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Sloan Corporate Finance Tutorial III

Cost of Capital

Jungsuk Han

http://phd.london.edu/jhan.phd2005/tutorial.htm

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Today’s Topic

1. CAPM and Risk Premium1. Beta and Systematic Risk2. Risk Premium

2. Market Efficiency1. Three forms of market efficiency2. Technical Analysis and Weak-form Efficiency

3. WACC and Capital Structure1. MM Theory 2. WACC, After-tax WACC3. Assumptions in WACC4. Industry WACC5. ‘Tesco’ Case

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1. CAPM (Capital Asset Pricing Model)

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1. CAPM and Risk Premium

E[rE] – rf = βE(E[rM]-rf)

(or, E[rE] = rf + βE(E[rM]-rf))

• Expected risk premium on an asset (E[rE] – rf )

= Quantity of risk (βE) * Price of risk (E[rM]-rf)

(interpreted similarly as “Value = Quantity * Price”)

• In the CAPM, the risk premium on the market portfolio measures the price of risk, while the beta states the quantity of risk.

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(1) Beta and Systematic Risk

• total risk = systematic risk + idiosyncratic risk • Beta Beta onlyonly measures systematic risk! measures systematic risk!• When beta = 1, it has the same systematic risk as the market

portfolio• Smaller beta of a portfolio means less systematic risk • Small beta does not guarantee small risk since it ignores

idiosyncratic risk. If a portfolio is diversified enough, there is no idiosyncratic risk any more. Only then, low beta means low risk

)(

),()(

M

eMe rVar

rrCovBeta

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Example: Risk Premium(From 2003 Final Exam)

• Question: What is a suitable number for the market risk premium in your view? What consideration lead you to this answer?

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How to measure Risk Premium (E[rM]-rf)?

1. How to find a market portfolio?• The market portfolio should in theory include all

types of assets that are held by anyone as an investment (including works of art, real estate, human capital, etc)

• Practically, it is impossible to find such a market portfolio.

We use the return on stock market index as a proxy (e.g., return on FTSE 100, FTSE 250, S&P 500, etc).

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How to measure Risk Premium (E[rM]-rf)?

2. How to estimate the expected market risk premium?

• Assume that the future will be like the past, and use past data

• Assume that the expected return on equities goes up if interest rates go up

We use historical data to estimate the risk premium on equities relative to Gilts, or T-bills

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Average Rate of Return (U.S,1900~2003)

Average Annual Rate of Return

Average Risk Premium

Nominal Real

Treasury bills 4.1% 1.1% 0.0%

Government bonds 5.2% 2.3% 1.2%

Common stocks 11.7% 8.5% 7.4%

(From Brealey, Meyers, and Allen)

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Where to Find Beta?

• Bloomberg terminal (available at LBS library)• CRSP• Datastream• Reuters (http://www.reuters.co.uk)• Valueline (http://www.valueline.com)• Google finance (http://finance.google.com)• Bloomberg website (http://www.bloomberg.com)• Your own stock broker (e.g., E-trade, Barclays, etc)Or,• Do it by yourself!

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Market Risk Premium vs. Individual Asset Risk Premium

Risk premium ofmarket portfolio

Risk premium of an individual asset

0

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Regression

Risk premium ofmarket portfolio

Risk premium of an individual asset

Slope = beta

0

Intercept= alpha

Risk premium of an asset = alpha + beta * market risk premium

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Tesco PLC

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Microsoft Corporation

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3M Corporation

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Northern Rock PLC

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FTSE 100

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T-Bills

http://www.bloomberg.com/markets/rates

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Gilts

http://www.bloomberg.com/markets/rates

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Tesco

• What is the expected return of Tesco PLC according to CAPM?

• Nominal return– Beta: 0.544– Expected Market Risk Premium: 6% ( As was given in the

class)– Risk-free rate: 5%– Expected return = 5% + 0.544*6%

= 9.26%

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Tesco

• Assume inflation is 3%

• Real return– Beta: 0.544– Expected Market Risk Premium: 6%– Risk-free rate: 2%– Expected return = 2% + 0.544*6%

= 6.26%

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Northern Rock

• Assume– Inflation: 3%– Risk-free Rate: 5%– Market Risk Premium: 6%

• What is the expected return on Northern Rock PLC according to CAPM?

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2. Market Efficiency

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Market Efficiency

• If market is efficient, it is impossible to beat the market.

Weak-form Efficiency

Semi-strong-form Efficiency

Strong-form Efficiency

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Three kinds of efficiency

• Weak-form efficiency: past price information does not predict how future prices will deviate from today’s price.

• Semi-strong-form efficiency: public information does not predict how future prices will deviate from today’s price.

• Strong-form efficiency: private information does not predict how future prices will deviate from today’s price.

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Alpha

• If market is efficient, CAPM implies that alpha must be zero.

• If alpha is significantly different from zero for a certain group of shares with similar characteristics, it is called anomaly. (momentum, size, value, etc)

• Alpha is also used to measure portfolio manager’s performance. (If alpha > 0, means the fund is performing better compared to its risk.)

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Alpha and SML

Security Market Line(SML)

Beta (β)

Expected return

0

Risk-free rate

Alpha

Realised return r* of an asset with β*

β*

r*

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Example: Technical Analysis and

Weak-form Market Efficiency (From 2003 Final Exam)

• Question: If a company’s share went down over each of last four weeks, would you expect it to be more likely to go down again or up?

4 weeks ago

time

Share price (£)

Momentum?

Reversal?

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Answer

• If market is efficient, past prices do not give any information. (Technical analysis is useless: weak-form efficiency)– Reason: If the price is expected to go up (down) according

to the past trend, rational investors will immediately buy (sell) the share until the price becomes the same as the expected price. Thus, the price should always reflect all the information from the past trend. (Arbitrage)

• But, if you do not believe that market is weak-form efficient, the past trend of share prices might give some information about the future trend. In other words, technical analysis might pay off. (N.B: If semi-strong-form efficiency does not hold, fundamental analysis might pay off.)

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Anomalies (Optional Reading)

• Momentum (Jagadeesh & Titman ’93): winners outperform losers in short-term return (3 to 12 months)

• Reversal (or Contrarian) (DeBondt & Thaler ’85, ’87): Losers outperform winners in long-term return (5 years)

• Recent studies shows that reversal is mostly caused by value effect. (High Book-to-Market firms outperforms low Book-to-Market firms.) However, momentum effect still persists!

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3. WACC

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Modigliani-Miller (MM) Theory

• Proposition I: Market value of a firm is irrelevant to its capital structure. (WACC does not change with capital structure)

• Proposition II: The expected return on a levered firm’s equity is a linear function of the firm’s debt-to-equity ratio.

rE=rA+(rA-rD)(D/E)• When the firm changes its mix of debt and equity securities, the

risk and expected returns of these securities change, but the company’s overall cost of capital does not change.

• Be ware that MM is assuming no transaction cost, no tax, no incentive, no information asymmetries, etc.

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WACC (Weighted Average Cost of Capital)

• Value (V) = Debt (D) + Equity (E) (Market value of Debt and Equity)• rA: Expected return on assets, rD: Expected return on debt, rE: Expected return on

equity

Expected return on assets = (proportion in debt × expected return on debt) + (proportion in equity × expected return on equity)

• Cost of Equity (CAPM): E[rE] = rf+βE(E[rM]-rf)

Asset Liabilities and Equity

Asset A Debt D

Equity E

V

Er

V

DrWACC ED

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After-tax WACC

• Tax shield: Interest paid on a firm’s borrowing can be deducted from taxable income.

• After-tax cost of debt: rD(1-TC) where TC is the marginal corporate tax rate.

• Use the after-tax cost of debt to compute the after-tax WACC:

V

Er

V

DTrWACC ECD )1(

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Assumptions of WACC

• Frictionless market – No tax effect– No financial distress– No agency costs– No information asymmetries– etc

If we are assuming there exist tax effects or some other effects (e.g., financial distress), calculating WACC with changed capital structure does not make sense!

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Adjusting WACC when debt ratios differ (Optional Reading)

• What do we do when capital structure has to change?– If there is no tax, WACC does not change with

capital structure (MM proposition I)– If there is tax,

• Step 1. Calculate opportunity cost of capital• Step 2. Estimate the cost of debt and the cost of equity

at the new debt ratio• Step 3. Recalculate WACC at the new financing weight

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Adjusting WACC when debt ratios differ (Optional Reading)

• The opportunity cost of capital (hurdle rate, cost of capital): Expected return that is forgone by investing in a project rather than in comparable financial securities

r = rD(D/V)+rE(E/V)

• The opportunity cost of capital depends only on business risk not capital structure (MM proposition I)

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Adjusting WACC when debt ratios differ (Optional Reading)

• Step 1. MM proposition I. Use old D, EOpportunity cost of capital = r = rD(D/V)+rE(E/V)

• Step 2. MM proposition II. Use new D, E

rE=r+(r-rD)(D/E)

• Step 3. Use new rD, rE, D, E, and include tax

V

Er

V

DTrWACC ECD )1(

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Common Mistakes in using WACC

• WACC assumes– Rebalancing: existing capital structure does not

change when debt is increased (i.e., increase equity together with debt proportionally)

– New investment has approximately the same business risk as the overall asset of the company

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Company vs. Industry WACC

• In case a company is composed of two very different divisions, the company WACC may not be a good criteria for a specific investment in one division.

• We often cannot find the beta for a division If we can assume the company and industry

have approximately the same business risk and financing, we can use industry WACC instead of company WACC.

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Tesco Example (Adopted from 2003 Final Exam)

• “Tesco” Data (£ unit: million):– Short-term debt: £5,271– Long-term debt: £3,052– Market Capitalization: £16,859– Beta of equity: 0.56– Expected risk premium (E[RM]-Rf): 6%– Risk free rate (Rf): 4.5%– Inflation rate: 2.2%– Assume there is NO tax effect

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Questions

• Q1: Estimate the cost of capital for Tesco• Q2: What would happened to the WACC if leverage

(or gearing) were significantly increased?• Q3: Suppose that Tesco were to plan a major

expansion of its Hungarian operations, and could fund 100% of the costs of this investment by borrowing locally. What would be the correct discount rate to use when appraising this plan?

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Tesco Example Q1: Answer (Nominal)

• We are using NOMINAL terms here (Just be consistent in any case!)

• Cost of Equity (CAPM)E[rE] = rf+βE(E[rM]-rf) = 4.5 + 0.56*6 = 7.86%

• Debt (D) = Long-term debt = 3,052 (As is discussed in the class. But, including short-term is also fine given some assumptions)

• Market value of debt is ideal, but it is usually unavailable. Thus, using the book value of debt is fine.

• Use market value of equity (Market capitalization)

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Tesco Example Q1: Answer (Nominal)

• Value (V) = Debt (D) + Equity (E) = 3,052 + 16,859 = 19,911

• LeverageD/V = 3,052/19,991 = 0.153 (about 15% debt, 85%

equity)

• WACC = 4.5*0.153 + 7.86*0.847 = 7.35%(If there is tax effect (e.g., tax rate = 30%), WACC = 4.5*0.153 (1-0.3) + 7.86*0.847 =

7.14%)

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Tesco Example Q1: Answer (Real)

• Just the same except for the risk free rate

• Real risk free rate = rf – inflation rate = 2.3%

• Cost of Equity (CAPM)E[rE] = rf+βE(E[rM]-rf) = 2.3 + 0.56*6 = 5.66%

• WACC = 2.3*0.153 + 5.66*0.847 = 5.15%

(If there is tax effect (e.g., tax rate = 30%),

WACC = 2.3*0.153 (1-0.3) + 5.66*0.847 = 5.04%)

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Tesco Example Q2: Answer

• Question 2: What would happened to the WACC if leverage (or gearing) were significantly increased?

• Answer:– Assuming M&M assumptions: WACC does not

change with leverage– Hence, WACC does not change at all

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Tesco Example Q2: Answer

– Assuming Tax effect: WACC probably falls because of tax shields

– (Optional) Assuming cost of financial distress: financial distress decreases company’s value. It is not sure whether it will increase or decrease WACC with debt.

– (Optional) Assuming incentive problem: (1) Debt mitigates agency costs related to private benefits of the manager => increase company value (2) another agency costs related to risk-shifting. => decrease company value (Also, It is not sure whether it will increase of decrease WACC with debt.)

MM needs to be modified by several factors including benefits of tax shields, costs of financial distress, incentives

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Tesco Example Q2(Optional) - Adjusting WACC when debt ratio changes

• Suppose debt (D) is increasing from £3,502mil to £4,052mil.• Step 1.

Opportunity cost of capital = r = rD(D/V)+rE(E/V)= 4.5*0.153 + 7.86*0.847 = 7.35%

• Step 2.

rE=r+(r-rD)(D/E) = 7.35+(7.35-4.5)(4,052/16,859) = 8.03%

• Step 3.

= 4.5*(1-0.3)*(4,052/(4,052+16,859))+8.03* (16,859/(4,052+16,859))= 7.08 %

V

Er

V

DTrWACC ECD )1(

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Tesco Example Q3

• Question 3: Suppose that Tesco were to plan a major expansion of its Hungarian operations, and could fund 100% of the costs of this investment by borrowing locally. What would be the correct discount rate to use when appraising this plan?

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Tesco Example Q3: Answer

• As long as the risk of the project is the same as the rest of Tesco’s business, the overall WACC is the correct discount rate.

• If the project has different risk (higher or lower beta) than the rest of Tesco, then you should use a cost of capital based on the beta for the project.

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Summary

• Risk Premium: Use historical data of stock market index minus T-bill rate

• Market Efficiency: According to weak-form efficiency, it is impossible to predict future prices using past price information.

• WACC: Rebalancing and the same risk are assumed