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If f is flotation cost in percent, the formula for the cost of new common stock is:

D

1

ke = Po(l-f) + g

EXAMPLE 10.4 Assume the same data as in Example 10.3, except the firm is trying to sell new issues of stock

A and its flotation cost is 10 percent. Then:

$4

@ +6% = -+ 11.11% + 6% = 17.11%

- 6%

$40(1 - 0.1) $36

The CAPM Approach. An alternative approach to measuring the cost of common stock is to use

the CAPM, which involves the following steps:

Estimate the risk-free rate, rf, generally taken to be the United States Treasury bill rate.

Estimate the stockâ€™s beta coefficient, b, which is an index of systematic (or nondiversifiable

market) risk.

Estimate the rate of return on the market portfolio such as the Standard & Poorâ€™s 500 Stock

Composite Index or Dow Jones 30 Industrials.

Estimate the required rate of return on the firmâ€™s stock, using the CAPM (or SML)

equation:

ke = rf+ b(rm - r f )

Again, note that the symbol r, is changed to k,.

EXAMPLE 10.5 Assuming that rf is 7 percent, b is 1.5, and r,,, is 13 percent, then:

+ 1.5(13% - 7%) = 16%

k , = r,+ b(r,,,- r f ) = 7%

This 16 percent cost of common stock can be viewed as consisting of a 7 percent risk-free rate plus a

9 percent risk premium, which reflects that the firmâ€™s stock price is 1.5 times more volatile than the market

portfolio to the factors affecting nondiversifiable, or systematic, risk.

The Bond Plus Approach. Still another simple but useful approach to determining the cost of

common stock is to add a risk premium to the firmâ€™s own cost of long-term debt, as follows:

k , = long-term bond rate + risk premium

= ki(1- t ) + risk premium

A risk premium of about 4 percent is commonly used with this approach.

EXAMPLE 10.6 Using the data found in Example 10.1, the cost of common stock using the bond plus

approach is:

k, = long-term bond rate + risk premium

= ki(1 - t ) + risk premium

= 5.14% + 4% = 9.14%

Cost of Retained Earnings

The cost of retained earnings, k,, is closely related to the cost of existing common stock, since the

cost of equity obtained by retained earnings is the same as the rate of return investors require on the

firmâ€™s common stock. Therefore,

k, = k,

283

CHAP. 101 COST OF CAPITAL

10.3 MEASURING THE OVERALL COST OF CAPITAL

The firmâ€™s overall cost of capital is the weighted average of the individual capital costs, with the

weights being the proportions of each type of capital used. Let k, be the overall cost of capital.

=cstructure

1

i

cost of capital

% of total capital

k, supplied by X for each source

of capital

each type of capital

+ wp.kp+ w;k, -+ ws*ks

= Wdâ€™kd

where wd = % of total capital supplied by debt

wp = % of total capital supplied by preferred stock

O

we = % of total capital supplied by external equity

w, = % of total capital supplied by retained earnings (or internal equity)

The weights can be historical, target, or marginal.

Historical Weights

Historical weights are based on a firmâ€™s existing capital structure. The use of these weights is based

on the assumption that the firmâ€™s existing capital structure is optimal and therefore should be maintained

in the future. Two types of historical weights can be used-book value weights and market value

weights.

Book Value Weights.The use of book value weights in calculating the firmâ€™s weighted cost of capital

assumes that new financings will be raised using the same method the firm used for its present capital

structure. The weights are determined by dividing the book value of each capital component by the sum

of the book values of all the long-term capital sources. The computation of overall cost of capital is

illustrated in the following example.

EXAMPLE 10.7 Assume the following capital structure for the Carter Company:

Mortgage bonds ($l,OOO par) $20,000,000

Preferred stock ($100 par) 5,000,000

Common stock ($40 par) 20,000,000

Retained earnings 5,000,000

Total $50.000.000

The book value weights and the overall cost of capital are computed as follows:

Book Value Weights Cost Weighted Cost

Source

$20,000,000

Debt 40% 5.14% 2.06%

5,000,000 10

Preferred stock 13.40% 1.34

17.I 1Yo

Common stock 40 6.84

20,000,000

5,000,000

Retained earnings 10 16.00% 1.60

$50,000,000

Totals 100% 11.84%

Overall cost of capital = k, = 11.84%

Market Value Weights. Market value weights are determined by dividing the market value of each

source by the sum of the market values of all sources. The use of market value weights for computing

a firmâ€™s weighted average cost of capital is theoretically more appealing than the use of book value

weights because the market values of the securities closely approximate the actual dollars to

be received from their sale.

284 COST OF CAPITAL [CHAP. 10

EXAMPLE 10.8 In addition to the data from Example 10.7, assume that the security market prices are as

follows:

Mortgage bonds = $1,100 per bond

Preferred stock = $90 per share

Common stock = $80 per share

The firmâ€™s number of securities in each category is:

Therefore, the market value weights are:

Number of Securities

Source Price Market Value

Debt 20,000 $1,100 $22,000,000

Preferred stock 50,000 $90 4,500,000

Common stock 500,000 $80 40,000,000

$66,500,000

The $40 million common stock value must be split in the ratio of 4 to 1 (the $20 million common stock versus the

$5 million retained earnings in the original capital structure), since the market value of the retained earnings has

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