27.Cost of Capital and Capital Structure Decision

The cost of capital is computed as a weighted average of the various capital components, which are items on the right-hand side of the balance sheet such as debt, preferred stock, common

C HAPTER 27

C OST OF C APITAL AND C APITAL

S TRUCTURE D ECISIONS

The cost of capital is defined as the rate of return that is necessary to maintain the market value of the firm (or price

of the firm’s stock) CFOs must know the cost of capital (the minimum required rate of return) in (1) making capital budgeting decisions, (2) helping to establish the optimal capital structure, and (3) making decisions such as leasing, bond refunding, and working capital management The cost of capital is used either as a discount rate under the NPV method or as a hurdle rate under the IRR method The cost of capital is computed as a weighted average

of the various capital components, which are items on the right-hand side of the balance sheet such as debt, preferred stock, common stock, and retained earnings

How do you compute individual costs

of capital?

Each element of capital has a component cost that is identified by:

ki = before-tax cost of debt

kd = k i(1− t) = after-tax cost of debt, where

t= tax rate

kp = cost of preferred stock

ks = cost of retained earnings (or internal equity)

ke = cost of external equity, or cost of issuing new common stock

k o = firm’s overall cost of capital, or a weighted average cost of capital

COST OF DEBT

The before-tax cost of debt can be found by determining the internal rate of return (or yield to maturity) on the bond cash flows

515

However, the following shortcut formula may be used for approximating the yield to maturity on a bond:

ki= I+ (M − V)/n(M

+ V)/2

where

I = annual interest payments in dollars

M= par or face value, usually $1,000 per bond

V = market value or net proceeds from the sale of a bond

n = term of the bond n years

Since the interest payments are tax-deductible, the cost

of debt must be stated on an after-tax basis The after-tax cost of debt is:

kd = k i(1− t)

where t is the tax rate.

E XAMPLE 27.1

Assume that the Carter Company issues a $1,000, 8 percent, 20-year bond whose net proceeds are $940 The tax rate is 40 percent Then, the before-tax cost of

debt, k i, is:

ki= I+ (M − V)/n(M

+ V)/2

= $80($1,000+ ($1,000 − $940)/20

$83

$970= 8.56%

Therefore, the after-tax cost of debt is:

k d = k i(1− t) = 8.56%(1 − 0.4) = 5.14%

COST OF PREFERRED STOCK

The cost of preferred stock,k p, is found by dividing the annual preferred stock dividend,dp, by the net proceeds from the sale of the preferred stock,p, as follows

kp=d p p

Since preferred stock dividends are not a tax-deductible expense, these dividends are paid after taxes Conse-quently, no tax adjustment is required

Cost of Equity Capital 517

E XAMPLE 27.2

Suppose that the Carter Company has preferred stock that pays a $13 dividend per share and sells for $100 per share in the market The flotation (or underwrit-ing) cost is 3 percent, or $3 per share Then the cost of preferred stock is:

kp=d p

P = $13$97= 13.4%

COST OF EQUITY CAPITAL

The cost of common stock, ke, is generally viewed as the rate of return investors require on a firm’s common stock Two techniques for measuring the cost of common

stock equity capital are widely used: (1) the Gordon’s

growth model and (2) the capital asset pricing model (CAPM)

approach

The Gordon’s growth model is:

Po= D1

r − g

where

Po= value (or market price) of common stock

D1= dividend to be received in one year

r = investor’s required rate of return

g = rate of growth (assumed to be constant over time) Solving the model forrresults in the formula for the cost of common stock:

r=D1

P o + g or k e=D1

P o + g

Note that the symbolris changed tok eto show that it

is used for the computation of cost of capital

E XAMPLE 27.3

Assume that the market price of the Carter Company’s stock is $40 The dividend to be paid at the end of the coming year is $4 per share and is expected to grow

at a constant annual rate of 6 percent Then the cost of this common stock is:

E XAMPLE 27.3 (continued)

ke= D1

Po + g =$40$4 + 6% = 16%

The cost of new common stock, or external equity capital, is higher than the cost of existing common

stock because of the flotation costs involved in selling

the new common stock Flotation costs, sometimes

called issuance costs, are the total costs of issuing and

selling a security that include printing and engraving, legal fees, and accounting fees

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

ke= D1

Po(1− f) + g

E XAMPLE 27.4

Assume the same data as in Example 27.3, except the firm is trying to sell new issues of stock A and its flotation cost is 10 percent Then:

k e= D1

Po(1− f) + g =

$4

$40(1− 0.1)+ 6% =

$4

$36 + 6%

= 11.11% + 6% = 17.11%

CAPITALASSETPRICINGMODEL(CAPM) APPROACH

An alternative approach to measuring the cost of common stock is to use the CAPM, which involves these four steps:

1 Estimate the risk-free rate,r f, generally taken to be the United States Treasury bill rate

2 Estimate the stock’s beta coefficient, b, which is

an index of systematic (or nondiversifiable market) risk

3 Estimate the rate of return on the market portfolio,r m, such as the Standard & Poor’s 500 Stock Composite Index or Dow Jones 30 Industrials

4 Estimate the required rate of return on the firm’s stock, using the CAPM equation:

k e = r f + b(r m − r f)

Again, note that the symbolris changed tok

Cost of Retained Earnings 519

E XAMPLE 27.5

Assuming thatrf is 7 percent,b is 1.5, andrm is 13 percent, then:

ke = r f + b(r m − r f)= 7% + 1.5 (13% − 7%) = 16%

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 firm’s stock price is 1.5 times more volatile than the market portfolio to the factors affecting nondiversifiable, or systematic risk

COST OF RETAINED EARNINGS

The cost of retained earnings,ks 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 firm’s common stock Therefore,

ke = k s

How is the overall cost of capital

determined?

The firm’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 Letko be the overall cost of capital

ko =
(percentage of the total capital structure supplied by each source of capital × cost of capital for each source)

=
wdkd + w pkp + w eke + w sks

where

wd= % of total capital supplied by debts

wp= % of total capital supplied by preferred stock

we= % of total capital supplied by external equity

ws = % 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 firm’s existing capital structure The use of these weights is based on the assumption that the firm’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 firm’s weighted cost of capital assumes that new financing will

be raised employing 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 Example 27.6

E XAMPLE 27.6

Assume the following capital structure and cost of each source of financing for the Carter Company:

Mortgage bonds

($1,000 par) $20,000,000 5.14% (Example 27.1) Preferred stock ($100 par) 5,000,000 13.40% (Example 27.2) Common stock ($40 par) 20,000,000 17.11% (Example 27.3) Retained earnings 5,000,000 16.00% (Example 27.4)

$50,000,000

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

Source Book value Weights Cost Weighted

cost

Debt $20,000,000 40%a 5.14% 2.06%b Preferred

stock 5,000,000 10 13.40% 1.34 Common

stock 20,000,000 40 17.11% 6.84 Retained

earnings 5,000,000 10 16.00% 1.60

$50,000,000 100% 11.84 Overall cost of capital= k o = 11.84%

a$20,000,000/$50,000,000 = 0.40 = 40%

b5.14% × 40% = 2.06%

Historical Weights 521

Market Value Weights

Market value weights are determined by dividing the market value of each source by the sum of the market val-ues of all sources The use of market value weights for com-puting a firm’s weighted average cost of capital is theoret-ically more appealing than the use of book value weights because the market values of the securities closely approx-imate the actual dollars to be received from their sale

E XAMPLE 27.7

In addition to the data from Example 27.6, assume that the security market prices are:

Mortgage bonds = $1,100 per bond

Preferred stock = $90 per share

Common stock = $80 per share

The firm’s number of securities in each category is:

Mortgage bonds = $20,000,000$1,000 = 20,000

Preferred stock = $5,000,000$100 = 50,000

Common stock = $20,000,000$40 = 500,000

Therefore, the market value weights are:

Source Number of Price Market

Securities 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 origi-nal capital structure), since the market value of the retained earnings has been impounded into the com-mon stock

The firm’s cost of capital is:

Source Market Value Weights Cost Weighted

Average

Debt $22,000,000 33.08% 5.14% 1.70% Preferred

stock 4,500,000 6.77 13.40% 0.91

E XAMPLE 27.7 (continued)

Source Market Value Weights Cost Weighted

Common

stock 32,000,000 48.12 17.11% 8.23 Retained

earnings 8,000,000 12.03 16.00% 1.92

$66,500,000 100.00% 12.76%

Overall cost of capital= k o = 12.76%

TARGET WEIGHTS

If the firm has a target capital structure (desired debt-equity mix) that is maintained over the long term, then that capital structure and associated weights can be used

in calculating the firm’s weighted cost of capital

MARGINAL WEIGHTS

Marginal weights involves use of the actual financial mix

used in financing the proposed investments In using tar-get weights, the firm is concerned with what it believes

to be the optimal capital structure or target percentage

In using marginal weights, the firm is concerned with the actual dollar amounts of each type of financing to

be needed for a given investment project This approach, though attractive, presents a problem The cost of cap-ital for the individual sources depends on the firm’s financial risk, which is affected by the firm’s financial mix If the company alters its present capital structure, the individual costs will change, which makes it more difficult to compute the weighted cost of capital The important assumption needed is that the firm’s financial mix is relatively stable and that these weights will closely approximate future financing practice

E XAMPLE 27.8

The Carter Company is considering raising $8 million for plant expansion The CFO estimates using the following mix for financing this project:

Debt $4,000,000 50% Common stock 2,000,000 25% Retained earnings 2,000,000 25%

EBIT-EPS Approach to Capital Structure Decisions 523

E XAMPLE 27.8 (continued)

The company’s cost of capital is computed as:

Source Marginal Cost Weighted

Weights Cost

Debt 50% 5.14% 2.57% Common stock 25 17.11% 4.28 Retained earnings 25 16.00% 4.00

100% 10.85%

Overall cost of capital= k o = 10.85%

How do you determine the firm’s

optimal capital structure?

The concepts to be covered in this chapter relate closely

to the cost of capital and also to the crucial problem

of determining the firm’s optimal capital structure We will cover three methods that show how to build an appropriate financing mix

EBIT-EPS APPROACH TO CAPITAL

STRUCTURE DECISIONS

This analysis is a practical tool that enables the CFO to evaluate alternative financing plans by investigating their effect on EPS over a range of EBIT levels Its primary objective is to determine the EBIT breakeven, or indif-ference, points between the various alternative financing plans The indifference point identifies the EBIT level at which the EPS will be the same regardless of the financing plan chosen by the CFO

This indifference point has major implications for cap-ital structure decisions At EBIT amounts in excess of the EBIT indifference level, the more heavily levered financing plan will generate a higher EPS At EBIT amounts below the EBIT indifference level, the financing plan involving less leverage will generate a higher EPS Therefore, it is of critical importance for the CFO to know the EBIT indif-ference level The indifindif-ference points between any two methods of financing can be determined by solving for EBIT in this equality:

(EBIT− I)(1 − t) − PD

S 1 =(EBIT− I)(1 − t) − PD

S 2 where

t = tax rate

PD = preferred stock dividends

S 1 and S 2= number of shares of common stock

outstanding after financing for plan 1 and plan 2, respectively

E XAMPLE 27.9

Assume that ABC Company, with long-term capital-ization consisting entirely of $5 million in stock, wants

to raise $2 million for the acquisition of special equip-ment by (1) selling 40,000 shares of common stock at

$50 each, (2) selling bonds at 10 percent interest, or (3) issuing preferred stock with an 8 percent dividend The present EBIT is $800,000, the income tax rate is 50 percent, and 100,000 shares of common stock are now outstanding To compute the indifference points, we begin by calculating EPS at a projected EBIT level of

$1 million

All All Debt All Common Preferred

EBIT $1,000,000 $1,000,000 $1,000,000 Interest 200,000

Earnings before

taxes (EBT) $1,000,000 $ 800,000 $1,000,000 Taxes 500,000 400,000 500,000 Earnings after

taxes (EAT) $ 500,000 $ 400,000 $ 500,000 Preferred stock

dividend 160,000 Earnings

available to

common

stockholders $ 500,000 $ 400,000 $ 340,000 Number of

shares 140,000 100,000 100,000 EPS $3.57 $4.00 $3.40

Now connect the EPSs at the level of EBIT of $1 million with the EBITs for each financing alternative

on the horizontal axis to obtain the EPS-EBIT graphs

We plot the EBIT necessary to cover all fixed financial costs for each financing alternative on the horizontal axis For the common stock plan, there are no fixed costs, so the intercept on the horizontal axis is zero For the debt plan, there must be an EBIT of $200,000

to cover interest charges For the preferred stock plan, there must be an EBIT of $320,000 [$160,000/(1 – 0.5)]

to cover $160,000 in preferred stock dividends at a

50 percent income tax rate; thus, $320,000 becomes the horizontal axis intercept (See Exhibit 27.1.) In this example, the indifference point between all common and all debt is:

EBIT-EPS Approach to Capital Structure Decisions 525

E XAMPLE 27.9 (continued)

(EBIT− I)(1 − t) − PD

S 1 = (EBIT− I)(1 − t) − PDS

2

(EBIT− 0)(1 − 0.5) − 0

140,000 = (EBIT− 200,000)(1 − 0.5) − 0100,000

Rearranging yields:

0.5(EBIT)(100,000) = 0.5(EBIT)(140,000)

−0.5(200,000)(140,000)

20,000 EBIT = 14,000,000,000

EBIT = $700,000

Similarly, the indifference point between all common and all preferred would be:

(EBIT− I)(1 − t) − PD

S 1 = (EBIT− I)(1 − t) − PDS

2

(EBIT− 0)(1 − 0.5) − 0

140,000 = (EBIT− 0)(1 − 0.5) − 160,000100,000

Rearranging yields:

0.5(EBIT)(100,000) = 0.5(EBIT)(140,000)

−160,000(140,000) 20,000 EBIT = 22,400,000,000

EBIT = $1,120,000

Based on the above computations and observing Exhibit 27.1, we can draw three conclusions:

1 At any level of EBIT, debt is better than preferred stock, since it gives a higher EPS

2 At a level of EBIT above $700,000, debt is better than common stock If EBIT is below $700,000, the reverse is true

3 At a level of EBIT above $1,120,000, preferred stock

is better than common At or below that point, the reverse is true

A Word of Caution

It is important to realize that financial leverage is a two-edge sword It can magnify profits, but it can also increase losses The EBIT-EPS approach helps the CFO examine the impact of financial leverage as a financing method Investment performance is crucial to the success-ful application of any leveraging strategy