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					CHAPTER 9
The Cost of Capital

 n   Sources of capital
 n   Component costs
 n   WACC
 n   Adjusting for flotation costs
 n   Adjusting for risk
     What sources of long-term
     capital do firms use?

                       Long-Term Capital
                       Long-Term Capital

Long-Term Debt
Long-Term Debt   Preferred Stock
                 Preferred Stock   Common Stock
                                   Common Stock

                     Retained Earnings
                     Retained Earnings     New Common Stock
                                           New Common Stock

Calculating the weighted
average cost of capital

    WACC = wdkd(1-T) + wpkp + wcks

n   The w’s refer to the firm’s capital
    structure weights.
n   The k’s refer to the cost of each

Should our analysis focus on before
-tax or after-tax capital costs?

n   Stockholders focus on A-T CFs.
    Therefore, we should focus on A-T
    capital costs, i.e. use A-T costs of
    capital in WACC. Only kd needs
    adjustment, because interest is tax

Should our analysis focus on
historical (embedded) costs or new
(marginal) costs?

n   The cost of capital is used primarily to
    make decisions that involve raising new
    capital. So, focus on today’s marginal
    costs (for WACC).

How are the weights determined?

    WACC = wdkd(1-T) + wpkp + wcks

n   Use accounting numbers or market
    value (book vs. market weights)?
n   Use actual numbers or target capital

Component cost of debt
    WACC = wdkd(1-T) + wpkp + wcks

n   kd is the marginal cost of debt capital.
n   The yield to maturity on outstanding L
    -T debt is often used as a measure of
    kd .
n   Why tax-adjust, i.e. why kd(1-T)?
    A 15-year, 12% semiannual coupon
    bond sells for $1,153.72. What is
    the cost of debt (kd)?
n   Remember, the bond pays a semiannual
    coupon, so kd = 5.0% x 2 = 10%.

INPUTS     30           -1153.72   60    1000
            N    I/YR     PV       PMT   FV
OUTPUT            5

Component cost of debt
n   Interest is tax deductible, so
       A-T kd = B-T kd (1-T)
               = 10% (1 - 0.40) = 6%
n   Use nominal rate.
n   Flotation costs are small, so ignore

Component cost of preferred
    WACC = wdkd(1-T) + wpkp + wcks

n   kp is the marginal cost of preferred
n   The rate of return investors require on
    the firm’s preferred stock.

What is the cost of preferred
n   The cost of preferred stock can be
    solved by using this formula:

      kp = D p / P p
         = $10 / $111.10
         = 9%

Component cost of preferred
n   Preferred dividends are not tax-
    deductible, so no tax adjustments
    necessary. Just use kp.
n   Nominal kp is used.
n   Our calculation ignores possible
    flotation costs.

Is preferred stock more or less
risky to investors than debt?
n   More risky; company not required to
    pay preferred dividend.
n   However, firms try to pay preferred
    dividend. Otherwise, (1) cannot pay
    common dividend, (2) difficult to raise
    additional funds, (3) preferred
    stockholders may gain control of firm.

Why is the yield on preferred
stock lower than debt?
n   Corporations own most preferred stock,
    because 70% of preferred dividends are
    nontaxable to corporations.
n   Therefore, preferred stock often has a lower
    B-T yield than the B-T yield on debt.
n   The A-T yield to an investor, and the A-T cost
    to the issuer, are higher on preferred stock
    than on debt. Consistent with higher risk of
    preferred stock.
Illustrating the differences between A
-T costs of debt and preferred stock
Recall, that the firm’s tax rate is 40%, and its
before-tax costs of debt and preferred stock
are kd = 10% and kp = 9%, respectively.

A-T kp = kp – kp (1 – 0.7)(T)
       = 9% - 9% (0.3)(0.4)         = 7.92%
A-T kd = 10% - 10% (0.4)            = 6.00%

A-T Risk Premium on Preferred       = 1.92%
Component cost of equity
    WACC = wdkd(1-T) + wpkp + wcks

n   ks is the marginal cost of common
    equity using retained earnings.
n   The rate of return investors require on
    the firm’s common equity using new
    equity is ke.

    Why is there a cost for
    retained earnings?
n   Earnings can be reinvested or paid out as
n   Investors could buy other securities, earn a
n   If earnings are retained, there is an
    opportunity cost (the return that
    stockholders could earn on alternative
    investments of equal risk).
    n   Investors could buy similar stocks and earn ks.
    n   Firm could repurchase its own stock and earn ks.
    n   Therefore, ks is the cost of retained earnings.
Three ways to determine the
cost of common equity, ks
n   CAPM: ks = kRF + (kM – kRF) β

n   DCF:   ks = D 1 / P 0 + g

n   Own-Bond-Yield-Plus-Risk Premium:
          ks = kd + RP

If the kRF = 7%, RPM = 6%, and the
firm’s beta is 1.2, what’s the cost of
common equity based upon the CAPM?

  ks = kRF + (kM – kRF) β
     = 7.0% + (6.0%)1.2 = 14.2%

If D0 = $4.19, P0 = $50, and g = 5%,
what’s the cost of common equity based
upon the DCF approach?

 D1 = D0 (1+g)
 D1 = $4.19 (1 + .05)
 D1 = $4.3995

 ks = D1 / P 0 + g
    = $4.3995 / $50 + 0.05
    = 13.8%
What is the expected future growth rate?
n   The firm has been earning 15% on equity
    (ROE = 15%) and retaining 35% of its
    earnings (dividend payout = 65%). This
    situation is expected to continue.

       g = ( 1 – Payout ) (ROE)
         = (0.35) (15%)
         = 5.25%

n   Very close to the g that was given before.
Can DCF methodology be applied if
growth is not constant?

n   Yes, nonconstant growth stocks are
    expected to attain constant growth at
    some point, generally in 5 to 10 years.
n   May be complicated to compute.

If kd = 10% and RP = 4%, what is ks
using the own-bond-yield-plus-risk-
premium method?
n   This RP is not the same as the CAPM
n   This method produces a ballpark
    estimate of ks, and can serve as a
    useful check.

       ks = kd + RP
       ks = 10.0% + 4.0% = 14.0%
What is a reasonable final
estimate of ks?
    Method      Estimate
    CAPM         14.2%
    DCF          13.8%
    kd + RP      14.0%
      Average    14.0%

Why is the cost of retained earnings
cheaper than the cost of issuing new
common stock?
n   When a company issues new common
    stock they also have to pay flotation costs
    to the underwriter.
n   Issuing new common stock may send a
    negative signal to the capital markets,
    which may depress the stock price.

If issuing new common stock incurs a
flotation cost of 15% of the proceeds,
what is ke?

Flotation costs
n   Flotation costs depend on the risk of the firm
    and the type of capital being raised.
n   The flotation costs are highest for common
    equity. However, since most firms issue
    equity infrequently, the per-project cost is
    fairly small.
n   We will frequently ignore flotation costs when
    calculating the WACC.

  Ignoring floatation costs, what is
  the firm’s WACC?

WACC =   wdkd(1-T) + wpkp + wcks
     =   0.3(10%)(0.6) + 0.1(9%) + 0.6(14%)
     =   1.8% + 0.9% + 8.4%
     =   11.1%

What factors influence a
company’s composite WACC?
n   Market conditions.
n   The firm’s capital structure and
    dividend policy.
n   The firm’s investment policy. Firms
    with riskier projects generally have a
    higher WACC.

Should the company use the
composite WACC as the hurdle rate
for each of its projects?
n   NO! The composite WACC reflects the risk
    of an average project undertaken by the
    firm. Therefore, the WACC only represents
    the “hurdle rate” for a typical project with
    average risk.
n   Different projects have different risks. The
    project’s WACC should be adjusted to
    reflect the project’s risk.

Risk and the Cost of Capital

What are the three types of
project risk?
n   Stand-alone risk
n   Corporate risk
n   Market risk

How is each type of risk used?
n   Market risk is theoretically best in most
n   However, creditors, customers,
    suppliers, and employees are more
    affected by corporate risk.
n   Therefore, corporate risk is also

Problem areas in cost of capital
n   Depreciation-generated funds
n   Privately owned firms
n   Measurement problems
n   Adjusting costs of capital for
    different risk
n   Capital structure weights

How are risk-adjusted costs of
capital determined for specific
projects or divisions?
n   Subjective adjustments to the firm’s
    composite WACC.
n   Attempt to estimate what the cost of
    capital would be if the project/division
    were a stand-alone firm. This requires
    estimating the project’s beta.

Finding a divisional cost of capital:
Using similar stand-alone firms to
estimate a project’s cost of capital
n   Comparison firms have the following
    n   Target capital structure consists of 40%
        debt and 60% equity.
    n   kd = 12%
    n   kRF = 7%
    n   RPM = 6%
    n   βDIV = 1.7
    n   Tax rate = 40%
        Calculating a divisional cost of capital

n   Division’s required return on equity
    n   ks = kRF + (kM – kRF)β
           = 7% + (6%)1.7 = 17.2%
n   Division’s weighted average cost of capital
    n   WACC = wd kd ( 1 – T ) + wc ks
             = 0.4 (12%)(0.6) + 0.6 (17.2%) =13.2%
n   Typical projects in this division are
    acceptable if their returns exceed 13.2%.

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