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Cost of Capital & Optimal Capital Structure

Module: Module 2 — Functional MasteryCode: CCOCS (DMA)Faculty: Prof. Debasish MaitraSessions: 3Status: ✅ Drafted

Big idea​

The cost of capital is the single most important number in corporate finance: it is the hurdle rate every project must clear to create value, and the discount rate used to translate future cash flows into present value. Prof. Debashish's frame builds it up component by component — cost of equity from CAPM (Ke=Rf+β(Rm−Rf)K_e = R_f + \beta(R_m - R_f)), cost of debt as the after-tax yield on borrowings, then the weighted blend in WACC. The optimal capital structure question — how much debt vs equity — then asks: at what mix does WACC minimise and firm value maximise? Modigliani–Miller's no-tax irrelevance result is the theoretical starting point; the real-world answer adds tax shields, financial distress costs, and agency considerations (the trade-off theory).

Key concepts​

  • WACC. WACC=EVKe+DVKd(1−T)WACC = \frac{E}{V} K_e + \frac{D}{V} K_d (1-T). Weight by market values, not book; use the after-tax cost of debt because interest is tax-deductible.
  • CAPM and beta. Ke=Rf+β(Rm−Rf)K_e = R_f + \beta(R_m - R_f). Beta measures systematic risk. Equity beta must be unlevered and re-levered when target capital structure differs from the comparable firm — the pure-play method.
  • Cost of debt. Risk-free rate plus credit spread. Use yield to maturity on existing bonds or rating-based spreads; remember the (1–T) tax adjustment, otherwise you'll over-state cost.
  • Divisional vs corporate WACC. A single firm-wide WACC misallocates capital across divisions of different risk. The Marriott case (lodging, restaurants, contract services) is the textbook example of how not to use one rate.
  • Modigliani–Miller propositions. In a frictionless world (no taxes, no bankruptcy costs, no asymmetric information), capital structure is irrelevant (M–M I). With taxes, debt is valuable because of the interest tax shield (M–M with taxes).
  • Trade-off theory of optimal capital structure. Firms balance the tax-shield benefit of debt against the expected costs of financial distress. The optimum sits where marginal benefit equals marginal cost — neither 100% debt nor zero debt.

Self-check​

A diversified conglomerate uses a single corporate WACC of 10% to evaluate all projects across its three divisions: a low-risk regulated utility (asset beta 0.4), a mid-risk manufacturing arm (asset beta 1.0), and a high-risk new-tech venture (asset beta 1.8). What is the predictable consequence over time?

  • A. No problem — a single WACC simplifies decision-making
  • B. The utility will be starved of capital (its projects look insufficiently profitable at 10%) and the high-risk venture will be over-invested (its risky projects clear the too-low hurdle and destroy value)
  • C. All three divisions will perform equally
  • D. The conglomerate will outperform peers
WACC formula
$WACC = \frac{E}{V} K_e + \frac{D}{V} K_d (1-T)$ where $V = E + D$ at market values, $K_e$ from CAPM, $K_d$ is the pre-tax cost of debt, and $T$ is the marginal corporate tax rate.

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Continue learning​

📊NYU Stern · DataDamodaran Online (Cost of Capital data)Industry betas, risk-free rates, equity risk premiums and country risk premiums updated monthly — the practitioner gold standard.📊HBS · CaseMarriott Corporation: The Cost of CapitalThe canonical case on divisional WACCs — the live workout for the pure-play method and unlever/re-lever drill.📄CFI · ReadCFI: WACC Formula & CalculationClean walk-through of WACC mechanics with downloadable Excel — the cleanest free primer for the formula side.🎓MIT OCW · CourseMIT 15.401 Finance Theory IAndrew Lo's full MIT MBA finance course on video — CAPM, WACC, MM theorems lectured at PhD-quality rigour, free.
🪞 Apply it — reflection prompts
  1. Pull your firm's most recent annual report. Compute WACC yourself using market values, current bond YTM, and a beta from Damodaran's dataset. How does your number compare with the rate finance actually uses?
  2. If your firm operates multiple businesses, are project hurdle rates set divisionally or as a single corporate WACC? Where is capital being silently misallocated as a result?
  3. Where is your firm on the trade-off curve — under-levered (leaving tax shield on the table) or over-levered (paying distress-premium spreads)? What would shift it to optimum?

📝 Going deeper. Brealey, Myers & Allen, Principles of Corporate Finance chapters on WACC and capital structure are the standard textbook; for the case-based workout, Marriott Corporation: The Cost of Capital (HBS 9-289-047) is essential. Damodaran's online dataset of industry betas and country risk premiums is the working reference for applied estimation.