Risk, Return and Capital Budgeting

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Risk, Return and Capital Budgeting

• Chapter 13 Classes 8 9

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Outline

• What Is the Firm's Opportunity Cost of Capital?
• Definitions and calculations
• Basic assumptions
• Estimating the Opportunity Cost of Capital (
  WACC).
• Calculating Costs and Financing Proportions
• Cost of debt
• Cost of preferred stock
• Cost of common equity
• Financing proportions
• Divisional and Project-Specific Opportunity Costs
• Divisional opportunity costs of capital
• Project-specific opportunity costs of capital
• WACC and liquidity

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Ex 1 The Hurdle Rate

• You are considering setting up a coffee shop in
  the Peters bldg. A used Starbucks Espresso
  machine costs 10,000.
• You will borrow the money at 10. The term of the
  loan is forever.

• Your annual gross profits (revenues less costs)
  are expected to be 1,200 in perpetuity. You pay
  no tax.
• Is the project worth undertaking?

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Time Line for the project

• Positive numbers at the top denote net yearly
  inflows..

1200
1200
1200
1200
1200
1200
-10,000
Yr 1
Yr 2
Yr 3
Yr 4
Yr n ? ?

• The return of the project 12 gt the interest
  rate (cost of capital) 10, so accept the project!

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The Cost of Capital

• The cost of capital is the hurdle rate for
  capital budgeting decisions.
• Cost of capital is the opportunity cost or the
  return that the investors could earn in another
  investment of similar risk.
• Return on the project must exceed opportunity
  cost (return required by providers of capital).
• Opportunity cost of capital is the weighted
  average of the cost of the last dollar of capital
  expected to be raised by the firm from each
  source of financing.

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The Cost of Capital (synonyms)
Alternative names
7
WACC
Definitions
market value of debt B pre-tax cost of
debt Kb market value of preferred stock P
post-tax cost of pref.stock Kps market value
of equity E post-tax cost of equity
Ke market value of the firm is V EBP
8
WACC Definition

• WACC is the overall return that the firm must
  earn on its existing assets to maintain the value
  of its stock.
• It is the interest rate that matches the
  riskiness of the firms operations.

• Notation
• kb - before tax cost of new debt
• ki kb (1-T) - after tax cost of new debt
• T is the marginal corp. tax rate
• kps - cost of new preferred shares
• ks - return required by current shareholders
  (cost of retained earnings)
• ke - cost of issuing new common stock
• wj proportion of debt, equity and preferred
  shares in the firm, based on market values of
  capital structure after financing has been
  raised.

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Market ( not Book) Value Weights

• The weight placed on common equity is the market
  value of equity divided by the value of the firm.
  
• The weight placed on preferred shares is the
  market value of these shares divided by the value
  of the firm.
• For debt issues, add up the market values of all
  the different bond issues (or estimate the market
  values on private issues). Divide this by the
  value of the firm to get the weight placed on
  debt.

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Basic Assumptions

• we want to look at the current cost to the firm.
  This is based on the beliefs of current
  investors. Therefore we need to use market and
  not book values.
• Need efficient markets because we need prices to
  reflect all current information available to the
  firm.

• Firm vs. project
• Can use firms WACC for evaluating a project as
  long as risk of project is similar to risk of
  firm.
• Why should we look at the capital structure of
  the firm instead of the capital structure of the
  project?
• Because security holders receive payment based on
  how well the firm does, not on the returns of the
  specific project.

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Basic Assumptions contd..

• In general k ( in our WACC formula) refers to
  marginal costs of capital I.e is the cost of the
  last 1 raised in debt, pref. stock or equity.
• We are interested in what the costs of capital
  are on the last 1 of financing raised.
• For example, if historical bond yields are 10,
  but the firm is now paying 18 on its debt, it is
  the 18 that is included in the firm's cost of
  raising new capital, not the historical 10.
• Returns on the project must be such that the firm
  can exceed 18, not 10.

• For example, suppose a project were to be
  entirely funded by debt.
• This would indeed change the return required by
  existing shareholders.
• If were to calculate the WACC to the project, we
  should not even consider the return required by
  shareholders.
• So we would end up underestimating the return
  required on the project.

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Some Examples (Ex 2 3)

• Reactive Industries has the following capital
  structure. Its corporate tax rate is 35. What is
  its WACC?

• Passive Footwear has a WACC of 12. Its debt
  sells at a YTM of 9, and its tax rate is 40.
  Its cost of equity is 15. If the firm is
  financed by debt and common equity only, what
  fraction of the firm is financed by equity?

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Cost of Debt (Ex 4)

• Consider a firm that borrows 1 million at 9.
  The corporate tax rate is 40.What is the cost of
  debt to this firm?
• Cost of debt

• The interest is tax deductible we call it the
  Interest Tax Shield.
• The interest tax shield reduces the cost of debt.
  
• So is the after tax cost of new debt.
• Why?

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Solutions

• Reactives WACC 8(1-.35)(20/80) 10(10/80)
  15(50/80) 11.9
• Reactives financing proportions .25 debt .125
  preferred stock .625 common stock or equity
• Passive Footwears fraction financed with equity
  X 68.75 since 12 9(1-.4)(1-X) 15X

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Cost of Debt

• Recall from Bus 383, that kb (if interest is
  paid annually) satisfies

• Here we make an adjustment to B. Use net bond
  price or Bnp. Use bond price minus flotation
  costs per bond

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YTM Approximation for kb

• The yield to maturity (YTM) or kb can be
  approximated by

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Two Examples (Ex 5 6)

• 1).In the mid 1990s, Union Gas had an annual
  bond outstanding with
• 27 years to maturity and
• a coupon rate of 8.65.
• The bond was currently selling for 134.58 of its
  face value.
• Union Gas tax rate is 35.
• What is Union Gas (approximate) cost of debt?

• 2). Armstrong Inc. is planning to issue new debt.
  Armstrong can currently issue debt that
• has an annual coupon interest rate of 10,
• pays interest semi-annually,
• has 20 years to maturity to net 1198 per bond.
• If the firms tax rate is 35, what is the firms
  approximate after tax cost of debt?

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Solutions use YTM Approximation

• Union Gas kb (86.50 (1000-1345.80)/27)/
  (10001345.80)/2 6.28
• Union Gas ki 6.28(1-.35) 4.08
• Armstrong kb (100 (1000-1198)/20)/(10001198)/
  2 8.2
• Armstrong ki 8.2(1-.35) 5.3
• Note If no mention of flotation costs, assume
  none. Approximation is insensitive to whether
  bond is annual or semiannual pay.

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After Tax Cost of Preferred Shares (Ex 7)

• Black Inc has an issue of preferred stock with a
  7 stated dividend that just sold for 95 per
  share.
• What is Blacks cost of preferred stock?
• 7/95 7.4

• Dividends are paid from after tax income no tax
  adjustment is required.
• Preferred stock pays level dividends of Dps each
  year.
• If Pnp are the proceeds from the sale of
  preferred stock then kps Dps / Pnp.

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Cost of Common Equity - Internally Generated
Funds and New Issues

• Do not adjust for taxes. Dividends are paid from
  after tax income therefore no tax shield to the
  firm
• Difficult to calculate because there is not
  stated interest or dividend rate and stock prices
  fluctuate over time.

• 3 approaches
• I.dividend valuation.
• II.CAPM.
• III.bond yield risk premium.

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I.Dividend Valuation

• Rearrange the Gordon growth model

• to solve for ks, firms cost of equity

• Growth rate is usually unknown estimate it from
  past growth or use analysts forecasts of future
  growth rates.
• Advantage simplicity.
• Disadvantage more difficult if firm does not pay
  dividends, or if growth is uneven. Method is
  extremely sensitive to expected growth rate.

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Dividend Valuation (Ex 8)

• The Chilton Oil Co.
• just issued a dividend of 3 per share on its
  common stock.
• is expected to maintain a constant 5 growth rate
  in its dividends.
• its stock sells for 60 a share
• what is the Chiltons cost of equity?

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II.CAPM Valuation

• Recall the CAPM formula

• Risk free rate from yield on T-bills, estimates
  of ? are published by several sources.
• Market return can be estimated as expected
  inflation expected real growth in economy
  expected risk premium. It has averaged between 7
  and 8 over last 60 years.
• Advantages explicitly adjusts for risk,
  applicable to firms other than those with steady
  dividend growth.
• Disadvantagesestimates both market risk premium
  and ?, relies on past performance to predict
  future.

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CAPM Valuation (Ex 9)

• The Bedrock Corporations common stock has a beta
  of 1.4.
• If the risk free rate is 5 and
• the market risk premium is 9
• what is Bedrocks cost of equity capital?
• 5 (9)1.4 17.6

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Cost of new equity

• Sometimes firms issue new equity (infrequent
  interpreted as a negative signal by the market,
  also expensive due to underpricing and floatation
  costs).
• Cost of capital same as internally generated
  equity (retained earnings) except adjustment for
  flotation costs. Retained earnings cheaper than
  new share issue.
• Using the dividend valuation method, replace
  current price of stock by net proceeds (Pnp) of
  sale.
• Difficult to use CAPM to calculate the cost of
  new equity, since price does not appear in
  formula.

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III. Bond Yield Plus Model

• Theoretical basis Stockholders require what the
  bondholders require and then some. But numerical
  value of the risk premium is a guess.
• ks bond yield expected risk premium of stocks
  over bonds.
• Again, since price does not appear, cannot use
  this approach to calculate cost of new shares.
• All 3 methods, however should give a similar
  rate of return.

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Example 10

• Stock in Eddy industries has a beta of 1.2.
• The market risk premium is 7.5
• T-bills are currently yielding 6.
• Eddys most recent dividend was 3.15 per share
• dividends are expected to grow at a 3 annual
  rate indefinitely.
• the stock sells for 27.50 per share
• what is your best estimate of Eddys cost of
  equity?
• CAPM 6(7.5)1.2 15
• Dividend Valuation(3.15(13)/27.50) 3
  14.8
• Use average 14.9

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Putting It All Together Ex 11

• Waters Beginning has 1 million shares of common
  outstanding with a market price of 12 per share.
• The firms outstanding bonds have
• a total face value of 5 million
• ten years to maturity,
• a coupon rate of 10, and
• sell for 985.

• The risk-free rate is 7,
• the analysts expected return for the market is
  14.
• WB stock has a beta of 1.2, and WB is in the 40
  tax bracket.
• Find Waters Beginning WACC.

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Putting It All Together Ex 12

• Fernandos has 7.2 million shares of common stock
  o/s.
• Fernandos also has 2 bond issues o/s, both make
  semi-annual payments.
• The first issue has a face value of 70 million,
  a 7 coupon and sells for 86 of par.
• The second issue has a face of 50 million, a
  6.5 coupon and sells for 82 of par.
• The first issue matures in 10 years, the second
  in 6 years.

• The current share price is 32 and the book value
  per share is 23.
• The firms most recent dividend was 3, and the
  dividend growth rate is 6.
• The overall cost of debt is simply the average of
  the costs of the 2 debt issues.
• The tax rate is 35.
• What is Fernandos WACC?

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Summary
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Firm versus Project Risks

• Motivation

• A firm-wide OCC should be used only to evaluate
  projects if they have approximately the same risk
  as the firm
• Divisional projects need to be adjusted for
  differences in risk so that they can be properly
  evaluated

• A firm-wide OCC will under-allocate
  (over-allocate) funds to low-risk (high-risk)
  divisions
• Why?

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Firm versus Project Risks (Continued)

• What if risk of the project/division is different
  from firm risk?
• If project risk lt WACC, reject profitable
  projects.
• If project risk gt WACC, accept unprofitable
  projects.
• Solution base project acceptance/rejection on
  divisional or project cost of capital.

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Calculating Project ? - Pure Play Approach 4
steps

• 1. Calculate ki for the firm. Firms capital
  structure, T, and ki apply across all of firms
  divisions.
• 2. Find a publicly traded firm exclusively
  involved in the industry of the divisional
  project i.e. a pure-play firm.
• The pure-play firm may have a different capital
  structure. Its effective tax rate may also be
  different. Risk of this firm is comprised of
  business risk and capital structure risk. We
  adjust for the capital structure risk as follows,
  obtaining the pure-plays unlevered or asset beta

Where T, B and S respectively refer to the
effective tax-rate, market values of debt and
equity of pure-play firm.
Debt equity ratio for pure play firm
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Calculating Project ? - Pure Play Approach
Continued
3. Divisional cost of equity is

• 4. Apply the firms financing weights to ki and
  kdivision to calculate the divisional WACC. Note
  that kdivision is the sole divisional specific
  parameter.

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Nexus between two debt ratios

• Debt-to-equity B/S vs. debt-to-total-capitalizat
  ion B/(BS)
• Know how to infer one from the other!
• B/S .5 implies B/(BS) .5/(.51) .33
• B/(BS) .4 or .4/(.4.6) implies B/S .4/.6
  .67
• Formulas B/S in beta adjustment versus B/(BS)
  in WACC

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Pure Play (Ex 13)

• In order to estimate the equity cost of capital
  for their electronics division, Li Industries has
  identified a pure-play firm. Pertinent data are
  as follows.

• If the pure play firms levered ? is 1.20, the
  risk free rate is 11 and the market risk premium
  is 9, what is the electronics divisions cost of
  equity capital?

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Solution Same equation used twice.

• Pure plays unlevered beta X 0.8633 since 1.2
  X (1(1-.35).6). The beta of the pure plays
  assets is 0.8633.
• Divisional levered beta X 1.1 since X
  0.8633(1(1-.45).5). If the division were a
  separately traded firm, the beta of its common
  stock would equal 1.1.
• Divisional cost of equity 11 9(1.1) 20.9

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Divisional Betas Another Example (Ex 14)

• Marriott Corp. needs an equity (levered) Beta for
  its restaurant division for capital budgeting.
  The corporation has debt and equity of B0.5B
  and S 1B.
• The corporate tax rate is 34. The risk free rate
  is 4 and the market risk premium is 8.4.

• What is the restaurant divisions cost of equity?
  Use the average of the unlevered betas of the
  pure play firms as the restaurant divisions
  asset beta.

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Restaurant Divisions Cost of Equity

• Burger Kings unlevered beta or X 0.73 since
  .75 X(1(1-.34)(.004/.096))
• McDonalds unlevered beta or X 0.835 since 1
  X(1(1-.34)(2.3/7.7))
• Wendys unlevered beta or X 0.92 since 1.08
  X(1(1-.34)(.21/.79))
• Restaurant Div.s asset beta .83 is average
  Relevered beta 1.104 .83(1(1-.34).5)
• Restaurant Div.s cost of equity 4 (8.4)
  1.104 13.3

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The Subjective Approach

• A firm may use a more ad hoc method to come up
  with divisional / project WACC.

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A Comprehensive Cost of Capital (Ex 15)

• Independence Mining Corp has
• 7 million shares of common stock o/s,
• 1 million shares of 6 preferred stock o/s with a
  face value of 100 and
• 100,000 9 semi annual bonds o/s, par value 1000
  each.
• The common stock currently sells for 35 a share
  and has a beta of 1.
• The preferred stock currently sells for 60 a
  share and
• the bonds have 15 years to maturity and sell for
  89 of par.

• The market risk premium is 8,
• T-bills are yielding 7 and
• Independence Minings tax rate is 34.
• What is the firms market value capital
  structure?
• If the firm is evaluating a new investment
  project that has the same risk as the firm, what
  rate should the firm use to discount the
  projects cash flows?

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Independence Min.s Capital Structure

• B100,000(890)89M
• P1M(60)60M
• S7M(35)245M
• V(8960245)M394M
• Debt weight 89/394 .226
• Preferred stock weight 60/394 .152
• Common stock weight 245/394 .622

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Independence Min.s WACC

• Pre-tax cost of debt (90 (1000-890)/15)/((1000
  890)/2) 10.3
• Cost of preferred 6(100)/60 10
• Cost of common 7 8(1) 15
• WACC 10.3(1-.34)(.226) 10(.152) 15(.622)
  12.4
• WACC is appropriate hurdle rate as project is of
  same risk as that of firm.

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Another Example (Ex 16)

• A firm is considering a project that will result
  in initial after tax cash savings of 6 million
  at the end of the first year, and these savings
  will grow at a rate of 3 indefinitely.
• The firm has a target debt-equity ratio of 1.5,
• a cost of equity of 17, and
• an after tax cost of debt of 6
• The cost-savings proposal is somewhat riskier
  than the usual project that the firm undertakes

• management uses a subjective approach and applies
  an adjustment factor of 2 to the cost of
  capital for projects of this risk
• Under what circumstances should the firm take
  this project?

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Undertake if investment lt 63.83M

• Capital structure B/(BS)1.5/(1.51).6
  S/(BS).4
• WACC6(.6)17(.4)10.4
• Hurdle rate10.4212.4
• PV of subsequent CFs
  6M/(12.4-3)63.83M
• NPVgt0 if initial investmentlt63.83M

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Yet Another Example (Ex 17)

• The XYZ Corporation intends to finance new
  investments in proportion of 50 debt, 10
  preferred shares and 40 equity that would come
  solely from retained earnings.
• The corporate tax rate is 40.
• Debt with a maturity of 12 years can be sold at
  face value at an interest rate of 14.
• Preferred shares would be sold at par with
  after-tax issue costs amounting to 1 of par
  value.
• The dividend yield to investors would be 10.

• New common shares could be sold at 15 below the
  current market price of 20.
• Additional after-tax issuing expenses amount to
  50 per share.
• Growth in dividends has been steady at 8 per
  year and it is expected that this will continue.
• The dividend at the end of the current year is
  expected to be 2.25 per share.
• What is the firms weighted average cost of
  capital?

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Some Comments

• Remember that a firms cost of capital will
  change over time as the risk of the projects it
  undertakes changes as the economy changes over
  time.

• For a given firm usually
• kblt kpslt ks (retained earnings)ltke(new shares).
• Sometimes because bonds more heavily taxed kb gt
  kps

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Reducing the Cost of Capital

• Cost of capital is
• Positively related to risk of firm/project.
• Negatively related to liquidity.

• Liquidity is the cost of buying and selling
  stock.
• Brokerage fees, bid-ask spread and market impact
  costs.
• Investors demand a higher return when trading
  stocks with higher costs ? increases rs and
  therefore increases WACC.

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Adverse Selection and Liquidity

• Adverse Selection
• Size of bid ask spread is positively correlated
  to the percentage of informed traders.

• What Firms Can Do
• Firm has incentive to lower trading costs to
  lower WACC.
• Firm can increase number of uninformed traders
• Use of stock splits.
• Facilitate on-line trading.
• Reduce information asymmetries.
• Release of information by firm.
• Role of analysts.

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Recap and Summary

• Divisional and Project-Specific Opportunity Costs

• What Is the Firm's Opportunity Cost of Capital?
• Definitions and calculations
• Basic assumptions
• Estimating the Opportunity Cost of Capital (
  WACC).
• Calculating Costs and Financing Proportions
• Cost of debt
• Cost of preferred stock
• Cost of common equity
• Financing proportions (weights)