10-1 chapter 10 the cost of capital sources of capital component costs wacc adjusting for flotation...

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CHAPTER 10The Cost of Capital

Sources of capital Component costs WACC Adjusting for flotation costs

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What sources of long-term capital do firms use?

Long-Term CapitalLong-Term Capital

Long-Term DebtLong-Term Debt Preferred StockPreferred Stock Common StockCommon Stock

Retained EarningsRetained Earnings New Common StockNew Common Stock

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Calculating the weighted average cost of capital

WACC = wdrd(1-T) + wprp + wcrs

The w’s refer to the firm’s capital structure weights.

The r’s refer to the cost of each component.

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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 Using or raising new funds.

The Weighted Average Cost of Capital

Capital Structure Weights

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Firm Capital Structure Weight

Assume the capital structure weight of the firm is 30% debt, 10% preferred stock and 60% equity

WACC = 0.3rdd(1-T) + 0.1rp + 0.6rs

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Component cost of debt


rd is the cost of debt capital. The yield to maturity on

outstanding L-T debt is often used as a measure of rd.

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Borrowing firm

= Yield to maturityCost of debt (rd)

Coupon interest Par value

“Tax deductible” - Partially subsidized

rd (1-T)

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A 15-year, 12% semiannual coupon bond sells for $1,153.72. What is the cost of debt (rd)?

The bond pays a semiannual coupon, so rd = 5.0% x 2 = 10%.

INPUTS

OUTPUT N

I/YR

PMTPV FV

30

5

60 1000-1153.72

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Component cost of debt

Why tax-adjust, i.e. why rd(1-T)?

WACC = wdrd(1-T) + wprp + wcrs Interest is tax deductible Assume Corp tax is 40% Interest is tax deductible, so

A-T rd = B-T rd (1-T)

= 10% (1 - 0.40) = 6%

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Borrowing firm

= Yield to maturity = 10%Cost of debt (rd)=6%

Coupon interest Par value

“Tax deductible” - Partially subsidized

rd (1-T)

= 10% (1 - 0.40) = 6%

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Component cost of preferred stock


rp is the cost of preferred stock, which is the return investors require on a firm’s preferred stock.

Preferred dividends are not tax-deductible, so no tax adjustments necessary. Just use nominal rp.

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What is the cost of preferred stock?

The cost of preferred stock can be solved by using this formula:

rp = Dp / Pp

= $10 / $111.10 = 9%

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Is preferred stock more or less risky to borrowing firm?

More risky; although the firm has the option not to pay preferred dividend under certain circumstances.

However, under company law, if preferred dividend is not paid (1) firm cannot pay common dividend, & (2) difficult to raise additional external funds.

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Component cost of equity


rs is the cost of common equity using retained earnings.

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Why is there a cost for retained earnings?

Earnings can be reinvested or paid out as dividends.

Investors could buy other securities, earn a higher return.

If earnings are retained, there is an opportunity cost (the return that stockholders could earn on alternative investments).

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To determine the cost of common equity, rs

CAPM: rs = rRF + (rM – rRF) b

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If the rRF = 7%, rM = 13%, and the firm’s beta is 1.2, what’s the cost of common equity based upon the CAPM?

rs = rRF + (rM – rRF) b

= 7.0% + (6.0%)1.2 = 14.2% ~14%

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Cost of issuing new common stock? When a company issues new

common stock they also have to pay flotation costs to the underwriter.

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Cost of issuing new common stock

WACC = wdrd(1-T) + wprp + wcre

re is the cost of common equity of issuing new common stock

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If issuing new common stock incurs a flotation cost of 15% of the proceeds, what is re?

15.4%

5.0% $42.50

$4.3995

5.0% 0.15)-$50(1

)$4.19(1.05

g F)-(1P

g)(1D r

0

0e

g P

g)(1D

0

0

≈

Flotation costfactor

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Flotation costs

Flotation costs are highest for common equity. However, since most firms issue equity infrequently,

We will frequently ignore flotation costs when calculating the WACC.

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Ignoring flotation costs, what is the firm’s WACC?


= 0.3(10%)(0.6) + 0.1(9%) + 0.6(14%)

= 1.8% + 0.9% + 8.4%= 11.1%

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The Marginal Cost & Investment Decisions

The Weighted Marginal Cost of Capital (WMCC) The WACC typically increases as the volume

of new capital raised within a given period increases.

This is true because companies need to raise the return to investors in order to entice them to invest more in the company ( ie. to compensate them for the increased risk introduced by larger volumes of capital raised.

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$2.5 $4.0 Total Financing (millions)

11.75%

11.25%

11.50%

WMCC11.76%

11.66%

11.13%


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The Weighted Marginal Cost of Capital (WMCC) In addition, the cost will eventually increase

when the firm runs out of cheaper retained equity and is forced to raise new, more expensive equity capital.

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WACC = ka = wiki + wpkp + wskr or n

The Weighted Average Cost of Capital

Capital Structure Weights

For example, assume the market value of the firm’s debt is $40

million, the market value of the firm’s preferred stock is $10

million, and the market value of the firm’s equity is $50 million.

Dividing each component by the total of $100 million gives us

market value weights of 40% debt, 10% preferred, and 50%

common.

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Finding the break points in the WMCC schedule will allow us to determine at what level of new financing the WACC will increase due to the factors listed above.

BPj = AFj/wj

where:

BPj = breaking point form financing source j

AFj = amount of funds available at a given cost

wj = target capital structure weight for source j

The Marginal Cost & Investment Decisions (cont.)

The Weighted Marginal Cost of Capital (WMCC) Finding Break Points

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The Weighted Marginal Cost of Capital (WMCC) Finding Break PointsAssume that the firm has $2 million of retained earnings

available. When it is exhausted, the firm must issue new (more

expensive) equity. Furthermore, the company believes it can

raise $1 million of cheap debt after which it will cost 7% (after-

tax) to raise additional debt.

Given this information, the firm can determine its break points as

follows:

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The Weighted Marginal Cost of Capital (WMCC) Finding Break Points

BPequity = $2,000,000/.50 = $4,000,000

BPdebt = $1,000,000/.40 = $2,500,000

This implies that the firm can fund up to $4 million of new investment before it is forced to issue new equity and $2.5 million of new investment before it is forced to raise more expensive debt.

Given this information, we may calculate the WMCC as follows:

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Range of total Source of Weighted

New Financing Capital Weight Cost Cost

$0 to $2.5 million Debt 40% 5.67% 2.268%

Preferred 10% 9.62% 0.962%

Common 50% 15.80% 7.900%

WACC 11.130%

$2.5 to $4.0 million Debt 40% 7.00% 2.800%

Preferred 10% 9.62% 0.962%

Common 50% 15.80% 7.900%

WACC 11.662%

over $4.0 million Debt 40% 7.00% 2.800%

Preferred 10% 9.62% 0.962%

Common 50% 16.00% 8.000%

WACC 11.762%

WACC for Ranges of Total New Financing


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$2.5 $4.0 Total Financing (millions)

11.75%

11.25%

11.50%

WMCC11.76%

11.66%

11.13%


New Debt was issued

New Equity was issued

10-1 chapter 10 the cost of capital sources of capital component costs wacc adjusting for flotation...

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