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8/8/2019 Cost of Captial
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The Cost of Capital
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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)
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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
!
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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. ( . ) . ( . ) . ( . ) .
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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
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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
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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:
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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%. . . . . . . .
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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
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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
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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
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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
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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
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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
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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