Hurdle rates for Firms

1
Hurdle rates for Firms

• 04/09/07
• Ch. 7

2
Investment decision

• Firms should invest in projects that creates
  value for the firms shareholders
• These are projects that yield a return greater
  than the minimum acceptable hurdle rate with
  adjustments for project riskiness.

3
Investment decision

• Components of the investment decision making
  process
• Determine the appropriate hurdle rate for the
  firm (Ch. 7)
• Make adjustments for project riskiness (Ch. 8)
• Calculate the cash flows associated with the
  project (Ch. 9)
• Employ the appropriate decision tools (Ch. 10)
• Evaluate project interactions (ch 12)

4
What is a hurdle rate?

• The hurdle rate for the firm represents the
  minimum rate of return that the firm as a whole
  must generate on its investments to satisfy its
  investors.
• This is sometimes referred to as the weighted
  average cost of capital (WACC) or simply the cost
  of capital.
• This hurdle rate is a function of (among other
  things)
• Type and mix of investors (equity, debt,
  preferred stock)
• Riskiness of the firm

5
What is a hurdle rate?

• This hurdle will be higher for riskier projects
  than for safer projects.
• A simple representation of the hurdle rate is as
  follows
• Hurdle rate Risk-free Rate Risk Premium
• The two basic questions that every risk and
  return model in finance tries to answer are, for
  each type of security
• How do you measure risk?
• How do you translate this risk measure into a
  risk premium?

6
Cost of equity

• Required rate of return for equity investors (or
  shareholders) is also referred to as the cost of
  equity
• For publicly traded firms, we initially assume
  that the these equity investors are diversified
  investors. Consequently,
• Only the firms risk relative to the market is
  relevant (systematic risk)
• Firm-specific risk is assumed to be diversified
  away
• We will later relax our diversified investor
  assumption

7
Cost of equity

• With our diversified investor assumption, the
  appropriate risk measure for a firm is beta (ß)
  which measures the firms systematic risk
• Although it has its limitations, the appropriate
  model to estimate the cost of equity is the
  Capital Asset Pricing Model (CAPM)
• where re is the cost of equity for a particular
  stock, rf is the risk free rate, and rm is the
  return on the market (SP 500 index for our
  purposes)

8
Cost of equity

• To calculate the cost of equity for a firm, we
  need estimates for each of its components
• Risk-free rate
• Market return, or alternatively the market risk
  premium, (rm-rf)
• Firms beta

9
Risk-free rate

• With the risk-free asset, the actual return and
  expected return do not vary.
• This asset assumes
• No default risk
• No reinvestment risk
• Ideally, this means that you should use a
  risk-free asset whose maturity matches the timing
  of cash flows

10
Risk-free rate

• Realistically, using a long-term government bond
  (even with coupon), such as a 30-year Treasury
  bond return, is adequate for long-term analyses.
• For short-term analyses, short term government
  securities, such as the 3-month Treasury bill,
  are appropriate.
• The current rates for these instruments are
  available from the Yahoo (or other financial
  information sources) and are represented by the
  yield.

11
Market risk premium

• The market risk premium represents the extra
  return beyond that of a risk-free asset that an
  investor demands for moving their funds from the
  risk-free asset to the risky (market portfolio)
  asset.
• As a general proposition, this premium should be
• greater than zero
• increase with the risk aversion of the investors
  in that market
• increase with the riskiness of the average
  risky investment

12
What is your risk premium?

• Assume that stocks are the only risky assets and
  that you are offered two investment options
• a riskless investment (say a Government
  Security), on which you can make 6
• a mutual fund of all stocks, on which the
  returns are uncertain
• How much of an expected return would you demand
  to shift your money from the riskless asset to
  the mutual fund?
• 6 or less
• 7
• 8
• 9
• 10
• 11 or more

13
Risk Aversion and Risk Premiums

• The risk premium is a weighted average of the
  risk premiums demanded by each and every
  investor.
• The weights will be determined by the magnitude
  of wealth that each investor has.
• As investors become more risk averse, you would
  expect the equilibrium premium to increase.

14
Risk Premiums do change..

• Go back to the previous example. Assume now that
  you are making the same choice but that you are
  making it in the aftermath of losing your job.
  Would you change your answer?
• I would demand a larger premium
• I would demand a smaller premium
• I would demand the same premium

15
Estimating the market risk premium

• There are two methods to estimate the market risk
  premium.
• historical risk premium
• Implied risk premium
• The majority of analyses tend to employ the
  historical method or some form of weighted
  average between the two.

16
The historical premium approach

• In most cases, historical market risk premiums
  can be estimated as follows
• define a time period for the estimation
  (1926-Present, 1962-Present....)
• calculate average returns on a stock index during
  the period with longer-term analyses use
  geometric returns
• calculate average (geometric) returns on a
  risk-free security over the same period
• The market risk premium is then the difference
  between the two, i.e., rm - rf.

17
Historical premium limitations

• The limitations of this approach are
• it assumes that the risk aversion of investors
  has not changed in a systematic way across time.
  (The risk aversion may change from year to year,
  but it reverts back to historical averages)
• it assumes that the riskiness of the risky
  portfolio (stock index) has not changed in a
  systematic way across time

18
Implied premium approach

• The implied risk premium approach estimates a
  risk premium based on current market values,
  dividends and growth rates.
• We can use a basic dividend discount model (DDM)
  to estimate the implied risk premium
• Index value Expected index dividends
• (RR on the index growth rate in
  dividends)
• The implied risk premium would then be
• RR on index current risk-free rate

19
Implied premium limitations

• The limitations of this approach are
• It assumes that the DDM is correct to value the
  market.
• It assumes that the market is currently correctly
  valued

20
What should we use as a risk premium?

• The historical risk premium (4.91) tends to be
  higher than the implied risk premium.
• An average of the two measures may serve as a
  good estimate for the risk premium because the
  historical risk premium is much too high to use
  in a market, where equities are currently priced
  with premiums that are closer to 3.

21
Estimating betas

• A firms beta represents the level of systematic
  risk inherent in the firm.
• It can be measured in two ways
• Historical measure (or top-down approach)
  measured by regressing historical stock returns
  of the firm on index (or market) returns
• Bottom-up approach estimated by measuring the
  average beta for firms within the same industry
  after adjusting for financial leverage

22
Historical betas

• The standard procedure for estimating historical
  betas is to regress stock returns (r) against
  market returns (rm) -
• where a is the regression intercept and b is the
  slope of the regression.
• The slope of the regression (b) corresponds to
  the beta of the stock, and measures the riskiness
  of the stock.
• Note Do not confuse this equation with the CAPM.
  This is simply a linear representation of the
  relationship between the return for the firm and
  the market return.

23
Setting up for the estimation

• Decide on an estimation period
• Services (such as Value-Line) use periods ranging
  from 2 to 5 years for the regression
• Longer estimation period provides more data, but
  firms change.
• Shorter periods can be affected more easily by
  significant firm-specific event that occurred
  during the period
• Decide on a return interval - daily, weekly,
  monthly
• Shorter intervals yield more observations, but
  suffer from more noise, monthly returns tend to
  work well.
• Noise is created by stocks not trading and biases
  all betas towards one.
• Estimate returns (including dividends) on stock
• Return (PriceEnd - PriceBeginning
  DividendsPeriod)/ PriceBeginning
• Included dividends only in ex-dividend month
• Choose a market index, and estimate returns
  (inclusive of dividends) on the index for each
  interval for the period.
• Run the regression

24
Applying the approach

• Data for periodic individual stock prices and
  market index values can be found on Yahoo and
  other financial websites
• In general, closing stock prices should be used.
• The SP 500 serves as a good market index.
• Ensure that the returns are calculated including
  dividends.
• This would mean using the adjusted closing prices
  for the index and stock in Yahoo
• You should include the dividends paid by the
  company in the month in which it was paid (if
  monthly returns are calculated).

25
Forward looking beta adjustment

• The regression-estimated betas represent betas
  that are calculated using historical (or past)
  stock prices and index values.
• Since the purpose of calculating these betas is
  to provide us with a hurdle rate for future
  decisions, sometimes these values are adjusted to
  be forward-looking.
• When making the forward-looking adjustment, we
  assume that as firms mature, their betas tend
  towards 1 (market beta).
• Forward-looking beta Regression beta 0.67
  1 0.33
• Many financial reporting agencies, such as Value
  Line, use this adjustment

26
Estimating performance

• The regression output (intercept and
  slope)provides a simple measure of performance
  during the period of the regression, relative to
  the capital asset pricing model.
• CAPM provides an expected return for the stock
• The regression model is a measure of the actual
  return for the stock

27
Estimating performance

• If
• a rf (1-ß) .... Stock did better than
  expected during regression period
• a rf (1-ß).... Stock did as well as expected
  during regression period
• a during regression period
• Alternatively, we can calculate Jensens alpha
  (a)
• a a - rf (1-ß)
• If this measure is greater (less) than 0, the
  company performed better (worse) than investors
  expected during the period from which the
  regression data was obtained.

28
Firm-specific and market risk

• The R-squared (R2) of the regression provides an
  estimate of the proportion of the risk (variance)
  of a firm that can be attributed to market risk.
• The balance (1 - R2) can be attributed to
  firm-specific risk.
• Diversified investors are only concerned about
  market risk. Undiversified investors care about
  both market and firm-specific risks.
• For undiversified investors, a total beta measure
  which accounts for both risks is more
  appropriate.

29
The Relevance of R2

• You are a diversified investor trying to decide
  whether you should invest in Home Depot or Bed,
  Bath and Beyond. Both firms provide equal
  returns. They both have betas of 1.404, but Home
  Depot has an R2 of 40 while Bed Bath and
  Beyonds R2 is only 15. Which one would you
  invest in?
• BBB, because it has the lower R2
• HD, because it has the higher R2
• You would be indifferent
• Would your answer be different if you were an
  undiversified investor?

30
Bottom-up betas

• The bottom-up approach relies on the fundamental
  characteristics of the firm to determine the
  riskiness of the firm and thus the firm beta.
• These fundamental characteristics include
• Type of Business Firms in more cyclical
  businesses or that sell products that are more
  discretionary to their customers will have higher
  betas than firms that are in non-cyclical
  businesses or sell products that are necessities
  or staples.
• Operating Leverage Firms with greater fixed
  costs (as a proportion of total costs) will have
  higher betas than firms with lower fixed costs
  (as a proportion of total costs)
• Financial Leverage Firms that borrow more
  (higher debt, relative to equity) will have
  higher betas than firms that borrow less.

31
Bottom-up betas

• The critical assumption we make in using the
  bottom-up approach is that the riskiness
  associated with the type of business and
  operating leverage will be similar across firms
  that are in the same industry and are of similar
  size.
• This assumption implies that the only difference
  in riskiness between firms in a particular
  industry comes from differences in financial
  leverage, or debt/equity mix.

32
Bottom-up betas

• The first component of a firms risk is that
  associated with its operations
• We can measure this risk by calculating the
  firms unlevered beta (ßU), i.e., a beta that
  removes the effect of financial leverage.
• This unlevered beta is also referred to as an
  asset beta as it represents the riskiness of a
  firms assets.

33
Bottom-up betas

• The second component of a firms risk is that
  associated with its financial leverage
• The greater the debt/equity ratio, the greater
  the financial leverage, and therefore financial
  leverage risk
• The firms levered (or bottom-up) beta provides
  us with an estimate of both operating and
  financial leverage risks.
• This levered beta (ßL), represents the firms
  risk and is equivalent (but not necessarily the
  same in value) to the historical beta calculated
  using the regression approach.

34
Bottom-up betas

• The levered beta can be estimated by doing the
  following
• Find out the industry that a firm operates in
• Find the unlevered betas of other comparable
  firms in this industry
• Take a weighted (by sales or market value)
  average of these unlevered betas
• Lever up using the firms debt/equity ratio
• This method is best for beta estimation for
  non-traded (private) firms since stock prices are
  not available to measure a historical beta.

35
Equity betas and leverage

• The following equation provides us with the
  mathematical relationship between the unlevered
  and levered beta
• where
• ?L Levered Beta
• ?u Unlevered Beta
• t Corporate marginal tax rate
• D Debt Value
• E Equity Value

36
Betas are weighted averages

• The beta of a portfolio is always the
  market-value weighted average of the betas of the
  individual investments in that portfolio.
• Thus, for example,
• the beta of a firm is the weighted average of the
  betas of the firms distinct divisions
• the beta of a firm after a merger is the
  market-value weighted average of the betas of the
  companies involved in the merger.

37
Is beta an adequate measure of risk for a private
firm?

• The owners of most private firms are not
  diversified. Beta measures the risk added on to a
  diversified portfolio. Therefore, using beta to
  arrive at a cost of equity for a private firm
  will
• Over estimate the cost of equity for the private
  firm
• Under estimate the cost of equity for the private
  firm
• Could under or over estimate the cost of equity
  for the private firm

38
Total risk versus market (systematic) risk

• For private firms (or firms where owners are not
  diversified), it would be more appropriate to use
  the firms total risk rather than just market
  risk.
• The adjustment to account for total risk is a
  relatively simple one, since the R2 of the
  regression measures the proportion of the risk
  that is market risk.
• For private firms where we do not have stock
  returns to run a regression, the R2 of comparable
  firms will suffice.

39
Bottom-up or regression (top-down) beta Which
one should we use?

• The bottom-up beta will give you a better
  estimate of the true beta when
• the firm is not substantially different
  fundamentally (size, operational characteristics,
  etc.) from the other firms in the industry
• the firm has reorganized or restructured itself
  substantially during the period of the regression

40
Summary of cost of equity estimation

• Determine an appropriate risk-free rate (the
  30-yr T-bond rate will usually suffice).
• Estimate an appropriate market risk premium
• Calculate firm beta either by
• Using a top-down or regression approach
• Bottom-up approach
• Make adjustments if necessary to account for
  undiversified investors or to make the value
  forward looking
• Calculate the cost of equity using the CAPM

41
From cost of equity to cost of capital

• The cost of capital is a composite cost to the
  firm of raising financing to fund its projects.
• In addition to equity, firms can raise capital
  from debt or hybrid securities

42
What is debt?

• General Rule Debt generally has the following
  characteristics
• Commitment to make fixed payments in the future
• The fixed payments are tax deductible
• Failure to make the payments can lead to either
  default or loss of control of the firm to the
  party to whom payments are due.
• As a consequence, debt should include
• Any interest-bearing liability, whether short
  term or long term.
• Any lease obligation, whether operating or
  capital.

43
Cost of debt vs. required rate of return for
debtholders

• The required rate of return for bondholders of a
  particular firm is a function of
• Current interest rate for the risk-free asset
  (30-yr. T-bond yield)
• Default risk associated with the firm, i.e., how
  likely is the firm to go bankrupt (risk premium).
• Bondholders are compensated in interest payments
  (or coupon payments) for this required rate of
  return. This represents the before-tax cost of
  debt (BT rd)
• Because from the firms perspective interest
  expense is tax-deductible, the after-tax cost of
  debt (rd) is
• BT rd (1 tax rate)

44
Estimating the cost of debt

• Depending on whether or not the firm in question
  has bonds that are publicly traded and on
  available information, there are three ways (in
  order of preference) to estimate the before-tax
  cost of debt
• Look for prices and yields of bonds outstanding
• Estimate the cost of debt from the firms credit
  rating
• Estimate the cost of debt by calculating a
  synthetic credit rating

45
Estimating the cost of debt

• If the firm has bonds outstanding, and the bonds
  are traded, the yield to maturity (YTM) on a
  long-term, straight (no special features) bond
  can be used as the before tax cost of debt.
• The YTM incorporates the risk-free rate and
  firm-specific default risk.
• Sources
• Look at the Corporate Bond excerpt in the WSJ or
  other publications
• Yahoo may also have this information
• rd YTM (1-t)

46
Estimating the cost of debt

• If the firm is rated, use the credit rating and a
  typical default spread on bonds with that rating
  to estimate the cost of debt.
• Standard Poors, Moodys and Fitch provide
  credit ratings for firms. The first of these
  ratings can be found at
• www.standardandpoors.com
• Default spreads can be found at
  www.bondsonline.com (premium service) OR inferred
  from bond spreads of other bonds with the same
  rating
• rd (30-yr. T-bond yield spread) (1-t)

47
Estimating the cost of debt

• If the firm is not rated,
• estimate a synthetic rating for the company, and
  use the synthetic rating to arrive at a default
  spread and a cost of debt

rd (30-yr. T-bond yield spread) (1-t)
48
Estimating synthetic credit ratings

• The rating for a firm can be estimated using the
  financial characteristics of the firm. In its
  simplest form, the rating can be estimated from
  the interest coverage ratio
• Interest Coverage Ratio EBIT / Interest
  Expenses
• Interest Coverage Ratio SP Rating
• 8.5 AAA
• 6.50 - 8.50 AA
• 5.50 6.50 A
• 4.25 5.50 A
• 3.00 4.25 A-
• 2.50 3.00 BBB
• 2.25 2.50 BB
• 2.00 2.25 BB
• 1.75 - 2.00 B
• 1.50 1.75 B
• 1.25 1.50 B-
• 0.80 1.25 CCC
• 0.65 0.80 CC

49
Cost of preferred stock

• The cost of preferred stock, which has some
  characteristics of debt and equity (specified
  dividend, not tax deductible, infinite life) is
  calculated as follows
• where rps, Dps, and Pps are the cost of
  preferred stock, dividend on preferred stock and
  current price per share of preferred stock,
  respectively.
• www.quantumonline.com has useful information
  about preferred stocks.

50
Estimating capital weights

• The firms cost of capital is a function of the
  cost of each type of financing the firm adopts
  and of the weights of each type of financing
• Book values (obtained from financial statements)
• Equity includes common stock and retained
  earnings
• Debt includes long term debt and the present
  value of leases
• Preferred Stock includes preferred stock
• Convertible bond value should be apportioned to
  equity and debt.

51
Estimating capital weights

• Market Values
• Market Value of Equity (E) and Preferred Stock
  (PS) should include the following
• Market Value of Shares outstanding
• Shares outstanding current stock price
• Market Value of Warrants outstanding
• 10-K filings (with the SEC) and annual reports
  should provide information about the shares
  outstanding, market value of warrants should be
  in the 10-Ks.
• Conversion option value of outstanding
  convertible bonds should be included in Equity.

52
Estimating capital weights

• Market value of debt (D) is more difficult to
  estimate because few firms have only publicly
  traded debt.
• Estimate the market value of debt from the book
  value by treating the entire debt as one coupon
  bond, with a coupon (C) set equal to interest
  expenses and maturity (n) equal to the average
  maturity of all debt outstanding and using the
  current before-tax cost of debt (BT rd).
• Market value of bonds (D)

53
Converting leases to debt

• The debt value of leases is the present value
  of the lease payments, at a rate that reflects
  their risk.
• In general, this rate will be close to or equal
  to the rate at which the company can borrow,
  i.e., pre-tax cost of debt.
• Capital leases are included in the balance sheet,
  operating leases are not.

54
Accounting for convertible bonds

• A convertible bond is a bond that can be
  converted into equity at the option of the
  bondholder.
• To incorporate a firms outstanding convertible
  bond issues into our cost of capital
  calculations, we separate the bond
• into 2 distinct components
• Straight debt, whose value is
• Conversion option Current bond price straight
  debt value

55
Accounting for convertible bonds

• The straight debt component is included in debt.
• The conversion option component is included in
  equity.

56
Cost of Capital

• The weighted average cost of capital (or firm
  hurdle rate) is then just the weighted average of
  the individual sources of capital
• rd represents an after-tax cost of debt
• Divisional costs of capital may be calculated if
  firms have distinct major divisions of operation

57
Choosing a Hurdle Rate

• Either the cost of equity or the cost of capital
  can be used as a hurdle rate, depending upon
  whether the returns measured are to equity
  investors or to all claimholders on the firm
  (capital)
• If returns are measured to equity investors, the
  appropriate hurdle rate is the cost of equity.
• If returns are measured to capital (or the firm),
  the appropriate hurdle rate is the cost of
  capital.

58
Chapter 7 sections NOT covered

• Riskless Rates When There is Sovereign Risk
• Currency Choices and Real Rates
• Historical risk premiums for other countries (pg.
  192-194) this section does not have a separate
  title
• Accounting Betas