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## Session 9: Valuation

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**Session 9: Valuation**C15.0008 Corporate Finance Topics**Outline**• Valuation with leverage • WACC • APV • FTE • Valuation using multiples**Approaches to Valuation**There are 3 equivalent (but not identical) approaches to valuation (of projects or firms) • WACC: weighted average cost of capital • APV: adjusted present value • FTE: flow to equity**Formulas**WACC: V = t UCFt / (1+rWACC)t APV: V = t UCFt / (1+r0)t + PV(financing effects) FTE: S = t LCFt / (1+rS)t**Cash Flows**• UCF--unlevered cash flows • Cash flows available to all security holders (equity, debt, etc.) • UCF = EBIT(1-T) + depr - capex - NWC = (1-b)EBIT(1-T) • Gives V • LCF--levered cash flows • Cash flows available to equity holders (dividends) • LCF = UCF - int exp(after-tax) - pref divLCF = (EBIT-int exp)(1-T) - pref div + depr - capex - NWC = (1-b)[(EBIT-int exp)(1-T) – pref div] • Gives S**Discount Rates**• WACC--weighted average cost of capital • Market value weights of permanent financing • After-tax • r0--required return on (cost of) unlevered equity • Asset required return • Can be backed out of rS • rS--required return on (cost of) equity • Dependent on financing**The Problem**Firm - No growth, UCF of 60 in perpetuity - Debt and equity financed 0 1 2 3 … 60 60 60 … What is the value of the firm?**WACC Approach**V = t UCFt / (1+rWACC)t UCF -- expected, after-tax, unlevered cash flow rWACC = wB rB(1-T)+wS rS Key assumption -- the weights are constant Inputs: (1) leverage ratio (weights), (2) component costs of capital, (3) cash flows**WACC Valuation**0 1 2 3 … 60 60 60 … rS = 11.2%, rB = 8%, wB = wS = 0.5, T = 40% rWACC = 0.5(8%)(1-0.4) + 0.5(11.2%) = 8% V = 60/0.08 = 750**APV Approach**V = t UCFt / (1+r0)t + PV(financing effects) PV(financing effects) = PV(tax shield) + PV(subsidies) - PV(fin. distress/agency costs) – PV (other side-effects) UCF -- expected, after-tax, unlevered cash flow r0 -- required return on unlevered equity Key assumption -- $ amount of debt known Inputs: (1) financing effects, (2) cost of unlevered equity, (3) cash flows**APV Valuation**0 1 2 3 … 60 60 60 … r0 = 10%, B = 375 (perpetual), rB = 8% V = 60/0.1 + 0.4(375) = 750**WACC and APV**Why did the WACC approach and APV approach yield the same answer? B = 375, V = 750 wB= 0.5 r0 = 10%, rS = 11.2%, rB = 8% Because rS = r0 + (1- TC)(B/S)(r0 - rB) MM w/ corporate taxes!**FTE Approach**S = t LCFt / (1+rS)t LCF -- expected, after-tax, levered cash flow rS -- required return on levered equity Key assumptions -- debt cash flows known, rS constant Inputs: (1) cost of levered equity, (2) cash flows**FTE Cash Flows**0 1 2 3 … UCF 60 60 60 … Int. exp. -30 -30 -30 … After-tax -18 -18 -18 … LCF 42 42 42 … Or reconstruct income statement!**FTE Valuation**0 1 2 3 … 42 42 42 … rS = 11.2%, B = 375 S = 42/0.112 = 375 V = B + S = 375 + 375 = 750**Issues**• Theoretically equivalent • Assumptions/inputs determine applicability • Constant leverage ratio WACC • $ value of debt APV • Both WACC, APV, FTE • In practice all methods are approximations**WACC Approach**Consider a firm with expected EBIT next year of 100, a payout ratio of 75%, an expected perpetual growth rate of 5%, a tax rate of 40%, a WACC of 10%, and current market value of debt of 250. What is the value of the equity?**The Solution**V = [(1-b)EBIT(1-T)]/(WACC-g) = [(0.75)100(1-0.4)]/(10%-5%) = 900 S = V - B = 900 - 250 = 650 Assumptions • Fixed leverage ratio, i.e., the debt will grow with firm value • b(EBIT) = capex + NWC - depr**APV Approach**Consider a firm with a single 1 year project, that requires 1000 in financing, will generate expected UCF of 2200, and has a required return of 10%. The financing will come from equity and 400 in subsidized debt. The cost of debt is 6%, but the government is offering a low interest loan of 2% in return for an origination fee of 5. Assume a tax rate of 40%. What is the NPV of the project?**The Solution**NPVU = -1000 + 2200/1.1 = 1000 Financing:01 400 -400 Int .exp -8 After-tax -4.8 CF 400 -404.8 PV(financing effects) = PV(tax shield) + PV(subsidy) – PV(financing costs) = 0.4(8)/1.06 + (24-8)/1.06 – 5 = 13.11 NPV = 1000 + 13.11 = 1013.11**FTE Approach**Consider a firm with expected EBIT next year of 100, interest expense of 25, a payout ratio of 40%, an expected perpetual growth rate of 3%, a tax rate of 40%, and a cost of equity of 13%. What is the value of the equity?**The Solution**S = [(1-b)(EBIT-Int. Exp.)(1-T)]/(rS-g) = [(0.40)(100-25)(1-0.4)]/(13%-3%) = 180 Assumptions • Fixed leverage ratio • Interest expense growing with value**Terminal Values**• Usually, cash flows and tax shields can be forecasted only for a certain number of years into the future. • Beyond that, you have to consider some terminal value of cash-flows and tax-shields, usually at a fixed or zero growth rate • Applicable to all DCF methods**Example**• Spreadsheet..**Multiple-Based Valuation**• Value target as a multiple of earnings, cash flows, revenues (sales), etc. • Multiple from comparable companies • Choice of multiple depends on industry and motivation**Logic**• DCF is truth! • Multiple-based valuation will give the correct answer if • The variable (e.g., sales) translates into cash flows (current and future) the same way in both companies • The discount rate (risk, capital structure) is the same for both companies**Implicit Assumptions**• UCF = EBIT(1-T) + depr – cap ex. – NWC • Sales • Same margin • Same WC management • Same growth (reinvestment rate, ROE) • Same WACC (risk, leverage) • EBITDA • No margin assumption needed but more calculations required**Advantages**• Easy • Correct if required assumptions are valid • Uses market-based expectations • Works even if firms are (consistently) mispriced**An Example: P/E Ratios**• Valuing the equity • For comparable firms, P/E = 15 For firm to be valued P = 15 EPS • Assumptions:P/E = (1-b)/(rS-g) g = b ROE • Same cost of equity (risk, leverage) • Same growth (reinvestment rate, investment opportunities, ROE)**Multiples**SalesP/SalesP/EM/B Wal-Mart 256 0.86 23.97 5.33 H.D. 65 1.35 19.56 3.99 Lowes 31 1.25 21.92 4.00 Target 48 0.96 23.07 3.70 Sears 41 0.31 21.12 1.98 Kmart 17 0.43 20.52 2.85**Assignments**• Chapter 29.1-29.10 • Case: USG