Corporate Issuers. Worth 6 to 9 percent of the exam. One session: the lesson, the rules, the method, then the questions.
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Five to ten minutes on this one unit: what the exam wants, the idea in plain words, then straight into the trap and the practice.
The exam wants you to calculate WACC from market-value weights and the correct after-tax cost of each capital source, describe what Modigliani-Miller's propositions say with and without taxes, contrast that with trade-off theory's U-shaped WACC, and identify which framework a question is actually testing from its stated assumptions.
WACC blends the cost of every capital source a firm uses, each weighted by its share of total market value: WACC = (E/V) x Re + (D/V) x Rd x (1 - T). A third term, (P/V) x Rp, is added when preferred stock exists. The tax adjustment, (1 - T), applies to debt alone. Interest is tax-deductible; neither preferred nor common dividends are. Applying that adjustment anywhere else is a structural error, not a rounding one. The cost of debt itself is always the current yield to maturity, never the bond's coupon rate. The coupon was fixed at issuance and reflects old conditions. Yield to maturity reflects what a lender demands today, given the bond's actual market price. Weights always use market values, never what was raised in the past; a firm's own stated target capital structure is an acceptable, often preferred, basis alongside current market values.
Modigliani and Miller's Proposition I, in a world with no taxes, no transaction costs, and no distress costs, says a firm's value is completely independent of how it splits financing between debt and equity. Proposition II explains the mechanism behind that result: as a firm substitutes debt for equity, the remaining equity becomes riskier, and its required return rises by precisely enough to leave WACC unchanged. Introduce corporate taxes and the conclusion flips entirely. Because interest is tax-deductible, adding debt now adds value, T x D, to the firm, and left unchecked this framework implies an extreme, unrealistic optimum: maximize debt, all the way to 100 percent. Reading whether a question specifies taxes or no taxes is the single decision that determines which of these two opposite conclusions applies.
Trade-off theory exists precisely because 100 percent debt is not what real firms do. It adds financial distress costs back into the model: firm value equals the unlevered value, plus the present value of the tax shield, minus the expected present value of financial distress costs. The optimal capital structure sits at the point where one more dollar of debt's marginal tax benefit exactly equals its marginal expected distress cost. This produces the shape the exam tests directly: WACC traces a U as leverage rises. It falls at first as cheap, tax-advantaged debt replaces more expensive equity, then rises again once financial distress risk starts to dominate, with the bottom of that U marking the optimal structure. A firm with stable cash flows and collateral-friendly, tangible assets can safely carry more debt before distress costs start to bite; a firm with volatile cash flows and few tangible assets reaches that turning point much sooner.
A firm's equity has a market value of $600 million and a cost of equity of 11 percent. Its debt has a market value of $400 million and a current yield to maturity of 6.5 percent. The tax rate is 25 percent. What is the firm's WACC? Total market value V = $600M + $400M = $1,000M. Equity weight = 600/1000 = 0.60. Debt weight = 400/1000 = 0.40. After-tax cost of debt = 6.5% x (1 - 0.25) = 4.875%. WACC = (0.60 x 11%) + (0.40 x 4.875%) = 6.6% + 1.95% = 8.55%.
Same firm: equity $600 million at 11 percent, debt $400 million at a 6.5 percent yield to maturity, tax rate 25 percent. Compute the weights and the after-tax cost of debt yourself, then finish WACC.
Equity $600M, Re = 11%. Debt $400M, YTM = 6.5%. Tax rate 25%. Find WACC.
A question naming both taxes and an optimal or moderate capital structure is testing trade-off theory, not pure Modigliani-Miller with taxes: under M-M with taxes and no distress cost added back in, the theoretical implication is maximum debt, never a moderate, balanced level.
Read these before the questions, not after them. Everything here traces to this module's own lesson and to the 2026 outline.
WACC = (E/V) x Re + (D/V) x Rd x (1 - T), where V is total market value of the firm's capital and Rd x (1 - T) is the after-tax cost of debt; a preferred-stock tranche adds a third term, (P/V) x Rp, with no tax adjustment, since neither preferred dividends nor common dividends are tax-deductible. Market-value weights are required over book-value weights because WACC is a forward-looking cost of raising capital today, not a record of past financing.
A bond's coupon rate was fixed at issuance and reflects historical conditions; the yield to maturity reflects what a lender demands today given the bond's current market price, which is the economically relevant, marginal cost of new debt. Only when a bond trades exactly at par do coupon rate and YTM coincide; otherwise using the coupon rate understates or overstates the true current cost of debt.
Without taxes, re_L = re_U + (re_U - rd) x (D/E): as a firm substitutes debt for equity, the remaining equity becomes riskier and its required return rises by precisely enough to leave WACC unchanged, which is the mechanism behind Proposition I's value-invariance result. With taxes, the formula gains a (1 - T) factor that dampens, but does not eliminate, this rising cost of equity.
Without taxes, WACC is flat regardless of capital structure. With taxes, and absent any offsetting distress cost, the interest tax shield (adding T x D to firm value) makes WACC fall as debt rises, implying an extreme, unrealistic conclusion, maximum debt is optimal, that motivates adding financial distress costs back into the model. Reading which assumption set a question specifies, taxes or no taxes, decides which of these two opposite directional answers is correct.
The base M-M framework assumes no transaction costs, no taxes (relaxed in the tax version), no costs of financial distress, and that both firms and individual investors can borrow at the same rate, the last of which enables homemade leverage: an investor can replicate any capital structure personally, which is the arbitrage mechanism that forces value equality across differently levered but otherwise identical firms.
Trade-off theory holds that value equals the unlevered firm value plus the present value of the tax shield minus the expected present value of financial distress costs; the optimal capital structure sits where the marginal tax benefit of one more dollar of debt exactly equals the marginal expected distress cost of that dollar. Firms with stable cash flows and tangible, collateral-friendly assets can sustain a higher optimal debt ratio than firms with volatile cash flows or mostly intangible assets, because their expected distress costs are lower at any given leverage level.
When a firm has a stated or evident target mix of debt and equity, that target is an acceptable, often preferred, basis for WACC weights alongside current market values, since it represents the firm's intended long-run financing structure rather than a snapshot that may be temporarily distorted by market conditions. Book-value weights remain the least preferred basis of the three.
A debt-to-equity ratio of 0.5 means debt is one-third of total capital, not one-half. Reading D/E as if it were the debt weight in WACC is the most common arithmetic slip on Proposition II questions.
The exam routinely supplies both the coupon rate and the current bond price. The coupon rate is the trap; the cost of debt for WACC is always the yield to maturity, then adjusted by (1 - T).
Interest is tax-deductible; dividends, preferred or common, are not. Applying (1-T) to a preferred or common equity cost is a structural error, not a rounding one.
Three distinct frameworks give three distinct answers to what happens to WACC as leverage rises. The exam signals which one applies by explicitly naming its assumptions.
The order to work a question of this type in, every time, before you touch the numbers.
The first is worked in full. The second gives you the setup and stops. After that the questions give you nothing, which is the point: the help fades on purpose, so the last thing you practise is the thing the exam actually asks of you.
According to Modigliani and Miller's Proposition I with no taxes, the value of a firm is most likely described as being determined by:
Answer B. The correct answer is The cash flows generated by its assets.
A firm has an unlevered cost of equity of 10% and a cost of debt of 6%. The firm's debt-to-equity ratio is 0.5. According to M-M Proposition II (no taxes), the firm's levered cost of equity is CLOSEST to:
Identify every capital source in the problem (debt, preferred, common equity) and confirm you have a market value for each.
Answer B. The correct answer is 12.0%.
Pick an answer, say how sure you are, then reveal. Being sure and wrong is the most useful thing that can happen in a session, so answer honestly: it sends the unit back to learning and puts it at the front of your revision queue.
Under Modigliani-Miller with corporate taxes, a firm should most likely theoretically:
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Unit: capital-structure
According to the trade-off theory of capital structure, the optimal capital structure is most likely where:
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Unit: capital-structure
A company's CFO argues that issuing equity would signal to the market that the stock is overvalued. This reasoning is MOST consistent with which capital structure theory?
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Unit: capital-structure
Which of the following is most likely NOT an assumption of the original Modigliani-Miller framework (no taxes)?
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Unit: capital-structure
Firm A is unlevered with a value of $50 million. The corporate tax rate is 30%. If the firm issues $20 million of debt and uses proceeds to repurchase equity, the value of the levered firm under M-M with taxes is closest to:
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Unit: capital-structure
Under M-M Proposition II without taxes, as a firm most likely increases its financial leverage, its weighted average cost of capital (WACC) will:
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Unit: capital-structure
Which of the following costs is most likely classified as an indirect cost of financial distress?
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Unit: capital-structure
According to the pecking order theory, which of the following financing sources would a company use LAST when it needs external capital, most likely?
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Unit: capital-structure
A highly profitable, asset-heavy industrial company with stable cash flows would most likely have a HIGHER optimal debt ratio compared to a high-growth technology startup according to the trade-off theory. Which factor BEST explains this?
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Unit: capital-structure
The MM framework assumes that both individuals and corporations can borrow at the same rate. What type of transaction does this assumption enable that underpins Proposition I, most likely?
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Unit: capital-structure
A company's stock trades at $40.00. It just paid a dividend of $2.00 (D0 = $2.00). Dividends are expected to grow at 5% annually. Using the dividend growth model, the company's cost of equity is closest to:
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Unit: capital-structure
An analyst is estimating the cost of equity for a private company that does not pay dividends and has no publicly traded debt. Which cost-of-equity estimation method is MOST appropriate?
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Unit: capital-structure
A company's 10-year bonds yield 7.5%. An analyst estimates the equity risk premium over the firm's bonds is 4.0%. Using the bond yield plus risk premium method, the cost of equity is closest to:
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Unit: capital-structure
Using CAPM, a stock has a beta of 1.3. The risk-free rate is 3.0% and the expected market return is 9.0%. The cost of equity is closest to:
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Unit: capital-structure
A company issues preferred stock with an annual dividend of $5.00 per share. The current market price is $62.50. Flotation costs are $2.50 per share. The cost of preferred stock, adjusted for flotation costs, is closest to:
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Unit: capital-structure
An analyst uses a historical beta of 1.5 for a stock. Applying the Bloomberg beta adjustment formula, the adjusted (predicted) beta is closest to:
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Unit: capital-structure
When estimating the cost of equity using the CAPM, the equity risk premium is most likely estimated using:
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Unit: capital-structure
According to CFA Institute, flotation costs for new equity issuance are most likely handled by:
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Unit: capital-structure
A stable utility company has a stock price of $50, an expected dividend next year of $3.00, and a long-run dividend growth rate of 4%. Its 20-year bonds yield 6.5%. Using the dividend growth model, the cost of equity is closest to:
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Unit: capital-structure
The sustainable growth rate for a company with ROE of 15% and a dividend payout ratio of 40% is closest to:
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Unit: capital-structure
Which of the following is most likely a LIMITATION of using the capital asset pricing model (CAPM) to estimate the cost of equity?
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Unit: capital-structure
A firm has a capital structure of $400 million in equity (market value) and $600 million in debt (market value). The firm's after-tax cost of debt is 4.8%, its cost of equity is 11.2%, and its marginal tax rate is 35%. The firm's WACC is closest to:
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Unit: capital-structure
A company has the following capital structure and costs: - Long-term debt: book value $200M, market value $180M, coupon rate 6%, yield to maturity 7%, tax rate 30% - Common equity: book value $300M, market value $420M, required return 13% Which of the following correctly calculates the weight of debt for WACC purposes? The value is closest to:
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Unit: capital-structure
A firm currently has a WACC of 8.5% with a D/E ratio of 0.4. The firm increases its D/E ratio to 1.0. Under Modigliani-Miller with corporate taxes, and assuming financial distress costs are negligible, which statement about the firm's WACC is most accurate?
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Unit: capital-structure
A firm's preferred stock has a par value of $50 and pays a quarterly dividend of $0.75. The stock currently trades at $45. What is the cost of preferred stock for WACC purposes, most likely?
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Unit: capital-structure
A firm uses the bond-yield-plus-risk-premium approach to estimate its cost of equity. The firm's 10-year bonds yield 6.5%. The typical risk premium over bond yield for similar firms is 3.5%. Using CAPM separately, with a beta of 1.2, risk-free rate of 3.0%, and market risk premium of 5.5%, what would the analyst most likely conclude about the cost of equity?
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Unit: capital-structure
A company has the following data: - Market value of debt: $500M at a pre-tax YTM of 6% - Market value of common equity: $750M with a required return of 12% - Market value of preferred stock: $250M with a dividend yield of 8% - Corporate tax rate: 40% the firm's WACC is closest to:
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Unit: capital-structure
Which of the following statements about the appropriate weights for WACC is most accurate?
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Unit: capital-structure
A project has an IRR of 9.2%. The firm's WACC is 8.5%. The firm's CFO argues that the project should be rejected because the company's target return for this division is 11%. Which of the following is the most appropriate response to the CFO?
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Unit: capital-structure
A firm is computing WACC using the dividend discount model to estimate its cost of equity. The stock price is $40, the most recent annual dividend was $2.00, and dividends are expected to grow at 4% per year indefinitely. The cost of equity is closest to:
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Unit: capital-structure
A firm's WACC is 9%. It is considering two independent projects: Project A costs $500,000 with an expected return of 10%; Project B costs $800,000 with an expected return of 8%. The combination of decisions most consistent with shareholder value maximization is most likely:
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Unit: capital-structure
Which of the following most likely explains why it is appropriate to use the marginal cost of capital rather than the historical (embedded) cost of capital when computing WACC for capital budgeting?
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Unit: capital-structure
A firm operates with an all-equity capital structure worth $50 million (Modigliani-Miller Proposition I, no taxes, assumed to hold). The firm then issues $20 million of debt and uses the proceeds to repurchase equity, with no change in operating cash flows. Combining MM Proposition I (no taxes) with MM Proposition II (no taxes), the firm's WACC after the recapitalization is most likely to:
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Unit: capital-structure
A firm operates in a world with corporate taxes (MM with taxes) and is currently unlevered with a firm value of $80 million and a 25% corporate tax rate. It is considering issuing $30 million in permanent debt and using the proceeds to repurchase equity. Combining MM Proposition I with taxes with the interest tax shield concept, the levered firm's value is most likely closest to:
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Unit: capital-structure