FIN 40153: Advanced Corporate Finance

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FIN 40153 Advanced Corporate Finance

• THE WEIGHTED AVERAGE COST OF CAPITAL
• (BASED ON RWJ CHAPTER 13)

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The Cost of Capital and Valuation

• Debt and Equity
• A company can get cash for investment by
  retaining earnings or selling either debt or
  equity.
• Does it make any difference how the firm raises
  money?
• What is the proper discount rate when the firm
  uses both debt and equity?
• How do we perform capital budgeting/valuation
  when the project has different risk and/or
  capital structure than the firm as a whole?

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Setting the stage
Assets Produce Cash Flows That Create Value
Cash Flows
Debt
Equity
The firms assets are a portfolio of the debt and
equity. Debt and equity just divide up the cash
flows (value) of the firm.
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The Weighted Average Cost Of Capital(WACC)

• When a firm has both debt and equity in its
  capital structure, the most frequent
  recommendation is to base the project discount
  rate on the weighted average cost of capital
  (WACC)

• where
• E is the market value of the firms stock
• D is the market value of the firms debt
• rE is the required rate of return on the firms
  stock
• rD is the required before tax rate of return on
  the firms debt
• TC is the firms marginal tax rate

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Why Is There A Tax Adjustment For Debt?

• Consider a firm that has earnings before interest
  and taxes each period of 1000. Under scenario A,
  the firm is all equity financed under scenario
  B, the firm has issued debt with a face value of
  1000 and a coupon rate of 10. The firm has a
  40 marginal tax rate.

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Why Is There A Tax Adjustment For Debt?

• In A, the firm can distribute a total of 600 to
  stakeholders.
• In B, the firm can distribute 100540640 to
  stakeholders.
• The tax shield from debt gives the firm 40 more
  to distribute. This tax shield lowers the
  effective interest payment on debt to
  60100(1-0.4) or 6 coupon rate.

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Calculation of the cost of debt (RDebt)

• The before tax cost of debt can be calculated as
  the yield to maturity (YTM) on the firms
  existing debt.
• Much debt is not publicly traded, so you do not
  have the current price to compute the YTM.
• YTM is basically the IRR of the debt.
• Can also be determined using the current interest
  rates applicable to bonds of companies with
  comparable financial structure and bond ratings.
• Wall Street Journal
• Moodys
• The after tax cost of debt is the before tax cost
  of debt multiplied by (1-Tc), where Tc is the
  firms effective marginal tax rate.

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Bond Ratings and Bond Yields
So on 3/1/2006 10 year AAA bonds pay 68 basis
points higher than 10 year than Treasuries, 4.59
0.68 5.27
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High Yield Bond Quotes
For Intelsat if the face a corporate tax rate of
35 their after tax cost of debt would be 9.467(1
0.35) 6.154
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Calculation of the cost of equity (rEquity)

• The cost of equity can be calculated using the
  Security Market Line (SML) from the CAPM.
• rE Rf b (ERM- Rf)
• Three inputs are required
• Firm Beta
• Risk free rate
• Market risk premium

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Applying the CAPM

• (i) An estimate of the risk free interest rate.
• Practitioners tend to favor the current yield on
  longer-term treasury bonds but adjust according
  to projects maturity.
• Remember to adjust the market risk premium
  accordingly.
• (ii) An estimate of the market risk premium, E(Rm
  - rf), the extra return investors expect to earn
  from holding the market instead of the risk-free
  bond.
• The theory calls for a forward looking measure
  (expected)
• Expectations are not observable.
• Generally use a historically estimated value.
• (iii) An estimate of beta. Is the project or a
  surrogate for it traded in financial markets? If
  so, gather data and run an OLS regression.

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How To Obtain Beta.

• Estimate beta from a regression equation.
• In practice, generally use last five years of
  monthly data. Some companies publish beta
  estimates on a regular basis
• Value Line
• Merrill Lynch Beta Book
• Internet Finance Websites
• What if the company is not publicly traded?
• Find a comparable company that is traded.
• Use accounting data (ROE) instead of stock
  returns
• Reason it out.

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Microsoft Return Versus SP 500
RMicrosoft
RSP
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Estimating Microsofts Beta
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Regression Results of Microsoft Return on SP 500
Return 2001-2004
This is Microsofts Beta
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What Determines Beta?

• Beta is a measure of sensitivity to the market.
• Companies with cyclical cash flows will tend to
  have higher betas.
• Higher operating leverage implies higher betas.
• operating leverage is the ratio of fixed costs to
  variable costs.
• Higher financial leverage also means higher
  equity beta.

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The Market Risk Premium

• The market risk premium measures the additional
  return that an investor needs to hold risky
  assets (i.e. stocks) rather than risk-free assets
  (treasuries).
• The Market Risk Premium is defined as
• Ideally, the MRP would be based on expectations
  of investors about the future. However,
  expectations are not observable.
• We can observe what has actually happened based
  on historical data.

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The Market Risk Premium (Excess Returns)

• Excess Returns
• The difference between the average return for an
  investment and the average return for a risk-free
  asset
• The extra return earned for holding a risky
  investment
• For U.S. data from 1928 to 2007

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The Market Risk Premium

• Recall that the standard deviation of returns on
  the SP 500 is approximately 20 per year.
• If we use data from 1928-2007 we have 80 years of
  data.
• The standard error of the risk premium estimate
  is about 0.20/sqrt(80)0.022
• This implies that our estimate of the risk
  premium is not very precise. The 95 confidence
  interval is
• 0.078 2 x 0.022
• The risk premium is between 3.3 and 12.2
• Note that these calculations assume that the
  process generating stock returns is stationary
  over time.
• What if it is not?

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The Market Risk Premium

• Should we use a longer sample?
• Some researchers have now been able to get U.S.
  stock return data back to the early 1800s. See
  for example Stocks for the Long Run by Jeremy
  Siegel http//www.wharton.edu/research/1998.html
• Also, do we want to create our sample estimate
  using only data from U.S. markets?
• The U.S. won the major wars, avoided communism
  or other major social upheaval. Could the U.S.
  market outcomes reflect what was expected, plus a
  bonus for doing so well?
• Lets look at some data from A Century of Global
  Stock Market Returns provided by William
  Goetzmann, Yale University.

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The US is clearly not typical

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Country Risk Premiums
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How do estimates of the market risk premium
change?

• If we add additional years to the sample using
  the Siegel data it suggests a risk premium
  relative to short-term treasuries of perhaps 6
  per year (compared to 7.78).
• The Goetzmann data suggest that the average U.S.
  stock return exceeds average world returns by
  about 2 per year.
• These findings suggest estimates of
• 6.0 relative to short-term treasuries.
• 4.5 relative to long-term treasuries .
• Finally, might the risk premium change over time
  -- higher at some points, lower at others?
• If the risk premium is not stationary then using
  a longer sample will not provide an accurate
  estimate of current expectations.
• But using only recent data increases the
  estimation error.

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Betas and Leverage

• We noted earlier that the beta of a portfolio is
  the average of the component betas. Also, we can
  think of the firms assets as a portfolio of the
  debt and equity claims. From these insights it
  follows that

• Where E is the market value of the stock
  (equity) and D is the
• market value of debt (borrowings).

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Risk of Debt and Equity
Assets Produce Cash Flows That Create
Value (Asset Beta)
Cash Flows
Debt (Debt Beta)
Equity (Equity Beta)
The firms assets are a portfolio of the debt and
equity. Debt and equity just divide up the cash
flows (value) of the firm.
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Beta and Leverage

• This formula can be used to find the asset beta
  given the equity and debt betas or to find the
  equity beta, given the asset and debt betas.
  Rearranging the formula gives
• Note that the equity beta increases as leverage
  (D/E) increases.
• It is often assumed that the debt has a zero beta
  (a big simplification). Then

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Beta and Leverage

• This formula can be used to find the asset beta
  given the equity and debt betas or to find the
  equity beta, given the asset and debt betas.
• For firms with risky debt (i.e., below investment
  grade), in practice it is often assumed that the
  debt beta is 0.25 to 0.30.

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Adjusting beta for different capital structures

• Example Gamma airlines equity beta is observed
  to be 1.31. Its equity is worth 25.0 million
  while its debt is worth 15.0 million. What is
  the beta of the underlying assets assuming a debt
  beta of zero?
• Note The asset beta is always less than or
  equal to the equity beta.

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Points to Note Regarding Beta and Leverage

• If the firm uses no debt (D0) the equity beta
  and the asset beta are equal.
• If the firm uses debt, the equity beta is
  increased relative to the asset beta
• implies
• (1) equity holders will require a higher rate of
  return,
• (2) when comparable firms are used to estimate
  beta, allowances for differing capital structures
  will be required.

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How to use the set of tools developed here to
select discount rates for capital budgeting.

• The cost of capital for each project should
  reflect the systematic risk of that project and
  the capital structure of the firm (or division)
  taking the project. So,
• Select a publicly traded company that is
  comparable in terms of the risk of the underlying
  business (i.e., the asset beta).
• Obtain the unlevered (asset) beta of the
  comparable.
• Obtain the corresponding project equity beta for
  your firm, reflecting your firms capital
  structure.
• Obtain the cost of equity and cost of debt for
  this project reflecting your firms capital
  structure.
• Calculate the WACC for the project and perform
  NPV analysis based on the expected cash flows
  with no leverage.

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EXAMPLEThe Story For BK Industries

• Remember BK Industries has been producing
  publishing equipment for some time now and the
  CEO believes that he has stumbled upon a valuable
  product innovation that embeds new features in
  text editing systems. BKs cost advantages and
  vast skill in marketing mean it would be
  difficult for competitors to undertake such a
  project.

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BK IndustriesIncremental Cash Flows

• Suppose that BK forecasts the following cash
  flows from operating a text editing business (
  millions).

Year 0 Year 1 Year 2 Year 3 Year 4 Year5
-26.00 3.98 5.42 6.69 5.99 22.46
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BK Industries Net Present Value (NPV)

• BK has estimated its company cost of capital to
  be 10. What is the NPV of the text editing
  business?

• NPV (_at_ r10)
• -26.00 3.98/(1.10) 5.42/(1.10)2
  6.69/(1.10)3
• 5.99/(1.10)4 22.46/(1.10)5 5.159 Million
• The NPV is greater than zero, so BK should
  proceed with the project.

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Example BK Industries Revisited

• Suppose that BK Industries is a conglomerate
  company with operations in a number of other
  products lines with no text editing business.
  Also suppose BKs current equity beta is 1.0. BK
  has and will maintain a debt/equity ratio of 1.0.
• Can we use the company cost of capital to value
  the text editing project?
• Latec Inc. is a firm that makes only text editing
  systems. Latecs equity beta is 1.35. Latec has
  a debt to equity ratio of 0.75.

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Delevered Betas with debt/equity ratios

• The formulas for obtaining asset betas from
  equity betas and vice versa provided earlier
  required dollars values for debt (D) and equity
  (E). What if you are only given the leverage
  ratio, L D/E? The formulas are restated as

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Delever Latecs Beta to obtain the Beta of
text-editing assets

• Latec has L 0.75and an equity beta of 1.35.

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Relever the asset Beta to reflect BKs capital
structure
Recalling that BK will keep its debt/equity
ratio equal to one, we can get

• This is the beta for a BK equity position in a
  text
• editing asset.
• Why is this equity beta greater than Latecs?

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BK Industries, Cont.

• Assume that the risk free rate is 8 and that
  BKs cost of debt is also 8. The market risk
  premium is 7 and the marginal tax rate is 45.
  The required return on BKs equity is

The weighted average cost of capital for the text
editing venture (using the fact that D/E 1
here) is
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• Finally, we can evaluate the NPV of the text
  editing venture using the WACC that reflects the
  risk associated with this particular business.
• The NPV of the text editing project is -21,329

• Notice that the selected discount rate of 11.59
  reflects
• The risk (beta) of text editing businesses, not
  BKs existing businesses.
• BKs capital structure, not that of the surrogate
  firm.

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COMPANY COST OF CAPITAL ANDPROJECT COST OF
CAPITAL
Required return
Security market line showing
required return on project
Risky Project
Safe Project
Company cost of capital
Project beta
Average beta
of firm's assets
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Some Common Errors to Avoid

• Using book value weights in the WACC.
• The weights should be based on market values
• The weights should reflect the firms target
  capital structure.
• Using incorrect leverage ratios for levering and
  unlevering betas and computing WACC.
• D/E versus D/(DE).
• Know which one you are using.

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Some Common Errors to Avoid

• Subtracting the current risk-free rate from the
  historical average market return to get the
  market-risk-premium.
• The MRP estimate should be based on the
  difference between the historical average of the
  market return and the historical average return
  on the risk-free bond.
• The current risk-free rate is used for the
  stand-alone Rf if the SML equation.

Historical difference between return on the
market and return on the risk-free bond
Current-Value