The Cost of Capital

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The Cost of Capital

• Timothy R. Mayes, Ph.D.
• FIN 3300 Chapter 11

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What is the Cost of Capital?

• 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 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

• 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. 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.
• 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.)
Because the current capital structure is optimal,
thefirm will raise funds as follows
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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.
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The Weighted Average Cost of Capital

• 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

7
Calculating RMMs WACC

• Using the numbers from the RMM example, we can
  calculate RMMs Weighted-Average Cost of Capital
  (WACC) as follows

• Note that this is the same as we found earlier

8
Finding the Weights

• 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

9
Book-value Weights

• 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
• 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
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Market-value Weights

• 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
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Market vs Book Values

• 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
  market-values 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

• 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

15
The Cost of Debt

• Recall that the formula for valuing bonds is

• 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

• 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 companys after-tax cost is only 66. The
  formula is

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The Cost of Preferred Equity

• As with debt, we calculate the cost of preferred
  equity by solving the valuation equation for kP

• 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

• Again, to find the cost of common equity we
  simply solve the valuation equation for kCS

• 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

• 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
• 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

• Simply subtract the flotation costs (F) from the
  price of the bonds, and calculate the cost of
  debt as usual

• Note that we still must adjust this calculation
  for taxes

21
The Cost of Preferred with Flotation Costs

• Simply subtract the flotation costs (F) from the
  price of preferred, and calculate the cost of
  preferred as usual

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The Cost of Common Equity with Flotation Costs

• Simply subtract the flotation costs (F) from the
  price of common, and calculate the cost of common
  as usual

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A Note on Flotation Costs

• 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

24
The Cost of Retained Earnings

• 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