1. Session 9: Valuation C15.0008 Corporate Finance Topics

2. Outline Valuation with leverage –WACC –APV –FTE Valuation using multiples

3. 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

4. Formulas WACC: V =  t UCF t / (1+r WACC ) t APV: V =  t UCF t / (1+r 0 ) t + PV(financing effects) FTE: S =  t LCF t / (1+r S ) t

5. 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 div LCF = (EBIT-int exp)(1-T) - pref div + depr - capex -  NWC = (1-b)[(EBIT-int exp)(1-T) – pref div] –Gives S

6. Discount Rates WACC--weighted average cost of capital –Market value weights of permanent financing –After-tax r 0 --required return on (cost of) unlevered equity –Asset required return –Can be backed out of r S r S --required return on (cost of) equity –Dependent on financing

7. The Problem Firm - No growth, UCF of 60 in perpetuity - Debt and equity financed 0 1 2 3… 606060… What is the value of the firm?

8. WACC Approach V =  t UCF t / (1+r WACC ) t UCF -- expected, after-tax, unlevered cash flow r WACC = w B r B (1-T)+w S r S Key assumption -- the weights are constant Inputs: (1) leverage ratio (weights), (2) component costs of capital, (3) cash flows

9. WACC Valuation 0 1 2 3… 606060… r S = 11.2%, r B = 8%, w B = w S = 0.5, T = 40% r WACC = 0.5(8%)(1-0.4) + 0.5(11.2%) = 8% V = 60/0.08 = 750

10. APV Approach V =  t UCF t / (1+r 0 ) 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 r 0 -- required return on unlevered equity Key assumption -- $ amount of debt known Inputs: (1) financing effects, (2) cost of unlevered equity, (3) cash flows

11. APV Valuation 0 1 2 3… 606060… r 0 = 10%, B = 375 (perpetual), r B = 8% V = 60/0.1 + 0.4(375) = 750

12. WACC and APV Why did the WACC approach and APV approach yield the same answer? B = 375, V = 750  w B = 0.5 r 0 = 10%, r S = 11.2%, r B = 8% Because r S = r 0 + (1- T C )(B/S)(r 0 - r B ) MM w/ corporate taxes!

13. FTE Approach S =  t LCF t / (1+r S ) t LCF -- expected, after-tax, levered cash flow r S -- required return on levered equity Key assumptions -- debt cash flows known, r S constant Inputs: (1) cost of levered equity, (2) cash flows

14. 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!

15. FTE Valuation 0 1 2 3… 424242… r S = 11.2%, B = 375 S = 42/0.112 = 375 V = B + S = 375 + 375 = 750

16. 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

17. 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?

18. 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

19. 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?

20. The Solution NPV U = -1000 + 2200/1.1 = 1000 Financing: 0 1 400 -400 Int.exp -8 After-tax -4.8 CF400-404.8 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

21. 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?

22. The Solution S = [(1-b)(EBIT-Int. Exp.)(1-T)]/(r S -g) = [(0.40)(100-25)(1-0.4)]/(13%-3%) = 180 Assumptions –Fixed leverage ratio –Interest expense growing with value

23. 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

24. Example Spreadsheet..

25. 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

26. 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

27. 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

28. Advantages Easy Correct if required assumptions are valid Uses market-based expectations Works even if firms are (consistently) mispriced

29. 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)/(r S -g)g = b ROE –Same cost of equity (risk, leverage) –Same growth (reinvestment rate, investment opportunities, ROE)

30. Multiples Sales P/Sales P/E M/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

31. Assignments Chapter 29.1-29.10 Case: USG