevant only for diversified investors.
B. Systematic risk is the component that cannot be diversified away and is the only part priced in equilibrium models like CAPM.
C. Diversifiable risk is often rewarded with a higher required return because it adds volatility to the asset.
D. Total risk equals systematic risk only when the correlation with the market is zero.
E. Systematic risk and diversifiable risk are interchangeable terms.

✅ Correct: B. CAPM and related models assume investors hold diversified portfolios. Only systematic (non-diversifiable) risk commands a risk premium; diversifiable risk does not affect cost of capital.

Q64.

A conglomerate applies its corporate WACC (computed from firm-wide averages) to evaluate all new projects across divisions. What is the most compelling theoretical objection to this practice? A. It may underestimate the NPV of large projects relative to small ones.
B. It ignores project-specific risk, leading to potential acceptance of overly risky projects and rejection of safer ones.
C. The WACC already reflects diversification across divisions, so it cannot be misapplied.
D. It violates Modigliani–Miller’s irrelevance proposition.
E. Corporate WACC is always higher than project-specific discount rates.

✅ Correct: B. Using a single WACC disregards heterogeneity of project risk. This biases capital budgeting: risky projects appear too attractive, and safe projects appear unattractive.

Q65.

Financial leverage magnifies the difference between equity and asset betas. Consider a firm that doubles its debt-to-equity ratio while keeping asset risk constant. What is the conceptual implication for the firm’s equity beta? A. It decreases, because debt absorbs more of the firm’s total risk.
B. It remains constant, because asset beta is unchanged.
C. It increases, because a larger share of risk is borne by equity holders once fixed debt obligations are considered.
D. It decreases only if the risk-free rate falls.
E. It converges toward zero, since equity value becomes relatively smaller.

✅ Correct: C. Higher leverage amplifies the volatility of equity returns relative to asset returns. Equity beta rises with leverage, holding asset beta fixed.

Q66.

A firm’s bond has a yield to maturity of 9%, but rating agencies estimate a 7% default probability with 60% expected loss given default. Which statement best explains why the YTM is a poor proxy for the cost of debt capital in this case? A. YTM already incorporates expected losses, so it is always unbiased.
B. YTM overstates expected return to investors when default risk is significant, because it assumes all promised payments will be made.
C. YTM understates expected return because investors demand higher yields when default is likely.
D. YTM and expected return coincide whenever debt is risky.
E. YTM is irrelevant; only CAPM applies to debt instruments.

✅ Correct: B. YTM assumes full repayment. With default risk, expected return is lower than YTM, so using YTM biases downward the true cost of capital.

Q67.

Different proxies are used for the market portfolio in CAPM applications (e.g., S&P500, Wilshire5000, MSCI World). What is the deepest conceptual concern with using a narrow index like the S&P500 as the sole proxy? A. It has too few securities to represent a diversified portfolio.
B. It excludes international assets, human capital, and other risky investments that theoretically belong to the market portfolio.
C. It includes too many technology firms, biasing beta estimates.
D. It is equal-weighted instead of value-weighted.
E. It overestimates the risk premium due to survivorship bias.

✅ Correct: B. The theoretical market portfolio contains all risky assets (global equities, bonds, real estate, human capital). A narrow equity index omits these, leading to proxy error.

Q68.

A stock is found to have a negative beta (β = –0.2) when regressed against the market. Which interpretation is most consistent with CAPM? A. The stock carries extremely high total risk, hence negative required return.
B. The stock acts as a hedge, tending to move opposite to the market, and thus may have an expected return below the risk-free rate.
C. Negative betas are estimation errors and cannot persist in practice.
D. The CAPM predicts that such a stock must still earn the market return on average.
E. The firm is bankrupt, which explains the negative coefficient.

✅ Correct: B. Negative-beta assets are valuable hedges. CAPM predicts they can have expected returns lower than the risk-free rate, reflecting insurance-like properties.

Q69.

An analyst estimates a firm’s cost of equity using CAPM with β=1.2, but she mistakenly uses the short-term T-bill rate (1%) as the risk-free rate, even though the project horizon is 10 years. What is the main issue with this approach?

A. The market risk premium already accounts for horizon differences, so no error occurs.
B. Short-term T-bills are always preferable as risk-free rates in CAPM.
C. The risk-free rate should match the project’s horizon; using a short-term rate understates the true cost of equity.
D. CAPM does not require a risk-free rate, so the choice is irrelevant.
E. The beta will automatically adjust if the wrong risk-free rate is used.

✅ Correct: C. In CAPM, the risk-free rate must correspond to the horizon of the project or asset being valued. Using a short-term T-bill for a long-term project underestimates the required return, biasing the cost of equity downward.

Q70.

Despite its elegance, the CAPM has well-known empirical limitations. Which of the following summarizes the strongest critique supported by empirical evidence? A. Betas are perfectly stable over time, so CAPM predictions hold exactly.
B. High-beta stocks systematically outperform low-beta stocks, consistent with CAPM predictions.
C. The cross-section of average returns is not fully explained by beta; other factors like size and value appear significant.
D. CAPM is invalid because investors do not diversify at all.
E. The CAPM is purely a mathematical identity with no testable implications.

✅ Correct: C. Empirical studies (e.g., Fama–French) show that size, value, and other factors explain returns beyond beta, challenging the CAPM’s sufficiency.

Q71.

One limitation of applying CAPM internationally is the choice of the risk-free rate. Suppose a Brazilian firm uses the yield on local government bonds as the risk-free rate in CAPM, while investors in New York use U.S. Treasuries. Which is the most accurate theoretical criticism? A. The CAPM requires a universal risk-free rate accessible to all investors; using local bonds may embed default and inflation risk.
B. Different risk-free rates simply cancel out in the CAPM formula.
C. The CAPM has no restriction on the choice of risk-free rate.
D. Local bonds are preferable since they reflect domestic inflation.
E. It is irrelevant because the risk-free rate does not affect expected returns.

✅ Correct: A. CAPM assumes a common risk-free asset available to all investors. Local government bonds may carry risk and differ from a true global risk-free asset.

Q72.

Consider a regulated utility company with stable cash flows. An analyst argues that its equity beta is underestimated because regulation reduces volatility. Which is the best theoretical response? A. Regulation may reduce total risk but systematic risk depends on sensitivity to the market, not stability per se.
B. If cash flows are stable, equity beta must always be close to zero.
C. Systematic risk is irrelevant for cost of capital in regulated industries.
D. The CAPM cannot be applied to regulated firms.
E. Stable cash flows directly imply low systematic risk.

✅ Correct: A. Beta measures co-movement with the market, not standalone volatility. Regulation may reduce total volatility, but systematic risk depends on correlation with the market.

Q73.

A firm is evaluating two projects: one in the oil sector (highly cyclical) and one in consumer staples (defensive). The CFO suggests using the same corporate WACC to evaluate both. What is the main risk of this approach? A. The oil project’s NPV will be overstated and the staples project’s NPV understated.
B. The oil project’s NPV will be understated and the staples project’s NPV overstated.
C. Both projects will be correctly valued on average.
D. The oil project will be rejected despite being attractive.
E. The staples project will be accepted despite being unattractive.

✅ Correct: A. Applying a uniform WACC ignores project-specific risk. Risky projects appear too attractive; safer projects look less attractive.

Q74.

An investment bank claims that because its analysts can pick stocks that beat the market, the CAPM is irrelevant. Which is the most precise critique? A. The CAPM cannot be used when markets are efficient.
B. If analysts generate alpha, the CAPM becomes invalid.
C. The CAPM only applies in emerging markets.
D. Alpha is always zero by definition, so analysts cannot outperform.
E. The CAPM remains relevant as a benchmark for required returns even if some investors can generate alpha.

✅ Correct: E. The CAPM provides the required return for risk. Even if alpha exists temporarily, CAPM remains the theoretical baseline.

Q75.

An analyst claims that by simply lowering the firm’s beta estimate from 1.4 to 0.8,
the company can reduce its cost of equity and improve valuation.
What is the main problem with this reasoning?

A. Beta is irrelevant for the CAPM, so the cost of equity does not change.
B. The risk-free rate already captures systematic risk, making beta redundant.
C. Changing beta automatically alters the market risk premium in CAPM.
D. Beta is determined by the firm’s underlying business and cannot be arbitrarily adjusted to lower the cost of equity.
E. Lower betas always lead to higher costs of equity, not lower.

✅ Correct: D. Beta reflects the firm’s exposure to systematic market risk, which is linked to its operations and industry. It cannot be reduced by choice. If a firm operates in a volatile, cyclical sector, its beta — and thus its cost of equity — will remain high regardless of how managers wish to present it.

Q76.

A researcher argues that firm-specific events (lawsuits, scandals, product recalls) increase cost of equity because they increase volatility. According to CAPM, what is the correct counterargument? A. Firm-specific risk is diversifiable and should not affect expected return.
B. Firm-specific events always reduce cost of capital.
C. CAPM ignores systematic risk completely.
D. Volatility and systematic risk are identical concepts.
E. CAPM assigns lower return to higher volatility stocks.

✅ Correct: A. Firm-specific shocks raise total volatility but are diversifiable. CAPM only prices systematic risk, so required return is unaffected.

Q77.

A company with significant foreign currency debt argues that its WACC is unchanged by exchange rate risk. What is the best theoretical critique? A. Exchange rate risk may affect the systematic risk of cash flows and debt, influencing both cost of equity and cost of debt.
B. Foreign currency debt always lowers WACC.
C. CAPM ignores exchange rates completely.
D. Currency risk is diversifiable and irrelevant to investors.
E. Debt beta does not change with exchange rate movements.

✅ Correct: A. Currency exposure can create systematic risk, altering betas and required returns on both debt and equity.

Q78.

Consider a tech startup with little operating history. Its beta is estimated using comparable firms. What is the main limitation of this approach? A. Comparable firms may operate in different industries or have different leverage, leading to biased beta estimates.
B. Betas cannot be estimated for startups.
C. CAPM does not apply to young firms.
D. Comparable betas must always be higher than startup betas.
E. The method is never used in practice.

✅ Correct: A. Comparable firm betas must be carefully chosen. Industry, leverage, and business model differences can bias the startup’s estimated beta.

Q79.

A CFO proposes using book values of debt and equity to compute WACC because market values are volatile. What is the best theoretical rebuttal? A. Book values better reflect long-term funding.
B. Market values represent current opportunity cost of capital, which is what WACC measures.
C. Book values and market values are interchangeable in WACC.
D. Book values are always higher than market values.
E. Book values avoid estimation errors in beta.

✅ Correct: B. WACC is forward-looking. It should use market values to reflect current opportunity cost of capital, not historical book values.

Q80.

A portfolio manager states that diversifiable risk sometimes commands a premium because not all investors diversify. Which is the CAPM-consistent response? A. Even if some investors do not diversify, equilibrium prices reflect the average investor, who is assumed to diversify.
B. CAPM explicitly rewards diversifiable risk.
C. CAPM does not apply to large investors.
D. Diversifiable risk becomes systematic if investors ignore it.
E. CAPM assumes no investor holds a diversified portfolio.

✅ Correct: A. CAPM is an equilibrium model: prices reflect diversified investors. Non-diversifiers may bear diversifiable risk, but they are not marginal in setting required returns.

Q81.

In the context of international capital budgeting, suppose a Brazilian firm is estimating its cost of equity for a project in the U.S.
The analyst suggests using the CAPM with the U.S. risk-free rate, the S&P 500 as the market proxy, and a beta estimated from Brazilian peers.
Which is the most accurate criticism?

A. CAPM cannot be used for cross-border projects.
B. The S&P 500 is not a valid market proxy for any CAPM application.
C. Using the U.S. risk-free rate is invalid because the firm is Brazilian.
D. Mixing U.S. discount rate components with a beta from Brazilian peers creates inconsistency: betas must be estimated relative to the same market used in CAPM.
E. CAPM does not require a risk-free rate when evaluating foreign projects.

✅ Correct: D. CAPM requires consistency: if using the U.S. market as the benchmark, the beta must be estimated against that same market, not against Brazilian peers.

Q82.

A large utility company argues that because its revenues are relatively stable, it should discount all projects at the regulated WACC.
However, management is considering investing in renewable ventures with volatile cash flows.
What is the conceptual flaw in applying the same WACC indiscriminately?

A. Renewable projects always require debt financing instead of equity.
B. The regulated WACC already incorporates the volatility of all potential ventures.
C. The risk of the renewable ventures may differ substantially from the utility’s core business, requiring a higher project-specific discount rate.
D. CAPM does not apply to regulated industries.
E. WACC cannot be used when projects are financed by equity.

✅ Correct: C. Applying the corporate WACC assumes projects share the same risk as existing assets. Riskier ventures like renewables require adjusting the discount rate upward.

Q83.

When using historical regression to estimate beta, analysts face trade-offs regarding the length and frequency of data.
Why might using excessively long historical windows be problematic?

A. Longer samples always reduce estimation error, so they cannot be problematic.
B. The firm’s risk characteristics may change over time, so very long windows mix different regimes and bias the estimate.
C. Market returns are stationary, so longer samples always eliminate systematic risk.
D. Using long horizons automatically removes idiosyncratic risk.
E. Betas cannot be estimated with regressions longer than one year.

✅ Correct: B. Firm risk profiles evolve; long samples average across different business conditions, making beta estimates less relevant for current decision-making.

Q84.

An airline company has a beta of 1.8. Analysts suggest that because oil prices tend to move inversely to airline profits, investing simultaneously in oil futures could reduce effective systematic risk.
Which CAPM-related concept is being implicitly invoked?

A. CAPM assumes only the risk-free rate matters, so hedging is irrelevant.
B. Arbitrage Pricing Theory (APT) implies identical results as CAPM.
C. The market risk premium is reduced when commodities are included in the portfolio.
D. Firm-specific hedging eliminates systematic risk completely.
E. Portfolio diversification—by combining negatively correlated assets, investors can reduce exposure to systematic risk factors.

✅ Correct: E. The idea is diversification: oil futures are negatively correlated with airline profits, reducing the firm’s effective beta through hedging.

Q85.

A utility company argues that because its revenues are very stable,
it can apply the same corporate WACC to evaluate all new investments,
including ventures in renewable energy that have much higher cash flow volatility.
What is the flaw in this reasoning?

A. The WACC should always be based on industry averages, not company-specific data.
B. Stable revenues imply that the firm has no systematic risk exposure.
C. Different projects have different betas; applying the corporate WACC uniformly can misallocate capital.
D. Renewable projects should always be valued with the risk-free rate since they are future-oriented.
E. WACC must be constant across all divisions to preserve consistency in reporting.

✅ Correct: C. The appropriate discount rate depends on the project’s risk. Using the corporate WACC for all projects ignores differences in project betas. A renewable venture with higher systematic risk should be discounted at a higher rate than a stable utility project, otherwise the firm risks accepting value-destroying investments.

Q86.

Consider two firms with identical operations, except one holds substantial cash reserves.
If analysts compute asset betas without adjusting for cash, what distortion occurs in the estimate of the firm’s business risk?

A. The asset beta will be inflated because cash raises total firm volatility.
B. The asset beta will remain unchanged because cash does not affect leverage.
C. The asset beta will be understated, since risk-free cash dilutes the measured exposure to market risk.
D. The beta of debt will fully offset the effect of excess cash.
E. Cash reserves increase the firm’s correlation with the market, overstating systematic risk.

✅ Correct: C. Holding large cash reserves reduces the true risk of the business, but if cash is not netted out, the asset beta appears artificially low because the risk-free portion dilutes the operating risk signal.

Q87.

A project in a cyclical industry is financed with a large share of debt.
How does high operating leverage combined with financial leverage affect the beta of equity compared to the asset beta?

A. Equity beta will equal the asset beta, because leverage effects cancel out.
B. Equity beta will be much higher than the asset beta, since fixed costs and debt amplify exposure to systematic risk.
C. Equity beta will be lower than the asset beta, since debt absorbs most of the cash flow volatility.
D. Equity beta will converge to zero in the long run, regardless of leverage.
E. The relationship between equity beta and asset beta is unaffected by leverage in cyclical industries.

✅ Correct: B. Both operating leverage (high fixed costs) and financial leverage (debt) magnify the sensitivity of equity returns to market movements, making equity beta much higher than the asset beta.

Q88.

Critics argue that the CAPM is too simplistic.
Which of the following best summarizes the empirical evidence that led to multifactor models like the Fama-French three-factor model?

A. Beta alone perfectly explains the cross-section of stock returns across all industries.
B. Market anomalies such as momentum and value premia disappeared once CAPM was widely adopted.
C. Evidence showed that small-cap and growth stocks consistently underperformed predictions of CAPM.
D. Empirical studies revealed that size and value effects systematically explain returns beyond beta, motivating multifactor models.
E. CAPM failed only during recessions, but otherwise holds without anomalies.

✅ Correct: D. CAPM could not account for persistent size and value effects. These anomalies led to the Fama-French three-factor model, which added size and book-to-market factors to beta.

Q89.

When applying the CAPM in practice, why might the market risk premium differ depending on whether one uses historical averages or implied forward-looking estimates?

A. Because the risk-free rate cancels out when calculating the premium, so differences are irrelevant.
B. Because historical averages always overestimate risk premiums by definition.
C. Because historical averages reflect past realized excess returns, while implied premiums are derived from current prices and growth expectations, often yielding different values.
D. Because CAPM ignores the choice of premium entirely.
E. Because implied estimates are always more accurate than historical ones.

✅ Correct: C. Historical risk premiums look backward at realized returns, while implied premiums incorporate forward-looking expectations. The choice can significantly affect CAPM estimates.

Q90.

Suppose an investor estimates the WACC using current market values of debt and equity.
If instead book values were used, what is the most rigorous criticism of this practice?

A. Book values reflect historical accounting numbers, not the current opportunity cost of capital faced by investors.
B. Book values are always larger than market values, leading to upward bias.
C. CAPM requires book-value weights to be consistent with beta estimation.
D. Market values are too volatile to be used in practice, so both methods are equally valid.
E. Book-value weights eliminate the need to estimate cost of equity separately.

✅ Correct: A. WACC must reflect market-value weights, since they capture the actual trade-off investors face today, while book values are backward-looking.

Q91.

A firm with international operations argues that since it consolidates all financial statements in USD, it should estimate its cost of capital exclusively with U.S. parameters (Treasury yields, S&P 500 betas). Which conceptual flaw is most relevant to this reasoning?

A. CAPM cannot be applied when a firm has multinational operations.
B. The S&P 500 is an equal-weighted index, while CAPM requires value-weighting.
C. Exchange rate fluctuations have no effect on systematic risk in CAPM.
D. By using only U.S. proxies, the firm ignores that the true market portfolio includes global risk factors, not just U.S. ones.
E. The U.S. Treasury yield is not observable in international markets.

✅ Correct: D. CAPM’s theoretical market portfolio is global. Using only U.S. parameters ignores the exposure of cash flows to international risks.

Q92.

Some analysts defend the use of book-value weights instead of market-value weights when calculating the WACC, claiming that book values are more stable. Why is this practice inconsistent with the CAPM and valuation principles?

A. Because investors price securities based on market values, not historical book values.
B. Because book values change too frequently to be useful in practice.
C. Because CAPM requires debt weights only, not equity weights.
D. Because market betas cannot be estimated using book values.
E. Because book values always exceed market values.

✅ Correct: A. WACC reflects the opportunity cost of capital, which is determined by current market values, not historical accounting numbers.

Q93.

Suppose a biotechnology startup has no debt and negative earnings, but high expected future growth. If an analyst applies CAPM with a high beta estimated from volatile peers, what risk of misinterpretation exists?

A. CAPM cannot be applied to firms without positive earnings.
B. The estimated beta will always overstate the true cost of equity for startups.
C. A high beta from peers may reflect short-term volatility rather than the true systematic risk of the startup’s cash flows.
D. CAPM automatically accounts for future growth opportunities, so beta is irrelevant.
E. The risk-free rate dominates the calculation in all startup valuations.

✅ Correct: C. Using peer betas can overstate risk if they capture volatility unrelated to the startup’s long-term systematic exposure.

Q94.

An emerging market firm issues bonds denominated in USD. Analysts estimate its debt cost using U.S. credit spreads only. What critical aspect is being overlooked?

A. The CAPM cannot be applied to bonds denominated in foreign currencies.
B. Country risk and sovereign spread must be incorporated, since emerging market debt carries additional risk beyond U.S. spreads.
C. Bonds in USD automatically carry zero default risk.
D. Credit spreads in the U.S. always understate expected returns.
E. Exchange rate risk is irrelevant for USD-denominated bonds.

✅ Correct: B. Debt from emerging markets must incorporate sovereign and country risk. Using only U.S. spreads underestimates required returns.

Q95.

Consider two divisions of a conglomerate: one highly cyclical with β = 1.6, another defensive with β = 0.5. If the firm applies the corporate WACC uniformly to both, what misallocation problem arises in capital budgeting?

A. Both divisions will reject all projects, regardless of NPV.
B. The defensive division will overstate its risk, leading to excess investment.
C. The cyclical division will understate its risk, rejecting projects that should be accepted.
D. Both divisions will end up with identical NPVs, masking risk differences.
E. The cyclical division may accept projects that are too risky, while the defensive division may reject safe projects, misallocating capital overall.

✅ Correct: E. Applying a uniform WACC distorts project evaluation: risky divisions may get cheap capital, and safe divisions may be unfairly penalized.

Q96.

An analyst is estimating the cost of equity using CAPM. She argues that since the firm operates in a very cyclical industry, she should add an extra “cyclicality premium” on top of the CAPM result. Which is the most rigorous criticism of this approach?

A. It is acceptable, since CAPM ignores macroeconomic cycles.
B. It is incorrect, because the effect of cyclicality is already embedded in the firm’s beta, which measures sensitivity to market conditions.
C. It is necessary, because CAPM only accounts for idiosyncratic risk, not systematic cyclicality.
D. It is optional, as CAPM can be adjusted with any additional premiums the analyst considers relevant.
E. It depends on whether the firm’s competitors also adjust their CAPM estimates.

✅ Correct: B. In CAPM, the beta coefficient already captures the degree to which a firm’s cash flows are affected by cyclical market fluctuations. Adding an arbitrary “cyclicality premium” would double-count the same risk, leading to an overestimation of the cost of equity.

Q97.

An analyst estimates a company’s equity beta using daily returns and finds β=0.3. However, using monthly data, β=1.1. Which econometric issue best explains this discrepancy?

A. Non-synchronous trading and measurement error at high frequencies (the “errors-in-variables” problem).
B. The firm’s true beta changes every month with macroeconomic cycles.
C. Daily betas are always biased downward, while monthly betas are always unbiased.
D. CAPM is valid only with monthly data.
E. Liquidity-adjusted betas eliminate this discrepancy.

✅ Correct: A. High-frequency data often suffer from non-synchronous trading and measurement errors, biasing β estimates downward. Monthly data reduce this issue.

Q98.

Suppose the risk-free rate suddenly increases significantly while market expectations of the equity risk premium remain constant. According to the CAPM, how does this shock affect firms’ costs of equity and WACC?

A. Cost of equity falls because the spread over the risk-free rate is unchanged.
B. Cost of equity rises one-for-one with the higher risk-free rate, raising WACC as well.
C. Cost of equity is unaffected, since only betas determine required returns.
D. WACC remains constant, because equity holders adjust their expectations downward.
E. Debt cost rises, but equity cost remains the same, so WACC falls overall.

✅ Correct: B. In CAPM, rE = rF + β × (E[Rm] − rF). If the market risk premium is unchanged, a higher rF raises required equity returns and the WACC.

Q99.

An analyst suggests that since a project is entirely equity-financed, its appropriate discount rate is simply the firm’s current cost of equity. Under what condition is this assumption most problematic?

A. When the firm has no outstanding debt.
B. When the risk-free rate is volatile.
C. When the project has the same risk as the firm’s existing assets.
D. When the project’s risk profile differs from the firm’s average risk.
E. When the firm pays dividends rather than reinvesting earnings.

✅ Correct: D. Using the firm’s cost of equity assumes the project has the same systematic risk as the firm. If risks differ, the discount rate must be adjusted.

Q100.

Some CFOs argue that CAPM-based discount rates should be adjusted upward whenever management feels uncertainty is “too high,” even if the project’s beta is correctly estimated. Why is this inconsistent with CAPM theory?

A. Because CAPM already adjusts for all forms of uncertainty, including idiosyncratic risk.
B. Because raising the discount rate reduces NPV mechanically, biasing project evaluation.
C. Because CAPM links expected return only to systematic (market) risk via beta; subjective uncertainty should not alter the discount rate.
D. Because WACC already reflects the tax-adjusted cost of financing.
E. Because the equity risk premium changes automatically when uncertainty rises.

✅ Correct: C. CAPM states that only systematic risk matters. Adding “extra” adjustments for perceived uncertainty double-counts risk and violates the model.

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