HFT 4464

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HFT 4464HFT 4464

Chapter 8Chapter 8

Cost of CapitalCost of Capital

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Chapter 8 Introduction

A firm’s long-term success depends upon the firm’s investments earning a sufficient rate of return. This sufficient or minimum rate of return necessary for a firm to succeed is called the cost of capital.

The cost of capital can also be viewed as the minimum rate of return required to keep investors satisfied.

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Organization of Chapter 8

Measure the cost of capital on a marginal, after-tax basis.

Estimating the cost of capital components Debt Preferred stock Common equity

Internal— new retained earnings External—new issues of common stock

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Organization of Chapter 8

Estimating the weighted average cost of capital

Separating the finance decision from the investment decision

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The Weighted Average Cost of Capital

The weighted average cost of capital is:

The firm’s minimum required rate of return on investments

Measured as a percentage rate (%) An average cost of the various sources of capital

employed by a firm Debt Preferred stock Retained earnings Common stock

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Also, the weighted average cost of capital is:

The cost of long-term sources of funds; long-term sources of funds are relevant because these are the funds used to make long-term investments.

Measured on an after-tax basis. Measured as a marginal cost of capital. We

want to measure the cost of new capital used to finance new investments.

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The weights used are determined by a firm’s target capital structure. A target capital structure is the % of various capital components a firm plans to use to fund investments.

An example is a firm may plan to raise 70% of capital from long-term debt and 30% from equity. Another firm may plan to raise 40% of capital from long-term debt, 10% from preferred stock, and 50% from equity.

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The basic weighted average cost of capital (ka) equation is:

ka = ( wd * kd ) + ( wp * kp ) + ( we * ke )

Cost of Capital = (%Debt * Cost of Debt) + (% P.S. * Cost of P.S.) + (%C.S. * Cost of C.S.)

Where the w’s represent the firm’s target capital structure and must add up to 100%.

And the k’s represent the cost of each capital component—debt, preferred stock, and common equity.

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Estimating the Cost of Capital Components

Components of a firm’s capital structure may include:

Long-term debt

Preferred stock

New retained earnings

Common stock

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A component’s cost of capital is a reflection of the investor-required rate of return.

A business loan at a 10% interest rate provides a 10% return to the investor (lender) and a 10% cost to the business plus any transaction costs the company may pay to process the loan.

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A component’s cost of capital is just the investor-required return plus an adjustment for transaction costs.

These transaction costs are called issuance or flotation costs and consist of fees paid to investment bankers and lawyers for assisting a firm in the issuance of securities.

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Seniority Risk and the Cost of Capital

Debt securities have the least seniority risk and common stock the most seniority risk of the 3 basic security types a corporation may issue.

Therefore investors demand the lowest returns on debt securities and the highest returns on common stock.

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Seniority Risk and the Cost of Capital

There is a clear ranking of cost for a firm’s funds raised by different security types.

The cost of debt securities is lowest due to their relatively low risk.

The cost of common stocks is the highest due to its relatively high risk to investors.

The cost of preferred stocks falls between the above two.

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The Cost of Debt

The interest cost of debt is a tax-deductible cost. We take this into account by multiplying a firm’s before-tax cost of debt by one minus the firm’s marginal tax rate:

kd = kdbt x (1 – t)

With a 10% before-tax cost and a 40% marginal tax rate the relevant after-tax cost of debt is:

kd = 10% x (1 – 40%) = 6%

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The Cost of Debt The before-tax interest cost on bonds can be computed

with the same method used to compute the yield to maturity on bonds in Chapter 6.

Net Proceeds = (Coupon * PVA) + (Face Value * PVLS)

Where Vnet is the net proceeds from the bond issuance after issuance costs are paid.

n

dbtdbt

ndbt

netk1

$1,000

k

k1

1 - 1

x C V

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The Cost of Debt Suppose a firm is considering the issuance of a 20-year

bond at a $1,000 price with a 9% coupon rate and issuance costs of $10 for each bond.

Kdbt = 9.11% and the after-tax cost of debt assuming a 40% tax rate is:

kd = 9.11% x (1 - 40%) = 5.47%

20

dbtdbt

20dbt

k1

$1,000

k

k1

1 - 1

x $90 $990

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The Cost of Preferred Stock

Preferred stock is sometimes considered a perpetuity, but many issues have a call feature or a sinking fund as described in Chapter 6.

We will show how to compute the cost of funds raised with preferred stock assuming the preferred stock is a perpetuity and also assuming there is a stated ending date for the preferred stock.

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Computing the cost of funds raised with preferred stock is similar to computing the investor’s rate of return as in Chapter 6. If the preferred stock is perpetual:

Cost of P.S. = P.S. Dividend / P.S. Net Proceeds

Where Vnet is the net proceeds from the preferred stock issuance after issuance costs are paid.

net

pp V

d k

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Suppose a firm is considering the issuance of preferred stock at $100 market price, with a 10% dividend rate and issuance costs of $3 per share. The par value is also $100 per share. What is the cost of raising funds with preferred stock in this case?

%31.10$97

$10

3 - $100

$100 x 10% kp

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The Cost of Preferred Stock Let’s consider the same example with one change. What

will be the cost of raising funds with preferred stock if all the preferred stock will be called at a $100 par value in 10 years? The computation is similar to the bond computation but without the tax impact!

Kp = 10.50%

10

pp

10p

k1

$100

k

k1

1 - 1

x $10 $97

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Common Equity

Funds provided from a firm’s common equity have 2 possible sources:

Funds provided by reinvestment of a firm’s profits are called new retained earnings. We call this internal equity because these funds come from the firm itself.

Funds provided by the sale of new common stock we call external equity.

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The Cost of Internal Equity The source of internal equity are profits not paid out as

dividends. Profits belong to the common stockholders. The stockholders could have used this money to make further investments of their own. Thus profits should only be reinvested if the firm can earn as much as stockholders could earn on their own. How much is this?

We will estimate this by the rate of return stockholders can expect when they buy the firm’s common stock at its current price. We will use this rate as the cost of funds raised from internal equity!

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The Cost of Internal Equity

How do we measure the rate of return investors expect when they buy a firm’s common stock? We will present 3 different methods for estimating this rate of return and thus the cost of using funds from internal equity:

The dividend valuation model

The capital asset pricing model

The bond yield plus risk premium method

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The constant growth dividend valuation model was presented in chapter 7:

We need to algebraically rearrange the terms to solve for investor rate of return:

gk

dP

e

10

gP

dk

0

1e

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Suppose a firm’s common stock is selling for $40 per share, pays a current dividend of $3.50 per share and earnings and dividends are expected to grow at a 4% rate into the foreseeable future. The cost of internal equity estimate is:

%10.13 4%$40

4%)(1 x $3.50ke

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The capital asset pricing model (CAPM) was presented in Chapter 4. The CAPM estimates investor-required rate of return on common stock as a function of the firm’s systematic risk as measured by beta.

investor-required rate of return = Risk Free Rate +

{ ( Market Rate – Risk Free Rate) * beta }

jfmfj x )RR(Rk

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Suppose a firm’s beta is estimated at 1.20, the expected risk-free rate of return is 5%, and the expected market return is 12%. The CAPM can be used to estimate the firm’s internal cost of equity:

13.4% x 5%)12%(5%ke

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The bond yield plus risk premium method of estimating the cost of internal equity:

Begins with an estimate of the firm’s before-tax bond yield.

A risk premium is added to the bond yield to estimate the cost of internal equity.

The difficulty is in estimating the appropriate risk premium. This risk premium may vary over time and across different firms.

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Suppose a firm has bonds trading at an 8.5% yield. The typical risk premium over bond yield for an average company is 4%. But we believe our firm to have above-average risk so we think 5% is a better estimate of its risk premium over bond yield. The cost of internal equity using the bond yield plus risk premium is:

ke = 8.5% + 5% = 13.5%

Cost of Internal Equity = Bond Yield + Risk Premium

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The Cost of External Equity

If retained earnings growth is not sufficient to meet a firm’s need for equity funding, then new shares of common stock may be sold to raise capital. We call this external equity since the funds come from outside the firm.

The cost of external equity should be the same as the cost of internal equity plus additional issuance costs. Of course issuance costs are not relevant to internal equity.

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The same general approach to handling issuance costs with bonds and preferred stock is used to in the cost estimation for external equity. The market price of the security is reduced by the amount of the issuance costs. The dividend valuation model uses market price to estimate the cost of equity:

gP

dk

net

1ne

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The Cost of External Equity Let’s use the same example as before. A firm’s

common stock is selling for $40 per share, expects to pay a dividend of $3.64 in 1 year, and growth rate is 4%. If the issuance costs are $6 per share, the cost is:

Remember, the cost of internal equity for this firm was 13.10% using the dividend valuation model.

%71.14%4$34

$3.64 4%

6 - $40

$3.64kne

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We just have this 1 model for estimating the cost of external equity, but we have 3 models for estimating the cost of internal equity! We should just estimate the cost adjustment for external equity (14.71%–13.10%) of 1.61% and add this to whatever estimate we use for internal equity.

For example, if you use the 13.4% estimate of cost of internal equity from the CAPM, then add 1.61% to this to estimate a cost of external equity of 15.01%!

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Now that we know how to compute the components’ cost of capital we are ready to complete the weighted average cost of capital estimation. Previously we presented the equation for this computation:

ka = wd x kd + wp x kp + we x ke

We also need to know a firm’s target capital structure so we can estimate the wi’s.

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Suppose our firm has a target capital structure of 40% long-term debt (wd), 10% preferred stock (wp), and 50% common equity (we).

Assume the firm has sufficient retained earnings growth to need no funds from a new common stock issuance.

Let’s use our previously computed 5.44% cost of long-term debt and 10.31% cost of funds from preferred stock.

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For the cost of internal equity let’s use an average of our 3 estimates:

%33.133

13.5% 13.4% 13.1%ke

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Now we have all the inputs we need to estimate the weighted average cost of capital:

ka = 0.4 x 5.47% + 0.1 x 10.31% + 0.5 x 13.33%

ka = 9.88%

Therefore, this firm should use 9.88% as the minimum required rate of return when evaluating investments.

An average return of 9.88% is required to pay off the firm’s contractual obligations on bonds and preferred stock and still have enough left over to satisfy common shareholders with a sufficient return!

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Let’s now consider how this computation will change if external equity becomes part of the equation.

Suppose the firm is considering investing up to $100 million in new projects. According to the target capital structure the following funds will be needed:

Long-term debt funding = 0.4 x $100 million = $40 million

Preferred stock funding = 0.1 x $100 million = $10 million

Common equity funding = 0.5 x $100 million = $50 million

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What if the firm expects to have only $20 million of new retained earnings to help finance this growth when up to $50 million of equity funding may be required?

The other $30 million of equity funding could be provided by a new issue of common stock—external common equity!

The cost adjustment for external equity we obtained was 1.61%. When added to our cost of internal equity, we obtain:

Ke = 13.33% + 1.61% = 14.94%

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The new estimate for the weighted average cost of capital is:

ka = .4x5.47% + 0.1x10.31% + 0.2x13.33%

+ .3x14.94% = 10.37%

We have broken up the weight for equity into 2 components:

20% for internal equity ($20/$50) 30% for external equity ($30/$50)

Therefore, this firm should use 10.37% as the minimum required rate of return when evaluating investments.

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Using The Weighted Average Cost of Capital

A weighted average cost of capital should always be used to evaluate an investment project even if all the capital components are not used to finance the project.

Thus, even if a project is financed with only debt, the project should still return at a minimum the weighted average cost of capital computed using the firm’s marginal cost of capital and its target capital structure.

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Summary of Chapter 8 Topics

Cost of capital measured as an average, marginal, after-tax cost of long-term sources of funds

The weights used to compute a firm’s weighted average cost of capital reflect the firm’s target capital structure.

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The components’ cost of capitals are reflections of investor-required rates of return. Show how to compute the cost of funds from:

Debt Preferred stock Common equity

Internal—new retained earnings External—new issues of common stock

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Estimate the weighted average cost of capital.

The finance decision should be separate from the investing decision.

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