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Cost of capital
1. The Cost of Capital
Timothy R. Mayes, Ph.D.
FIN 3300: Chapter 11
2. 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 return
y 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)
3. The Appropriate Hurdle Rate: An Example
y 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.
y 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?
5. RMM Example (Cont.)
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.
6. 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:
7. Calculating RMM’s WACC
y 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) + 0.10(010) + 0.50(012) = 0.098
. .
y Note that this is the same as we found earlier
8. 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:
• Book-value weights
• Market-value weights
9. Book-value Weights
y One potential source of these weights is the firm’s
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
the proportion that each source of capital is of the
total capital
11. 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. Therefore, market
values are more appropriate
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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13. 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 represent the 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 its decision making process
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14. 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 capital
y To do this, we simply solve the valuation equations
for the required rates of return
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15. The Cost of Debt
y Recall that the formula for valuing bonds is:
y We cannot solve this equation directly for kd, so we
must use an iterative trial and error procedure (or,
use a calculator)
y 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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16. 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 expense
y As an example, consider a company in the 34%
marginal tax bracket that pays $100 in interest
y The company’s after-tax cost is only $66. The formula
is:
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17. The Cost of Preferred Equity
y As with debt, we calculate the cost of preferred
equity by solving the valuation equation for kP:
y Note that preferred dividends are not tax-deductible,
so there is no tax adjustment for the cost of preferred
equity
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18. The Cost of Common Equity
y Again, to find the cost of common equity we simply
solve the valuation equation for kCS:
y Note that common dividends are not tax-deductible,
so there is no tax adjustment for the cost of common
equity
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19. Flotation Costs
y When a company sells securities to the public, it must
use the services of an investment banker
y 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
y The cost of these services are referred to as “flotation
costs,” and they must be accounted for in the WACC
y 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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20. 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:
y Note that we still must adjust this calculation for
taxes
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21. 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:
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22. 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:
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23. 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 lower
y 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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24. The Cost of Retained Earnings
y The firm may choose to finance new projects using
only internally generated funds (retained earnings)
y These funds are not free because they belong to the
common shareholders (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:
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