Cost of capital Study Guide

📖 Core Concepts Cost of Capital – The required return that investors demand for providing a firm’s debt and equity; serves as the discount rate for project evaluation. Weighted Average Cost of Capital (WACC) – The firm‑wide blended cost of capital, weighted by market values of debt and equity. Risk‑Adjusted Return – Required return = risk‑free rate + risk premium (captures time value of money and risk). Opportunity Cost Perspective – Use the firm’s average cost of capital for projects with similar risk; use a project‑specific rate when risk differs. Tax Shield of Debt – Interest expense is tax‑deductible, lowering the after‑tax cost of debt and thus the overall WACC. 📌 Must Remember After‑tax Cost of Debt: $kd = (r{\text{risk‑free}} + \text{default premium}) \times (1 - Tc)$ CAPM Cost of Equity: $ke = rf + \beta (rm - rf)$ Dividend Capitalization Cost of Equity: $ke = \frac{D1}{P0} + g$ WACC Formula: $WACC = \frac{E}{V}ke + \frac{D}{V}kd(1 - Tc)$ where $V = E + D$ Positive NPV Rule: Accept a project only if its NPV (using cost of capital as discount rate) > 0. Tax Benefit Increases with Higher $Tc$ – More corporate tax → larger debt tax shield → lower after‑tax cost of debt. 🔄 Key Processes Estimate Cost of Debt Start with risk‑free rate → add default premium → apply after‑tax adjustment. Estimate Cost of Equity Choose model (CAPM, Fama–French, dividend capitalization). For CAPM: plug in $rf$, $\beta$, and market risk premium $(rm - rf)$. Compute WACC Determine market values $E$ and $D$. Apply WACC formula, ensuring debt component is after‑tax. Project Evaluation Discount projected free cash flows at WACC. Calculate NPV; accept if NPV > 0, reject otherwise. 🔍 Key Comparisons Debt vs. Equity Cost Debt: Fixed interest, tax‑deductible, lower required return, rises with default risk. Equity: No tax shield, higher required return, reflects market risk via $\beta$. CAPM vs. Dividend Model CAPM: Uses market risk factors, works even when dividends are irregular. Dividend Model: Relies on stable dividend growth, simple when $D1$, $P0$, $g$ known. WACC vs. Management Hurdle Rate WACC: Market‑based, objective benchmark. Hurdle Rate: Internal target, may be higher/lower than WACC. ⚠️ Common Misunderstandings “Cost of debt = coupon rate.” – The correct cost is the market‑based yield plus default premium, adjusted for taxes. “WACC uses book values.” – Use market values for both equity and debt. “Higher debt always lowers WACC.” – Excessive debt raises default risk, increasing $kd$ and the cost of other capital, potentially raising WACC. “Dividends reduce cost of capital.” – Only the required return on equity changes; paying dividends shifts earnings from retained to paid but does not magically lower $ke$. 🧠 Mental Models / Intuition “Bridge” Analogy: Think of WACC as the minimum load a bridge (firm) must support; any project must carry a load (return) higher than this to be safe. Tax Shield as a Discount: Debt interest is a “coupon” that the tax authority refunds; the more you borrow (up to a safe point), the bigger the discount on your overall cost. Beta as a Sensitivity Dial: $\beta = 1$ = moves exactly with market; >1 = amplified swings; <1 = muted swings. Adjust $ke$ accordingly. 🚩 Exceptions & Edge Cases Project‑Specific Risk: Use a higher or lower discount rate than firm‑wide WACC when the project’s risk deviates substantially from the firm’s average. High Tax Rate Environments: Debt tax shield becomes more valuable; optimal capital structure may shift toward more leverage. Negative Market Risk Premium: In rare periods of expected market decline, $rm - rf$ could be negative, yielding a lower (or even negative) $ke$ in CAPM—interpret with caution. 📍 When to Use Which CAPM – Standard choice when reliable $\beta$ and market risk premium are available. Fama–French – Prefer when firm’s size/value characteristics are pronounced and CAPM fit is poor. Dividend Model – Use for mature firms with stable, predictable dividend policies. After‑Tax Debt Formula – Always apply when computing WACC; ignore tax shield only for tax‑exempt entities. WACC vs. Hurdle Rate – Use WACC for valuation/NVP analysis; use hurdle rate for internal budgeting when management wants a safety margin. 👀 Patterns to Recognize Rising Debt → Rising Default Premium → Higher $kd$ – Look for this chain in questions about leverage changes. Higher $\beta$ → Higher $ke$ – Whenever $\beta$ is given, instantly adjust equity cost upward. Tax Rate Increase → Larger $(1 - Tc)$ factor → Lower after‑tax $kd$ – Spot this in scenarios with tax policy shifts. Positive NPV ⇔ Return > WACC – Quick check: compare project IRR to WACC. 🗂️ Exam Traps Using Book Value in WACC – Test‑writers often include book values to tempt you; remember to use market values. Forgetting the Tax Shield – Omitting the $(1 - Tc)$ factor on debt underestimates the benefit of leverage. Mixing Pre‑Tax and After‑Tax Costs – Ensure all debt costs in WACC are after‑tax; equity costs are always pre‑tax. Applying CAPM without Adjusting for Project Risk – If a project is riskier than the firm, the CAPM $ke$ must be increased; failure to do so yields an inflated NPV. Assuming Debt Always Lowers WACC – Over‑leveraging can raise default premiums enough to offset tax shields; watch for statements that “more debt always reduces WACC.”