cost of captial

8/8/2019 Cost of Captial

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The Cost of Capital


2/24

What is the Cost of Capital?

y When we talk about the cost of capital, we are talking about

the required rate of return on invested funds

y It is also referred to as a hurdle rate because this is the

minimum acceptable rate of returny Any investment which does not cover the firms cost of funds

will reduce shareholder wealth (just as if you borrowed

money at 10% to make an investment which earned 7%

would reduce your wealth)


3/24

The Appropriate Hurdle Rate: An Example

y The managers of RMM Corp are considering the purchase of a new tract of

land which will be held for one year. The purchase price of the land is $10,000.

RMMs capital structure is currently made up of 40% debt, 10% preferred

stock, and 50% common equity. This capital structure is considered to be

optimal, so any new funds will need to be raised in the same proportions.

y Before making the decision, RMMs managers must determine the appropriate

require rate of return. What minimum rate of return will simultaneously satisfy

all of the firms capital providers?


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RMM Example (cont.)

Source of

Funds

Amount Dollar

Cost

After-tax

Cost

Debt $4,000 $280 7%

Preferred $1,000 $100 10%Common $5,000 $600 12%

Total $10,000 $980 9.8%

Be ca use the cur r e n t capita l str uctur e is o ptim a l, thefirm wil l ra ise fun d s a s fo l lo ws:


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RMM Example (Cont.)

Rate of Return 8% 9.8% 11%

Total Funds Available $10,800 $10,980 $11,100

Less: Debt Costs $4,280 $4,280 $4,280

Less: Preferred Costs $1,100 $1,100 $1,100

= Remainder to Common $5,420 $5,600 $5,720

The following table shows three possible scenarios:

Obviously, the firm must earn at least 9.8%. Any less,and the common shareholders will not be satisfied.


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The Weighted Average Cost of Capital

y We now need a general way to determine the minimum

required return

y Recall that 40% of funds were from debt. Therefore, 40% of

the required return must go to satisfy the debtholders.Similarly, 10% should go to preferred shareholders, and 50%

to common shareholders

y This is a weighted-average, which can be calculated as:

WACC w k w k w k d d p p cs cs

!


7/24

Calculating RMMs WACC

y Using the numbers from the RMM example, we can calculate

RMMs Weighted-Average Cost of Capital (WACC) as

follows:

Noteth tthis is the s e s we ou earlier

WACC ! !0 40 0 07 0 10 0 10 0 50 0 12 0 098. ( . ) . ( . ) . ( . ) .


8/24

Finding the Weights

y The weights that we use to calculate the WACC will

obviously affect the result

y Therefore, the obvious question is: where do the weights

come from?y There are two possibilities:

y Book-value weights

y Market-value weights


9/24

Book-value Weights

y One potential source of these weights is the firms balance

sheet, since it lists the total amount of long-term debt,

preferred equity, and common equity

y

We can calculate the weights by simply determining theproportion that each source of capital is of the total capital


10/24

Book-value Weights (cont.)

Source Total Book Value % of Total

Long-term Debt $400,000 40%Preferred Equity $100,000 10%Common Equity $500,000 50%

Grand Totals $1,000,000 100%

The following table shows the calculation of thebook-value weights for RMM:


11/24

Market-value Weights

y The problem with book-value weights is that the book values

are historical, not current, values

y The market recalculates the values of each type of capital on

a continuous basis.T

herefore, market values are moreappropriate

y Calculation of market-value weights is very similar to the

calculation of the book-value weights

y The main difference is that we need to first calculate the total

market value (price times quantity) of each type of capital


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Calculating the Market-value Weights

Source Price perUnit

Units Total MarketValue

% ofTotal

Debt $ 905 400 $362,000 31.15%Preferred $ 100 1,000 $100,000 8.61%Common $ 70 10,000 $700,000 60.24%

Totals $1,162,000 100.00%

The following table shows the current market prices:

WACC ! ! !0 3115 0 07 0 0861 0 10 0 6024 0 1 2 0 1027 10 27%. . . . . . . .


13/24

Market vs Book Values

y It is important to note that market-values is always preferred

over book-value

y The reason is that book-values represent the historical

amount of securities sold, whereas market-values representthe current amount of securities outstanding

y For some companies, the difference can be much more

dramatic than for RMM

y

Finally, note that RMM should use the 10.27 WACC in itsdecision making process


14/24

The Costs of Capital

y As we have seen, a given firm may have more than one

provider of capital, each with its own required return

y In addition to determining the weights in the calculation of

the WACC, we must determine the individual costs of capitaly To do this, we simply solve the valuation equations for the

required rates of return


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The Cost of Debt

y Recall that the formula for valuing bonds is:

V Pmt

k

k

FV

kB

d

N

d d

N!

-

1 11

1

We cannot solvethis equation irectly or k so weust usean iterativetrialanderror procedure (or,

usea calculator)

Notethat kd is nottheappropriate costofdebtto usein calculatingtheWACC, instead we should usetheafter-tax costofdebt


16/24

The After-tax Cost of Debt

y Recall that interest expense is tax deductible

y Therefore, when a company pays interest, the actual cost is

less than the expensey As an example, consider a company in the 34% marginal tax

bracket that pays $100 in interest

y The companys after-tax cost is only $66.The formula is:

After tax k efore tax k td d ! 1


17/24

The Cost of Preferred Equity

y As with debt, we calculate the cost of preferred equity bysolving the valuation equation for kP:

k DV

P

P

!

Notethat preferreddividends arenottax-deductible,sothere is notaxadjustmentforthe costof preferred

equity


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The Cost of Common Equity

y Again, to find the cost of common equity we simply solve thevaluation equation for kCS:

k

g

Vg

Vg

S

S S

!

! 0 1

1

Notethat commondividends arenottax-deductible,sothere is notaxadjustmentforthe costof common

equity


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Flotation Costs

y When a company sells securities to the public, it must use theservices of an investment banker

y The investment banker provides a number of services for the firm,including:

y Setting the price of the issue, and

y Selling the issue to the public

y The cost of these services are referred to as flotation costs, and

they must be accounted for in the WACCy Generally, we do this by reducing the proceeds from the issue by

the amount of the flotation costs, and recalculating the cost ofcapital


20/24

The Cost of Debt with Flotation Costs

y Simply subtract the flotation costs (F) from the price of the

bonds, and calculate the cost of debt as usual:

V F Pmt

k

k

FV

kB

d

N

d d

N !

-

1 11

1

Notethat we stillmustadjustthis calculationfortaxes


21/24

The Cost of Preferred with Flotation Costs

y Simply subtract the flotation costs (F) from the price of

preferred, and calculate the cost of preferred as usual:

k

D

V FP

P

!


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The Cost of Common Equity with Flotation Costs

y Simply subtract the flotation costs (F) from the price of

common, and calculate the cost of common as usual:

kD g

V Fg

D

V Fg

C

C C

!

!

0 1

1


23/24

A Note on Flotation Costs

y The amount of flotation costs are generally quite low for debt

and preferred stock (often 1% or less of the face value)

y For common stock, flotation costs can be as high as 25% for

small issues, for larger issue they will be much lowery Note that flotation costs will always be given, but they may

be given as a dollar amount, or as a percentage of the selling

price


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The Cost of Retained Earnings

y The firm may choose to finance new projects using only

internally generated funds (retained earnings)

yThese funds are not free because they belong to the commonshareholders (i.e., there is an opportunity cost)

y Therefore, the cost of retained earnings is exactly the same as

the cost of new common equity, except that there are no

flotation costs:

k

D g

Vg

D

Vg

RE

C C

!

! 0 11

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