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preferred stock, and of the weights in the cost of capital formulation are explored in detail

in Chapter 4. To summarize:

The cost of equity should reflect the riskiness of an equity investment in the

â€¢

company. The standard models for risk and return â€“â€“ the capital asset pricing model

and the arbitrage pricing model â€“â€“ measure risk in terms of market risk, and convert

the risk measure into an expected return.

â€¢ The cost of debt should reflect the default risk of the firm - the higher the default risk,

the greater the cost of debt - and the tax advantage associated with debt - interest is

tax deductible.

Cost of Debt = Pre-tax Interest Rate on Borrowing (1 - tax rate)

â€¢ The cost of preferred stock should reflect the preferred dividend and the absence of

tax deductibility.

Cost of Preferred Stock = Preferred Dividend / Preferred Stock Price

â€¢ The weights used for the individual components should be market value weights

rather than book value weights.

The Role of Cost of Capital in Investment Analysis and Valuation

In order to understand the relationship between the cost of capital and optimal

capital structure, we first have to establish the relationship between firm value and the

cost of capital. In chapter 5, we noted that the value of a project to a firm could be

computed by discounting the expected cash flows on it at a rate that reflected the

riskiness of the cash flows, and that the analysis could be done either from the viewpoint

of equity investors alone or from the viewpoint of the entire firm. In the latter approach,

we discounted the cash flows to the firm on the project, i.e., the project cash flows prior

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to debt payments but after taxes, at the projectâ€™s cost of capital. Extending this principle,

the value of the entire firm can be estimated by discounting the aggregate expected cash

flows over time at the firmâ€™s cost of capital. The firmâ€™s aggregate cash flows can be

estimated as cash flows after operating expenses, taxes and any capital investments

needed to create future growth in both fixed assets and working capital.

Cash Flow to Firm = EBIT (1-t) - (Capital Expenditures - Depreciation) - Change

in Working Capital

The value of the firm can then be written as â€“

t=n

CF to Firm

! (1+ WACC)tt

Value of Firm =

t =1

The value of a firm is therefore a function of its cash flows and its cost of capital. In the

specific case where the cash flows to the firm are unaffected as the debt/equity mix is

changed, and the cost of capital is reduced, the value of the firm will increase. If the

objective in choosing the financing mix for the firm is the maximization of firm value,

this can be accomplished, in this case, by minimizing the cost of capital. In the more

general case where the cash flows to the firm are a function of the debt-equity mix, the

optimal financing mix is the one that maximizes firm value.7

The optimal financing mix for a firm is simple to compute if one is provided with

a schedule that relates the costs of equity and debt to the leverage of the firm.

Illustration 8.2: WACC, Firm Value, and Leverage

Assume that you are given the costs of equity and debt at different debt levels for

Belfanâ€™s, a leading manufacturer of chocolates and other candies, and that the cash flows

to this firm are currently $200 million. Belfanâ€™s is in a relatively stable market, and these

cash flows are expected to grow at 6% forever, and are unaffected by the debt ratio of the

firm. The WACC schedule is provided in Table 8.1, along with the value of the firm at

each level of debt.

Table 8.1: WACC, Firm Value and Debt Ratios

D/(D+E) Cost of Equity Cost of Debt WACC Firm Value

7 In other words, the value of the firm might not be maximized at the point that cost of capital is minimized,

if firm cash flows are much lower at that level.

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0 10.50% 4.80% 10.50% $4,711

10% 11.00% 5.10% 10.41% $4,807

20% 11.60% 5.40% 10.36% $4,862

30% 12.30% 5.52% 10.27% $4,970

40% 13.10% 5.70% 10.14% $5,121

50% 14.00% 6.30% 10.15% $5,108

60% 15.00% 7.20% 10.32% $4,907

70% 16.10% 8.10% 10.50% $4,711

80% 17.20% 9.00% 10.64% $4,569

90% 18.40% 10.20% 11.02% $4,223

100% 19.70% 11.40% 11.40% $3,926

Note that the value of the firm = Cash flows to firm*(1+g)/ (WACC - g)

= $200 * 1.06 / (WACC - .06)

The value of the firm increases (decreases) as the WACC decreases (increases), as

illustrated in Figure 8.2.

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WACC AND FIRM VALUE AS A FUNCTION OF LEVERAGE

11.40% $6,000

11.20%

$5,000

11.00%

10.80%

$4,000

10.60%

Firm Value

WACC

10.40% $3,000

10.20%

$2,000

10.00%

9.80%

$1,000

9.60%

9.40% $0

0

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

D/(D+E)

WACC Firm Value

While this illustration makes the choice of an optimal financing mix seem trivial, it

obscures some real problems that may arise in its applications. First, an analyst typically

does not have the benefit of having the entire schedule of costs of financing prior to an

analysis. In most cases, the only level of debt about which there is any certainty about the

cost of financing is the current level. Second, the analysis assumes implicitly that the

level of cash flows to the firm is unaffected by the financing mix of the firm and,

consequently, by the default risk (or bond rating) for the firm. While this may be

reasonable in some cases, it might not in others. For instance, a firm that manufactures

consumer durables (cars, televisions etc.) might find that its sales drop if its default risk

increases because investors are reluctant to buy its products.

8.1. â˜ž: Minimizing Cost of Capital and Maximizing Firm Value

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A lower cost of capital will lead to a higher firm value only if

a. the operating income does not change as the cost of capital declines

b. the operating income goes up as the cost of capital goes down

c. any decline in operating income is offset by the lower cost of capital

Steps in the Cost of Capital Approach

We need three basic inputs to compute the cost of capital â€“ the cost of equity, the

after-tax cost of debt and the weights on debt and equity. The costs of equity and debt

change as the debt ratio changes, and the primary challenge of this approach is in

estimating each of these inputs.

Let us begin with the cost of equity. In chapter 4, we argued that the beta of equity

will change as the debt ratio changes. In fact, we estimated the levered beta as a function

of the debt to equity ratio of a firm, the unlevered beta and the firmâ€™s marginal tax rate:

Î²levered = Î²unlevered [1+(1-t)Debt/Equity]

Thus, if we can estimate the unlevered beta for a firm, we can use it to estimate the

levered beta of the firm at every debt ratio. This levered beta can then be used to compute

the cost of equity at each debt ratio.

Cost of Equity = Riskfree rate + Î²levered (Risk Premium)

The cost of debt for a firm is a function of the firmâ€™s default risk. As firms borrow

more, their default risk will increase and so will the cost of debt. If we use bond ratings as

our measure of default risk, we can estimate the cost of debt in three steps. First, we

estimate a firmâ€™s dollar debt and interest expenses at each debt ratio; as firms increase

their debt ratio, both dollar debt and interest expenses will rise. Second, at each debt

level, we compute a financial ratio or ratios that measures default risk and use the ratio(s)

to estimate a rating for the firm; again, as firms borrow more, this rating will decline.

Third, a default spread, based upon the estimated rating, is added on to the riskfree rate to

arrive at the pre-tax cost of debt. Applying the marginal tax rate to this pre-tax cost yields

an after-tax cost of debt.

Once we estimate the costs of equity and debt at each debt level, we weight them

based upon the proportions used of each to estimate the cost of capital. While we have

not explicitly allowed for a preferred stock component in this process, we can have

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preferred stock as a part of capital. However, we have to keep the preferred stock portion

fixed, while changing the weights on debt and equity. The debt ratio at which the cost of

capital is minimized is the optimal debt ratio.

In this approach, the effect on firm value of changing the capital structure is

isolated by keeping the operating income fixed and varying only the cost of capital. In

practical terms, this requires us to make two assumptions. First, the debt ratio is

decreased by raising new equity and retiring debt; conversely, the debt ratio is increased

by borrowing money and buying back stock. This process is called recapitalization.

Second, the pre-tax operating income is assumed to be unaffected by the firmâ€™s financing

mix and, by extension, its bond rating. If the operating income changes with a firm's

default risk, the basic analysis will not change, but minimizing the cost of capital may not

be the optimal course of action, since the value of the firm is determined by both the

cashflows and the cost of capital. The value of the firm will have to be computed at each

debt level and the optimal debt ratio will be that which maximizes firm value.

Illustration 8.3: Analyzing the Capital Structure for Disney: March 2004

The cost of capital approach can be used to find the optimal capital structure for a

firm, as we will for Disney in March 2004. Disney had $13,100 million in debt on its

books. The estimated market value of this debt was $12,915 million was added the

present value of operating leases, of $1,753 million to arrive at a total market value for

the debt of $14,668 million. 8 The market value of equity at the same time was $55,101

million; the market price per share was $ 22.26, and there were 2475.093 million shares

outstanding. Proportionally, 21.02% of the overall financing mix was debt, and the

remaining 78.98% was equity.

The beta for Disney's stock in March 2004, as estimated in chapter 7, was 1.2456.

The treasury bond rate at that time was 4%. Using an estimated market risk premium of

4.82%, we estimated the cost of equity for disney to be 10.00%:

Cost of Equity = Riskfree rate + Beta * (Market Premium)

=4.00% + 1.2456 (4.82%) = 10.00%

8 The details of this calculation are in illustration 4.15 in chapter 4.

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Disneyâ€™s senior debt was rated BBB+. Based upon this rating, the estimated pre-tax cost

of debt for Disney is 5.25%. The tax rate used for the analysis is 37.30%.

Value of Firm = 14,668+ 55,101 = $ 69,769 million

After-tax Cost of debt = Pre-tax interest rate (1- tax rate)

= 5.25% (1- 0.373) = 3.29%

The cost of capital was calculated using these costs and the weights based upon market value:

WACC = Cost of Equity (Equity/(Equity + Debt)) + After-tax Cost of Debt (Debt/(Debt

+Equity))

= 10.00%* [55,101/69.769] + 3.58% *[14,668/69,769] = 8.59%

8.2. â˜ž: Market Value, Book Value and Cost of Capital

Disney had a book value of equity of approximately $ 16.5 billion. Using the book value

of debt of $ 13.1 billion, estimate the cost of capital for Disney using book value weights.

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