Cost of Capital.pdf

8/16/2019 Cost of Capital.pdf

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Cost of CapitalCost of Capital


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An Overview of the Cost of CapitalAn Overview of the Cost of Capital

The cost of capital acts as a link between the firm’slong-term investment decisions and the wealth of theowners as determined by investors in themarketplace.

It is the “magic number” that is used to decidewhether a proposed investment will increase ordecrease the firm’s stock price.

Formally, the cost of capital is the rate of return thata firm must earn on the projects in which it invests to

maintain the market value of its stock.


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The Firm’s Capital StructureThe Firm’s Capital Structure


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Some Key AssumptionsSome Key Assumptions

Business Risk—the risk to the firm of beingunable to cover operating costs—is assumed to beunchanged. This means that the acceptance of agiven project does not affect the firm’s ability to

meet operating costs. Financial Risk—the risk to the firm of being

unable to cover required financial obligations—isassumed to be unchanged. This means that the

projects are financed in such a way that the firm’sability to meet financing costs is unchanged.

After-tax costs are considered relevant—the costof capital is measured on an after-tax basis.


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Assume the ABC company has the following investment opportunity:

- Initial Investment = $100,000

- Useful Life = 20 years

- IRR = 7%

- Least cost source of financing, Debt = 6%

Given the above information, a firm’s financial manger would be inclined toaccept and undertake the investment.

The Basic ConceptThe Basic Concept

Why do we need to determine a company’s overall“weighted average cost of capital?”


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Imagine now that only one week later, the firm has another available investmentopportunity

- Initial Investment = $100,000

- Useful Life = 20 years

- IRR = 12%

- Least cost source of financing, Equity = 14%

Given the above information, the firm would reject this second, yet clearly moredesirable investment opportunity.

The Basic Concept (cont.)The Basic Concept (cont.)



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The Basic Concept (cont.)The Basic Concept (cont.)


As the above simple example clearly illustrates, usingthis piecemeal approach to evaluate investmentopportunities is clearly not in the best interest of thefirm’s shareholders.

Over the long haul, the firm must undertakeinvestments that maximize firm value.

This can only be achieved if it undertakes projects thatprovide returns in excess of the firm’s overall weightedaverage cost of financing (or WACC).


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Should we focus onShould we focus on beforebefore--taxtax ororafterafter--taxtax capital costs?capital costs?

Tax effects associated with financing can

be incorporated either in capital budgetingcash flows or in cost of capital.

Most firms incorporate tax effects in thecost of capital. Therefore, focus on after-

tax costs.

Only cost of debt is affected.


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Specific Sources of Capital:Specific Sources of Capital:TheThe Cost of LongCost of Long--Term DebtTerm Debt

The pretax cost of debt is equal to the yield-to-maturity on thefirm’s debt adjusted for flotation costs.

Recall that a bond’s yield-to-maturity depends upon a number

of factors including the bond’s coupon rate, maturity date, parvalue, current market conditions, and selling price.

After obtaining the bond’s yield, a simple adjustment must bemade to account for the fact that interest is a tax-deductibleexpense.

This will have the effect of reducing the cost of debt.


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P9-17 Dillon Labs has asked its financial manager to measure the cost

of each specific type of capital as well as the weighted average cost of

capital. The weighted average cost of capital to be measured by using

the following weights: 40% Long Term Debt, 50% Common Stock

Equity (Retained Earnings, New Common Stock or Both). The Firm Tax

Rate is 40%

Specific Sources of Capital:Specific Sources of Capital:The Cost of LongThe Cost of Long--Term Debt (cont.)Term Debt (cont.)

Debt: The firm can sell for $980 a 10 year, $1,000 par value bondpaying annual interest at a 10% coupon rate. A flotation cost of 3% of

the par value is required in addition to the discount of $20 per bond


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Before-Tax Cost of Debt

Using Cost Quotations

When the net proceeds from the sale of a bond equal its parvalue, the before-tax cost equals the coupon interest rate.

A second quotation that is sometimes used is the yield-to-

maturity (YTM) on a similar risk bond.



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Calculating the Cost

This approach finds the before-tax cost of debt by

calculating the internal rate of return (IRR).

As discussed in earlier in the text, YTM can be calculated

using: (a) trial and error, (b) a financial calculator, or (c) a

spreadsheet.



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Approximating the Cost



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Find the after-tax cost of debt for Dillon Labassuming it has a 40% tax rate:

ri = 9.4% (1-.40) = 5.6%

This suggests that the after-tax cost of raising debtcapital for Dillon Lab is ≈ 6.50%



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Dillon Lab is contemplating the issuance of a 8% (annual

dividend) preferred stock having a par value $100 that is

expected to sell for its $65-per share value. An additional fee

of $2 per share must be paid to underwriters

rP = DP/Np = $8/$63 ≈ 12.70%

Specific Sources of Capital:Specific Sources of Capital:The Cost of Preferred StockThe Cost of Preferred Stock


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Specific Sources of Capital:Specific Sources of Capital:The Cost of Common StockThe Cost of Common Stock

There are two forms of common stock financing: retained

earnings and new issues of common stock.

In addition, there are two different ways to estimate the cost

of common equity: any form of the dividend valuation model,and the capital asset pricing model (CAPM).

The dividend valuation models are based on the premise that

the value of a share of stock is based on the present value of all

future dividends.


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Earnings can be reinvested or paid out as dividends.

Investors could buy other securities, earn a return.

Thus, there is an opportunity cost if earnings arereinvested.

Opportunity cost: The return stockholders could earnon alternative investments of equal risk.

They could buy similar stocks and earn ks, or companycould repurchase its own stock and earn ks. So, ks, isthe cost of reinvested earnings and it is the cost ofequity.

Why is there a cost for reinvested earnings?Why is there a cost for reinvested earnings?


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rS = (D1/P0) + g

rE = rF + b(rM - rF).

We can also estimate the cost of common equityusing the CAPM:

Specific Sources of Capital:Specific Sources of Capital:The Cost of Common Stock (cont.)The Cost of Common Stock (cont.)

Using the constant growth model, we


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The CAPM differs from dividend valuation models in that itexplicitly considers the firm’s risk as reflected in beta.

On the other hand, the dividend valuation model does notexplicitly consider risk.

Dividend valuation models use the market price (P0) as areflection of the expected risk-return preference of investors inthe marketplace.



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Although both are theoretically equivalent, dividendvaluation models are often preferred because the data

required are more readily available. The two methods also differ in that the dividend

valuation models (unlike the CAPM) can easily beadjusted for flotation costs when estimating the cost

of new equity.

This will be demonstrated in the examples that follow.



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rs = D1/P0 + g

rS = ($4/$50.00) + 7.10%≈15.10%.

Specific Sources of Capital:Specific Sources of Capital:Cost of Retained Earnings (Cost of Retained Earnings (rrEE))

Constant Dividend Growth Model

The firm’s common stock is currently selling for $50/ share. The dividend

expected to be paid at the end of the coming year (2013) is $4. Itsdividend payments, which have been approximately 60% of earnings per

share in each of the past 5 years, were as shown in the following table

Year Dividend

2012 $3.75

2011 $3.50

2010 $3.30

2009 $3.15

2008 $2.85


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rs = rF + b(rM - rF).

For example, if the 3-month T-bill rate is currently 5.0%, the market

risk premium is 9%, and the firm’s beta is 1.20, the firm’s cost of

retained earnings will be:

rs = 5.0% + 1.2 (9.0%) = 15.8%.

Cost of Retained Earnings (rE)

Security Market Line Approach



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The previous example indicates that our estimate of the cost

of retained earnings is somewhere between 15.5% and 15.8%.At this point, we could either choose one or the other estimate

or average the two.

Using some managerial judgment and preferring to err on the

high side, we will use 15.10% as our final estimate of the cost

of retained earnings.


Cost of Retained Earnings (rE)


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rn = D1/Nn + g

Continuing with the previous example, it is expected that to

attract buyers new common stock must be underpriced $5 per

share, an the firm also paid $3 per share in flotation cost.Dividend payments are expected to continue at 60% of earnings

rn = [$4/($45.00 - $3.00)] + 7.10% ≈ 16.62

Cost of New Equity (rn)

Constant Dividend Growth Model



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WACC = ra = wiri + wprp + wsrr or n

The weights in the above equation are intended to represent a

specific financing mix (where wi = % of debt, wp = % of preferred, and

ws= % of common).

Specifically, these weights are the target percentages of debt and

equity that will minimize the firm’s overall cost of raising funds.

The Weighted Average Cost of CapitalThe Weighted Average Cost of Capital

Capital Structure Weights


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One method uses book values from the firm’s balance sheet. For example, to estimate

the weight for debt, simply divide the book value of the firm’s long-term debt by the

book value of its total assets.

To estimate the weight for equity, simply divide the total book value of equity by the

book value of total assets.


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A second method uses the market values of the firm’s debt andequity. To find the market value proportion of debt, simply multiply

the price of the firm’s bonds by the number outstanding. This is

equal to the total market value of the firm’s debt.

Next, perform the same computation for the firm’s equity by

multiplying the price per share by the total number of shares

outstanding.





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Using the costs previously calculated along with the market

value weights, we may calculate the weighted average cost of

capital as follows:

WACC = .40(10.77%) + .10(12.70%) + .50(15.10%)

≈ 11.35%

This assumes the firm has sufficient retained earnings to fund

any anticipated investment projects. Or ≈ 12.11% if the firm

issuing new stock


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$2.5 $4.0 Total Financing (millions)

11.75%

11.25%

11.50%

WMCC11.76%

11.66%

11.13%

The Marginal CostThe Marginal Cost& Investment Decisions (cont.)& Investment Decisions (cont.)


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Initial Cumulative

Project IRR Ivestment Investment

A 13.0% 1,000,000$ 1,000,000$

B 12.0% 1,000,000$ 2,000,000$

C 11.5% 1,000,000$ 3,000,000$

D 11.0% 1,000,000$ 4,000,000$

E 10.0% 1,000,000$ 5,000,000$


Investment Opportunities Schedule (IOS)

Now assume the firm has the following investmentopportunities available:


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$2.5 $4.0 Total Financing (millions)

WACC

11.66%

11.13%

$1.0

13.0% AB

$2.0 $3.0

C

D

11.5%

11.0%

12.0%

This indicates

that the firm can

accept only

Projects A & B.



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FigureFigure 11 WMCC ScheduleWMCC Schedule


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TableTable 33 Investment Opportunities ScheduleInvestment Opportunities Schedule

(IOS) for Duchess Corporation(IOS) for Duchess Corporation


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FigureFigure 22 IOS and WMCC SchedulesIOS and WMCC Schedules

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