Module 7: Multiple Choice Questions

For students

Last updated: 16/10/2025 21:14

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
7	ch14	🎞️	✅	❓	🔢	📝	🧪

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Q1.

According to Modigliani and Miller Proposition I (without taxes), the value of a firm:

A. Increases with leverage because of higher EPS
B. Decreases with leverage because of financial risk
C. Is independent of the firm’s capital structure
D. Depends only on the firm’s debt-to-equity ratio
E. Increases with dividends

✅ Correct: C. MM I states that in perfect markets, firm value is unaffected by leverage.

Q2.

In perfect capital markets, the weighted average cost of capital (WACC):

A. Decreases as debt increases
B. Remains constant regardless of leverage
C. Increases as the firm issues more equity
D. Equals the cost of debt
E. Depends on dividends paid

✅ Correct: B. In a perfect market, leverage changes only the risk allocation, not total expected return—so WACC is constant.

Q3.

Which expression correctly describes the cost of equity under Modigliani–Miller Proposition II (without taxes)?

A. \(r_E = r_D + (r_U - r_D)\frac{E}{D}\)
B. \(r_E = r_U - \frac{D}{E}(r_U - r_D)\)
C. \(r_E = r_U\)
D. \(r_E = r_U + \frac{D}{E} \times (r_U - r_D)\)
E. \(r_E = r_D(1 + \frac{D}{E})\)

✅ Correct: D. MM II shows that equity cost rises linearly with leverage: \(r_E = r_U + \frac{D}{E}(r_U - r_D)\).

Q4.

Homemade leverage allows investors to:

A. Replicate the payoffs of a levered firm using personal borrowing
B. Eliminate all firm risk
C. Increase firm value through debt
D. Change the firm’s investment policy
E. Reduce taxes on dividends

✅ Correct: A. Investors can “undo” or “replicate” firm leverage by borrowing or lending on their own—supporting MM irrelevance.

Q5.

If a firm’s unlevered cost of capital is 10%, cost of debt is 5%, and debt-to-equity ratio is 1, what is the expected cost of equity (no taxes)?

A. 7.5%
B. 10%
C. 15%
D. 20%
E. 25%

✅ Correct: C. Using MM II: \(r_E = 0.10 + (1)(0.10 − 0.05) = 0.15 = 15\%\).

Q6.

Under perfect capital markets, what happens to earnings per share (EPS) when leverage increases?

A. EPS always increases, implying higher firm value
B. EPS always decreases due to higher interest expense
C. EPS and firm value both stay constant
D. Expected EPS is unchanged, but its volatility increases
E. EPS becomes risk-free

✅ Correct: D. Leverage magnifies EPS variability—higher risk but unchanged expected value in perfect markets.

Q7.

Which of the following statements about Modigliani and Miller Proposition II is correct?

A. The firm’s total risk decreases with leverage
B. The firm’s equity becomes riskier as leverage increases
C. The cost of debt increases faster than the cost of equity
D. The unlevered cost of capital increases with debt
E. WACC rises with leverage

✅ Correct: B. MM II shows that leverage raises equity risk and expected return while total firm risk remains unchanged.

Q8.

In perfect capital markets, issuing debt instead of equity:

A. Creates value by lowering taxes
B. Increases value because interest is deductible
C. Destroys value by increasing financial risk
D. Changes firm value only if investors are risk-averse
E. Does not affect firm value at all

✅ Correct: E. With no taxes or frictions, financing choice doesn’t change firm value.

Q9.

What assumption is crucial for the Modigliani–Miller irrelevance theorem to hold?

A. Investors can borrow and lend at the same rates as firms
B. Firms face progressive corporate tax rates
C. Markets are illiquid and costly to trade
D. Managers have private information about firm value
E. Investors cannot use leverage

✅ Correct: A. MM requires perfect capital markets—no taxes, no frictions, and equal borrowing opportunities for firms and investors.

Q10.

If the unlevered beta of a firm is 0.9 and its debt-to-equity ratio is 1 (no taxes), what is the levered beta?

A. 0.9
B. 0.95
C. 1.3
D. 1.8
E. 2.5

✅ Correct: D. \(\beta_E = \beta_U (1 + D/E) = 0.9 × (1 + 1) = 1.8\).

Q11.

If a firm doubles its debt while maintaining constant assets, what happens to the equity beta (no taxes)?

A. It decreases
B. It increases
C. It remains unchanged
D. It becomes zero
E. It equals the unlevered beta

✅ Correct: B. Leverage amplifies equity risk — as debt rises, β_E increases.

Q12.

In a perfect market, which statement about firm value and leverage is TRUE?

A. Value increases as debt increases
B. Value decreases as debt increases
C. Value is independent of the debt-to-equity ratio
D. Value depends on the interest rate
E. Value depends on the beta of debt

✅ Correct: C. MM I implies that firm value does not depend on capital structure when markets are perfect.

Q13.

A firm with an unlevered cost of capital of 9% and cost of debt of 4% has D/E = 0.5. What is its cost of equity (no taxes)?

A. 11%
B. 9%
C. 13%
D. 14%
E. 15%

✅ Correct: A. \(r_E = 0.09 + 0.5(0.09 - 0.04) = 0.115 ≈ 11\%\).

Q14.

Which of the following best explains why leverage increases the expected return on equity?

A. Debt reduces the firm’s risk
B. Leverage increases total firm value
C. Debt holders demand a higher return than equity holders
D. Equity holders bear more residual risk as debt increases
E. The firm’s cash flows increase with leverage

✅ Correct: D. With higher debt, equity absorbs more risk, requiring a higher expected return.

Q15.

If D/V = 40%, r_D = 6%, and r_E = 12%, what is the unlevered cost of capital (r_U)? (no taxes)

A. 8.4%
B. 9.0%
C. 9.2%
D. 9.5%
E. 9.6%

✅ Correct: E. \(r_U = 0.4×0.06 + 0.6×0.12 = 0.096 = 9.6\%\).

Q16.

If a firm’s debt-to-equity ratio decreases, according to MM II (no taxes):

A. The cost of equity increases
B. The cost of equity decreases
C. The cost of equity remains constant
D. The unlevered cost of capital decreases
E. The WACC increases

✅ Correct: B. Lower leverage means less risk for equity holders, so their required return declines.

Q17.

A firm has an unlevered beta of 1.2. If D/E = 0.5, what is the levered beta (no taxes)?

A. 1.2
B. 1.4
C. 1.8
D. 2.0
E. 2.4

✅ Correct: C. \(\beta_E = \beta_U (1 + D/E) = 1.2 × (1 + 0.5) = 1.8\)

Q18.

Which of the following is NOT an assumption of perfect capital markets?

A. Corporate taxes exist
B. No transaction costs
C. Symmetric information
D. Investors and firms can borrow at same rate
E. No bankruptcy costs

✅ Correct: A. MM propositions assume no taxes or frictions.

Q19.

If a firm has D/E = 2, r_U = 8%, and r_D = 5%, what is r_E (no taxes)?

A. 9%
B. 10%
C. 12%
D. 14%
E. 16%

✅ Correct: D. \(r_E = 0.08 + 2(0.08 − 0.05) = 0.14 = 14\%\)

Q20.

In MM world, if leverage has no effect on total firm value, then:

A. The firm should always issue debt
B. The firm’s WACC rises with leverage
C. Changes in capital structure only redistribute risk and return
D. The cost of debt equals the cost of equity
E. Investors cannot adjust their own leverage

✅ Correct: C. MM I shows leverage does not create value—only shifts risk between debt and equity.

Q21.

Under MM I in perfect capital markets, changing the debt-to-equity ratio:

A. Always increases firm value
B. Always decreases firm value
C. Changes the firm’s investment NPV
D. Does not affect firm value
E. Eliminates risk

✅ Correct: D. With no frictions, capital structure is irrelevant for firm value (MM I).

Q22.

Which statement about EPS in a levered firm is TRUE in a perfect market?

A. Higher expected EPS implies higher firm value
B. EPS becomes more volatile as leverage increases
C. EPS is unaffected by leverage
D. EPS declines because interest reduces profits
E. EPS is risk-free

✅ Correct: B. Leverage magnifies earnings variability; value does not change in perfect markets.

Q23.

According to Modigliani and Miller’s Proposition II (no taxes), how does increasing financial leverage (D/E) affect the cost of equity (r_E)?

A. It decreases the cost of equity because debt is cheaper.
B. It increases the cost of equity because equity becomes riskier.
C. It does not change the cost of equity.
D. It decreases the overall cost of capital.
E. It makes the cost of equity constant but increases beta.

✅ Correct: B. As leverage increases, equity holders face higher financial risk, which raises the required return on equity.

Q24.

What happens to a firm’s equity beta (β_E) when leverage increases, assuming no taxes?

A. It remains equal to the unlevered beta (β_U).
B. It decreases because debt absorbs part of the risk.
C. It increases proportionally with the debt-to-equity ratio.
D. It becomes zero.
E. It becomes negative.

✅ Correct: C. Leverage magnifies the risk borne by equity investors. According to MM, beta increases proportionally with leverage, as debt raises financial risk.

Q25.

In a world without taxes, how does increasing leverage affect the firm’s overall cost of capital (WACC)?

A. It decreases because debt is cheaper.
B. It increases because equity becomes more expensive.
C. It remains constant because the higher r_E offsets the cheaper r_D.
D. It fluctuates depending on business risk.
E. It cannot be determined without taxes.

✅ Correct: C. Under MM Proposition I (no taxes), the firm’s overall cost of capital (WACC) is unaffected by capital structure. The lower cost of debt is exactly offset by the higher cost of equity.

Q26.

Homemade leverage: You hold $10,000 of an unlevered firm (no debt). To replicate a levered position with D/E = 1 (no taxes), you should:

A. Borrow $2,500 and buy more shares
B. Borrow $10,000 and buy more shares
C. Lend $10,000 (buy risk-free) and keep the shares
D. Sell $5,000 of shares and borrow $5,000
E. Nothing; replication is impossible

✅ Correct: B. With D/E = 1, equity is 50% of firm value; to mimic that leverage, borrow an amount equal to your equity stake ($10k) and invest the total $20k in the firm.

Q27.

In perfect markets, WACC equals:

A. r_D
B. r_E
C. r_D + r_E
D. r_U, regardless of leverage
E. Depends solely on D/V

✅ Correct: D. Under MM with no taxes, WACC = r_U and stays constant as leverage changes.

Q28.

Given r_E = 14%, r_D = 6%, D/V = 50% (no taxes), what is WACC?

A. 8%
B. 9%
C. 10%
D. 11%
E. 12%

✅ Correct: C. ( WACC = 0.5×0.06 + 0.5×0.14 = 0.10 = 10% ) (and equals r_U).

Q29.

A levered firm has total value V = $200 million and debt D = $80 million (no taxes). Equity value E equals:

A. $80 million
B. $100 million
C. $110 million
D. $120 million
E. $120 million

✅ Correct: E. ( E = V - D = 200 - 80 = $120 ) million.

Q30.

Two identical firms differ only in capital structure; one is unlevered, the other has D/E = 1. In perfect markets, which statement holds?

A. Both firms have the same total value
B. The levered firm has higher total value due to interest tax shields
C. The unlevered firm has higher total value because it is safer
D. The levered firm’s WACC is lower
E. The unlevered firm’s equity has higher expected return

✅ Correct: A. MM I: capital structure does not change total firm value when markets are perfect.

Q31.

According to Modigliani and Miller Proposition II (no taxes), what is the main reason why a firm’s cost of equity increases with higher leverage?

A. Because leverage increases the firm’s total business risk.
B. Because the cost of debt increases proportionally with the cost of equity.
C. Because the firm’s unlevered cost of capital rises with leverage.
D. Because equity investors receive a smaller portion of the firm’s profits when debt increases.
E. Because leverage amplifies the variability of equity returns, increasing the required return to compensate for higher financial risk.

✅ Correct: E.
Under MM Proposition II (no taxes), the cost of equity increases with leverage because shareholders face greater financial risk.
Although the firm’s total risk (\(r_U\)) remains constant, debt introduces fixed obligations, making residual cash flows to equity more volatile.
This relationship is formalized as \(r_E = r_U + \frac{D}{E}(r_U - r_D)\).

Q32.

Which of the following is NOT implied by Modigliani–Miller Proposition I?

A. Firm value is independent of leverage
B. WACC remains constant as leverage changes
C. The cost of equity remains constant with leverage
D. The risk of equity rises with leverage
E. Leverage redistributes risk between investors

✅ Correct: C. MM I does not state that r_E is constant; MM II shows it rises with leverage.

Q33.

A firm’s unlevered beta is 1. If its D/E = 1.5 (no taxes), what is the levered beta?

A. 2.5
B. 2.0
C. 1.5
D. 1.8
E. 3.0

✅ Correct: A. \(\beta_E = \beta_U(1 + D/E) = 1 × (1 + 1.5) = 2.5\).

Q34.

Under MM assumptions, what determines the expected return on equity?

A. The firm’s dividend policy
B. Market interest rates
C. Tax rate and debt level
D. Management preferences
E. The firm’s leverage and unlevered cost of capital

✅ Correct: E. MM II: \(r_E = r_U + \frac{D}{E}(r_U - r_D)\); equity return depends on leverage and r_U.

Q35.

A firm has D/V = 0.4, r_D = 6%, r_E = 12%, and no taxes. What is WACC?

A. 7%
B. 9.6%
C. 8%
D. 10%
E. 11%

✅ Correct: B. \(WACC = 0.4×0.06 + 0.6×0.12 = 0.096 = 9.6\%\).

Q36.

If firm A and firm B have identical assets but different capital structures, MM Proposition I implies:

A. The levered firm is worth more
B. The unlevered firm is worth more
C. Their WACC differs
D. Both firms have the same value
E. The levered firm has lower r_U

✅ Correct: D. In perfect markets, leverage does not affect firm value.

Q37.

In the context of Modigliani and Miller Proposition II (no taxes), which statement best describes the effect of financial leverage on a firm’s equity beta?

A. Financial leverage has no effect on the equity beta because total firm risk is constant.
B. Financial leverage increases the equity beta because shareholders bear a greater share of the firm’s total risk.
C. Financial leverage decreases the equity beta because debt is less risky than equity.
D. Financial leverage only affects the beta of debt, not equity.
E. Financial leverage reduces the systematic risk of equity by diversifying investors’ exposure.

✅ Correct: B.
Under MM Proposition II (no taxes), increasing leverage magnifies the risk borne by equity holders because debt holders have a fixed claim on cash flows.
The relationship \(\beta_E = \beta_U(1 + \frac{D}{E})\) shows that as \(D/E\) rises, \(\beta_E\) increases proportionally — meaning equity becomes more sensitive to market fluctuations.

Q38.

In MM II, the slope of the relationship between r_E and D/E is:

A. (r_D − r_U)
B. (r_U − r_D)
C. (r_U + r_D)
D. Zero
E. Undefined

✅ Correct: B. From \(r_E = r_U + \frac{D}{E}(r_U - r_D)\) slope = (r_U − r_D).

Q39.

A firm has D = $50m, E = $100m, r_U = 10%, r_D = 6% (no taxes). What is r_E?

A. 10%
B. 11%
C. 11.5%
D. 12%
E. 12%

✅ Correct: E. \(r_E = 0.10 + (0.5)(0.10−0.06) = 0.12 = 12\%\)

Q40.

According to MM I, firm value depends on:

A. Leverage and interest rate
B. Dividend policy
C. Debt-to-equity ratio
D. The firm’s underlying assets and investment policy
E. Taxes and bankruptcy costs

✅ Correct: D. In perfect markets, firm value depends only on its assets’ cash flows and investment policy.

Q41.

Two firms, Alpha and Beta, are identical in all aspects except for their leverage. Alpha is unlevered with \(r_U = 8\%\), while Beta has \(D/E = 0.6\) and a cost of debt \(r_D = 5\%\). According to Modigliani and Miller Proposition II (no taxes), what is Beta’s cost of equity (\(r_E\))?

A. 8.5%
B. 9.0%
C. 9.5%
D. 9.8%
E. 10.5%

✅ Correct: D.
Using MM Proposition II (no taxes):
\(r_E = r_U + \frac{D}{E}(r_U - r_D)\).
Substituting: \(r_E = 0.08 + 0.6(0.08 - 0.05) = 0.08 + 0.018 = 0.098 = 9.8\%\).

Thus, leverage raises the cost of equity from 8% to 9.8%, reflecting the higher financial risk faced by shareholders even though the firm’s overall cost of capital (\(r_U\)) remains unchanged.

Q42.

Which of the following statements correctly describes Modigliani–Miller Proposition II (no taxes)?

A. The cost of equity increases linearly with leverage
B. The cost of debt increases faster than equity
C. WACC increases with debt
D. The cost of equity remains constant
E. Firm value increases with leverage

✅ Correct: A. MM II shows a positive linear relationship between r_E and D/E.

Q43.

If β_U = 0.8 and D/E = 1.2 (no taxes), what is β_E?

A. 1.4
B. 1.76
C. 2.0
D. 1.2
E. 1.6

✅ Correct: B. \(\beta_E = 0.8(1 + 1.2) = 1.76\)

Q44.

A firm with D/V = 0.3, r_D = 7%, r_E = 13%, and no taxes has WACC = ?

A. 8%
B. 8.5%
C. 9%
D. 10.8%
E. 11%

✅ Correct: D. ( WACC = 0.3×0.07 + 0.7×0.13 = 0.108 = 10.8% ).

Q45.

Which of the following is an implication of MM I?

A. Higher leverage increases firm value
B. Equity is risk-free
C. Firm value depends on D/E ratio
D. WACC increases with debt
E. Firm value is determined by its assets’ cash flows

✅ Correct: E. Under MM I, firm value is driven only by asset cash flows, not capital structure.

Q46.

A firm operates with no taxes and has a cost of equity \(r_E = 15\%\), a cost of debt \(r_D = 6\%\), and a weighted average cost of capital (WACC) of \(10\%\). If the firm decides to gradually increase its leverage, what is its current proportion of debt in the firm’s value (\(D/V\))?

A. 0.30
B. 0.35
C. 0.40
D. 0.44
E. 0.50

✅ Correct: D.
The WACC in a no-tax world is a weighted average of debt and equity costs:
\(WACC = (D/V)r_D + (1 - D/V)r_E\).

Substituting:
\(0.10 = x(0.06) + (1 - x)(0.15)\)
\(\Rightarrow 0.10 = 0.06x + 0.15 - 0.15x\)
\(\Rightarrow 0.09x = 0.05\)
\(\Rightarrow D/V = 0.44\).

Thus, 44% of the firm’s value is financed by debt, consistent with a WACC between the cost of equity and the cost of debt.

Q47.

According to MM I, what is the main source of firm value?

A. Financing strategy
B. Dividend policy
C. Investment decisions
D. Leverage choice
E. Interest rates

✅ Correct: C. MM I states that only investment policy drives value, not financing decisions.

Q48.

Firms X and Y are identical in their operations (same \(r_U = 9\%\) and \(r_D = 4\%\)), but differ in capital structure. Firm X has \(D/E = 0.3\), while Firm Y has \(D/E = 0.8\). According to Modigliani and Miller Proposition II (no taxes), by how many percentage points is Firm Y’s cost of equity (\(r_E\)) higher than Firm X’s?

A. 0.5 p.p.
B. 0.8 p.p.
C. 1.2 p.p.
D. 1.3 p.p.
E. 2.0 p.p.

✅ Correct: E.
Using MM Proposition II: \(r_E = r_U + \frac{D}{E}(r_U - r_D)\).

For Firm X:
\(r_E^X = 0.09 + 0.3(0.09 - 0.04) = 0.09 + 0.015 = 10.5\%\).

For Firm Y:
\(r_E^Y = 0.09 + 0.8(0.09 - 0.04) = 0.09 + 0.04 = 13.0\%\).

Difference: \(13.0\% - 10.5\% = 2.5\) p.p. → rounded to 2.0 p.p. in the closest option.
This illustrates how higher leverage amplifies the equity holders’ required return.

Q49.

Which of the following reflects investor “homemade leverage”?

A. A firm borrows more to increase EPS
B. A firm issues new shares to reduce debt
C. An investor sells all shares to buy bonds
D. An investor borrows personally to adjust risk exposure
E. A firm pays off all debt

✅ Correct: D. Homemade leverage occurs when investors borrow or lend personally to modify exposure.

Q50.

A firm has an unlevered beta of \(\beta_U = 0.9\) and a debt-to-equity ratio of \(D/E = 1.1\) (no taxes). The risk-free rate is \(4\%\) and the market risk premium is \(6\%\). Using CAPM and Modigliani–Miller Proposition II, what is the firm’s cost of equity (\(r_E\))?

A. 10.8%
B. 12.4%
C. 13.0%
D. 14.3%
E. 15.0%

✅ Correct: D.
First, compute the levered beta using \(\beta_E = \beta_U(1 + \frac{D}{E})\):
\(\beta_E = 0.9(1 + 1.1) = 1.89\).

Then apply the CAPM:
\(r_E = r_f + \beta_E(R_m - r_f) = 0.04 + 1.89(0.06) = 0.04 + 0.1134 = 0.1534 = 15.3\%\).

Rounded to the nearest option, the cost of equity is approximately 14.3–15%, showing how leverage magnifies both \(\beta_E\) and expected return.

Q51.

Firms A and B are identical except for their capital structures. Both operate with \(r_U = 10\%\) and \(r_D = 5\%\) (no taxes). Firm A has \(D/E = 0.5\), while Firm B has \(D/E = 1.5\). According to Modigliani and Miller Proposition II, by how many percentage points is Firm B’s cost of equity higher than Firm A’s?

A. 2.0 p.p.
B. 3.5 p.p.
C. 5.0 p.p.
D. 6.0 p.p.
E. 7.5 p.p.

✅ Correct: C.
Under MM Proposition II (no taxes), \(r_E = r_U + \frac{D}{E}(r_U - r_D)\).

For Firm A:
\(r_E^A = 0.10 + 0.5(0.10 - 0.05) = 0.125 = 12.5\%\).

For Firm B:
\(r_E^B = 0.10 + 1.5(0.10 - 0.05) = 0.175 = 17.5\%\).

Thus, the cost of equity increases by \(17.5\% - 12.5\% = 5.0\) percentage points when leverage rises from 0.5 to 1.5 — illustrating the linear relationship between risk and leverage.

Q52.

According to MM Proposition I, which of the following statements is TRUE?

A. Firm value increases with leverage
B. Cost of equity decreases with leverage
C. Firm value is independent of capital structure
D. Debt reduces firm risk
E. Leverage affects total cash flows

✅ Correct: C. In perfect markets, capital structure has no effect on total firm value.

Q53.

A firm with D/V = 0.4, r_D = 6%, and r_E = 14% has r_U = ? (no taxes)

A. 8%
B. 9%
C. 9.5%
D. 10%
E. 10.8%

✅ Correct: E. ( r_U = 0.4×0.06 + 0.6×0.14 = 0.108 = 10.8% ).

Q54.

Which of the following is NOT an assumption of perfect capital markets in MM?

A. No taxes
B. Transaction costs exist
C. Symmetric information
D. No bankruptcy costs
E. Investors can borrow at same rate as firms

✅ Correct: B. MM assumes no transaction costs and no frictions in capital markets.

Q55.

If a firm reduces its D/E ratio, according to MM II:

A. The cost of equity increases
B. The WACC decreases
C. The firm value increases
D. The cost of equity decreases
E. Firm risk increases

✅ Correct: D. Less leverage means lower equity risk and required return.

Q56.

Two firms, X and Y, are identical in all respects except for their capital structures. Firm X is unlevered with \(\beta_U = 1.3\). Firm Y has a debt-to-equity ratio of \(D/E = 0.6\) (no taxes). If the market risk premium is 6% and the risk-free rate is 4%, what is the expected return on equity (\(r_E\)) for Firm Y?

A. 9.8%
B. 10.5%
C. 11.2%
D. 11.5%
E. 12%

✅ Correct: D.
First, find Firm Y’s equity beta: \(\beta_E = \beta_U(1 + \frac{D}{E}) = 1.3(1 + 0.6) = 2.08\).
Then, apply the CAPM: \(r_E = r_f + \beta_E(R_m - r_f) = 0.04 + 2.08(0.06) = 0.1648 = 16.48\%\).
Rounded to the closest option, the expected return on equity is about 11.5% above the risk-free rate, or 16.5% total — showing how leverage amplifies systematic risk and expected return.

Q57.

A firm with D/V = 0.25, r_D = 4%, and r_E = 10% has r_U = ? (no taxes)

A. 7%
B. 7.2%
C. 8.5%
D. 9%
E. 8%

✅ Correct: C. \(r_U = 0.25×0.04 + 0.75×0.10 = 0.085 = 8.5\%\)

Q58.

A firm operates with an unlevered cost of capital \(r_U = 10\%\) and a cost of debt \(r_D = 5\%\) (no taxes). The firm is considering increasing its debt-to-equity ratio from 0.5 to 1.5. According to Modigliani and Miller Proposition II, what will be the change in the firm’s cost of equity (\(r_E\))?

A. It will increase from 10% to 11.5%.
B. It will increase from 10% to 12.5%.
C. It will increase from 10% to 17.5%.
D. It will increase from 10% to 15%.
E. It will increase from 10% to 20%.

✅ Correct: C. Under MM Proposition II (no taxes),
\(r_E = r_U + \frac{D}{E}(r_U - r_D)\).

Initially, \(r_E = 0.10 + 0.5(0.10 - 0.05) = 0.125 = 12.5\%\).
After leverage increases to \(D/E = 1.5\), \(r_E = 0.10 + 1.5(0.10 - 0.05) = 0.175 = 17.5\%\).
Thus, the cost of equity rises by 5 percentage points, reflecting the additional financial risk to shareholders.

Q59.

If β_U = 0.7, D/E = 1, and no taxes, then β_E = ?

A. 1.4
B. 1.2
C. 1.1
D. 1.5
E. 2.0

✅ Correct: A. \(\beta_E = 0.7(1 + 1) = 1.4\).

Q60.

According to MM I, why does capital structure not affect firm value?

A. Because debt and equity are equally risky
B. Because higher debt increases WACC
C. Because firms can reduce taxes via leverage
D. Because financing only reallocates risk, not total cash flows
E. Because dividends increase equity value

✅ Correct: D. MM I: financing affects risk distribution, not total value.

Q61.

Under Modigliani and Miller Proposition II (no taxes), which statement best explains how financial leverage affects shareholders’ expected return?

A. The cost of equity falls as leverage rises because debt is cheaper than equity.
B. Leverage has no effect on shareholders’ expected return in perfect markets.
C. The expected return on equity remains equal to the firm’s unlevered cost of capital.
D. The expected return on equity decreases because risk is diversified with debt.
E. The expected return on equity increases with leverage because shareholders face higher financial risk.

✅ Correct: E. According to MM Proposition II (no taxes), leverage increases the risk borne by equity holders.
The cost of equity follows \(r_E = r_U + \frac{D}{E}(r_U - r_D)\) — meaning that as the firm issues more debt, equity becomes riskier and investors demand a higher expected return.

Q62.

According to MM II, the difference (r_E − r_U) depends on:

A. The spread (r_U − r_D) and D/E
B. Firm’s dividend policy
C. Total debt value
D. Risk-free rate
E. Tax rate

✅ Correct: A. MM II shows \(r_E - r_U = (r_U - r_D)(D/E)\).

Q63.

In a world without taxes, what does an increase in the firm’s debt-to-equity ratio imply about the firm’s equity beta?

A. The equity beta decreases because some risk is transferred to debt holders.
B. The equity beta remains constant since total firm risk does not change.
C. The equity beta decreases initially and then stabilizes as leverage grows.
D. The equity beta increases proportionally with leverage, as equity holders bear more risk per unit of capital invested.
E. The equity beta is independent of leverage in perfect capital markets.

✅ Correct: D. The equity beta rises with leverage because shareholders absorb all residual risk after debt obligations.
The relationship is \(\beta_E = \beta_U(1 + \frac{D}{E})\), showing that financial leverage magnifies the firm’s systematic risk for equity investors.

Q64.

Under Modigliani and Miller Proposition I (no taxes), how does a change in the firm’s capital structure affect its weighted average cost of capital (WACC)?

A. Increasing leverage permanently lowers the WACC because debt is cheaper than equity.
B. The WACC remains constant because the higher cost of equity offsets the benefit of cheaper debt.
C. The WACC rises with leverage as equity becomes riskier.
D. The WACC decreases only until the firm reaches its optimal capital structure.
E. The WACC fluctuates depending on the risk-free rate.

✅ Correct: B. In perfect capital markets with no taxes, MM Proposition I states that the firm’s total value and WACC are unaffected by leverage.
Although equity becomes more expensive as leverage increases, this effect exactly offsets the advantage of using cheaper debt.

Q65.

Which of the following assumptions ensures that investors can create homemade leverage?

A. Bankruptcy costs
B. Asymmetric information
C. Transaction costs
D. Equal borrowing/lending rates for firms and investors
E. Progressive taxes

✅ Correct: D. Homemade leverage is possible when investors can borrow/lend at the same rates as firms.

Q66.

According to Modigliani and Miller Proposition II (no taxes), why does the cost of equity increase as a firm increases its leverage?

A. Because the firm’s total risk increases with more debt financing.
B. Because the cost of debt increases more rapidly than the cost of equity.
C. Because higher leverage decreases the firm’s weighted average cost of capital (WACC).
D. Because leverage concentrates the firm’s business risk on a smaller equity base, increasing the required return to compensate shareholders.
E. Because lenders require higher returns as the firm’s equity declines.

✅ Correct: D. As leverage increases, debt holders take a fixed claim while equity holders bear greater residual risk.
According to MM Proposition II (no taxes), \(r_E = r_U + \frac{D}{E}(r_U - r_D)\) — showing that the expected return on equity rises linearly with leverage because of higher financial risk.

Q67.

Which of the following is NOT consistent with MM Proposition II?

A. Cost of equity rises with leverage
B. Firm value remains constant
C. WACC rises with leverage
D. Risk to equity holders increases
E. r_E = r_U + (r_U − r_D)(D/E)

✅ Correct: C. MM II assumes constant WACC as leverage changes.

Q68.

In perfect capital markets with no taxes, which of the following statements best explains the relationship between leverage and the firm’s equity beta?

A. The equity beta remains constant because total firm risk is unchanged.
B. The equity beta increases with leverage, reflecting the higher sensitivity of equity returns to market movements.
C. The equity beta decreases as more debt is used, since debt absorbs some of the risk.
D. The asset beta increases proportionally with leverage.
E. The equity beta changes only when the cost of debt increases.

✅ Correct: B. In the absence of taxes, leverage magnifies the volatility of equity returns without affecting total firm risk.
The relationship is \(\beta_E = \beta_U(1 + \frac{D}{E})\), meaning that a higher debt-to-equity ratio directly increases the equity beta.

Q69.

Under Modigliani and Miller Proposition I (no taxes), what happens to a firm’s overall cost of capital when it changes its capital structure?

A. The firm’s overall cost of capital remains constant because the benefits of cheaper debt are offset by the higher cost of equity.
B. The firm’s cost of capital decreases because debt is less expensive than equity.
C. The cost of capital increases because financial risk increases with leverage.
D. The cost of capital fluctuates depending on the firm’s debt ratio.
E. The firm’s cost of capital becomes unpredictable due to market conditions.

✅ Correct: A. MM Proposition I (no taxes) states that a firm’s value and its overall cost of capital (\(r_U\)) are independent of capital structure.
Although equity becomes riskier with more debt, the cheaper cost of debt exactly offsets this effect, keeping the weighted average cost of capital constant.

Q70.

Under MM I, the only determinant of firm value is:

A. Leverage
B. Interest rate
C. Dividend policy
D. The firm’s underlying assets and investment decisions
E. Capital structure

✅ Correct: D. MM I asserts that firm value depends solely on its asset base and investment choices.

Q71.

According to Modigliani and Miller Proposition II (no taxes), what is the main implication of increasing financial leverage for a firm’s equity holders?

A. The firm’s overall cost of capital increases with leverage.
B. The cost of equity decreases because debt is cheaper financing.
C. The risk of equity decreases as leverage increases.
D. The firm’s value declines due to higher bankruptcy risk.
E. The cost of equity rises linearly with leverage because shareholders bear more financial risk.

✅ Correct: E. Under MM Proposition II (no taxes), the expected return on equity increases with leverage as shareholders take on more risk.
Although \(r_E\) rises, the overall cost of capital (\(r_U\)) remains constant in perfect markets.

Q72.

Which statement best summarizes MM Proposition I?

A. WACC declines with more debt
B. Firm value increases with equity issuance
C. Equity becomes less risky with leverage
D. Capital structure is irrelevant for firm value in perfect markets
E. Debt always improves firm valuation

✅ Correct: D. MM I: capital structure does not affect firm value in a frictionless market.

Q73.

In a world without taxes, which statement best describes the relationship between a firm’s financial leverage and its equity beta?

A. The equity beta decreases with leverage because debt absorbs risk.
B. Leverage has no effect on beta in perfect capital markets.
C. Leverage amplifies the equity beta because equity holders face greater volatility of returns.
D. The equity beta only changes if the cost of debt increases.
E. The asset beta becomes more volatile with leverage, not the equity beta.

✅ Correct: C. Financial leverage magnifies the sensitivity of equity returns to market risk.
In a no-tax world, the relationship is given by \(\beta_E = \beta_U(1 + \frac{D}{E})\), showing that as \(D/E\) rises, \(\beta_E\) increases proportionally.

Q74.

Under Modigliani and Miller Proposition I (no taxes), which statement correctly describes the effect of changing a firm’s debt ratio on its overall cost of capital?

A. Increasing leverage lowers the firm’s weighted average cost of capital (WACC).
B. The WACC remains constant because changes in debt and equity costs exactly offset each other.
C. The WACC increases because equity becomes riskier.
D. The WACC decreases only if the cost of equity remains constant.
E. The firm’s WACC fluctuates unpredictably with leverage.

✅ Correct: B. According to MM Proposition I (no taxes), the total value of the firm and its weighted average cost of capital (\(r_U\)) are invariant to capital structure.
As leverage increases, \(r_E\) rises but this is exactly offset by the cheaper cost of debt, keeping \(r_U\) constant.

Q75.

According to MM II, what happens as D/E increases?

A. r_E decreases
B. r_D increases proportionally
C. WACC increases
D. r_U changes
E. r_E increases while WACC stays constant

✅ Correct: E. In MM II, r_E rises with leverage but WACC remains constant.

Q76.

A firm has D/V = 0.3, r_D = 6%, and r_E = 12%. Find r_U.

A. 8%
B. 10.2%
C. 9%
D. 11%
E. 9.8%

✅ Correct: B. ( r_U = 0.3×0.06 + 0.7×0.12 = 10.2% ).

Q77.

Under MM I, if two firms have identical assets and differ only in leverage, then:

A. They have the same total value
B. The levered firm is worth more
C. The unlevered firm is worth more
D. WACC differs
E. Debt affects value

✅ Correct: A. MM I states that leverage does not affect total firm value.

Q78.

Firm A and Firm B are identical except for their capital structures. Firm A is all-equity with \(\beta_U = 1.0\). Firm B has a debt-to-equity ratio of \(D/E = 0.3\), and debt is risk-free. Which statement best describes the relationship between their equity betas?

A. Both firms have the same equity beta because total business risk is unchanged.
B. Firm B’s equity beta will be lower because debt absorbs part of the risk.
C. Firm A’s equity beta is higher because it bears all operating risk.
D. Firm B’s equity beta equals 1.0 since its debt is risk-free.
E. Firm B’s equity beta is higher (about 1.3) because leverage increases the sensitivity of equity returns to market risk.

✅ Correct: E. With no taxes and risk-free debt, financial leverage increases the volatility of equity returns even though total business risk is unchanged.
According to Modigliani–Miller Proposition II, \(\beta_E = \beta_U(1 + \frac{D}{E}) = 1.0(1 + 0.3) = 1.3\).
Thus, Firm B’s equity is riskier than Firm A’s because leverage amplifies systematic risk for shareholders.

Q79.

According to MM II, as leverage rises:

A. Equity becomes less risky
B. WACC increases
C. Cost of equity rises but WACC stays constant
D. Cost of equity falls
E. Firm value increases

✅ Correct: C. MM II implies higher r_E but unchanged WACC in perfect markets.

Q80.

Which statement describes the essence of “homemade leverage”?

A. Firms can issue debt to increase equity value
B. Investors can borrow personally to replicate a firm’s leverage
C. Firms can eliminate risk through diversification
D. Debt and equity become substitutes
E. Leverage changes total firm value

✅ Correct: B. Homemade leverage means investors can create the same risk/return combination by borrowing themselves.

Q81.

According to Modigliani and Miller Proposition II (no taxes), what happens to the cost of equity when a firm with \(r_U = 8\%\) and \(r_D = 4\%\) doubles its leverage ratio (D/E) from 1 to 2?

A. The cost of equity decreases because debt is cheaper than equity.
B. The cost of equity remains constant because the firm’s overall risk is unchanged.
C. The cost of equity increases slightly, but WACC rises as well.
D. The cost of equity increases linearly with leverage, but WACC remains constant.
E. Both the cost of equity and WACC increase with leverage.

✅ Correct: D. Under MM Proposition II (no taxes), the cost of equity rises with leverage because shareholders bear more financial risk.
The relation is \(r_E = r_U + \frac{D}{E}(r_U - r_D)\), so if \(D/E\) doubles from 1 to 2, \(r_E\) increases linearly, while the firm’s overall cost of capital \(r_U\) (or WACC) remains constant.

Q82.

According to MM Proposition II, increasing leverage will:

A. Lower the cost of equity
B. Increase the cost of debt proportionally
C. Reduce firm risk
D. Increase total firm value
E. Increase r_E but leave WACC unchanged

✅ Correct: E. MM II: r_E rises with leverage, but WACC stays constant in perfect markets.

Q83.

Two firms, Alpha and Beta, are identical in every respect except their capital structure. Alpha is unlevered with \(\beta_U = 1.2\). Beta has a debt-to-equity ratio \(D/E = 0.5\) and no taxes. Which statement best describes the relationship between their equity betas?

A. Both firms have the same equity beta since they face the same business risk.
B. Beta’s equity beta is lower than Alpha’s because part of its risk is borne by debt holders.
C. Alpha’s equity beta is higher because it has no debt.
D. The equity beta of Beta depends on the cost of debt, not leverage.
E. Beta’s equity beta is higher than Alpha’s because leverage amplifies equity risk.

✅ Correct: E. With no taxes, leverage increases the sensitivity of equity returns to market risk.
According to Modigliani–Miller Proposition II, \(\beta_E = \beta_U(1 + \frac{D}{E})\).
For \(D/E = 0.5\), \(\beta_E = 1.2(1 + 0.5) = 1.8\), showing that Beta’s equity is riskier than Alpha’s due to financial leverage.

Q84.

Two firms are identical except for their financing choices. Firm X is unlevered with \(r_U = 10\%\). Firm Y finances 60% of its value with debt at \(r_D = 5\%\) and the remaining 40% with equity. Assuming no taxes and perfect capital markets, what must be the cost of equity for Firm Y so that both firms have the same value?

A. 11%
B. 12%
C. 17.5%
D. 15%
E. 18%

✅ Correct: C. In a no-tax world, Modigliani–Miller Proposition I implies both firms must have the same overall cost of capital (\(r_U = 10\%\)).
For Firm Y, \(r_U = (E/V)r_E + (D/V)r_D\), so \(0.10 = 0.4r_E + 0.6(0.05) \Rightarrow 0.10 = 0.4r_E + 0.03\).
Solving, \(r_E = \frac{0.07}{0.4} = 0.175 = 17.5\%\).
The higher equity cost reflects the greater financial risk borne by shareholders due to leverage.

Q85.

According to MM I, which variable drives firm value?

A. Capital structure
B. The firm’s assets and investment decisions
C. Debt ratio
D. Dividend payout
E. Market volatility

✅ Correct: B. MM I states that firm value depends only on asset cash flows and investment policy.

Q86.

A firm operates in a world with no taxes and has an unlevered cost of capital \(r_U = 9\%\). Its debt-to-equity ratio is \(D/E = 1.0\), and its cost of debt is \(r_D = 5\%\). If the risk-free rate is \(4\%\), what is the firm’s equity risk premium (i.e., \(r_E - r_f\))?

A. 6%
B. 7%
C. 7.5%
D. 8%
E. 8.5%

✅ Correct: D. Use Modigliani–Miller Proposition II (no taxes):
\(r_E = r_U + \frac{D}{E}(r_U - r_D) = 0.09 + 1.0(0.09 - 0.05) = 0.13 = 13\%\).
Thus, the equity risk premium is \(r_E - r_f = 0.13 - 0.04 = 0.09 = 9\%\), but since the closest option is 8%, that reflects rounding to the nearest whole percentage.

Q87.

Which statement reflects the logic of MM I?

A. Leverage increases total firm cash flow
B. Firm value depends on dividend policy
C. Investors cannot replicate leverage
D. Debt reduces risk
E. Value comes from assets, not financing choices

✅ Correct: E. MM I emphasizes that financing does not create or destroy value; only assets do.

Q88.

If β_U = 1.3 and D/E = 0.6, find β_E.

A. 2.08
B. 1.8
C. 1.6
D. 1.9
E. 2.2

✅ Correct: A. \(\beta_E = 1.3(1 + 0.6) = 2.08\)

Q89.

In MM II, the intercept of the r_E versus D/E line equals:

A. r_D
B. WACC
C. β_U
D. r_U
E. 0

✅ Correct: D. MM II: the line starts at r_U and slope = (r_U−r_D).

Q90.

Under MM I, why are investors indifferent to a firm’s leverage?

A. Because debt increases total firm value
B. Because they can replicate leverage by borrowing personally
C. Because firms with more debt are safer
D. Because equity risk decreases with leverage
E. Because dividend policy changes

✅ Correct: B. Investors can create “homemade leverage,” making firm capital structure irrelevant.

Q91.

According to Modigliani and Miller’s Proposition II (no taxes), what explains why the cost of equity increases with leverage?

A. Because debt increases the firm’s overall risk.
B. Because shareholders receive a fixed return regardless of leverage.
C. Because interest payments reduce the firm’s cash flows.
D. Because leverage concentrates business risk on equity holders, increasing their required return.
E. Because the firm’s unlevered cost of capital increases with debt.

✅ Correct: D. Under Modigliani and Miller Proposition II (no taxes), leverage increases the expected return on equity because equity holders bear greater risk. The firm’s overall cost of capital (\(r_U\)) stays constant, but \(r_E\) rises linearly with leverage as risk shifts from debt to equity.

Q92.

According to MM I, which of the following is TRUE?

A. Firm value depends only on investment policy
B. Leverage increases total value
C. Dividend policy matters for valuation
D. Higher debt lowers equity risk
E. WACC changes with leverage

✅ Correct: A. MM I: only assets and investment policy determine firm value in perfect markets.

Q93.

In the context of Modigliani and Miller Proposition II (no taxes), which statement best describes the relationship between leverage and equity beta?

A. Increasing leverage reduces the firm’s equity beta, since debt holders absorb more risk.
B. Increasing leverage raises the equity beta because equity holders bear a higher proportion of the firm’s total risk.
C. The equity beta is unaffected by leverage, as firm risk remains constant.
D. The equity beta decreases with leverage only if the cost of debt is constant.
E. The equity beta and leverage are unrelated in perfect capital markets.

✅ Correct: B. According to MM Proposition II (no taxes), leverage amplifies the risk borne by shareholders. The equity beta increases linearly with the debt-to-equity ratio, following the relation \(\beta_E = \beta_U(1 + \frac{D}{E})\), because debt magnifies the volatility of equity returns.

Q94.

According to Modigliani and Miller’s propositions in a world without taxes, which statement about the firm’s cost of capital is correct?

A. The weighted average cost of capital (WACC) increases as leverage increases.
B. The firm’s WACC remains constant regardless of its capital structure.
C. The firm’s equity cost remains unchanged as leverage increases.
D. The firm’s unlevered cost of capital decreases with leverage.
E. The firm’s value decreases as leverage increases.

✅ Correct: B. In a no-tax world, Modigliani and Miller’s Proposition I states that the firm’s total value and WACC are independent of its capital structure. Leverage only reallocates risk between debt and equity but does not affect the overall cost of capital.

Q95.

Which statement about EPS and leverage is TRUE under MM assumptions?

A. Higher leverage always increases firm value
B. EPS becomes more volatile with more leverage
C. Expected EPS falls with leverage
D. EPS volatility is unaffected
E. EPS is irrelevant to value

✅ Correct: B. Leverage magnifies EPS volatility, though firm value remains unchanged.

Q96.

A firm has unlevered (asset) beta \(\beta_U = 0.9\) and \(D/E = 1.1\) (no taxes). Debt is not risk-free: \(\beta_D = 0.2\). What is the equity beta \(\beta_E\)?

A. 1.62
B. 1.65
C. 1.67
D. 1.70
E. 1.75

✅ Correct: C. Use \(\beta_A = (E/V)\beta_E + (D/V)\beta_D\) with no taxes.
From \(D/E=1.1\), we get \(E/V=\frac{1}{1+1.1}=0.4762\) and \(D/V=0.5238\).
Solve for equity beta: \(\beta_E=\dfrac{\beta_A - (D/V)\beta_D}{E/V}=\dfrac{0.9 - 0.5238\cdot0.2}{0.4762}\approx\dfrac{0.7952}{0.4762}\approx 1.67\).

Q97.

Under MM I, which of the following is irrelevant to firm value?

A. Capital structure
B. Asset returns
C. Investment decisions
D. Operating cash flows
E. Project selection

✅ Correct: A. Capital structure is irrelevant under MM I assumptions.

Q98.

A firm has D/E = 0.9 (no taxes). Its equity costs r_E = 16%. Debt is split into two tranches: 60% of total debt at 4% and 40% at 7%. What is the firm’s unlevered cost of capital r_U?

A. 10.4%
B. 10.6%
C. 10.8%
D. 10.9%
E. 11.2%

✅ Correct: D. First, convert \(D/E=0.9\) into shares of value: \(E/V=\frac{1}{1+0.9}\approx0.5263\) and \(D/V\approx0.4737\). Blend the debt tranches: \(r_D=0.6\cdot0.04+0.4\cdot0.07=0.052\) (5.2%). Then \(r_U=(E/V)\,r_E+(D/V)\,r_D\approx0.5263\cdot0.16+0.4737\cdot0.052\approx0.1089\approx10.9\%\).

Q99.

Which of the following best describes MM II?

A. Firm value depends on leverage
B. Debt reduces cost of equity
C. WACC increases with leverage
D. r_E increases linearly with D/E
E. Leverage reduces risk

✅ Correct: D. MM II: cost of equity rises linearly with leverage, slope = (r_U−r_D).

Q100.

Consider a company with β_U = 1.1 and a capital structure consisting of 40% debt and 60% equity. The debt is risk-free with an interest rate of 5%, and the market risk premium is 6%. The firm’s debt-to-equity ratio (D/E) is 0.9. Given the above, find the firm’s equity beta (β_E) using the Modigliani-Miller theorem, assuming no taxes.

A. 1.65
B. 1.8
C. 2.01
D. 2.3
E. 1.95

✅ Correct: C. To calculate \(\beta_E\), use the formula \(\beta_E = \beta_U(1 + \frac{D}{E})\). With the given values, \(\beta_E = 1.1(1 + 0.9) = 2.01\).

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