chapter outline

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chapter outline

• Chapter 14 Cost of Capital
• Read Chapter 14 (except section 14.6)
• 1. Definition and overview
• 2. The Cost of Equity
• 2.1 Dividend growth model approach
• 2.2 The SML approach
• 3. The Cost of Debt and Preferred Stock
• 4. The weighted average cost of capital (WACC)
  
• 5. Some fine-tuning

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1. Definition and overview

• Key Issues
• What do we mean by cost of capital?
• How can we estimate cost of capital?
• Cost of capital, appropriate discount rate,
  required rate of return
• ? minimum rate of return that a firm (or
  investors) requires on firms project
• Rate of return on alternative project with
  similar risk.
• WACC (Weighted average cost of capital)
• A measure of the cost of capital.

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1. Definition and overview..

• Who owns the firm?
• Shareholders required rate of return ? RE
• Bondholders required rate of return ? RD
• A firms cost of capital reflects both its cost
  of debt and equity.
• We first look at these costs separately, and then
  combine them to obtain the weighted cost of
  capital of a firm.
• Since we are always interested in valuing
  after-tax cash flows, we will focus on after-tax
  cost of capital.

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1. Definition and overview..

• An accurate estimate of the cost of capital is
  required for
• Capital budgeting
• NPV and IRR rules require the appropriate
  discount rate.
• Performance evaluation
• One can use the cost of capital as a benchmark
  rate of return for management to meet.
• Operating decisions
• Regulatory agencies use cost of capital to
  determine the "fair return" in some regulated
  industries (e.g., electric utilities)

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2. The cost of equity

• There are two approaches to estimate RE
• 2.1 Dividend growth model approach
• Recall
• Rearranging yields

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2.1 Dividend growth model..

• Implementation
• D0 and P0 observable from data
• Growth rate, g Estimate it using past data or
  analysts forecast.
• Example
• Geometric growth rate 4(1g)4 5.65. Solve
  for g 8.969
• Average growth rate (10.00 7.95 10.53
  7.62)/4 9.025.

 
 
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2.1 Dividend growth model..

• Pros/Cons
• Model is simple and easy to understand.
• However, the model is applicable only to firms
  with reasonably stable growth.
• The model is sensitive to the estimated growth
  rate.
• It does not explicitly consider risk, i.e., there
  is no allowance for the degree of uncertainty on
  the estimated growth rate in dividends.

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2.2 The SML approach

• Recall CAPM E(RE) Rf ?E E(Rm) Rf  
• Implementation
• Estimate ?E, risk-free rate (typically T-bill
  rate) and market risk premium based on past data.
  
• Pros/Cons
• The model adjusts for risk, and is applicable for
  firms other than those with stable dividend
  growth.
• Estimates based on past data might not be very
  reliable in a rapidly changing environment.
• Estimates might be sensitive to the choice of
  time periods.
• However, ?E is reasonably stable in a period of 5
  years.

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2.2 The SML approach..

• Example Cost of equity 
• Air BC has a beta of 1.25. Current stock price
  is 42 per share.
• The market risk premium is 6.5.
• T-bills are currently yielding 5.5.
• Air BCs most recent dividend was 2.20.
• Dividends are expected to grow at a 4 p.a.
  indefinitely.
• What is the best estimate of Air BCs cost of
  equity?
•  
• Growth model RE D0 (1g)/P g
• 2.20(14)/42 4 9.45.
• SML E(RE) Rf ?E E(Rm) Rf
• 5.5 1.256.5 13.625

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3. The cost of debt and preferred stock

• Cost of debt is simply the interest rate that
  lenders require on firms new borrowing.
• It is normally observable.
• The yield to maturity (YTM) on existing bonds,
  or
• Interest rate on new borrowings of similarly
  rated bonds.
• The coupon rate on existing bond is irrelevant
  it reflects the firms cost of debt at the time
  of issuance. You want to use todays yield as a
  proxy for cost of debt today.
• Preferred stocks pay fixed amount of dividend.
  So, dividend yield (dividend/current price) is a
  reasonable proxy for cost of preferred stock.

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3. The cost of debt and preferred stock..

• Example Cost of debt and preferred stock
• (1) KEC issued a 20-year, 8 semi-annual bond
  seven years ago. The bond currently sells for
  110 of its face value of 1,000. Tax rate is
  35. Find out the pretax and after-tax cost of
  debt.
• First find out IRR for the bond KEC will pay
  40 every six months.
• 1,100 PV(40 each at the end of 26 periods)
• PV(1,000 at the end of 26 periods). 
• IRR6.83 p.a. pre-tax cost of debt 6.83 p.a.
• Since interests are tax deductible, after-tax
  cost of debt is
• 6.83(1 Tc) 6.83(1 0.35) 4.44.

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3. The cost of debt and preferred stock..

• (2) White Teck Co (WTC)s preferred stock price
  is 95 per share.
• There is a 7 stated dividend.
• What is WKCs cost of preferred stock?
•  
• Cost of preferred stock 7/95 7.37

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4. The weighted average cost of capital (WACC)

• WACC
• 1. Let E ? the market value of the equity.
• D ? the market value of the debt.
• Then V E D, so E/V D/V 100
• 2. Proportion of E and D in firms value V are
  E/V and D/V.
• 3. Interest payments on debt are tax-deductible,
  so the
• After-tax cost of debt the pretax cost (1 -
  corporate tax rate).
• RD ? (1 - Tc)
• 4. Thus the weighted average cost of capital is
  
• WACC (E/V) ? RE (D/V) ? RD ? (1 - Tc)

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4. The weighted average cost of capital (WACC)

• Example after-tax cost of debt ABC borrows
  1,000 at 10 p.a., TC 40. After-tax
  interest is 10 (1 TC). Why?
• 100 interest is tax deductible and it will
  reduce the tax bill by 40. So after tax interest
  is 10 (1 TC).

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4. The weighted average cost of capital (WACC)

• When we say WACC, we refer to the after tax
  weighted average cost of capital. The table
  summarizes discussion so far.

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4. The weighted average cost of capital (WACC)

• Example Finding the WACC
•  
• 5 million shares of common shares at 40, and ?E
  1.2.
• 750,000 shares of 7 preferred stock selling at
  75.
• 250,000 units of 11 semi-annual bonds, par value
  1,000,
• 15 years-to-maturity selling at 93.5 of the
  par.
•  E(Rm) Rf 6, Rf 4, TC 34.
• Step 1 find out market value of common,
  preferred stocks and bonds. See column 1 of
  table.
• Step 2 find out fraction in total firm value.
  See column 2.
• Step 3 find out after tax cost of common,
  preferred stocks and bonds. See column 3.

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4. The weighted average cost of capital (WACC)

• (a) RE Rf ?E(Rm) Rf
• 4 1.2 6 11.2
•  
• (b) To obtain RD, first find out the bond yield
  using following approximation formula (or using
  financial calculator)
•  
• Yield Coupon (Face value Price)/maturity
  
• / (Price Face value)/2
• 110 (1,000 935)/15 / (1,000
  935)/2 11.8
• Yield (from a financial calculator) 11.94
• After-tax 11.94 (1 TC) 11.94 (66)
  7.88

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4. The weighted average cost of capital (WACC)

• Step 4 calculate the weighted average of cost.
  See column 4.

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4. The weighted average cost of capital (WACC)

• Example Using the WACC
• WallStores expansion will cost 50,000 and
  generate 10,000 p.a. in perpetuity after-tax.
  Target debt/equity ratio of .50 required return
  on equity of 15 return on bond of 10. Tax
  rate is 34.
• WACC (E/V) RE (D/V) RD (1 TC)
• 2/3 15 1/3 10 (1 .34) 12.2.
• WACC is appropriate to use, only when the
  proposed project is in the same risk class as the
  firm.

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4. The weighted average cost of capital (WACC)

• Summary of WACC  The required return on the
  firm as a whole. It is the appropriate discount
  rate for cash flows similar in risk to the firm.
• I. The Cost of Equity, RE
• A. Dividend growth model approach RE D1/P0
  g
• B. SML approach E(RE) Rf ?E E(Rm) Rf
   
• II. The Cost of Debt, RD
• Use the yield to maturity on existing debt or
  similarly rated bonds.
• III. The Weighted Average Cost of Capital (WACC)
• WACC (E/V) RE (D/V) RD (1 - Tc)
• where Tc is the corporate tax rate, E is the
  market value of the firms equity, D is the
  market value of debt, and V E D. So, E/V is
  the of the firms financing (in market value
  terms) in equity, and D/V is the in debt.

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5. Some fine-tuning

• What if a project risk is substantially different
  from the overall firms risk? One can not use
  firms overall WACC for the project.
• What if you still use overall WACC in this case?
  
• See next slide and find out what will happen.
• (Example) divisional cost of capital
• Several divisions in a company with different
  risk should use different cost of capital
  (conglomerate food division, computer division).
  

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5. Some fine-tuning
Required return of A 7 0.68 11.8.
Actual return is 14. Required return of B 7
1.28 16.6. Actual return is 16.
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5. Some fine-tuning

• There are two approaches to remedy the problem 
• Pure play approach pure play ? a company that
  focuses on a single line of business, e.g. oil
  drilling, gas exploration, etc.
• Subjective approach The firm places projects
  into one of several risk classes. The firm
  determines discount rates for each risk class by
  adding (for high risk) or subtracting (for low
  risk) an adjustment factor to or from the firms
  WACC.  
• Project category Adjustment Factor Discount
  Rate
• High risk 6 20
• Medium risk 0 14
• Low risk -4 10
• Mandatory n.a. n.a.

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5. Some fine-tuning..
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5. Some fine-tuning..

• Example SML and WACC An all-equity firm with
  14 cost of capital considers the projects
•  
• (1) If the firm uses 14 WACC which project does
  it accept? Project Y. 
• (2) When the firm considers risk of the
  projects, which project should it accept?
• CAPM E(X) 5 0.85(14 ? 5) 12.65 lt
  expected return 13
• CAPM E(Y) 5 1.15(14 ? 5) 15.35 gt
  expected return 15
• So the firm will choose Project X.

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6. Questions

• Example Eastman Chemicals WACC Eastman
  Chemical has 78.26 million shares of common stock
  outstanding. The book value per share is 22.40
  but the stock sells for 58. The market value of
  equity is 4.54 billion. Eastmans stock beta is
  .90. T-bills yield 4.5, and the market risk
  premium is assumed to be 9.2.
• The firm has four debt issues outstanding.
• Coupon Book Value Market Value Yield-to-Maturity
• 6.375 499m 501m 6.32
• 7.250 495m 463m 7.83
• 7.635 200m 221m 6.76
• 7.600 296m 289m 7.82
• Total 1,490m 1,474m

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6. Questions..

• Example Eastman Chemicals WACC
• Cost of equity (SML approach)
• RE .045 .90 ? (.092) .045 .0828 12.78
• Cost of debt
• Multiply the proportion of total debt
  represented by each issue by its yield to
  maturity the weighted average cost of debt
  7.15
• Capital structure weights
• Market value of equity 78.26 m ? 58
  4.539 billionMarket value of debt 501m
  463m 221m 289m 1.474 b
• V 4.539 b 1.474 b 6.013 b
• D/V 1.474b/6.013b .2451
• E/V 4.539b/6.013b .7549
• WACC .7549 (12.78) .2451 ? 7.15 ?(1 - .35)
  10.79

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6. Questions..

• Some concept questions
• 1. What is the relationship between cost of
  capital and firm value?
• Given other things being constant, the lower
  the cost of capital, the higher the value of the
  firm.
• 2. When we use the dividend growth model to
  estimate the firms cost of equity, we make a key
  assumption about future dividends of the firm.
  What is that assumption?
• We assume that dividends will grow at a
  constant growth rate, g.
• 3. What happens if we use the WACC to evaluate
  all potential investment projects, regardless of
  their risk?
• Estimated NPVs will be understated (overstated)
  for projects which are less risky (riskier) than
  the firm.

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6. Questions..

• Problem 14.16 Elway Mining Corporation has
• 8 m shares of common stock selling at 35 with a
  beta of 1.0,
• 1 m shares of 6 preferred selling at 60, and
• 100,000 9 semiannual coupon bonds, par value
  1,000 each.
• the bonds have 15 years to maturity and sell for
  89 percent of par.
• The market risk premium is 8 percent,
• T-bills are yielding 5 percent, and the firms
  tax rate is 34 percent.
• a. What is the firms market value capital
  structure?
• b. If the firm is evaluating a new investment
  project that has the same risk as the firms
  typical project, what rate should the firm use to
  discount the projects cash flows?

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6. Questions..

• Solution to Problem 14.16 (continued)
• a. MVD 100,000 (1,000) (.89) 89M
• MVE 8M(35) 280M
• MVp 1M(60) 60M
• V 89M 280M 60M 429M
• D/V 89M/429M .207,
• E/V 280M/429M .653, and
• P/V 60M/429M .140.

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6. Questions..

• Problem 14.16 b.
• For projects as risky as the firm itself, the
  WACC is the appropriate discount rate. So, find
  out the WACC.
• RE .05 1.0(.08) 13
• Bond YTM 890 45(PVIFARD,30)
  1,000(PVIFRD,30)
• RD 10.474, and RD (1 - Tc) (.10474)(1 -
  .34) 6.91
• RP 6/60 .10 10
• WACC .653 (13) .207 (6.91) .14 (10)
  11.32

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6. Questions..

• Problem 14.17 An all-equity firm is considering
  the following projects. Assume the T-bill rate is
  5 and the market expected return is 12.
• Project Beta
  Expected Return ()
• W .60 11
• X .85 13
• Y 1.15 13
• Z 1.50 19
• a. Which projects have a higher expected
  return than the firms 12 cost of capital?
• b. Which projects should be accepted?
• c. Which projects would be incorrectly
  accepted or rejected if the firms overall cost
  of capital is used as a hurdle rate?

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6. Questions..

• Problem 14.17 (concluded)
• a. Projects X, Y, and Z with expected returns of
  13, 13, and 19, respectively, have higher
  returns than the firms 12 cost of capital.
• b. Using the firms overall cost of capital as a
  hurdle rate, accept projects W, X, and Z. Compute
  required returns considering risk via the SML
• Project W .05 .60(.12 - .05) .092 lt .11,
  so accept W.Project X .05 .85(.12 - .05)
  .1095 lt .13, so accept X.Project Y .05
  1.15(.12 - .05) .1305 gt .13, so reject
  Y.Project Z .05 1.50(.12 - .05) .155 lt
  .19, so accept Z.
• c. Project W would be incorrectly rejected and
  Project Y would be incorrectly accepted.

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6. Questions..

• Problem 14.20 True North, Inc. 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 5 per year indefinitely.
• The firm has a target debt/equity ratio of .5, a
  cost of equity of 18 , and an after-tax cost of
  debt of 6 .
• The cost-saving proposal is somewhat riskier than
  the usual project the firm undertakes management
  uses the subjective approach and applies an
  adjustment factor of 2 to the cost of capital
  for such risky projects.
• Under what circumstances should True North take
  on the project?

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6. Questions..

• Problem 14.20
• WACC (.3333)(.06) (.6666)(.18) .14
• Project discount rate .14 .02 .16
• NPV - cost PV (cash savings)
• PV (cash savings) 6M/(.16 - .05) 54.55M
• So the project should only be undertaken if its
  cost is less than 54.55M.