# The Cost of Capital

The Cost of Capital

n       Sources of capital

n       Component costs

n       WACC

What sources of long-term capital do firms use?

Calculating the weighted average cost of capital

E                               D
WACC =              * Ke   +                      * Kd (1-T)
D + E                     D + E

n    The k’s refer to the cost of each component.

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 deductible.

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)?

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% annual coupon bond sells for \$1,153.72.  What is the cost of debt (kd)?

n    Annual coupon Payment:

\$1000 X 12% = \$120

n    kd = \$120/\$1153.72 = 10.40%.

Component cost of debt

n    Interest is tax deductible, If the tax rate is 40%, then

A-T kd = B-T kd (1-T)

= 10.40% (1 – 0.40) = 6.24%

Component cost of preferred stock

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

n    kp is the marginal cost of preferred stock.

n    The rate of return investors require on the firm’s preferred stock.

What is the cost of preferred stock?

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

kp = Dp / Pp

= \$10 / \$111.10

= 9%

Component cost of preferred stock

n    Preferred dividends are not tax-deductible, so no tax adjustments necessary.  Just use kp.

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.

Three ways to determine the cost of common equity, ks

n    CAPM: ks = kRF + (kM – kRF) ?

n    DCF:     ks = D1 / P0 + g

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) ?

= 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 / P0 + 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%

What is a reasonable final estimate of ks?

Method Estimate

CAPM               14.2%

DCF                 13.8%

Average            14.0%

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.

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