Ch 13 Risk, Cost of Capital, and Capital Budgeting

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Ch 13 Risk, Cost of Capital, and Capital Budgeting

• 1. The Cost of Equity Capital
• 2. Estimation of Beta
• 3. Determinants of Beta
• 4. Extensions of the Basic Model
• 5. Estimating Cost of Capital
• 6. Reducing the Cost of Capital
• 7. Summary and Conclusions

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Main Idea

• Time value of money reflects
• (1) opportunity cost of money,
• (2) risky cash flow.
• We discuss the appropriate discount rate for
  risky cash flows.

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1. The Cost of Equity Capital

• A firm with excess cash can either pay a dividend
  or make a capital investment.
• Stockholders can reinvest the dividend in risky
  financial assets.
• The expected return on a project should be the
  expected return on a financial asset of
  comparable risk.

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Example The Cost of Equity

• Assume a 100-equity firm. ABC Co. has a beta of
  2.5. The risk-free rate is 5 and a market risk
  premium is 10. What is the appropriate discount
  rate for an expansion of this firm?

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Example (continued)

• Suppose ABC is evaluating the following
  non-mutually exclusive projects. Each costs 100
  and lasts one year.

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Using the SML to Estimate the Risk-Adjusted
Discount Rate for Projects

• ABC should accept projects A and B, and reject
  project C.

Good project
Project IRR
Bad project
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Firms risk (beta)
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2. Estimation of Beta

• The beta is given by
• Example

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Example (continued)

• E(rGT) 0.07 E(rm) -0.10
• cov (rGT, rm) 0.109/3
• var (rm) 0.260/3.
• beta cov (rGT, rm) / var (rm)
• 0.109/0.260 0.419
• In practice, people use regression to estimate
  beta (characteristic line).

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About beta

• A firms beta change due to changes in
• product line, technology, market condition (e.g.
  airline deregulation) financial leverage.
• Betas are generally stable for firms remaining in
  the same industry.
• If you believe that the operations of the firm
  are similar to the operations of the rest of the
  industry, you may well use the industry beta.

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3. Determinants of Beta

• Where does beta come from?
• Business risks depend on both on the
  responsiveness of the firms revenue to the
• business cycle (cyclicity of revenues), and
• operating leverage
• Financial Risk
• Financial leverage

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Cyclicality of Revenues

• Highly cyclical stocks have high betas.
• Retailers and high-tech firms fluctuate with the
  business cycle.
• Utilities and food companies are less dependent
  upon the business cycle.
• Note that cyclicality is not the same as
  variability.
• Movie studios Revenues depend upon whether
  they produce hits or flops, but their
  revenues are not especially dependent upon the
  business cycle.
• Stocks with high standard deviations need not
  have high betas.

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Operating Leverage

• The degree of operating leverage measures how
  sensitive a firms cash flow (or project) is to
  its fixed costs.
• Operating leverage increases as fixed costs rise
  and variable costs fall.
• Operating leverage magnifies the effect of
  cyclicity on beta.
• The degree of operating leverage is given by

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Operating Leverage
? EBIT
Total costs

? Volume
Fixed costs
Volume
Operating leverage increases as fixed costs rise
and variable costs fall.
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Financial Leverage and Beta

• Operating leverage refers to the sensitivity of
  the firms cash flow to the firms fixed costs of
  production.
• Financial leverage is the sensitivity of a firms
  cash flow to the firms fixed costs of financing.
• The relationship between the betas of the firms
  debt, equity, and assets is given by
• Set ?D 0. ?e ?a (1 Debt/Equity). Equity ?
  is always greater than the asset ? with financial
  leverage.

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Financial Leverage and Beta Example

• XYZ Co. is currently all-equity and has a beta of
  0.90.
• The firm has decided to lever up to a capital
  structure of 1 part debt to 1 part equity.
• Suppose its asset beta remains at 0.90.
• Assuming a zero beta for its debt, its equity
  beta would become twice as large

bEquity
2 0.90 1.80
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4. Extensions of the Basic Model

• So far, we have considered
• projects with same risk as the firm,
• 100 equity firm.
• We now consider more general cases.

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The Firm versus the Project

• A project should generate return, comparable to
  return on asset with similar risk.
• If a projects beta is different from that of the
  firm, do not use corporate discount rate the
  project should be discounted at a rate
  commensurate with its risk.
• The use of a single corporate discount rate for
  all different divisions in the firm is
  problematic. (See the next figure.)

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Capital Budgeting Project Risk

• A firm that uses one discount rate for all
  projects may over time increase the risk of the
  firm while decreasing its value.

Project IRR
The SML can tell us why
Hurdle rate
Firms risk (beta)
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Example Capital Budgeting Project Risk

• Suppose JDL Co. has a cost of capital of 17
  based on the CAPM. The risk-free rate is 4 the
  market risk premium is 10 and the firms beta is
  1.3.
• This is a breakdown of the companys investment
  projects
• 1/3 Automotive retailer b 2.0
• 1/3 Computer Hard Drive Mfr. b 1.3
• 1/3 Electric Utility b 0.6
• Average b of assets 1.3
• When evaluating a new electrical generation
  investment, which cost of capital should be used?

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Capital Budgeting Project Risk
SML
Project IRR
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Investments in hard drives or auto retailing
should have higher discount rates.
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10
Projects risk (b)
1.3
2.0
0.6
r 4 0.6(14 4 ) 10 10 reflects the
opportunity cost of capital on an investment in
electrical generation, given the unique risk of
the project.
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The Cost of Capital with Debt

• The weighted average cost of capital is given by
• Interest expense is tax-deductible. So we
  multiply the last term by (1 Tc)

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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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Example Finding the WACC

• (a) RE Rf ?E(Rm) Rf
• 4 1.2 6 11.2
• (b) To obtain RD, first find out the bond yield,
  using financial calculator Yield 11.94
• After-tax 11.94 (1 TC)
• 11.94 (66) 7.88

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Example Finding the WACC

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

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6. Reducing the Cost of Capital

• What is Liquidity?
• Liquidity, Expected Returns and the Cost of
  Capital
• Liquidity and Adverse Selection
• What the Corporation Can Do

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What is Liquidity?

• Result the expected return and the firms cost
  of capital are positively related to risk.
• New idea The more liquid a firms shares, the
  lower expected return and lower cost of capital.
• Liquidity The trading costs of a firms shares.
  The costs include brokerage fees, the bid-ask
  spread and market impact costs.

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Liquidity, expected returns and the cost of
capital

• The cost of trading an illiquid stock reduces the
  total return that an investor receives.
• Investors demand a high expected return when
  investing in stocks with high trading costs.
• This high expected return implies a high cost of
  capital to the firm.

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Liquidity and the Cost of Capital
Cost of Capital
Liquidity
An increase in liquidity, i.e. a reduction in
trading costs, lowers a firms cost of capital.
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Liquidity and Adverse Selection

• One of factors that determine the liquidity of a
  stock is adverse selection.
• This refers to the notion that informed traders
  can pick off specialists and other uninformed
  traders.
• The informed traders raise the required return on
  equity, and thereby increasing the cost of
  capital.

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What the Corporation Can Do

• The corporation has an incentive to raise
  liquidity of its shares, since higher liqudity
  would reduce the cost of capital.
• (1) Firm can bring in more uninformed traders.
• (a) A stock split would make the shares more
  attractive to small (uninformed) traders.
• More uninformed traders means lower adverse
  selection costs and lowe bid-ask spreads.

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What the Corporation Can Do

• (b) Companies can also facilitate stock
  purchases through the Internet.
• Direct stock purchase plans and dividend
  reinvestment plans handles on-line allow small
  investors the opportunity to buy securities
  cheaply.
• (2) The companies can also disclose more
  information, especially to security analysts, to
  narrow the gap between informed and uninformed
  traders. This should reduce spreads.

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7. Summary and Conclusions

• The expected return on any capital budgeting
  project should be the expected return on a
  financial asset of comparable risk. Otherwise the
  shareholders would prefer the firm to pay a
  dividend.
• The expected return on any asset is dependent
  upon b.
• A projects required return depends on the
  projects b.
• A projects b can be estimated by considering
  comparable industries or the cyclicality of
  project revenues and the projects operating
  leverage.
• If the firm uses debt, the discount rate to use
  is the rWACC.
• In order to calculate rWACC, the cost of equity
  and the cost of debt applicable to a project must
  be estimated.

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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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Questions

• 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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Solution

• 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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• Problem 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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• Problem 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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• Problem 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.