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

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

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Models and methods to estimate the appropriate r

Remember the guiding principle: The r should reflect the riskiness of the cash flows

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

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

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

How do we estimate CAPM?

- Expected Return Model (CAPM)
- Realized Return Model (Index Model)

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?

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)

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

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

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)

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

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)

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?

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!

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?

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?

“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”)

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

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

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?

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.

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?

WACC

- FTE
- Equity income=cash flow minus after tax cost of debt

APV: One approach (r based on who receives flow)

- Second approach (r based on origin of flow)

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