Discounted cash flow Study Guide

📖 Core Concepts Discounted Cash Flow (DCF) – Valuation method that converts future cash flows into today’s dollars using a discount rate (cost of capital). Net Present Value (NPV) – Sum of all discounted cash flows; the present‑value “price” of a project or firm. Free Cash Flow (FCF) – Cash generated after operating expenses and capital expenditures; the cash stream DCF works with. Discount Rate – Reflects time value of money + risk; often the Weighted Average Cost of Capital (WACC) for the firm or the cost of equity for equity‑only valuations. Terminal Value (TV) – Value of cash flows beyond the explicit forecast period; typically a large share of total value. --- 📌 Must Remember Single‑period DCF: $DPV = \dfrac{FV}{(1+r)^{n}}$ Multi‑period NPV: $NPV = \sum{t=1}^{T} \dfrac{FV{t}}{(1+r)^{t}}$ Growing perpetuity TV: $TV = \dfrac{FCF{n+1}}{r - g}$ (valid when $r > g$). CAPM (cost of equity): $r{e} = r{f} + \beta (r{m} - r{f})$ WACC: $WACC = \frac{E}{E+D} r{e} + \frac{D}{E+D} r{d} (1 - T{c})$ APV approach: Value = $NPV{unlevered} + PV(\text{tax shield})$. Equity‑approach: Discount cash flows to equity (CFE) using cost of equity. Total‑cash‑flow approach: Discount FCF to the firm using WACC. --- 🔄 Key Processes Project FCF Forecast Estimate operating cash flow → subtract capital expenditures → obtain FCF for each forecast year. Select Discount Rate For firm value: compute WACC (combine cost of equity & after‑tax cost of debt). For equity value: use cost of equity (CAPM). Discount Cash Flows Apply $DPV$ formula to each year’s FCF. Compute Terminal Value Choose growth model (usually Gordon growth). Apply $TV = \dfrac{FCF{n+1}}{r - g}$. Sum to Get NPV $NPV = \sum{t=1}^{T} DPV{t} + \dfrac{TV}{(1+r)^{T}}$. Interpret Result $NPV > 0$ → value‑creating; $NPV < 0$ → reject. --- 🔍 Key Comparisons Equity‑Approach vs. Total‑Cash‑Flow Approach Equity‑Approach: Discounts cash flows after debt service; uses cost of equity. Total‑Cash‑Flow: Discounts all firm cash flows; uses WACC. Adjusted Present Value (APV) vs. WACC APV: Separates operating value (unlevered NPV) from financing benefits (tax shields). WACC: Blends operating and financing costs into a single discount rate. Terminal Value (Gordon Growth) vs. Exit Multiple (not in outline but common) Gordon: Uses perpetual growth rate $g$; sensitive to $r-g$ gap. Exit Multiple: Applies market multiple to final year’s metric (outside current outline). --- ⚠️ Common Misunderstandings “Higher discount rate always lowers value” – True, but a higher rate also reflects higher risk; don’t arbitrarily pick a low rate to inflate value. Confusing cost of equity with WACC – Cost of equity ignores debt; WACC accounts for both equity and debt (after‑tax). Using $r = g$ in terminal value – Division by zero; ensure $r > g$ for the Gordon growth formula. Treating terminal value as a “guess” – It’s a systematic calculation; sensitivity analysis is essential because TV often dominates NPV. --- 🧠 Mental Models / Intuition “Money today is worth more than money tomorrow” – The discount rate is simply the “interest” you could earn elsewhere; think of each future cash flow as a loan you’re receiving later. “Firm value = Operating value + Financing side effects” – APV splits these two ideas; WACC blends them, like mixing two colors into one shade. “Terminal value is a perpetuity” – Visualize the firm as a river that continues flowing forever; the Gordon growth formula is the cross‑section of that endless flow. --- 🚩 Exceptions & Edge Cases Negative cash flows in early years – Still discount each period; the NPV may be negative initially but become positive later. High‑growth firms with $g$ close to $r$ – Small denominator in TV formula → extreme sensitivity; consider alternative exit methods. Tax shields when debt is not tax‑deductible – APV’s tax‑shield component disappears; use unlevered cash flows only. --- 📍 When to Use Which Use Equity‑Approach when you need the value attributable solely to shareholders (e.g., stock valuation, buy‑outs). Use Total‑Cash‑Flow (WACC) Approach for firm‑wide valuation (M&A, project appraisal with mixed financing). Use APV when the capital structure is changing over time or when you want to isolate the impact of financing side‑effects. --- 👀 Patterns to Recognize TV dominates NPV → Look for problems where the terminal value is >70% of total value; focus on $r$ and $g$ assumptions. CAPM inputs appear together – $rf$, $\beta$, and market risk premium always in the cost‑of‑equity formula. WACC denominator $E+D$ – Whenever equity or debt values change, recalculate the weightings; the formula is linear in $E$ and $D$. --- 🗂️ Exam Traps Mixing up $r$ (discount rate) with $g$ (growth rate) – Answer choices may swap them in the TV formula; remember TV = $FCF{n+1} / (r-g)$. Using pre‑tax cost of debt in WACC – Forgetting the $(1-Tc)$ tax shield leads to an overly high WACC. Assuming $r = re$ for firm valuation – Firm‑wide NPV requires WACC, not just cost of equity. Neglecting the timing of cash flows – Treating a cash flow occurring at the end of year t as if it were at the beginning yields a higher (incorrect) NPV. ---