Cost of Capital Models and methods to estimate the appropriate r Remember the guiding principle: The r should reflec

1. Cost of Capital Models and methods to estimate the appropriate r Remember the guiding principle: The r should reflect the riskiness of the cash flows

2. Dividend Growth Model Approach Re=(D1/P0) +g • Typically used for equity • Future dividends? • Future growth rates? • Analyst forecasts • Analyst are optimists! (Realized growth 40-60% lower) • Historical growth rates • Other models

3. Capital Asset Pricing Model (CAPM) • Perfect Competition • All investors hold the universe of publicly traded assets and have unlimited access to borrowing/lending at the risk-free rate • No taxes or transactions costs • All investors plan for one identical holding period • All investors are mean-variance optimizers • All investors have homogeneous expectations

4. Implementing the CAPM Approach • Theoretically can be used on any asset (equity, debt, assets, etc.) – typically used on equity • Ri=Rf+Bi(Rm-Rf) • Only systematic risk (beta) is priced in equilibrium • Computing the components • Risk-free rate: Treasury rates • Market risk premium: Expected return on broad based index such as the S&P 500 or Wilshire 5000 • Beta • Many services estimate equity betas: READ THEIR METHODOLOGIES!!! • Estimate with historical equity data

5. How do we estimate CAPM? • Expected Return Model (CAPM) • Realized Return Model (Index Model)

6. Estimation Issues • Beta is non-stationary • What estimation period? • How often do you revise? • Beta moves toward one • Data Frequency • Daily, Weekly, Monthly? • Market portfolio • S&P 500? • Other equity indices? • Other real assets?

7. Return on Debt • Opportunity Cost of Debt Financing • Use the YTM of outstanding debt which reflects opportunity cost • Historical borrowing costs are irrelevant • Coupon rate is irrelevant • Use credit ratings to estimate cost of debt • Find firms with similar debt risk (probability of bankruptcy)

8. Other Asset Pricing Models • Many other models both proprietary and scholarly • APT: Arbitrage Pricing Theory • Fama/French Model • 3 Factor: Market return, small stock versus big stocks and high versus low book/market (value versus growth stocks) • 4 Factor: Additional momentum factor discovered by Carhart

9. Risk is Difficult to Empirically Measure • Data is necessary for empirical observations • Usually estimate equity betas because of data availability (asset beta is difficult to observe) • Equity risk comparables are difficult to find • Need to have the same capital structure • Adjust for different capital structure by levering and unlevering beta • Need to have the same business (asset) risk • Industry Estimation: May use industry mean/median • Other companies, other projects, divisions, etc. • Usually these measures are a combination of asset or business risk and other types of risk (i.e., capital structure) • Adjust by levering and unlevering beta

10. How Do We Manage This Problem? • We use the relationship between the total firm market value (V), asset (A), equity (E), debt (D) and the NPV of the capital structure/financing (D) • Think of the firm value expressed as V=A+D= E+D • The NPV of the capital structure/financing is the value created by the capital structure choice of the firm • In our simple world with no bankruptcy costs, this is basically the tax shield of debt • In perfect capital markets NPV of financing is zero (no taxes) • The firm (assets) can be viewed as a portfolio of its financing (assume equity, debt and NPV of capital structure/financing)

11. The Relationship • The beta of a portfolio is the weighted average of the components therefore • The return of a portfolio is also the weighted average of the components • Substitute return (r) for beta (B) in the relationship • Note: The use of this relationship is typically called levering and unlevering

12. What is the risk of financing NPV(D)? • Assume BA=BD (Case 1) • Assume BD=BD (Case 2) • Assume BD=BD and D=tD (Case 3)

13. Assumptions about NPV of financing (D) • BA=BD • Asset (business) risk related to the financing risk? • More likely if leverage is constant proportion of market value • BD=BD • Debt risk related to the financing risk? • More likely if leverage is constant dollar amount • Assume BD=BD and D=tD • Most restrictive assumptions • rd is the appropriate rate, debt is constant dollar amount and a tax deductible perpetuity (tD= tDrd/rd) • How about floating rate debt? • Reasonable assumptions?

14. Additional Assumptions • What is the beta of debt? • Can we assume it is zero? • If the firm has fixed rate debt and a low probability of bankruptcy, its very close to zero • Rule of thumb: Keep the assumptions to a minimum, in other words, lever and unlever only when necessary!

15. Computing An Asset Beta • Asset beta is usually difficult to observe • How do we estimate an asset beta? • Strip out the asset risk by unlevering the beta • Or find an all equity (pure play) firm • Find the Beta for a new hotel project. The industry Be is 1.5%, average industry debt level is 20% and Bd is 0.2%. (assume Case 1). • Assume Rf is 3% and Rm is 13%. Does this relationship hold for R also?

16. Estimate return on equity for a new capital structure • Use when you can reasonably estimate • New capital structure • Changes in cost of debt • From the previous example, the industry Ra is 15.4%. Your hotel project is going to have a debt level of 40% and the Rd is 7%. What is your Re?

17. “Whole Firm” Risk Measures • From portfolio theory • Portfolio risk is the weighted average of the components’ risk • Works with beta and return (but not volatility) • Think of the “whole firm” as components of... • Financing: Debt, equity, other financing (i.e., WACC) • Value: Business (unlevered) and financing flows • Other logical breakouts? • Divisions/business units • Assets in place and growth opportunities • Look to the available data and logical economic components • Used for any complex asset (does not have to be “whole firm”)

18. Weighted Average Cost of Capital • When is WACC the appropriate discount rate? • Proposed investment project is similar to the overall business activities of the firm • Project is financed with same capital structure weights as the firm • Target weights versus actual weights • Represents cost of the next dollar a firm would raise • Simplify the capital structure to debt and equity • View the firm as a portfolio of securities • Cost of Equity • Cost of Debt • WACC reflects average riskiness of firm's securities

19. What if the projects are not similar to company risk?WACC may lead to poor decisions! • Incorrect Investment Decisions B A Firm’s overall cost of capital Rf Project’s security market line

20. Weighted Average Cost of Capital (WACC) Capital Structure weights (portfolio weights) Use market values WACC (not adjusted) = value-weighted average of cost of capital WACC = (E/V)Re + (D/V)Rd WACC (adjusted) = value-weighted average of after tax cost of capital Tax-Advantage of Debt Implies: WACC = (E/V)Re + [(D/V)Rd*(1-tc)] Estimates of Corporate tax rate?

21. Bringing it all together: Cash flow and r? • FCF using WACC • Cash flows are the flows to the total firm • WACC is based on the firm’s existing capital structure (RHS of the balance sheet) • Adjusted Present Value (APV) • Most common use: Break the flows into flows to assets and flows to financing • NPV plus PV (other benefits or costs) • Flow to Equity Approach (FTE) • Only estimate the flows to the equity holders • The appropriate r is the return on equity.

22. Comparison of 3 methods • Assume the project is financed with $50 of debt which costs 8% and $50 of equity which costs 12%. The yearly perpetual project cash flow is $8.8, the tax rate is 30% and assume you can perpetually take advantage of the tax shield of debt. • What is the NPV?

23. WACC • FTE • Equity income=cash flow minus after tax cost of debt

24. APV: One approach (r based on who receives flow) • Second approach (r based on origin of flow)