cost of cap notes

8/3/2019 Cost of Cap Notes

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CHAPTER 12COST OF CAPITAL

CHAPTER ORGANIZATION

The appropriate discount rate to use when evaluating a capital budgeting project depends largely on the risk of theproject. The new project will have a positive NPV only if its return exceeds what the financial markets offer onnvestments of similar risk. We called this minimum required return the cost of capitalassociated with the project. T

weighted average cost of capital(WACC) is the cost of capital for the firm as a whole, and it can be interpreted as tequired return on the overall firm. In discussing the WACC, we will recognize the fact that a firm will normally raiapital in a variety of forms and that these different forms of capital may have different costs associated with them.

Taxes are an important consideration in determining the required return on an investment, because we are alwaysnterested in valuing the aftertax cash flows from a project. We will therefore discuss how to incorporate taxesxplicitly into our estimates of the cost of capital.

2.1 The Cost of Capital: Some Preliminaries

An accurate estimate of the cost of capital is important for various reasons:

good capital budgeting decisions neither the NPV rule nor the IRR rule can be implemented withoutknowledge of the appropriate discount rate.

financing decisions the optimal/target capital structure minimizes the cost of capital.

operating decisions cost of capital is used by regulatory agencies in order to determine the fair return insome regulated industries (e.g. electric utilities.

Required Return versus Cost of Capital: Cost of capital, required return, and appropriate discount rate ardifferent phrases that all refer to the opportunity cost of using capital in one way as opposed to alternativfinancial market investments of the same systematic risk. Required return is from an investors point oview; cost of capital is the same return from the firms point of view; appropriate discount rate is thesame return used in a PV calculation.

The cost of capital depends primarily on the use of the funds, not the source.

The investment decisions of the firm are separate from the financing decisions.

Financial Policy and Cost of Capital: The particular mixture of debt and equity a firm chooses to employreferred to as its capital structure; this is a managerial variable. For now, we will take the firm's financipolicy as given. In particular, we will assume that the firm has a fixed debt-equity ratio that it maintains.This ratio reflects the firm's target or optimal capital structure. Given that a firm uses both debt and equitcapital, this overall cost of capital will be a mixture of the returns needed to compensate its creditors andstockholders. In other words, a firm's cost of capital will reflect both its cost of debt capital and its cost oequity capital.

2.2 The Cost of Equity: The firm's overall cost of equity is difficult to estimate since there is no way of directlyobserving the return that the firm's equity investors require on their investment.

The Dividend Growth Model Approach

According to the constant growth model,

P0 = D0(1 + g) / (RE g) = D1 / RE g.

Prepared by Jim Keys


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Rearranging terms and solving for the cost of equity gives:

RE = (D1 / P0) + g ,

which equals the dividend yield plus the growth rate (capital gains yield).

Of the required data, only g is not directly observable [Note: D1 = D0(1 + g)]. The deficiencies of thisapproach are (1) it assumes that dividends grow at a constant rate; (2) the value of g must be estimated an

forecasting errors impact the value of RE; and (3) risk is not explicitly considered.

To use the dividend growth model, we must come up with an estimate forg, the growth rate. There areessentially two ways of doing this: (1) use historical growth rates or (2) use analysts' forecasts of futuregrowth rates. Analysts' forecasts are available from a variety of sources.

(Example from Yahoo! Finance:IBM; from Zacks: IBM).

Alternatively, we might observe dividends for the previous, say, five years, calculate the year-to-yeargrowth rates, and average them. For example, suppose we observe the following for some company:

Year Dividend $ Change % Change200

4$4.00 - -

2005

$4.40 $.40 10.00%

2006

$4.75 $.35 7.95%

2007

$5.25 $.50 10.53%

2008

$5.65 $.40 7.62%

Arithmetic average growth rate = (10.00% + 7.95% + 10.53% + 7.62%) / 4 = 9.025%

Geometric average growth rate = ($5.65 / $4.00)(1/4) 1 = 9.018%

The Boos Co. just issued a dividend of $2.40 per share on its common stock. The company is expected to maintain aonstant 6 percent growth rate in its dividends indefinitely. If the stock sells for $48 a share, what is the company's c

of equity?

With the information given, we can find the cost of equity, using the dividend growth model. Using this model, the

of equity is:

RE = [ $2.40(1.06) / $48 ] + .06

RE = ($2.544 / $48) + .06

RE = .053 + .06 = .1130 or 11.30%

The SML Approach - The required or expected return on a risky investment depends on three things:

http://finance.yahoo.com/q/ae?s=IBMhttp://finance.yahoo.com/q/ae?s=IBMhttp://www.zacks.com/research/report.php?PHPSESSID=594ec652e9adb5efdeedd602a1fe57d9&t=ibm&type=estimateshttp://finance.yahoo.com/q/ae?s=IBMhttp://www.zacks.com/research/report.php?PHPSESSID=594ec652e9adb5efdeedd602a1fe57d9&t=ibm&type=estimates


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(1) The risk-free rate, Rf(2) The market risk premium, E(RM) Rf(3) The systematic risk of the asset relative to average, which we called its beta coefficient,

Using the SML, we can write the expected return on the company's equity, E(RE), as:

E(RE) = Rf+ E[E(RM) Rf]

or simply

RE = Rf+ E(RM Rf)

Betas are widely available and T-bill rates are often used for Rf. The expected market risk premium, E(RM) is the more difficult number to come up with. One of the problems is that we really do need an expectation, bwe only have past information, and market risk premiums do vary through time. Early in 2000, Federal ReseChairman, Alan Greenspan, indicated that part of his concern with the current state of the U.S. stock marketsthe reduction in the market risk premium. He felt that investors were either becoming less risk averse, or theydid not truly understand the risk they were taking by investing in the stock. Nonetheless, the historical averagis often used as an estimate for the expected market risk premium.

- This approach explicitly adjusts for risk in a fashion that is consistent with capital market history.- It is applicable to virtually all publicly-traded stocks for which the value of can be determined.- The main disadvantage is that the past is not a perfect predictor of the future, and both beta and the market premium vary through time.

ceberg Corporation's common stock has a beta of 1.30. If the risk-free rate is 5 percent and the expected return on tmarket is 13 percent, what is the company's cost of equity capital?

Here we have information to calculate the cost of equity, using the CAPM. The cost of equity is:

RE = .05 + 1.30(.13 .05)

RE = .05 + .104 = .1540 or 15.40%

2.3 The Costs of Debt and Preferred Stock

The Cost of Debt - The cost of debt is the return that the firm's creditors demand on new borrowing.

Unlike a firm's cost of equity, its cost of debt can normally be observed either directly or indirectly, because

cost of debt is simply the interest rate the firm must pay on new borrowing, and we can observe interest ratethe financial markets. For example, if the firm already has bonds outstanding, then the yield to maturity onthose bonds is the market-required rate on the firm's debt.

Alternatively, if we knew that the firm's bonds were rated, say, AA, then we could simply find out what theinterest rate on newly issued AA-rated bonds was. Either way, there is no need to actually estimate a beta fothe debt since we can directly observe the rate we want to know.

The coupon rate on the firm's outstanding debt is irrelevant here. That just tells us roughly what the firm's coof debt was back when the bonds were issued, not what the cost of debt is today. This is why we have to loo



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the yield on the debt in today's marketplace. For consistency with our other notation, we will use the symbolfor the cost of debt.

CU Window, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with seven years tomaturity that is quoted at 93 percent of face value. The issue makes semiannual payments and has an embedded cos

.6 percent annually. What is ICU's pretax cost of debt? If the tax rate is 38 percent, what is the aftertax cost of debt

The pretax cost of debt is the YTM of the companys bonds, so:

P0 = $930 = $28(PVIFAR%,14) + $1,000(PVIFR%,14)R = 3.438%YTM = 2 3.438%YTM = 6.88%

**********************************************************************

N = 2 x 7 = 14PV = .93 x 1,000 = -930PMT = (.056 x $1,000) / 2 = 28FV = 1000

/YR = 3.4383 x 2 = 6.8767

And the aftertax cost of debt is:

RD(1 TC) = .068767(1 .38)

RD(1 TC)= .042636 or 4.26%

The Cost of Preferred Stock The cost of preferred stock financing can also be observed in the financialmarkets. A firm which expects to issue preferred stock would compute the yield for either its own currenoutstanding preferred stock issue or for preferred stock issued by other firms with ratings similar to theproposed offering.

Preferred stock is generally considered to be a perpetuity, so you rearrange the perpetuity equation to gethe cost of preferred, RP:

RP = D / P0

Sixth Fourth Bank has an issue of preferred stock with a $6 stated dividend that just sold for $94 per share. What is ank's cost of preferred stock?

RP = $6 / $94 = .0638 = 6.38%

2.4 The Weighted Average Cost of Capital



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The Capital Structure Weights

E = market value of the firms equity = # outstanding shares times price per shareD = market value of the firms debt = # bonds times price per bondV = combined market value of the firms equity and debt = E + D (Assuming that there is no preferred st

and current liabilities are negligible. If this is not the case, then you need to include thesecomponents as well. This is really just the market value version of the balance sheet identity. market value of the firms assets = market value of liabilities + market value of equity.)

Using the symbol V(forvalue) to stand for the combined market value of the debt and equity:

V = E + D

If we divide both sides by V, we can calculate the percentages of the total capital represented by the debt andequity:

100% = E/V + D/V

These percentages can be interpreted just like portfolio weights, and they are often called the capital structu

weights. For example, if the total market value of a company's stock were calculated as $200 million and thetotal market value of the company's debt were calculated as $50 million, then the combined value would be$250 million. Of this total, E/V = $200/250 = 80%, so 80 percent of the firm's financing would be equity andthe remaining 20 percent would be debt. We emphasize here that the correct way to proceed is to use the mavalues of the debt and equity. Under certain circumstances, such as when considering a privately ownedcompany, it may not be possible to get reliable estimates of these quantities, and book values must be used.

Taxes and the Weighted Average Cost of Capital We are always concerned with aftertax cash flows. Iwe are determining the discount rate appropriate to those cash flows, then the discount rate also needs toexpressed on an aftertax basis. Interest is a tax-deductible expense, while dividends paid to stockholders not tax-deductible. Therefore, the cost of capital calculation must be adjusted to reflect this differential ta

treatment.

Weighted average cost of capital = WACC = (E/V)(RE) + (D/V)(RD)(1 TC)

Note: The after-tax cost of debt = (RD)(1 TC)

If the firm also uses preferred stock in its capital structure, then the WACC is as follows:

WACC = (E/V)(RE) + (P/V)(RP) + (D/V)(RD)(1 TC)

Note: The cost of preferred stock = RP and the percentage of preferred stock in the capital structure = P/V

The WACC is the overall return the firm must earn on its existing assets to maintain the value of the stock. It

a market rate that is based on the markets perception of the risk of the firms assets.



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Mullineaux Corporation has a target capital structure of 70 percent common stock, 5 percent preferred stock, and 25ercent debt. Its cost of equity is 14 percent, the cost of preferred stock is 6 percent, and the cost of debt is 7.5 perce

The relevant tax rate is 35 percent.

. What is Mullineaux's WACC?

Using the equation to calculate the WACC, we find:

WACC = .70(.14) + .05(.06) + .25(.075)(1 .35)

WACC = .098 + .003 + .0122 = .1132 = 11.32%

. The company president has approached you about Mullineaux's capital structure. He wants to know why theompany doesn't use more preferred stock financing, since it costs less than debt. What would you tell the president

Since interest is tax deductible and dividends are not, we must look at the aftertax cost of debt, which is:

RD = .075(1 .35) = .0488 = 4.88%

Hence, on an aftertax basis, debt is cheaper than the preferred stock.



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Solving the Warehouse Problem and Similar Capital Budgeting Problems

The warehouse problem employs the WACC as the discount rate in an NPV calculation. This is onlyappropriate if the warehouse has approximately the same risk characteristics as the overall firm. A secondassumption that is often discussed in financial literature is that the project should be financed with the sameproportion of debt versus equity as used in the WACC. However, as discussed earlier, the appropriatediscount rate for a project depends on the risk of the project, not on how it is paid for. The WACC is the bestestimate we have of the markets perception about the risk of the firm and the required return, given that riskConsequently, the key assumption is that the project is the same risk as the firms current assets.

Calculating the WACC for Eastman Chemical: (pages 385 390)

2.5 Divisional and Project Costs of Capital

The SML and the WACC: The WACC is the appropriate discount rate only if the proposed investment issimilar risk as the firms existing assets; riskier (less risky) projects should be evaluated against higher(lower) capital costs.

The security market line, SML, and the weighted average cost of capital, WACC

Divisional Cost of Capital

When a firm has different operating divisions with different risks, its WACC is an average of thedivisional required returns. In such cases, the cost of capital for projects of average risk in each divisineeds to be established.



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If you do use the firms WACC across divisions, then riskier divisions will receive the bulk of thefunding while less-risky divisions will have to forego what would be good projects if the appropriatediscount rate were used. This will lead to an increase in risk for the overall firm.

The Pure Play Approach - A pure play is a company that has a single line of business. The idea is to findrequired return on a near substitute investment.

The Subjective Approach - Assigns investments to risk categories that have higher or lower riskpremiums than the firm as a whole.

Finding the WACC. Given the following information for Janicek Power Co., find the WACC. Assume the companax rate is 35 percent.

Debt: 6,500 8.5 percent coupon bonds outstanding, $1,000 par value, 25 years to maturity,selling for 104 percent of par; the bonds make semiannual payments.

Common

stock:150,000 shares outstanding, selling for $78 per share; beta is 1.15.

Preferred

stock:10,000 shares of 6.25 percent preferred stock outstanding, currently selling for $80 pershare.

Market: 8 percent market risk premium and 5.25 percent risk-free rate.

1) Determine the market value of each source of financing:2) Find the cost of equity, RE, using the CAPM:3) Compute the YTM of the outstanding bonds; this is RD:4) Calculate the cost of preferred stock, RP:5) Compute the WACC:


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