Transcript The Cost of Capital

The Cost of Capital
Timothy R. Mayes, Ph.D.
FIN 3300: Chapter 11
1
What is the “Cost” of Capital?
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When we talk about the “cost” of capital, we are
talking about the required rate of return on invested
funds
It is also referred to as a “hurdle” rate because this is
the minimum acceptable rate of return
Any investment which does not cover the firm’s 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
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The managers of Rocky Mountain Motors 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. RMM’s 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.
Before making the decision, RMM’s managers must determine
the appropriate require rate of return. What minimum rate of
return will simultaneously satisfy all of the firm’s capital
providers?
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RMM Example (cont.)
Because the current capital structure is optimal, the
firm will raise funds as follows:
Source of
Funds
Debt
Preferred
Common
Total
Amount
Dollar
Cost
After-tax
Cost
$4,000
$1,000
$5,000
$10,000
$280
$100
$600
$980
7%
10%
12%
9.8%
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RMM Example (Cont.)
The following table shows three possible scenarios:
Rate of Return
Total Funds Available
Less: Debt Costs
Less: Preferred Costs
= Remainder to Common
8%
9.8%
$10,800 $10,980
$4,280 $4,280
$1,100 $1,100
$5,420 $5,600
11%
$11,100
$4,280
$1,100
$5,720
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
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We now need a general way to determine the
minimum required return
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
This is a weighted-average, which can be calculated
as:
WACC  w d k d  w p k p  w cs k cs
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Calculating RMM’s WACC

Using the numbers from the RMM example, we can
calculate RMM’s Weighted-Average Cost of Capital
(WACC) as follows:
WACC  0.40(0.07)  010
. (010
. )  0.50(012
. )  0.098

Note that this is the same as we found earlier
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Finding the Weights
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The weights that we use to calculate the WACC will
obviously affect the result
Therefore, the obvious question is: “where do the
weights come from?”
There are two possibilities:
• Book-value weights
• Market-value weights
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Book-value Weights
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One potential source of these weights is the firm’s
balance sheet, since it lists the total amount of longterm debt, preferred equity, and common equity
We can calculate the weights by simply determining
the proportion that each source of capital is of the
total capital
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Book-value Weights (cont.)
The following table shows the calculation of the
book-value weights for RMM:
Source
Long-term Debt
Preferred Equity
Common Equity
Grand Totals
Total Book Value
$400,000
$100,000
$500,000
$1,000,000
% of Total
40%
10%
50%
100%
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Market-value Weights
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The problem with book-value weights is that the
book values are historical, not current, values
The market recalculates the values of each type of
capital on a continuous basis. Therefore, market
values are more appropriate
Calculation of market-value weights is very similar
to the calculation of the book-value weights
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
The following table shows the current market prices:
Source
Debt
Preferred
Common
Totals
Price per Units Total Market
% of
Unit
Value
Total
$ 905
400
$362,000 31.15%
$ 100 1,000
$100,000
8.61%
$ 70 10,000
$700,000 60.24%
$1,162,000 100.00%
WACC  0.31150.07  0.0861010
.   0.6024012
.   01027
.
 10.27%
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Market vs Book Values
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It is important to note that market-values is always
preferred over book-value
The reason is that book-values represent the
historical amount of securities sold, whereas marketvalues represent the current amount of securities
outstanding
For some companies, the difference can be much
more dramatic than for RMM
Finally, note that RMM should use the 10.27 WACC
in its decision making process
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The Costs of Capital
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As we have seen, a given firm may have more than
one provider of capital, each with its own required
return
In addition to determining the weights in the
calculation of the WACC, we must determine the
individual costs of capital
To do this, we simply solve the valuation equations
for the required rates of return
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The Cost of Debt

Recall that the formula for valuing bonds is:
1  1

N

1  kd  

FV
VB  Pmt 

N
k
1

k


d


d



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We cannot solve this equation directly for kd, so we
must use an iterative trial and error procedure (or,
use a calculator)
Note that kd is not the appropriate cost of debt to use
in calculating the WACC, instead we should use the
after-tax cost of debt
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The After-tax Cost of Debt
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Recall that interest expense is tax deductible
Therefore, when a company pays interest, the actual
cost is less than the expense
As an example, consider a company in the 34%
marginal tax bracket that pays $100 in interest
The company’s after-tax cost is only $66. The formula
is:
After  tax k d  Before  tax k d 1  t 
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The Cost of Preferred Equity
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As with debt, we calculate the cost of preferred
equity by solving the valuation equation for kP:
D
kP 
VP
Note that preferred dividends are not tax-deductible,
so there is no tax adjustment for the cost of preferred
equity
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The Cost of Common Equity
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Again, to find the cost of common equity we simply
solve the valuation equation for kCS:
k CS 

D 0 1  g
VCS
D1
g
g
VCS
Note that common dividends are not tax-deductible,
so there is no tax adjustment for the cost of common
equity
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Flotation Costs
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When a company sells securities to the public, it must
use the services of an investment banker
The investment banker provides a number of services
for the firm, including:
• Setting the price of the issue, and
• Selling the issue to the public
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The cost of these services are referred to as “flotation
costs,” and they must be accounted for in the WACC
Generally, we do this by reducing the proceeds from
the issue by the amount of the flotation costs, and
recalculating the cost of capital
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The Cost of Debt with Flotation Costs
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Simply subtract the flotation costs (F) from the price
of the bonds, and calculate the cost of debt as usual:
1  1

N

1  k d    FV
V

F

Pmt
 B 


N
k
1

k
d

 
d



Note that we still must adjust this calculation for
taxes
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The Cost of Preferred with Flotation Costs
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Simply subtract the flotation costs (F) from the price
of preferred, and calculate the cost of preferred as
usual:
D
kP 
 VP  F
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The Cost of Common Equity with Flotation Costs
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Simply subtract the flotation costs (F) from the price
of common, and calculate the cost of common as
usual:
k CS
D 0 1  g
D1

g
g
 VCS  F
 VCS  F
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A Note on Flotation Costs
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The amount of flotation costs are generally quite low
for debt and preferred stock (often 1% or less of the
face value)
For common stock, flotation costs can be as high as
25% for small issues, for larger issue they will be
much lower
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
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The firm may choose to finance new projects using
only internally generated funds (retained earnings)
These funds are not free because they belong to the
common shareholders (i.e., there is an opportunity
cost)
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 RE 
D0 1  g
VCS
D1
g
g
VCS
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