BFC2140 · Corporate Finance
Capital Structure
Capital structure asks whether the mix of debt and equity changes the value of the firm — and the Modigliani-Miller (MM) propositions are the benchmark answer. This chapter covers leverage and equity risk, business versus financial risk, MM Propositions I and II without tax, MM with corporate tax and the interest tax shield, trade-off theory with financial-distress costs, and the agency and signalling roles of debt. It is examined as Section B numerical questions (MM II cost of equity, the value of the tax shield) and Section C reasoning about why structure is irrelevant in a perfect market and what makes it matter in practice.
What this chapter covers
- 01Leverage = D/(D + E); how financial leverage raises equity risk and the cost of equity
- 02Business risk versus financial risk
- 03Perfect-capital-market assumptions (no taxes, no transaction costs, fixed cash flows)
- 04MM Proposition I (no tax): V_L = V_U — capital structure is irrelevant
- 05MM Proposition II (no tax): rₑ = r_A + (D/E)(r_A − r_D), WACC constant
- 06MM with corporate tax: the interest tax shield gives V_L = V_U + T·D
- 07Trade-off theory: tax-shield benefit versus financial-distress and bankruptcy costs
- 08Agency and signalling roles of debt (disciplining managers, reducing free cash flow)
MM Propositions with and without corporate tax
- 1 markApply MM Proposition I (no tax): firm value is unchanged by leverage, so V_L = V_U = $50m.
- 1 markFind the equity value after issuing debt: E = V_L − D = 50 − 20 = $30m.
- 1 markApply MM Proposition II (no tax): rₑ = r_A + (D/E)(r_A − r_D) = 12 + (20/30)(12 − 6).
- 1 markCompute the new cost of equity: rₑ = 12 + (0.6667)(6) = 12 + 4 = 16.00% (and WACC stays at 12%).
- 1 markApply MM with corporate tax: the interest tax shield adds value, V_L = V_U + T·D = 50 + 0.30 × 20.
- 1 markCompute the levered value with tax: V_L = 50 + 6 = $56m — debt adds $6m through the present value of the tax shield.
Key terms
- Financial leverage
- The use of debt in the capital structure, measured by D/(D + E). Adding leverage magnifies returns to equity but also raises the riskiness — and therefore the required return — of the remaining equity.
- Business vs financial risk
- Business risk is the inherent variability of a firm's operating earnings, independent of how it is financed; financial risk is the additional variability in returns to shareholders created by using fixed-cost debt. Leverage adds financial risk on top of business risk.
- MM Proposition I (no tax)
- In a perfect market with no taxes, the value of the firm is independent of its capital structure: V_L = V_U. The way the cash flows are sliced between debt and equity does not change the size of the pie.
- MM Proposition II (no tax)
- The cost of equity rises linearly with leverage: rₑ = r_A + (D/E)(r_A − r_D). The increase in the cost of equity exactly offsets the use of cheaper debt, so the WACC remains constant — consistent with Proposition I.
- Interest tax shield
- The tax saving from deducting interest, which makes debt valuable once corporate tax is introduced. For perpetual debt its present value is T·D, so the levered firm is worth V_L = V_U + T·D.
- Trade-off theory
- The view that an optimal capital structure balances the marginal tax-shield benefit of more debt against the rising expected costs of financial distress and bankruptcy. The optimum is where the net benefit of additional debt is maximised.
Capital Structure FAQ
What does MM Proposition I actually say, and why?
In a perfect capital market with no taxes, transaction costs or bankruptcy costs, the total value of a firm does not depend on how it is financed: V_L = V_U. The intuition is that capital structure only divides the firm's cash flows between debtholders and shareholders — it does not change the total cash the assets generate. Investors can replicate or undo any corporate leverage themselves (homemade leverage), so they will not pay a premium or accept a discount for the firm's particular debt-equity mix. The pie is the same size however it is sliced.
If debt is cheaper than equity, why doesn't more debt lower the WACC (no tax)?
Because of MM Proposition II. As the firm takes on more debt, the equity that remains becomes riskier — its claim is now behind a larger fixed debt obligation — so the cost of equity rises by exactly enough to offset the greater use of cheaper debt. The formula rₑ = r_A + (D/E)(r_A − r_D) captures this: the rise in rₑ is proportional to D/E. The result is a constant WACC equal to r_A, fully consistent with the irrelevance of structure in Proposition I.
How does corporate tax change the MM conclusion?
Tax breaks the irrelevance result because interest is tax-deductible while dividends are not. Each dollar of interest reduces the firm's tax bill, creating an interest tax shield whose present value for perpetual debt is T·D. So the levered firm is worth more: V_L = V_U + T·D. Taken literally this implies firms should be financed almost entirely with debt, which is clearly not what we observe — and that gap is what the trade-off theory and the costs of financial distress are introduced to explain.
What is the trade-off theory of capital structure?
It resolves the tension between MM-with-tax (which favours maximum debt) and reality (where firms hold moderate debt). The benefit of more debt is the growing interest tax shield; the cost is the rising probability and expected cost of financial distress and bankruptcy — both direct (legal and administrative) and indirect (lost customers, forced asset sales, under-investment). The optimal capital structure is the debt level where the marginal tax-shield benefit just balances the marginal expected distress cost. Agency and signalling effects (debt disciplining managers and reducing free cash flow, or signalling confidence) add further reasons structure matters.
How is capital structure examined in BFC2140?
It is the Week 11 topic, drawn from Berk Ch 16 and Brigham & Ehrhardt Ch 17, and is emphasised on the final. Expect Section B numerical questions applying MM Proposition II (the levered cost of equity) or computing the tax-shield value V_L = V_U + T·D, and Section C reasoning about why structure is irrelevant in a perfect market, how tax and distress costs make it relevant (trade-off theory), and the agency/signalling roles of debt. MM propositions are listed among the high-yield recurring exam skills.
Exam move
Learn capital structure as a story in two acts. Act one is the perfect market: MM Proposition I (value is fixed, structure irrelevant) and Proposition II (the cost of equity rises with leverage so WACC stays constant) — practise the rₑ = r_A + (D/E)(r_A − r_D) calculation until it is automatic and be able to explain the homemade-leverage intuition. Act two introduces frictions: corporate tax adds the interest tax shield (V_L = V_U + T·D), then financial-distress and bankruptcy costs pull the other way, giving the trade-off theory's optimum, with agency and signalling as further real-world forces. Keep the no-tax and with-tax results clearly separated, as mixing them is the commonest error. For Section C, rehearse the conceptual chain in words — irrelevance, why it breaks, what restores an interior optimum — because the applied exam rewards that reasoning as much as the numbers.
